Robust control
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control theory Control theory is a field of mathematics that deals with the control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a ...
, robust control is an approach to controller design that explicitly deals with uncertainty. Robust control methods are designed to function properly provided that uncertain parameters or disturbances are found within some (typically
compact Compact as used in politics may refer broadly to a pact or treaty; in more specific cases it may refer to: * Interstate compact * Blood compact, an ancient ritual of the Philippines * Compact government, a type of colonial rule utilized in British ...
) set. Robust methods aim to achieve robust performance and/or
stability Stability may refer to: Mathematics *Stability theory, the study of the stability of solutions to differential equations and dynamical systems **Asymptotic stability **Linear stability **Lyapunov stability **Orbital stability **Structural stabilit ...
in the presence of bounded modelling errors. The early methods of Bode and others were fairly robust; the state-space methods invented in the 1960s and 1970s were sometimes found to lack robustness, prompting research to improve them. This was the start of the theory of robust control, which took shape in the 1980s and 1990s and is still active today. In contrast with an
adaptive control Adaptive control is the control method used by a controller which must adapt to a controlled system with parameters which vary, or are initially uncertain. For example, as an aircraft flies, its mass will slowly decrease as a result of fuel consumpt ...
policy, a robust control policy is static, rather than adapting to measurements of variations, the controller is designed to work assuming that certain variables will be unknown but bounded. (Section 1.5) In German; an English version is also available


Criteria for robustness

Informally, a controller designed for a particular set of parameters is said to be robust if it also works well under a different set of assumptions. High-gain feedback is a simple example of a robust control method; with sufficiently high gain, the effect of any parameter variations will be negligible. From the
closed-loop transfer function A closed-loop transfer function in control theory is a mathematical expression (algorithm) describing the net result of the effects of a closed (feedback) loop on the input signal to the plant under control. Overview The closed-loop transfer func ...
perspective, high open-loop gain leads to substantial disturbance rejection in the face of system parameter uncertainty. Other examples of robust control include sliding mode and terminal sliding mode control. The major obstacle to achieving high loop gains is the need to maintain system closed-loop stability. Loop shaping which allows stable closed-loop operation can be a technical challenge. Robust control systems often incorporate advanced topologies which include multiple feedback loops and feed-forward paths. The control laws may be represented by high order
transfer function In engineering, a transfer function (also known as system function or network function) of a system, sub-system, or component is a function (mathematics), mathematical function that mathematical model, theoretically models the system's output for ...
s required to simultaneously accomplish desired disturbance rejection performance with the robust closed-loop operation. High-gain feedback is the principle that allows simplified models of
operational amplifier An operational amplifier (often op amp or opamp) is a DC-coupled high-gain electronic voltage amplifier with a differential input and, usually, a single-ended output. In this configuration, an op amp produces an output potential (relative to c ...
s and emitter-degenerated
bipolar transistor A bipolar junction transistor (BJT) is a type of transistor that uses both electrons and electron holes as charge carriers. In contrast, a unipolar transistor, such as a field-effect transistor, uses only one kind of charge carrier. A bipolar t ...
s to be used in a variety of different settings. This idea was already well understood by Bode and
Black Black is a color which results from the absence or complete absorption of visible light. It is an achromatic color, without hue, like white and grey. It is often used symbolically or figuratively to represent darkness. Black and white have o ...
in 1927.


The modern theory of robust control

The theory of robust control system began in the late 1970s and early 1980s and soon developed a number of techniques for dealing with bounded system uncertainty. Probably the most important example of a robust control technique is
H-infinity loop-shaping H-infinity loop-shaping is a design methodology in modern control theory. It combines the traditional intuition of classical control methods, such as Bode's sensitivity integral, with H infinity, H-infinity optimization techniques to achieve contro ...
, which was developed by Duncan McFarlane and
Keith Glover Keith Glover FRS, FREng, FIEEE is a British electrical engineer. He is an emeritus professor of control engineering at the University of Cambridge. He is notable for his contributions to robust controller design and model order reduction. ...
of
Cambridge University , mottoeng = Literal: From here, light and sacred draughts. Non literal: From this place, we gain enlightenment and precious knowledge. , established = , other_name = The Chancellor, Masters and Schola ...
; this method minimizes the sensitivity of a system over its frequency spectrum, and this guarantees that the system will not greatly deviate from expected trajectories when disturbances enter the system. An emerging area of robust control from application point of view is
sliding mode control In control systems, sliding mode control (SMC) is a nonlinear control