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| | ==开环和闭环(反馈)控制== | | ==开环和闭环(反馈)控制== |
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| − | [[File:Feedback loop with descriptions.svg|thumb|right|400px|A [[block diagram]] of a [[negative feedback]] [[control system]] using a [[feedback loop]] to control the process variable by comparing it with a desired value, and applying the difference as an error signal to generate a control output to reduce or eliminate the error.]] | + | [[File:Feedback loop with descriptions.svg|thumb|right|400px|负反馈控制系统的框图，使用反馈回路通过比较期望值来控制程序变数，并将差值作为一个错误信号来产生控制输出，以减少或消除错误]] |
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| − | A [[block diagram of a negative feedback control system using a feedback loop to control the process variable by comparing it with a desired value, and applying the difference as an error signal to generate a control output to reduce or eliminate the error.]]
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| − | 一个[负反馈控制系统的框图，使用反馈回路通过比较期望值来控制程序变数，并将差值作为一个错误信号来产生控制输出，以减少或消除错误]
| + | [[File:Industrial control loop.jpg|thumb|400px|单个工业控制回路的例子; 显示过程流程的连续调制控制]] |
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| − | [[File:Industrial control loop.jpg|thumb|400px|Example of a single industrial control loop; showing continuously modulated control of process flow.]] | |
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| − | Example of a single industrial control loop; showing continuously modulated control of process flow.
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| − | 单个工业控制回路的例子; 显示过程流程的连续调制控制。
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| | 从根本上讲，控制回路有两种类型：开环控制和闭环（反馈）控制。 | | 从根本上讲，控制回路有两种类型：开环控制和闭环（反馈）控制。 |
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| | :<math>P(s) = \frac{A}{1 + sT_P}</math> | | :<math>P(s) = \frac{A}{1 + sT_P}</math> |
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| − | where <math>A</math> and <math>T_P</math> are some constants. The plant output is fed back through
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| − | where <math>A</math> and <math>T_P</math> are some constants. The plant output is fed back through
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| | 其中<math>A</math>和<math>T_P</math>是一些常数。系统的输出通过 | | 其中<math>A</math>和<math>T_P</math>是一些常数。系统的输出通过 |
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| − | Plugging <math>P(s)</math>, <math>F(s)</math>, and <math>C(s)</math> into the closed-loop transfer function <math>H(s)</math>, we find that by setting
| + | 把<math>P(s)</math>， <math>F(s)</math>，<math>C(s)</math>输入到闭环传递函数<math>H(s)</math>中，我们通过设置 |
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| − | Plugging <math>P(s)</math>, <math>F(s)</math>, and <math>C(s)</math> into the closed-loop transfer function <math>H(s)</math>, we find that by setting
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| − | 把<math>P(s)</math>， <math>F(s)</math>，<math>C(s)</math>输入到闭回路传递函数<math>H(s)</math>中，我们通过设置 | |
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| | :<math>K = \frac{1}{A}, T_I = T_F, T_D = T_P</math> | | :<math>K = \frac{1}{A}, T_I = T_F, T_D = T_P</math> |
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| | 控制理论可分为两个分支: | | 控制理论可分为两个分支: |
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| − | * ''[[Linear control theory]]'' – This applies to systems made of devices which obey the [[superposition principle]], which means roughly that the output is proportional to the input. They are governed by [[linear equation|linear]] [[differential equation]]s. A major subclass is systems which in addition have parameters which do not change with time, called ''[[linear time invariant]]'' (LTI) systems. These systems are amenable to powerful [[frequency domain]] mathematical techniques of great generality, such as the [[Laplace transform]], [[Fourier transform]], [[Z transform]], [[Bode plot]], [[root locus]], and [[Nyquist stability criterion]]. These lead to a description of the system using terms like [[Bandwidth (signal processing)|bandwidth]], [[frequency response]], [[eigenvalue]]s, [[gain (electronics)|gain]], [[resonant frequency|resonant frequencies]], [[zeros and poles]], which give solutions for system response and design techniques for most systems of interest.
| + | 控制理论领域可以分为两个分支： |
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| | + | *[[线性控制理论]]–适用于由遵循叠加原理的系统，这意味着输出大致与输入成比例，系统由线性微分方程控制。其中最重要的一个子系统是具有不随时间变化的参数的系统，称为线性时不变 LTI 系统。这些系统使用通用且强大的频域数学技术，例如Laplace变换， Fourier变换，Z变换，Bode图，根轨迹和奈奎斯特稳定性判据。使用这些技术有助于使用带宽，频率响应，特征值，增益，谐振频率，零点和极点等术语对系统进行描述，从而为大多数目标系统提供了系统响应解决方案和设计方式。 |
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| | + | *[[非线性控制理论]]–涵盖了不遵循叠加原理的更广泛的系统类别，并适用于更多实际系统，因为所有实际控制系统都是非线性的。这些系统通常由非线性微分方程控制。为处理这些问题而开发的几种数学技术更加困难，而且通用性较低，通常仅适用于很少类别的系统。其中包括极限环理论，庞加莱图，李雅普诺夫稳定性定理和描述函数。通常在计算机上使用数值方法来分析非线性系统<ref>[http://www.mathworks.com/help/toolbox/simulink/slref/trim.html trim point]</ref>。如果仅关注稳定点附近的解决方案，则通常可以使用微扰理论通过线性系统对非线性系统进行近似来线性化非线性系统，并且可以使用线性理论的方式进行求解。[16] |
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| − | | + | ==分析技术-频域和时域== |
| − | * ''[[Nonlinear control theory]]'' – This covers a wider class of systems that do not obey the superposition principle, and applies to more real-world systems because all real control systems are nonlinear. These systems are often governed by [[nonlinear differential equation]]s. The few mathematical techniques which have been developed to handle them are more difficult and much less general, often applying only to narrow categories of systems. These include [[limit cycle]] theory, [[Poincaré map]]s, [[Lyapunov function|Lyapunov stability theorem]], and [[describing function]]s. Nonlinear systems are often analyzed using [[numerical method]]s on computers, for example by [[simulation|simulating]] their operation using a [[simulation language]]. If only solutions near a stable point are of interest, nonlinear systems can often be [[linearization|linearized]] by approximating them by a linear system using [[perturbation theory]], and linear techniques can be used.<ref>[http://www.mathworks.com/help/toolbox/simulink/slref/trim.html trim point]</ref>
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| − | ==Analysis techniques - frequency domain and time domain== | |
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| − | ==Analysis techniques - frequency domain and time domain==
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| − | 分析技术. 频域和时域
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| − | Mathematical techniques for analyzing and designing control systems fall into two different categories:
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| − | Mathematical techniques for analyzing and designing control systems fall into two different categories:
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| | 分析和设计控制系统的数学技术可分为两类: | | 分析和设计控制系统的数学技术可分为两类: |
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| − | * ''[[Frequency domain]]'' – In this type the values of the [[state variable]]s, the mathematical [[variable (mathematics)|variables]] representing the system's input, output and feedback are represented as functions of [[frequency]]. The input signal and the system's [[transfer function]] are converted from time functions to functions of frequency by a [[transform (mathematics)|transform]] such as the [[Fourier transform]], [[Laplace transform]], or [[Z transform]]. The advantage of this technique is that it results in a simplification of the mathematics; the ''[[differential equation]]s'' that represent the system are replaced by ''[[algebraic equation]]s'' in the frequency domain which is much simpler to solve. However, frequency domain techniques can only be used with linear systems, as mentioned above. | + | *频域状态空间表示法–在这种类型的状态变量中，数学变量代表系统输入，输出和反馈表示为频率函数。输入信号与系统的传递函数是从时间函数到频率的函数通过转换得到的变换，如Laplace变换， Fourier变换，Z变换。这种变换的优点是可以简化数学公式表达。为了方便计算，在频域中，微分方程在系统被替换为代数方程。如上所述，频域技术只能与线性系统一起使用。 |
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| | + | *时域状态空间表示法–在这种类型中，状态变量的值表示为时间的函数。使用此模型，所分析的系统由一个或多个微分方程表示。由于频域技术仅限于线性系统，因此时域被广泛用于分析现实世界的非线性系统。尽管这些问题更难解决，但现代计算机模拟技术（例如Simulink）可以相对方便的对系统进行分析。 |
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| | + | 与经典控制理论的频域分析相反，现代控制理论利用时域状态空间表示，是物理系统的数学模型，它是由一阶微分方程相关的一组输入，输出和状态变量。为了从输入，输出和状态的数量中抽象出来，变量被表示为矢量，并且微分方程和代数方程以矩阵形式编写（后者仅在动力系统为线性时才可行）。状态空间表示（也称为“时域方法”）提供了一种方便而紧凑的方式来建模和分析具有多个输入和输出的系统，如我们使用Laplace变换对含输入输出系统的所有信息进行编码。与频域方法不同，状态空间表示和使用不限于具有线性分量和零初始条件的系统。“状态空间”是指其轴为状态变量的空间。系统的状态可以表示为该空间内的一个点<ref>{{cite book|title=State space & linear systems|series=Schaum's outline series |publisher=McGraw Hill|author=Donald M Wiberg|isbn=978-0-07-070096-3}}</ref><ref>{{cite journal|author=Terrell, William|title=Some fundamental control theory I: Controllability, observability, and duality —AND— Some fundamental control Theory II: Feedback linearization of single input nonlinear systems|journal=American Mathematical Monthly|volume=106|issue=9|year=1999|pages=705–719 and 812–828|url=http://www.maa.org/programs/maa-awards/writing-awards/some-fundamental-control-theory-i-controllability-observability-and-duality-and-some-fundamental|doi=10.2307/2589614|jstor=2589614}}</ref>。 |
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| − | * ''[[Time-domain state space representation]]'' – In this type the values of the [[state variable]]s are represented as functions of time. With this model, the system being analyzed is represented by one or more [[differential equation]]s. Since frequency domain techniques are limited to [[linear function|linear]] systems, time domain is widely used to analyze real-world nonlinear systems. Although these are more difficult to solve, modern computer simulation techniques such as [[simulation language]]s have made their analysis routine.
| + | ==SISO和MIMO== |
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| − | In contrast to the frequency domain analysis of the classical control theory, modern control theory utilizes the time-domain [[state space (controls)|state space]] representation, a mathematical model of a physical system as a set of input, output and state variables related by first-order differential equations. To abstract from the number of inputs, outputs, and states, the variables are expressed as vectors and the differential and algebraic equations are written in matrix form (the latter only being possible when the dynamical system is linear). The state space representation (also known as the "time-domain approach") provides a convenient and compact way to model and analyze systems with multiple inputs and outputs. With inputs and outputs, we would otherwise have to write down Laplace transforms to encode all the information about a system. Unlike the frequency domain approach, the use of the state-space representation is not limited to systems with linear components and zero initial conditions. "State space" refers to the space whose axes are the state variables. The state of the system can be represented as a point within that space.<ref>{{cite book|title=State space & linear systems|series=Schaum's outline series |publisher=McGraw Hill|author=Donald M Wiberg|isbn=978-0-07-070096-3}}</ref><ref>{{cite journal|author=Terrell, William|title=Some fundamental control theory I: Controllability, observability, and duality —AND— Some fundamental control Theory II: Feedback linearization of single input nonlinear systems|journal=American Mathematical Monthly|volume=106|issue=9|year=1999|pages=705–719 and 812–828|url=http://www.maa.org/programs/maa-awards/writing-awards/some-fundamental-control-theory-i-controllability-observability-and-duality-and-some-fundamental|doi=10.2307/2589614|jstor=2589614}}</ref>
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| − | In contrast to the frequency domain analysis of the classical control theory, modern control theory utilizes the time-domain state space representation, a mathematical model of a physical system as a set of input, output and state variables related by first-order differential equations. To abstract from the number of inputs, outputs, and states, the variables are expressed as vectors and the differential and algebraic equations are written in matrix form (the latter only being possible when the dynamical system is linear). The state space representation (also known as the "time-domain approach") provides a convenient and compact way to model and analyze systems with multiple inputs and outputs. With inputs and outputs, we would otherwise have to write down Laplace transforms to encode all the information about a system. Unlike the frequency domain approach, the use of the state-space representation is not limited to systems with linear components and zero initial conditions. "State space" refers to the space whose axes are the state variables. The state of the system can be represented as a point within that space.
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| − | 与经典控制理论的频域分析不同，现代控制理论利用时域状态空间，一个物理系统的数学模型，作为一组输入、输出和状态变量，由一阶微分方程相关联。为了从输入、输出和状态的数量中抽象出来，变量被表示为向量，微分方程和代数方程被写成矩阵形式(后者只有当动力系统是线性的时候才可能)。状态空间模型(也称为“时域方法”)提供了一种方便而紧凑的方式来建模和分析具有多个输入和输出的系统。对于输入和输出，否则我们将不得不写下拉普拉斯转换来对系统的所有信息进行编码。与频域方法不同，状态空间表示的使用并不局限于具有线性分量和零初始条件的系统。“状态空间”是指其轴为状态变量的空间。系统的状态可以表示为该空间中的一个点。
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| − | ==System interfacing - SISO & MIMO==
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| − | ==System interfacing - SISO & MIMO==
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| − | 系统接口 -SISO & MIMO
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| − | Control systems can be divided into different categories depending on the number of inputs and outputs.
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| − | Control systems can be divided into different categories depending on the number of inputs and outputs.
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| | 根据输入和输出的数量，控制系统可以分为不同的类别。 | | 根据输入和输出的数量，控制系统可以分为不同的类别。 |
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| − | * [[Single-input single-output system|Single-input single-output]] (SISO) – This is the simplest and most common type, in which one output is controlled by one control signal. Examples are the cruise control example above, or an [[audio system]], in which the control input is the input audio signal and the output is the sound waves from the speaker. | + | *单输入单输出 SISO –这是最简单，最常见的类型，其中一个输出由一个控制信号控制。示例是上面的巡航控制示例，或者是音频系统，其中控制输入是输入音频信号，输出是来自扬声器的声波。 |
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| − | * [[MIMO|Multiple-input multiple-output]] (MIMO) – These are found in more complicated systems. For example, modern large [[telescope]]s such as the [[Keck telescopes|Keck]] and [[MMT Observatory|MMT]] have mirrors composed of many separate segments each controlled by an [[actuator]]. The shape of the entire mirror is constantly adjusted by a MIMO [[active optics]] control system using input from multiple sensors at the focal plane, to compensate for changes in the mirror shape due to thermal expansion, contraction, stresses as it is rotated and distortion of the [[wavefront]] due to turbulence in the atmosphere. Complicated systems such as [[nuclear reactor]]s and human [[cell (biology)|cells]] are simulated by a computer as large MIMO control systems.
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| − | ==Topics in control theory==
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| − | ==Topics in control theory==
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| − | 控制理论主题
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| − | ===Stability===
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| − | ===Stability===
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| − | 稳定性
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| | + | *多输入多输出 MIMO –在更复杂的系统中可以找到。例如，现代大型望远镜（例如Keck和MMT）具有由许多独立的部分组成的反射镜，每个部分都由致动器控制。MIMO 主动控制系统使用焦平面上多个传感器的输入不断调整整个反射镜的位置，以补偿由于热膨胀，收缩，旋转时的应力以及反射镜变形引起的反射镜形状变化。复杂的系统，例如核反应堆和人体细胞可以由计算机模拟为大型MIMO控制系统。 |
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| | + | ==控制理论主题== |
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| − | The ''stability'' of a general [[dynamical system]] with no input can be described with [[Lyapunov stability]] criteria.
| + | ===稳定性== |
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| − | The stability of a general dynamical system with no input can be described with Lyapunov stability criteria.
| + | 没有输入的一般动力系统的稳定性可以用Lyapunov稳定性标准来描述。 |
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| − | 一个没有输入的一般动力系统的稳定性可以用李雅普诺夫稳定性标准来描述。
| + | *一个线性系统如果对于任何有界输入都舒服于有界的输出中，被称为有界输入有界输出 BIBO 稳定。 |
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| − | *A [[linear system]] is called [[BIBO stability|bounded-input bounded-output (BIBO) stable]] if its output will stay [[bounded function|bounded]] for any bounded input. | + | *输入状态的非线性系统的稳定性是输入状态稳定性 ISS，它结合了Lyapunov稳定性和类似于BIBO稳定性的概念。 |
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| | + | 为简单起见，下面的描述集中于连续和离散时间线性系统。 |
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| | + | 在数学上，这意味着一个线性系统要稳定，其传递函数的所有极点都必须有负实值，即每个极点的实数部分必须小于零。实际上，稳定性意味着传递函数具有复极点 |
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| − | *Stability for [[nonlinear system]]s that take an input is [[input-to-state stability]] (ISS), which combines Lyapunov stability and a notion similar to BIBO stability. | + | *当使用Laplace变换获得传递函数时，在连续时间的复数平面的左半部分中保持不变。 |
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| | + | *使用Z变换时，离散时间下的单位圆包含的稳定性不变。 |
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| | + | 这两种情况之间的区别仅仅是对连续时间和离散时间传递函数的表示方法。连续的Laplace变换是在笛卡尔坐标系中，其中<math>x</math>轴是实轴，离散变换的<math>z</math>变换是在圆坐标系中，其中<math>\rho</math>轴是实轴。 |
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| − | | + | 当满足上述适当条件时，系统被称为渐近稳定的，渐近稳定控制系统的变量总是表现为它们的初始值减少，且不表现永久的振荡。当极点的实部精确等于零(在连续时间情况下)或模量等于1(在离散时间情况下)时，就会发生永久振荡。如果一个简单稳定的系统响应既不随时间衰减也不随时间增长，并且没有振荡，那么它是边际稳定的; 在这种情况下，系统传递函数在复平面原点处具有非重复极点(即在连续时间情况下，它们的实数和复数分量为零。当实部等于零的极点的虚部不等于零时，就存在振荡。 |
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| − | For simplicity, the following descriptions focus on continuous-time and discrete-time '''linear systems'''.
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| − | For simplicity, the following descriptions focus on continuous-time and discrete-time linear systems.
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| − | 为简单起见，下面的描述集中于连续时间和离散时间线性系统。
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| − | Mathematically, this means that for a causal linear system to be stable all of the [[Pole (complex analysis)|poles]] of its [[transfer function]] must have negative-real values, i.e. the real part of each pole must be less than zero. Practically speaking, stability requires that the transfer function complex poles reside
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| − | Mathematically, this means that for a causal linear system to be stable all of the poles of its transfer function must have negative-real values, i.e. the real part of each pole must be less than zero. Practically speaking, stability requires that the transfer function complex poles reside
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| − | 在数学上，这意味着一个因果线性系统要稳定，其传递函数的所有极点都必须有负实值，即。每个极点的真实部分必须小于零。实际上，稳定性要求存在传递函数复极点
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| − | * in the open left half of the [[complex plane]] for continuous time, when the [[Laplace transform]] is used to obtain the transfer function.
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| − | * inside the [[unit circle]] for discrete time, when the [[Z-transform]] is used.
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| − | The difference between the two cases is simply due to the traditional method of plotting continuous time versus discrete time transfer functions. The continuous Laplace transform is in [[Cartesian coordinates]] where the <math>x</math> axis is the real axis and the discrete Z-transform is in [[circular coordinates]] where the <math>\rho</math> axis is the real axis.
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| − | The difference between the two cases is simply due to the traditional method of plotting continuous time versus discrete time transfer functions. The continuous Laplace transform is in Cartesian coordinates where the <math>x</math> axis is the real axis and the discrete Z-transform is in circular coordinates where the <math>\rho</math> axis is the real axis.
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| − | 这两种情况之间的区别仅仅是由于传统的绘制连续时间和离散时间传递函数的方法。连续的拉普拉斯变换是在笛卡尔坐标系中，其中数学 x / math 轴是实轴，离散 z 变换是在圆坐标系中，其中数学 rho / math 轴是实轴。
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| − | When the appropriate conditions above are satisfied a system is said to be [[asymptotic stability|asymptotically stable]]; the variables of an asymptotically stable control system always decrease from their initial value and do not show permanent oscillations. Permanent oscillations occur when a pole has a real part exactly equal to zero (in the continuous time case) or a modulus equal to one (in the discrete time case). If a simply stable system response neither decays nor grows over time, and has no oscillations, it is [[marginal stability|marginally stable]]; in this case the system transfer function has non-repeated poles at the complex plane origin (i.e. their real and complex component is zero in the continuous time case). Oscillations are present when poles with real part equal to zero have an imaginary part not equal to zero.
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| − | When the appropriate conditions above are satisfied a system is said to be asymptotically stable; the variables of an asymptotically stable control system always decrease from their initial value and do not show permanent oscillations. Permanent oscillations occur when a pole has a real part exactly equal to zero (in the continuous time case) or a modulus equal to one (in the discrete time case). If a simply stable system response neither decays nor grows over time, and has no oscillations, it is marginally stable; in this case the system transfer function has non-repeated poles at the complex plane origin (i.e. their real and complex component is zero in the continuous time case). Oscillations are present when poles with real part equal to zero have an imaginary part not equal to zero.
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| − | 当满足上述适当条件时，系统被称为渐近稳定的，渐近稳定控制系统的变量总是从它们的初始值减少，并且不表现永久的振荡。当极点的实部精确等于零(在连续时间情况下)或模量等于一(在离散时间情况下)时，就会发生永久振荡。如果一个简单稳定的系统响应既不随时间衰减也不随时间增长，并且没有振荡，那么它是边际稳定的; 在这种情况下，系统传递函数在复平面原点处具有非重复极点(即:。在连续时间情况下，它们的实数和复数分量为零。当实部等于零的极点的虚部不等于零时，就存在振荡。
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| − | If a system in question has an [[impulse response]] of
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| − | If a system in question has an impulse response of
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| | 如果一个系统的脉冲响应为 | | 如果一个系统的脉冲响应为 |
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| | :<math>\ x[n] = 0.5^n u[n]</math> | | :<math>\ x[n] = 0.5^n u[n]</math> |
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| − | <math>\ x[n] = 0.5^n u[n]</math>
| + | 然后 z 变换(参见本例)为 |
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| − | 数学[ n ]0.5 ^ u [ n ] / math
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| − | then the Z-transform (see [[Z-transform#Example 2 (causal ROC)|this example]]), is given by
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| − | then the Z-transform (see this example), is given by
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| − | 然后 z 变换(参见本例)由 | |
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| | :<math>\ X(z) = \frac{1}{1 - 0.5z^{-1}}</math> | | :<math>\ X(z) = \frac{1}{1 - 0.5z^{-1}}</math> |
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| − | <math>\ X(z) = \frac{1}{1 - 0.5z^{-1}}</math>
| + | 在<math>z = 0.5</math>零虚部)中有一个极点。这个系统是 BIBO (渐近)稳定的，因为极点在单位圆内。 |
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| − | 数学 x (z) frac {1}{1-0.5 z ^ {1} / math
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| − | which has a pole in <math>z = 0.5</math> (zero [[imaginary number|imaginary part]]). This system is BIBO (asymptotically) stable since the pole is ''inside'' the unit circle.
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| − | which has a pole in <math>z = 0.5</math> (zero imaginary part). This system is BIBO (asymptotically) stable since the pole is inside the unit circle.
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| − | 在数学 z0.5 / math (零虚部)中有一个极点。这个系统是 BIBO (渐近)稳定的，因为极点在单位圆内。
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| − | However, if the impulse response was
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| − | However, if the impulse response was
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| − | 然而，如果冲动反应是
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| | + | 然后，如果冲激反应是 |
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| | :<math>\ x[n] = 1.5^n u[n]</math> | | :<math>\ x[n] = 1.5^n u[n]</math> |
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| − | <math>\ x[n] = 1.5^n u[n]</math> | + | 那么<math>z</math>变换是 |
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| − | 数学[ n ]1.5 ^ u [ n ]
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| − | then the Z-transform is
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| − | then the Z-transform is
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| − | 那么 z 变换是
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| | :<math>\ X(z) = \frac{1}{1 - 1.5z^{-1}}</math> | | :<math>\ X(z) = \frac{1}{1 - 1.5z^{-1}}</math> |
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| − | <math>\ X(z) = \frac{1}{1 - 1.5z^{-1}}</math>
| + | 它的极点在<math>z = 1.5</math>上，不是 BIBO 稳定的，因为极点的模严格大于1。 |
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| − | 1-1.5 z ^ {-1} / math
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| − | which has a pole at <math>z = 1.5</math> and is not BIBO stable since the pole has a modulus strictly greater than one.
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| − | which has a pole at <math>z = 1.5</math> and is not BIBO stable since the pole has a modulus strictly greater than one.
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| − | 它的极点在数学 z1.5 / math 上，不是 BIBO 稳定的，因为极点的模严格大于1。
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| − | Numerous tools exist for the analysis of the poles of a system. These include graphical systems like the [[root locus]], [[Bode plot]]s or the [[Nyquist plot]]s.
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| − | Numerous tools exist for the analysis of the poles of a system. These include graphical systems like the root locus, Bode plots or the Nyquist plots.
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| − | 有许多工具可用来分析系统的极点。这些包括图形系统，如根轨迹，波德图或奈奎斯特图。
| + | 有许多工具可用来分析系统的极点。这些包括图形系统，如根轨迹，Bode图或Nyquist图。 |
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| − | Mechanical changes can make equipment (and control systems) more stable. Sailors add ballast to improve the stability of ships. Cruise ships use [[Ship stability#Stabilizer fins|antiroll fins]] that extend transversely from the side of the ship for perhaps 30 feet (10 m) and are continuously rotated about their axes to develop forces that oppose the roll.
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| − | Mechanical changes can make equipment (and control systems) more stable. Sailors add ballast to improve the stability of ships. Cruise ships use antiroll fins that extend transversely from the side of the ship for perhaps 30 feet (10 m) and are continuously rotated about their axes to develop forces that oppose the roll.
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| | 机械的改变可以使设备(和控制系统)更加稳定。水手们增加压舱物以改善船只的稳定性。游轮使用从船侧横向延伸约30英尺(10米)的防侧翻鳍，并不断地绕轴旋转，以产生阻止侧翻的力。 | | 机械的改变可以使设备(和控制系统)更加稳定。水手们增加压舱物以改善船只的稳定性。游轮使用从船侧横向延伸约30英尺(10米)的防侧翻鳍，并不断地绕轴旋转，以产生阻止侧翻的力。 |
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| − | | + | ===可控性和可观察性=== |
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| − | ===Controllability and observability=== | |
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| − | ===Controllability and observability===
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| − | 可控性和可观察性
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| − | {{Main| Controllability|Observability}}
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| − | [[Controllability]] and [[observability]] are main issues in the analysis of a system before deciding the best control strategy to be applied, or whether it is even possible to control or stabilize the system. Controllability is related to the possibility of forcing the system into a particular state by using an appropriate control signal. If a state is not controllable, then no signal will ever be able to control the state. If a state is not controllable, but its dynamics are stable, then the state is termed ''stabilizable''. Observability instead is related to the possibility of ''observing'', through output measurements, the state of a system. If a state is not observable, the controller will never be able to determine the behavior of an unobservable state and hence cannot use it to stabilize the system. However, similar to the stabilizability condition above, if a state cannot be observed it might still be detectable.
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| − | Controllability and observability are main issues in the analysis of a system before deciding the best control strategy to be applied, or whether it is even possible to control or stabilize the system. Controllability is related to the possibility of forcing the system into a particular state by using an appropriate control signal. If a state is not controllable, then no signal will ever be able to control the state. If a state is not controllable, but its dynamics are stable, then the state is termed stabilizable. Observability instead is related to the possibility of observing, through output measurements, the state of a system. If a state is not observable, the controller will never be able to determine the behavior of an unobservable state and hence cannot use it to stabilize the system. However, similar to the stabilizability condition above, if a state cannot be observed it might still be detectable.
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| | 能控性和能观性是系统分析中的主要问题，它直接影响到系统的可控性和稳定性。可控性与使用适当的控制信号使系统进入特定状态的可能性有关。如果一个状态是不可控的，那么没有信号将永远能够控制该状态。如果一个状态是不可控的，但它的动力学是稳定的，那么这个状态称为可稳定的。相反，可观测性与通过输出测量观测系统状态的可能性有关。如果一个状态不可观测，控制器将永远不能确定一个不可观测状态的行为，因此不能使用它来稳定系统。然而，类似于上面的稳定性条件，如果一个状态不能被观察到，它仍然可能是可检测的。 | | 能控性和能观性是系统分析中的主要问题，它直接影响到系统的可控性和稳定性。可控性与使用适当的控制信号使系统进入特定状态的可能性有关。如果一个状态是不可控的，那么没有信号将永远能够控制该状态。如果一个状态是不可控的，但它的动力学是稳定的，那么这个状态称为可稳定的。相反，可观测性与通过输出测量观测系统状态的可能性有关。如果一个状态不可观测，控制器将永远不能确定一个不可观测状态的行为，因此不能使用它来稳定系统。然而，类似于上面的稳定性条件，如果一个状态不能被观察到，它仍然可能是可检测的。 |
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| − | | + | 从几何的角度来看，看待控制系统的每个变量的状态，这些变量的每个“坏”状态必须是可控和可观测的，以确保在闭环系统中的状态表达。也就是说，如果闭环系统的特征值之一不是可控和可观测的，这部分动态将保持不变。如果这样一个特征值不稳定，这个特征值的动力学将在闭环系统中将表示为不稳定的。在状态空间表示的传递函数实现中，不可观测的极点并不存在，这就是为什么在动力系统分析中有时倾向于后者的原因。 |
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| − | From a geometrical point of view, looking at the states of each variable of the system to be controlled, every "bad" state of these variables must be controllable and observable to ensure a good behavior in the closed-loop system. That is, if one of the [[eigenvalues]] of the system is not both controllable and observable, this part of the dynamics will remain untouched in the closed-loop system. If such an eigenvalue is not stable, the dynamics of this eigenvalue will be present in the closed-loop system which therefore will be unstable. Unobservable poles are not present in the transfer function realization of a state-space representation, which is why sometimes the latter is preferred in dynamical systems analysis.
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| − | From a geometrical point of view, looking at the states of each variable of the system to be controlled, every "bad" state of these variables must be controllable and observable to ensure a good behavior in the closed-loop system. That is, if one of the eigenvalues of the system is not both controllable and observable, this part of the dynamics will remain untouched in the closed-loop system. If such an eigenvalue is not stable, the dynamics of this eigenvalue will be present in the closed-loop system which therefore will be unstable. Unobservable poles are not present in the transfer function realization of a state-space representation, which is why sometimes the latter is preferred in dynamical systems analysis.
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| − | 从几何的角度来看，看待控制系统的每个变量的状态，这些变量的每个“坏”状态必须是可控和可观测的，以确保在闭环系统中的良好行为。也就是说，如果系统的特征值之一不是可控和可观测的，这部分动态将保持不变的闭环系统。如果这样一个特征值不稳定，这个特征值的动力学将出现在闭环系统中，因此将是不稳定的。在状态空间表示的传递函数实现中，不可观测的极点并不存在，这就是为什么在动力系统分析中有时倾向于后者的原因。
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| − | Solutions to problems of an uncontrollable or unobservable system include adding actuators and sensors.
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| − | Solutions to problems of an uncontrollable or unobservable system include adding actuators and sensors.
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| | 解决不可控或不可观测系统问题的方法包括增加执行器和传感器。 | | 解决不可控或不可观测系统问题的方法包括增加执行器和传感器。 |
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| | + | ===控制方法=== |
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| | + | 在过去的几年里，人们设计了几种不同的控制策略。这些控制器同最简单的PID控制器到对于复杂系统或非常规系统（尤其是机器人技术或飞机巡航控制）都是有一定差别的。 |
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| | + | 控制问题可以有几种规格。当然，始终存在稳定性。无论开环稳定性如何，控制器都必须确保闭环系统稳定。控制器选择不当甚至会恶化开环系统的稳定性，通常必须避免这种情况。有时希望在闭环中获得特定的动力学：即极点具有<math>Re[\lambda] < -\overline{\lambda}</math>,其中 <math>\overline{\lambda}</math，是一个严格大于零的固定值，而不是简单地要求<math>Re[\lambda]<0</math>。 |
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| | + | 另一个典型的特性是抑制阶跃扰动，包括开环系统中的积分器(即直接在系统控制之前)很容易做到这一点。其他类型的扰动需要包括不同类型的子系统。 |
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| − | ===Control specification===
| + | 其他“经典”控制理论规范考虑了闭环系统的时域响应。其中包括上升时间(控制系统在扰动后达到期望值所需的时间)、峰值时间、超调量(响应达到期望值之前达到的最高值)和稳定时间等其他稳态性能。频域规范通常与鲁棒性有关。 |
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| − | ===Control specification===
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| − | 控制规格
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| − | Several different control strategies have been devised in the past years. These vary from extremely general ones ([[PID controller]]), to others devoted to very particular classes of systems (especially [[robotics]] or aircraft cruise control).
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| − | Several different control strategies have been devised in the past years. These vary from extremely general ones (PID controller), to others devoted to very particular classes of systems (especially robotics or aircraft cruise control).
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| − | 在过去的几年里，人们设计了几种不同的控制策略。这些不同从非常一般的(PID 控制器) ，其他致力于非常特殊类型的系统(特别是机器人或飞机巡航控制)。
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| − | A control problem can have several specifications. Stability, of course, is always present. The controller must ensure that the closed-loop system is stable, regardless of the open-loop stability. A poor choice of controller can even worsen the stability of the open-loop system, which must normally be avoided. Sometimes it would be desired to obtain particular dynamics in the closed loop: i.e. that the poles have <math>Re[\lambda] < -\overline{\lambda}</math>, where <math>\overline{\lambda}</math> is a fixed value strictly greater than zero, instead of simply asking that <math>Re[\lambda]<0</math>.
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| − | A control problem can have several specifications. Stability, of course, is always present. The controller must ensure that the closed-loop system is stable, regardless of the open-loop stability. A poor choice of controller can even worsen the stability of the open-loop system, which must normally be avoided. Sometimes it would be desired to obtain particular dynamics in the closed loop: i.e. that the poles have <math>Re[\lambda] < -\overline{\lambda}</math>, where <math>\overline{\lambda}</math> is a fixed value strictly greater than zero, instead of simply asking that <math>Re[\lambda]<0</math>.
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| − | 一个控制问题可以有几个规范。当然，稳定总是存在的。控制器必须确保闭环系统是稳定的，而不管开环的稳定性。控制器的选择不当甚至会恶化开环系统的稳定性，这是通常必须避免的。有时需要在闭环中获得特定的动力学:。极点有数学 Re [ lambda ]- overline { lambda } / math，其中 math overline { lambda } / math 是一个严格大于零的固定值，而不是简单地问数学 Re [ lambda ]0 / math。
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| − | Another typical specification is the rejection of a step disturbance; including an [[integrator]] in the open-loop chain (i.e. directly before the system under control) easily achieves this. Other classes of disturbances need different types of sub-systems to be included.
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| − | Another typical specification is the rejection of a step disturbance; including an integrator in the open-loop chain (i.e. directly before the system under control) easily achieves this. Other classes of disturbances need different types of sub-systems to be included.
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| − | 另一个典型的特性是抑制阶跃扰动，包括开环链中的积分器(即。直接在系统控制之前)很容易做到这一点。其他类型的扰动需要包括不同类型的子系统。
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| − | Other "classical" control theory specifications regard the time-response of the closed-loop system. These include the [[rise time]] (the time needed by the control system to reach the desired value after a perturbation), peak [[overshoot (signal)|overshoot]] (the highest value reached by the response before reaching the desired value) and others ([[settling time]], quarter-decay). Frequency domain specifications are usually related to [[robust control|robustness]] (see after).
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| − | Other "classical" control theory specifications regard the time-response of the closed-loop system. These include the rise time (the time needed by the control system to reach the desired value after a perturbation), peak overshoot (the highest value reached by the response before reaching the desired value) and others (settling time, quarter-decay). Frequency domain specifications are usually related to robustness (see after).
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| − | 其他“经典”控制理论规范考虑了闭环系统的时间响应。其中包括上升时间(控制系统在扰动后达到期望值所需的时间)、峰值超调(响应达到期望值之前达到的最高值)和其他(稳定时间、四分之一衰减)。频域规范通常与健壮性有关(见后)。
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| − | Modern performance assessments use some variation of integrated tracking error (IAE, ISA, CQI).
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| − | Modern performance assessments use some variation of integrated tracking error (IAE, ISA, CQI).
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| | 现代的性能评估使用一些综合跟踪误差的变体(IAE，ISA，CQI)。 | | 现代的性能评估使用一些综合跟踪误差的变体(IAE，ISA，CQI)。 |
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| | + | ===模式辨识与鲁棒性=== |
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| | + | 控制系统必须具有一定的鲁棒性。一个鲁棒控制器是具有将和其数学特性不同的变量加入控制过程中，其鲁棒特性不变。这一要求很重要，因为没有任何一个真正的物理系统能够用数学表示的一系列微分方程那样真正地表现出来。为了简化计算，通常会选择简化的数学模型，否则，真正的系统动力学可能会非常复杂，以至于不可能建立一个完整的模型。 |
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| | + | :系统辨识 |
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| | + | 确定控制模型动力学方程的过程称为系统辨识。这可以离线完成：例如，执行一系列测量以从中计算近似的数学模型，通常是其传递函数或矩阵。但是，从输出中进行的这种识别不能考虑不可观察的动态。有时，模型是直接从已知的物理方程式开始构建的，例如，在质量弹簧-阻尼器系统的情况下，我们知道<math> m \ddot(t) = - K x(t) - \Beta \dot{x}(t)</math>。即使假设在设计控制器时使用了“完整”模型，这些方程中包含的所有参数（称为“标称/名义参数”）也从来不是绝对精确的；即使连接到物理系统的真实参数值与标称值不同，控制系统也必须正确运行。 |
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| − | ===Model identification and robustness===
| + | 一些先进的控制技术包括“在线”识别过程。当控制器本身运行时，模型的参数被计算(“辨识”)。通过这种方式，如果参数发生剧烈变化，例如，如果机器人的手臂释放一个重量，控制器将自我调整，以确保正确的性能。 |
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| − | ===Model identification and robustness===
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| − | 模型辨识与鲁棒性
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| − | A control system must always have some robustness property. A [[robust control]]ler is such that its properties do not change much if applied to a system slightly different from the mathematical one used for its synthesis. This requirement is important, as no real physical system truly behaves like the series of differential equations used to represent it mathematically. Typically a simpler mathematical model is chosen in order to simplify calculations, otherwise, the true system dynamics can be so complicated that a complete model is impossible.
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| − | A control system must always have some robustness property. A robust controller is such that its properties do not change much if applied to a system slightly different from the mathematical one used for its synthesis. This requirement is important, as no real physical system truly behaves like the series of differential equations used to represent it mathematically. Typically a simpler mathematical model is chosen in order to simplify calculations, otherwise, the true system dynamics can be so complicated that a complete model is impossible.
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| − | 控制系统必须具有一定的鲁棒性。一个鲁棒控制器是这样的，其性质不会改变很多，如果应用到一个系统略有不同的数学之一用于其综合。这一要求很重要，因为没有任何一个真正的物理系统能够像用于数学表示的一系列微分方程那样真正地表现出来。为了简化计算，通常会选择一个更简单的数学模型，否则，真正的系统动力学可能会非常复杂，以至于不可能建立一个完整的模型。
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| − | ;System identification
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| − | System identification
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| − | 系统辨识
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| − | {{details|System identification}}
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| − | The process of determining the equations that govern the model's dynamics is called [[system identification]]. This can be done off-line: for example, executing a series of measures from which to calculate an approximated mathematical model, typically its [[transfer function]] or matrix. Such identification from the output, however, cannot take account of unobservable dynamics. Sometimes the model is built directly starting from known physical equations, for example, in the case of a [[Damping#Example: mass–spring–damper|mass-spring-damper]] system we know that <math> m \ddot{{x}}(t) = - K x(t) - \Beta \dot{x}(t)</math>. Even assuming that a "complete" model is used in designing the controller, all the parameters included in these equations (called "nominal parameters") are never known with absolute precision; the control system will have to behave correctly even when connected to a physical system with true parameter values away from nominal.
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| − | The process of determining the equations that govern the model's dynamics is called system identification. This can be done off-line: for example, executing a series of measures from which to calculate an approximated mathematical model, typically its transfer function or matrix. Such identification from the output, however, cannot take account of unobservable dynamics. Sometimes the model is built directly starting from known physical equations, for example, in the case of a mass-spring-damper system we know that <math> m \ddot(t) = - K x(t) - \Beta \dot{x}(t)</math>. Even assuming that a "complete" model is used in designing the controller, all the parameters included in these equations (called "nominal parameters") are never known with absolute precision; the control system will have to behave correctly even when connected to a physical system with true parameter values away from nominal.
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| − | 确定支配模型动力学的方程式的过程被称为系统辨识。这可以离线完成: 例如，执行一系列的措施，从中计算一个近似的数学模型，通常是它的传递函数或矩阵。然而，这种对输出的识别不能考虑不可观测的动态性。有时候模型直接从已知的物理方程出发建立，例如，在质量-弹簧-阻尼系统的情况下，我们知道 math m-dot (t)-kx (t)- Beta-dot { x }(t) / math。即使假设在设计控制器时使用”完整”模型，这些方程中包括的所有参数(称为”名义参数”)也从来不是绝对精确的; 即使控制系统连接到远离名义参数值的真实参数值的物理系统，也必须正确地工作。
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| − | Some advanced control techniques include an "on-line" identification process (see later). The parameters of the model are calculated ("identified") while the controller itself is running. In this way, if a drastic variation of the parameters ensues, for example, if the robot's arm releases a weight, the controller will adjust itself consequently in order to ensure the correct performance.
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| − | Some advanced control techniques include an "on-line" identification process (see later). The parameters of the model are calculated ("identified") while the controller itself is running. In this way, if a drastic variation of the parameters ensues, for example, if the robot's arm releases a weight, the controller will adjust itself consequently in order to ensure the correct performance.
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| − | 一些先进的控制技术包括“在线”识别过程(见后文)。当控制器本身运行时，模型的参数被计算(“辨识”)。通过这种方式，如果参数发生剧烈变化，例如，如果机器人的手臂释放一个重量，控制器将自我调整，以确保正确的性能。
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| − | ;Analysis
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| − | Analysis
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| − | 分析
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| − | Analysis of the robustness of a SISO (single input single output) control system can be performed in the frequency domain, considering the system's transfer function and using [[Nyquist diagram|Nyquist]] and [[Bode diagram]]s. Topics include [[Bode plot#Gain margin and phase margin|gain and phase margin]] and amplitude margin. For MIMO (multi-input multi output) and, in general, more complicated control systems, one must consider the theoretical results devised for each control technique (see next section). I.e., if particular robustness qualities are needed, the engineer must shift his attention to a control technique by including them in its properties.
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| − | Analysis of the robustness of a SISO (single input single output) control system can be performed in the frequency domain, considering the system's transfer function and using Nyquist and Bode diagrams. Topics include gain and phase margin and amplitude margin. For MIMO (multi-input multi output) and, in general, more complicated control systems, one must consider the theoretical results devised for each control technique (see next section). I.e., if particular robustness qualities are needed, the engineer must shift his attention to a control technique by including them in its properties.
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| − | 考虑系统的传递函数，利用奈奎斯特图和伯德图，可以在频域上对单输入单输出控制系统的鲁棒性进行分析。主题包括增益和相位裕度和振幅裕度。对于 MIMO (多输入多输出)和一般更复杂的控制系统，必须考虑为每种控制技术设计的理论结果(见下一节)。也就是说，如果需要特定的鲁棒性质，工程师必须将注意力转移到控制技术上，将其包含在控制技术的属性中。
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| − | ;Constraints
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| − | Constraints
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| − | 约束
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| − | A particular robustness issue is the requirement for a control system to perform properly in the presence of input and state constraints. In the physical world every signal is limited. It could happen that a controller will send control signals that cannot be followed by the physical system, for example, trying to rotate a valve at excessive speed. This can produce undesired behavior of the closed-loop system, or even damage or break actuators or other subsystems. Specific control techniques are available to solve the problem: [[model predictive control]] (see later), and [[anti-wind up system (control)|anti-wind up systems]]. The latter consists of an additional control block that ensures that the control signal never exceeds a given threshold.
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| − | A particular robustness issue is the requirement for a control system to perform properly in the presence of input and state constraints. In the physical world every signal is limited. It could happen that a controller will send control signals that cannot be followed by the physical system, for example, trying to rotate a valve at excessive speed. This can produce undesired behavior of the closed-loop system, or even damage or break actuators or other subsystems. Specific control techniques are available to solve the problem: model predictive control (see later), and anti-wind up systems. The latter consists of an additional control block that ensures that the control signal never exceeds a given threshold.
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| − | 一个特别的鲁棒性问题是控制系统在存在输入和状态约束的情况下正确执行的要求。在物理世界中，每个信号都是有限的。控制器可能会发出物理系统无法跟踪的控制信号，例如，试图以过高的速度旋转阀门。这可能导致闭环系统的不良行为，甚至损坏或破坏执行机构或其他子系统。特定的控制技术可以解决这个问题: 模型预估计控制控制系统(见后面) ，和反上风系统。后者包括一个额外的控制块，确保控制信号永远不超过给定的阈值。
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| − | ==System classifications==
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| − | ==System classifications==
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| − | 系统分类
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| − | ===Linear systems control===
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| − | ===Linear systems control===
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| − | 线性系统控制
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| − | {{Main|State space (controls)}}
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| − | For MIMO systems, pole placement can be performed mathematically using a [[State space (controls)|state space representation]] of the open-loop system and calculating a feedback matrix assigning poles in the desired positions. In complicated systems this can require computer-assisted calculation capabilities, and cannot always ensure robustness. Furthermore, all system states are not in general measured and so observers must be included and incorporated in pole placement design.
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| − | For MIMO systems, pole placement can be performed mathematically using a state space representation of the open-loop system and calculating a feedback matrix assigning poles in the desired positions. In complicated systems this can require computer-assisted calculation capabilities, and cannot always ensure robustness. Furthermore, all system states are not in general measured and so observers must be included and incorporated in pole placement design.
| + | ;分析 |
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| − | 对于多输入多输出系统，极点配置可以通过使用开环系统的状态空间并计算反馈矩阵在期望位置的极点配置来实现。在复杂系统中，这可能需要计算机辅助计算能力，并且不能总是确保健壮性。此外，所有的系统状态一般不能测量，因此观测器必须包括在极点配置设计中。
| + | 考虑系统的传递函数并使用Nyquist和Bode图，可以在频域中对SISO控制系统的鲁棒性进行分析。包括增益和相位裕度以及幅度裕度。对于MIMO以及通常更复杂的控制系统，必须考虑针对每种控制技术设计的理论结果（请参阅下一节）。即如果需要特殊的鲁棒性，程师必须将注意力转移到控制技术上，将注意力转移到控制技术的属性中。 |
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| | + | ;约束条件 |
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| | + | 一个特殊的鲁棒性问题是要求控制系统在存在输入和状态约束的情况下正确运行。在物理世界中，每个信号都是有限的。控制器可能会发送物理系统无法跟踪的控制信号，例如，试图以超高速旋转阀门。这可能会导致闭环系统发生不良行为，甚至损坏或损坏执行器或其他子系统。可以使用特定的控制技术来解决该问题：模型预测控制（请参阅下文）和反缠绕系统。后者包括一个附加的控制块，可确保控制信号从不超过给定的阈值。 |
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| − | ===Nonlinear systems control=== | + | ==系统分类== |
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| − | ===Nonlinear systems control=== | + | ===[[线性系统控制]]=== |
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| − | 非线性系统控制
| + | 对于MIMO系统，可以使用开环系统的状态空间表示并通过计算分配给期望位置中的极点的反馈矩阵，以数学方式执行极点放置。在复杂的系统中，这可能需要计算机辅助的计算功能，并且不能始终确保鲁棒性。此外，所有的系统状态一般不能测量，因此观测器必须包括在极点配置设计中。 |
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| − | {{Main|Nonlinear control}}
| + | ===[[非线性系统控制]]=== |
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| | + | 机器人技术和航空航天工业等行业的流程通常具有强烈的非线性动力学。在控制理论中，有时可以将这类系统线性化并应用线性技术，但在许多情况下，有必要从头设计允许控制非线性系统的理论。这些控制方法，例如，反馈线性化控制、滑膜控制、轨迹线性化控制通常利用了基于李亚普诺夫理论的结果。微分几何已经被广泛地用作一种工具，将众所周知的线性控制概念推广到非线性情况，以及展示使它成为一个更具挑战性的问题的微妙之处。控制理论也被用来解释指导认知状态的神经机制<ref name=Shi_Gu_et_al>{{cite journal |author1 = Gu Shi|year = 2015 |title = Controllability of structural brain networks (Article Number 8414) |journal = Nature Communications |volume = 6 |quote = Here we use tools from control and network theories to offer a mechanistic explanation for how the brain moves between cognitive states drawn from the network organization of white matter microstructure. |lay-url = http://www.nature.com/ncomms/2015/151001/ncomms9414/full/ncomms9414.html |doi = 10.1038/ncomms9414|issue = 6 |display-authors=etal|arxiv = 1406.5197|bibcode = 2015NatCo...6E8414G |pmid = 26423222 |pmc = 4600713 |page = 8414}}</ref>。 |
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| | + | ===分散式系统控制=== |
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| − | Processes in industries like [[robotics]] and the [[aerospace industry]] typically have strong nonlinear dynamics. In control theory it is sometimes possible to linearize such classes of systems and apply linear techniques, but in many cases it can be necessary to devise from scratch theories permitting control of nonlinear systems. These, e.g., [[feedback linearization]], [[backstepping]], [[sliding mode control]], trajectory linearization control normally take advantage of results based on [[Lyapunov's theory]]. [[Differential geometry]] has been widely used as a tool for generalizing well-known linear control concepts to the non-linear case, as well as showing the subtleties that make it a more challenging problem. Control theory has also been used to decipher the neural mechanism that directs cognitive states.<ref name=Shi_Gu_et_al>{{cite journal |author1 = Gu Shi|year = 2015 |title = Controllability of structural brain networks (Article Number 8414) |journal = Nature Communications |volume = 6 |quote = Here we use tools from control and network theories to offer a mechanistic explanation for how the brain moves between cognitive states drawn from the network organization of white matter microstructure. |lay-url = http://www.nature.com/ncomms/2015/151001/ncomms9414/full/ncomms9414.html |doi = 10.1038/ncomms9414|issue = 6 |display-authors=etal|arxiv = 1406.5197|bibcode = 2015NatCo...6E8414G |pmid = 26423222 |pmc = 4600713 |page = 8414}}</ref>
| + | 当系统由多个控制器控制时，问题是分散控制问题。地方分权在许多方面都很有帮助，例如，它帮助控制系统在更大的范围内运行。分散控制系统中的智能体可以利用通信信道进行交互并协调其行为。 |
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| − | Processes in industries like robotics and the aerospace industry typically have strong nonlinear dynamics. In control theory it is sometimes possible to linearize such classes of systems and apply linear techniques, but in many cases it can be necessary to devise from scratch theories permitting control of nonlinear systems. These, e.g., feedback linearization, backstepping, sliding mode control, trajectory linearization control normally take advantage of results based on Lyapunov's theory. Differential geometry has been widely used as a tool for generalizing well-known linear control concepts to the non-linear case, as well as showing the subtleties that make it a more challenging problem. Control theory has also been used to decipher the neural mechanism that directs cognitive states.
| + | ===确定性和随机性系统控制=== |
| | + | 随机控制问题是一种状态变量的演变受到系统外部随机冲击的问题。确定性控制问题不受外部随机信号的影响。 |
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| − | 机器人技术和航空航天工业等行业的流程通常具有强烈的非线性动力学。在控制理论中，有时可以将这类系统线性化并应用线性技术，但在许多情况下，有必要从头设计允许控制非线性系统的理论。这些控制方法，例如，回授线性化控制、反推控制、滑动模式控制控制、轨迹线性化控制通常利用了基于李亚普诺夫理论的结果。微分几何已经被广泛地用作一种工具，将众所周知的线性控制概念推广到非线性情况，以及展示使它成为一个更具挑战性的问题的微妙之处。控制理论也被用来解释指导认知状态的神经机制。
| + | ==主要控制策略== |
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| | + | 每个控制系统首先必须保证闭环行为的稳定性。对于线性系统，这可以通过直接配置极点来实现。非线性控制系统使用特定的理论(通常基于李亚普诺夫理论)来确保系统的稳定性，而不考虑系统的内部动态。实现不同规格的可能性不同于所考虑的模型和所选择的控制策略。 |
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| | + | ;主要控制技术清单 |
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| | + | *自适应控制使用过程参数的在线识别或控制器增益的修改，从而获得强大的鲁棒性。1950年代，自适应控制首次应用于航空航天业，并在该领域取得了特别的成功。 |
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| | + | *分级控制系统是一种类型的控制系统，其中一组设备和管理软件的被布置在分层 树。当树中的链接由计算机网络实现时，该分层控制系统也是网络控制系统的一种形式。 |
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| − | ===Decentralized systems control=== | + | *智能控制使用各种AI计算方法，例如人工神经网络，贝叶斯概率，模糊逻辑，<ref>{{cite journal | title=A novel fuzzy framework for nonlinear system control| journal=Fuzzy Sets and Systems | year=2010 | last=Liu |first1=Jie |author2=Wilson Wang |author3=Farid Golnaraghi |author4=Eric Kubica | volume=161 | issue=21 | pages=2746–2759 | doi=10.1016/j.fss.2010.04.009}}</ref> 机器学习，进化计算和遗传算法或这些方法的组合（例如神经模糊算法）来控制动态系统。 |
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| − | ===Decentralized systems control===
| + | *最优控制是一种特殊的控制技术，其中控制信号优化某个“成本指标”：例如，在卫星的情况下，将其推向消耗最少燃料的所需轨迹所需的喷射推力。两种最优控制设计方法已在工业应用中广泛使用，因为已证明它们可以保证闭环稳定性。这些是模型预测控制 MPC 和线性二次高斯控制 LQG 。第一个可以更明确地考虑对系统中信号的约束，这是许多工业过程中的重要特征。但是，MPC中的“最佳控制”结构只是实现这种结果的一种手段，因为它没有优化闭环控制系统的真实性能指标。与PID控制器一起，MPC系统是过程控制中使用最广泛的控制技术。 |
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| − | 分散式系统控制
| + | *鲁棒控制明确地解决了控制器设计方法的不确定性。使用鲁棒控制方法设计的控制器往往能够应对真实系统与用于设计的标称模型之间的微小差异。<ref>{{cite journal|last1=Melby|first1=Paul|last2=et.|first2=al.|title=Robustness of Adaptation in Controlled Self-Adjusting Chaotic Systems |journal=Fluctuation and Noise Letters |volume=02|issue=4|pages=L285–L292|date=2002|doi=10.1142/S0219477502000919}}</ref> Bode和其他人的早期方法相当可靠；有时发现1960年代和1970年代发明的状态空间方法缺乏鲁棒性。现代鲁棒控制技术的例子包括H-无穷回路整形通过邓肯麦克法兰和开发基思格洛弗，滑模控制由显影（SMC）瓦迪姆Utkin和安全协议，旨在控制智能电网应用中的大量异构负载<ref name='TCL1'>{{cite journal|title=Safe Protocols for Generating Power Pulses with Heterogeneous Populations of Thermostatically Controlled Loads |author=N. A. Sinitsyn. S. Kundu, S. Backhaus |journal=[[Energy Conversion and Management]]|volume=67|year=2013|pages=297–308|arxiv=1211.0248|doi=10.1016/j.enconman.2012.11.021}}</ref> 。鲁棒法旨在在存在小的建模误差的情况下实现稳健的性能和/或稳定性。 |
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| − | {{Main|Distributed control system}}
| + | *随机控制处理模型不确定的控制设计。在典型的随机控制问题中，假设模型和控制器中存在随机噪声和干扰，并且控制设计必须考虑这些随机偏差。 |
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| | + | *能量整形控制将工厂和控制器视为能量转换设备。为了实现期望的行为，根据互连制定了控制策略。 |
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| | + | *自组织的临界控制可以定义为试图干扰自组织系统耗散能量的过程。 |
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| − | When the system is controlled by multiple controllers, the problem is one of decentralized control. Decentralization is helpful in many ways, for instance, it helps control systems to operate over a larger geographical area. The agents in decentralized control systems can interact using communication channels and coordinate their actions.
| + | ==系统和控制的科学家== |
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| − | When the system is controlled by multiple controllers, the problem is one of decentralized control. Decentralization is helpful in many ways, for instance, it helps control systems to operate over a larger geographical area. The agents in decentralized control systems can interact using communication channels and coordinate their actions.
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| − | 当系统由多个控制器控制时，问题是分散控制问题。地方分权在许多方面都很有帮助，例如，它帮助控制系统在更大的经纬度范围内运行。分散控制系统中的智能体可以利用通信信道进行交互并协调其行为。
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| − | ===Deterministic and stochastic systems control=== | |
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| − | ===Deterministic and stochastic systems control===
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| − | 确定性和随机性系统控制
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| − | {{Main|Stochastic control}}
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| − | A stochastic control problem is one in which the evolution of the state variables is subjected to random shocks from outside the system. A deterministic control problem is not subject to external random shocks.
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| − | A stochastic control problem is one in which the evolution of the state variables is subjected to random shocks from outside the system. A deterministic control problem is not subject to external random shocks.
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| − | 统计控制问题是指状态变量的演化受到系统外部随机冲击的问题。确定性控制问题不受外部随机冲击的影响。
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| − | ==Main control strategies==
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| − | ==Main control strategies==
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| − | 主要控制策略
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| − | Every control system must guarantee first the stability of the closed-loop behavior. For [[linear system]]s, this can be obtained by directly placing the poles. Non-linear control systems use specific theories (normally based on [[Aleksandr Lyapunov]]'s Theory) to ensure stability without regard to the inner dynamics of the system. The possibility to fulfill different specifications varies from the model considered and the control strategy chosen.
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| − | Every control system must guarantee first the stability of the closed-loop behavior. For linear systems, this can be obtained by directly placing the poles. Non-linear control systems use specific theories (normally based on Aleksandr Lyapunov's Theory) to ensure stability without regard to the inner dynamics of the system. The possibility to fulfill different specifications varies from the model considered and the control strategy chosen.
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| − | 每个控制系统首先必须保证闭环行为的稳定性。对于线性系统，这可以通过直接放置极点来实现。非线性控制系统使用特定的理论(通常基于亚历山大·李亚普诺夫理论)来确保系统的稳定性，而不考虑系统的内部动态。实现不同规格的可能性不同于所考虑的模型和所选择的控制策略。
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| − | ;List of the main control techniques
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| − | List of the main control techniques
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| − | 主要控制技术清单
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| − | *[[Adaptive control]] uses on-line identification of the process parameters, or modification of controller gains, thereby obtaining strong robustness properties. Adaptive controls were applied for the first time in the [[aerospace industry]] in the 1950s, and have found particular success in that field.
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| − | *A [[hierarchical control system]] is a type of [[control system]] in which a set of devices and governing software is arranged in a [[hierarchical]] [[tree (data structure)|tree]]. When the links in the tree are implemented by a [[computer network]], then that hierarchical control system is also a form of [[networked control system]].
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| − | *[[Intelligent control]] uses various AI computing approaches like [[artificial neural networks]], [[Bayesian probability]], [[fuzzy logic]],<ref>{{cite journal | title=A novel fuzzy framework for nonlinear system control| journal=Fuzzy Sets and Systems | year=2010 | last=Liu |first1=Jie |author2=Wilson Wang |author3=Farid Golnaraghi |author4=Eric Kubica | volume=161 | issue=21 | pages=2746–2759 | doi=10.1016/j.fss.2010.04.009}}</ref> [[machine learning]], [[evolutionary computation]] and [[genetic algorithms]] or a combination of these methods, such as [[neuro-fuzzy]] algorithms, to control a [[dynamic system]].
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| − | *[[Optimal control]] is a particular control technique in which the control signal optimizes a certain "cost index": for example, in the case of a satellite, the jet thrusts needed to bring it to desired trajectory that consume the least amount of fuel. Two optimal control design methods have been widely used in industrial applications, as it has been shown they can guarantee closed-loop stability. These are [[Model Predictive Control]] (MPC) and [[linear-quadratic-Gaussian control]] (LQG). The first can more explicitly take into account constraints on the signals in the system, which is an important feature in many industrial processes. However, the "optimal control" structure in MPC is only a means to achieve such a result, as it does not optimize a true performance index of the closed-loop control system. Together with PID controllers, MPC systems are the most widely used control technique in [[process control]].
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| − | *[[Robust control]] deals explicitly with uncertainty in its approach to controller design. Controllers designed using ''robust control'' methods tend to be able to cope with small differences between the true system and the nominal model used for design.<ref>{{cite journal|last1=Melby|first1=Paul|last2=et.|first2=al.|title=Robustness of Adaptation in Controlled Self-Adjusting Chaotic Systems |journal=Fluctuation and Noise Letters |volume=02|issue=4|pages=L285–L292|date=2002|doi=10.1142/S0219477502000919}}</ref> The early methods of [[Hendrik Wade Bode|Bode]] and others were fairly robust; the state-space methods invented in the 1960s and 1970s were sometimes found to lack robustness. Examples of modern robust control techniques include [[H-infinity loop-shaping]] developed by [[Duncan McFarlane]] and [[Keith Glover]], [[Sliding mode control]] (SMC) developed by [[Vadim Utkin]], and safe protocols designed for control of large heterogeneous populations of electric loads in Smart Power Grid applications.<ref name='TCL1'>{{cite journal|title=Safe Protocols for Generating Power Pulses with Heterogeneous Populations of Thermostatically Controlled Loads |author=N. A. Sinitsyn. S. Kundu, S. Backhaus |journal=[[Energy Conversion and Management]]|volume=67|year=2013|pages=297–308|arxiv=1211.0248|doi=10.1016/j.enconman.2012.11.021}}</ref> Robust methods aim to achieve robust performance and/or [[Stability theory|stability]] in the presence of small modeling errors.
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| − | *[[Stochastic control]] deals with control design with uncertainty in the model. In typical stochastic control problems, it is assumed that there exist random noise and disturbances in the model and the controller, and the control design must take into account these random deviations.
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| − | *[[Energy-shaping control]] view the plant and the controller as energy-transformation devices. The control strategy is formulated in terms of interconnection (in a power-preserving manner) in order to achieve a desired behavior.
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| − | *[[Self-organized criticality control]] may be defined as attempts to interfere in the processes by which the [[self-organized]] system dissipates energy.
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| − | ==People in systems and control==
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| − | ==People in systems and control==
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| − | 系统和控制中的人
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| − | {{Main|People in systems and control}}
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| − | Many active and historical figures made significant contribution to control theory including
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| − | Many active and historical figures made significant contribution to control theory including
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| | 许多活跃的历史人物对防治理论作出了重要贡献，其中包括 | | 许多活跃的历史人物对防治理论作出了重要贡献，其中包括 |
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| − | * [[Pierre-Simon Laplace]] invented the [[Z-transform]] in his work on [[probability theory]], now used to solve discrete-time control theory problems. The Z-transform is a discrete-time equivalent of the [[Laplace transform]] which is named after him. | + | *皮埃尔·西蒙·拉普拉斯 Pierre-Simon Laplace 在概率论研究中发明了Z变换，现在用于解决离散时间控制理论问题。Z变换与以他命名的Laplace变换的离散时间等效。 |
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| − | * [[Irmgard Flugge-Lotz]] developed the theory of [[bang-bang control|discontinuous automatic control]] and applied it to [[autopilot|automatic aircraft control systems]].
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| − | * [[Alexander Lyapunov]] in the 1890s marks the beginning of [[stability theory]].
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| − | * [[Harold Stephen Black|Harold S. Black]] invented the concept of [[negative feedback amplifier]]s in 1927. He managed to develop stable negative feedback amplifiers in the 1930s.
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| − | * [[Harry Nyquist]] developed the [[Nyquist stability criterion]] for feedback systems in the 1930s.
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| | + | *Irmgard Flugge-Lotz提出了不连续自动控制的理论，并将其应用于飞机自动控制系统。 |
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| − | * [[Richard Bellman]] developed [[dynamic programming]] since the 1940s.<ref>{{cite magazine |author=Richard Bellman |date=1964 |title=Control Theory |url=http://www.nature.com/scientificamerican/journal/v211/n3/pdf/scientificamerican0964-186.pdf |magazine=[[Scientific American]] |volume=211 |issue=3 |pages=186–200|author-link=Richard Bellman }}</ref> | + | *1890年代的Lyapunov标志着稳定性理论的诞生。 |
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| | + | *Harold S. Black在1927年发明了负反馈放大器的概念。他在1930年代成功开发了稳定的负反馈放大器。 |
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| | + | *哈里·奈奎斯特 Harry Nyquist 在1930年代为反馈系统制定了奈奎斯特稳定性标准。 |
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| − | * [[Andrey Kolmogorov]] co-developed the [[Wiener filter|Wiener–Kolmogorov filter]] in 1941. | + | *理查德·贝尔曼 Richard Bellman 从1940年代开始开发动态编程<ref>{{cite magazine |author=Richard Bellman |date=1964 |title=Control Theory |url=http://www.nature.com/scientificamerican/journal/v211/n3/pdf/scientificamerican0964-186.pdf |magazine=[[Scientific American]] |volume=211 |issue=3 |pages=186–200|author-link=Richard Bellman }}</ref> |
| | + | 。 |
| | + | *Andrey Kolmogorov于1941年共同开发了Wiener–Kolmogorov过滤器。 |
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| | + | *诺伯特·维纳（Norbert Wiener）共同开发了维纳-柯尔莫哥洛夫滤波器，并在1940年代创造了控制论一词。 |
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| | + | *John R. Ragazzini在1950年代（由Laplace发明）在控制理论中介绍了数字控制和Z变换的使用。 |
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| − | * [[Norbert Wiener]] co-developed the Wiener–Kolmogorov filter and coined the term [[cybernetics]] in the 1940s. | + | *列夫·庞特里亚金（Lev Pontryagin）介绍了最大原理和爆炸原理。 |
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| | + | *Pierre-Louis Lions 将粘度解决方案开发为随机控制和最佳控制方法。 |
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| | + | *鲁道夫·卡尔曼 Rudolf Kalman 率先采用状态空间方法来进行系统和控制。介绍了可控性和可观察性的概念。开发用于线性估计的卡尔曼滤波器。 |
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| − | * [[John R. Ragazzini]] introduced [[digital control]] and the use of [[Z-transform]] in control theory (invented by Laplace) in the 1950s. | + | *Ali H. Nayfeh 是非线性控制理论的主要贡献者之一，并出版了许多有关微扰方法的书 |
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| | + | *Jan C. Willems引入了耗散性概念，将Lyapunov函数推广到输入/状态/输出系统。称为Lyapunov函数的类似物的存储函数的构造导致了控制理论中线性矩阵不等式（LMI）的研究。他开创了数学系统理论的行为方法。 |
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| | + | ==另请参阅== |
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| − | * [[Lev Pontryagin]] introduced the [[Pontryagin's minimum principle|maximum principle]] and the [[Bang-bang control|bang-bang principle]].
| + | ;控制系统的例子 |
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| − | * [[Pierre-Louis Lions]] developed [[viscosity solutions]] into stochastic control and [[optimal control]] methods.
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| − | * [[Rudolf Kalman]] pioneered the [[state-space]] approach to systems and control. Introduced the notions of [[controllability]] and [[observability]]. Developed the [[Kalman filter]] for linear estimation.
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| − | * [[Ali H. Nayfeh]] who was one of the main contributors to Non-Linear Control Theory and published many books on Perturbation Methods
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| − | * [[Jan Camiel Willems|Jan C. Willems]] Introduced the concept of dissipativity, as a generalization of [[Lyapunov function]] to input/state/output systems.The construction of the storage function, as the analogue of a Lyapunov function is called, led to the study of the [[linear matrix inequality]] (LMI) in control theory. He pioneered the behavioral approach to mathematical systems theory.
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| − | ==See also==
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| − | ==See also==
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| − | 参见
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| − | {{Portal|Systems science}}
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| − | ;Examples of control systems | |
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| − | Examples of control systems
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| − | 控制系统的例子 | |
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| | {{colbegin}} | | {{colbegin}} |
| − | | + | [[自动化]] |
| − | | + | [[无差拍控制器]] |
| − | | + | [[分布式参数系统]] |
| − | * [[Automation]]
| + | [[分数阶控制]] |
| − | | + | [[H无穷控制]] |
| − | | + | [[分级控制系统]] |
| − | | + | [[模型预测控制]] |
| − | * [[Deadbeat controller]]
| + | [[最优控制]] |
| − | | + | [[过程控制]] |
| − | | + | [[鲁棒控制]] |
| − | | + | [[伺服机构]] |
| − | * [[Distributed parameter systems]]
| + | [[状态空间表达]] |
| − | | + | [[矢量控制]] |
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| − | * [[Fractional-order control]]
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| − | * [[H-infinity loop-shaping]]
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| − | * [[Hierarchical control system]]
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| − | * [[Model predictive control]]
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| − | * [[Optimal control]]
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| − | * [[PID controller]]
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| − | * [[Process control]]
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| − | * [[Robust control]]
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| − | * [[Servomechanism]]
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| − | * [[State space (controls)]]
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| − | * [[Vector control (motor)|Vector control]]
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| − | ;Topics in control theory | + | ;控制理论主题 |
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| − | Topics in control theory
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| − | 控制理论主题 | |
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| − | | + | [[系数图法]] |
| − | | + | [[控制重新配置]] |
| − | * [[Coefficient diagram method]]
| + | [[插入定理]] |
| − | | + | [[反馈]] |
| − | | + | [[H无穷]] |
| − | | + | [[奇异值]] |
| − | * [[Control reconfiguration]]
| + | [[超前滞后补偿器]] |
| − | | + | [[小循环反馈]] |
| − | | + | [[多回路反馈]] |
| − | | + | [[根]] |
| − | * [[Cut-insertion theorem]]
| + | [[信号流图]] |
| − | | + | [[稳定多项式]] |
| − | | + | [[状态空间表示]] |
| − | | + | [[稳定状态]] |
| − | * [[Feedback]]
| + | [[瞬态响应]] |
| − | | + | [[暂态]] |
| − | | + | Y[[oula–Kucera参数化]] |
| − | | + | [[马尔可夫链]] |
| − | * [[H infinity]]
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| − | * [[Hankel singular value]]
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| − | * [[Krener's theorem]]
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| − | * [[Lead-lag compensator]]
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| − | * [[Minor loop feedback]]
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| − | * [[Minor loop feedback|Multi-loop feedback]]
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| − | * [[Positive systems]]
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| − | * [[Radial basis function]]
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| − | * [[Root locus]]
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| − | * [[Signal-flow graph]]s
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| − | * [[Stable polynomial]]
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| − | * [[State space representation]]
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| − | * [[Steady state]]
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| − | * [[Transient response]]
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| − | * [[Transient state]]
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| − | * [[Underactuation]]
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| − | * [[Youla–Kucera parametrization]]
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| − | * [[Markov chain approximation method]]
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| − | | + | [[自适应系统]] |
| − | | + | [[自动化和远程控制]] |
| − | * [[Adaptive system]]
| + | [[控制工程]] |
| − | | + | [[控制论]] |
| − | | + | [[智能控制]] |
| − | | + | [[数学系统理论]] |
| − | * [[Automation and remote control]]
| + | [[负反馈放大器]] |
| − | | + | [[系统理论]] |
| − | | + | [[时间尺度演算]] |
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| − | * [[Bond graph]]
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| − | * [[Control engineering]]
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| − | * [[Control–feedback–abort loop]]
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| − | * [[Controller (control theory)]]
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| − | * [[Cybernetics]]
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| − | * [[Intelligent control]]
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| − | * [[Mathematical system theory]]
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| − | * [[Negative feedback amplifier]]
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| − | * [[People in systems and control]]
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| − | * [[Perceptual control theory]]
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| − | * [[Systems theory]]
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| − | * [[Time scale calculus]]
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| − | 参考资料
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| | {{Reflist}} | | {{Reflist}} |
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| − | | + | ==进一步阅读== |
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| − | == Further reading == | |
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| − | == Further reading ==
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| − | 进一步阅读
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| − | | 编辑-最后一个 Levine
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| − | | editor-first = William S.
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| − | | 编辑-第一个威廉 s。
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| | | title = The Control Handbook | | | title = The Control Handbook |
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| − | | title = The Control Handbook
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| − | 控制手册
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| − | | publisher = CRC Press
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| | | publisher = CRC Press | | | publisher = CRC Press |
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| − | 出版商 CRC 出版社
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| | | place = New York | | | place = New York |
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| − | | place = New York
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| − | 纽约
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| − | | year = 1996
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| | | year = 1996 | | | year = 1996 |
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| − | 1996年
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| − | | isbn = 978-0-8493-8570-4
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| | | isbn = 978-0-8493-8570-4 | | | isbn = 978-0-8493-8570-4 |
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| − | | isbn 978-0-8493-8570-4
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| | * {{cite book |author1=Karl J. Åström |author2=Richard M. Murray | year = 2008 | title = Feedback Systems: An Introduction for Scientists and Engineers.| publisher = Princeton University Press | url = http://www.cds.caltech.edu/~murray/books/AM08/pdf/am08-complete_28Sep12.pdf | isbn = 978-0-691-13576-2 }} | | * {{cite book |author1=Karl J. Åström |author2=Richard M. Murray | year = 2008 | title = Feedback Systems: An Introduction for Scientists and Engineers.| publisher = Princeton University Press | url = http://www.cds.caltech.edu/~murray/books/AM08/pdf/am08-complete_28Sep12.pdf | isbn = 978-0-691-13576-2 }} |
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| | * {{cite book | author= Christopher Kilian | title= Modern Control Technology | publisher= Thompson Delmar Learning | year= 2005 | isbn=978-1-4018-5806-3 }} | | * {{cite book | author= Christopher Kilian | title= Modern Control Technology | publisher= Thompson Delmar Learning | year= 2005 | isbn=978-1-4018-5806-3 }} |
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| | * {{cite book | author= Vannevar Bush | title= Operational Circuit Analysis | publisher= John Wiley and Sons, Inc. | year= 1929 }} | | * {{cite book | author= Vannevar Bush | title= Operational Circuit Analysis | publisher= John Wiley and Sons, Inc. | year= 1929 }} |
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| | *{{cite book | author= Robert F. Stengel | title= Optimal Control and Estimation | publisher= Dover Publications | year= 1994 | isbn=978-0-486-68200-6 }} | | *{{cite book | author= Robert F. Stengel | title= Optimal Control and Estimation | publisher= Dover Publications | year= 1994 | isbn=978-0-486-68200-6 }} |
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| | * {{cite book |last=Franklin |title=Feedback Control of Dynamic Systems |origyear= |accessdate= |edition=4 |year=2002 |publisher=Prentice Hall |location=New Jersey |language= |isbn=978-0-13-032393-4 |doi = |pages= |chapter= |url= |quote = |display-authors=etal }} | | * {{cite book |last=Franklin |title=Feedback Control of Dynamic Systems |origyear= |accessdate= |edition=4 |year=2002 |publisher=Prentice Hall |location=New Jersey |language= |isbn=978-0-13-032393-4 |doi = |pages= |chapter= |url= |quote = |display-authors=etal }} |
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| | * {{cite book |author1=Joseph L. Hellerstein |author2=Dawn M. Tilbury |author3=Sujay Parekh | title= Feedback Control of Computing Systems | publisher= John Wiley and Sons | year= 2004 | isbn=978-0-471-26637-2}} | | * {{cite book |author1=Joseph L. Hellerstein |author2=Dawn M. Tilbury |author3=Sujay Parekh | title= Feedback Control of Computing Systems | publisher= John Wiley and Sons | year= 2004 | isbn=978-0-471-26637-2}} |
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| | *{{cite book | author= [[Diederich Hinrichsen]] and Anthony J. Pritchard | title= Mathematical Systems Theory I – Modelling, State Space Analysis, Stability and Robustness | publisher= Springer | year= 2005 | isbn=978-3-540-44125-0 }} | | *{{cite book | author= [[Diederich Hinrichsen]] and Anthony J. Pritchard | title= Mathematical Systems Theory I – Modelling, State Space Analysis, Stability and Robustness | publisher= Springer | year= 2005 | isbn=978-3-540-44125-0 }} |
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| | *{{cite journal | author = Andrei, Neculai | title = Modern Control Theory – A historical Perspective | version = | year = 2005 | url = http://camo.ici.ro/neculai/history.pdf | accessdate = 2007-10-10 }} | | *{{cite journal | author = Andrei, Neculai | title = Modern Control Theory – A historical Perspective | version = | year = 2005 | url = http://camo.ici.ro/neculai/history.pdf | accessdate = 2007-10-10 }} |
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| | *{{cite book | last = Sontag | first = Eduardo | authorlink = Eduardo D. Sontag | year = 1998 | title = Mathematical Control Theory: Deterministic Finite Dimensional Systems. Second Edition | publisher = Springer | url = http://www.sontaglab.org/FTPDIR/sontag_mathematical_control_theory_springer98.pdf | isbn = 978-0-387-98489-6 }} | | *{{cite book | last = Sontag | first = Eduardo | authorlink = Eduardo D. Sontag | year = 1998 | title = Mathematical Control Theory: Deterministic Finite Dimensional Systems. Second Edition | publisher = Springer | url = http://www.sontaglab.org/FTPDIR/sontag_mathematical_control_theory_springer98.pdf | isbn = 978-0-387-98489-6 }} |
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| | * {{cite book | last = Goodwin | first = Graham | year = 2001 | title = Control System Design | publisher = Prentice Hall | isbn = 978-0-13-958653-8 }} | | * {{cite book | last = Goodwin | first = Graham | year = 2001 | title = Control System Design | publisher = Prentice Hall | isbn = 978-0-13-958653-8 }} |
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| | * {{cite book | author= Christophe Basso | year = 2012 | title = Designing Control Loops for Linear and Switching Power Supplies: A Tutorial Guide.| publisher = Artech House | url = http://cbasso.pagesperso-orange.fr/Spice.htm | isbn = 978-1608075577 }} | | * {{cite book | author= Christophe Basso | year = 2012 | title = Designing Control Loops for Linear and Switching Power Supplies: A Tutorial Guide.| publisher = Artech House | url = http://cbasso.pagesperso-orange.fr/Spice.htm | isbn = 978-1608075577 }} |
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| | <!-- * {{cite book | author = Briat, Corentin | year = 2015 | title = Linear Parameter-Varying and Time-Delay Systems. Analysis, Observation, Filtering & Control | publisher = Springer Verlag Heidelberg | isbn = 978-3-662-44049-0}}--> | | <!-- * {{cite book | author = Briat, Corentin | year = 2015 | title = Linear Parameter-Varying and Time-Delay Systems. Analysis, Observation, Filtering & Control | publisher = Springer Verlag Heidelberg | isbn = 978-3-662-44049-0}}--> |
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| | * {{cite book |author1=Boris J. Lurie |author2=Paul J. Enright |title=Classical Feedback Control with Nonlinear Multi-loop Systems |origyear= |accessdate= |edition=3 |year=2019 |publisher=CRC Press |isbn=978-1-1385-4114-6 }} | | * {{cite book |author1=Boris J. Lurie |author2=Paul J. Enright |title=Classical Feedback Control with Nonlinear Multi-loop Systems |origyear= |accessdate= |edition=3 |year=2019 |publisher=CRC Press |isbn=978-1-1385-4114-6 }} |
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| | ; For Chemical Engineering | | ; For Chemical Engineering |
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| − | For Chemical Engineering
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| − | 化学工程
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| | * {{cite book | last = Luyben | first = William | year = 1989 | title = Process Modeling, Simulation, and Control for Chemical Engineers | publisher = McGraw Hill | isbn = 978-0-07-039159-8 }} | | * {{cite book | last = Luyben | first = William | year = 1989 | title = Process Modeling, Simulation, and Control for Chemical Engineers | publisher = McGraw Hill | isbn = 978-0-07-039159-8 }} |
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| − | | + | ==其他链接== |
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| − | == External links == | |
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| − | == External links ==
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| − | 外部链接
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| | {{Wikibooks|Control Systems}} | | {{Wikibooks|Control Systems}} |
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| | {{Commons category|Control theory}} | | {{Commons category|Control theory}} |
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| | * [http://www.engin.umich.edu/class/ctms/ Control Tutorials for Matlab], a set of worked-through control examples solved by several different methods. | | * [http://www.engin.umich.edu/class/ctms/ Control Tutorials for Matlab], a set of worked-through control examples solved by several different methods. |
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| | * [https://controlguru.com/ Control Tuning and Best Practices] | | * [https://controlguru.com/ Control Tuning and Best Practices] |
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| | * [https://www.pidlab.com/ Advanced control structures, free on-line simulators explaining the control theory] | | * [https://www.pidlab.com/ Advanced control structures, free on-line simulators explaining the control theory] |
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| − | * "[http://delivery.acm.org/10.1145/2820000/2814734/p50-li.pdf Applying control theory to manage flash erasures/lifespan]" {{dead link|date=January 2016}}
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| | * [https://cbasso.pagesperso-orange.fr/Downloads/PPTs/Chris%20Basso%20APEC%20seminar%202012.pdf The Dark Side of Loop Control Theory], a professional seminar taught at APEC in 2012 (Orlando, FL). | | * [https://cbasso.pagesperso-orange.fr/Downloads/PPTs/Chris%20Basso%20APEC%20seminar%202012.pdf The Dark Side of Loop Control Theory], a professional seminar taught at APEC in 2012 (Orlando, FL). |
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| − | <small>This page was moved from [[wikipedia:en:Control theory]]. Its edit history can be viewed at [[控制理论/edithistory]]</small></noinclude>
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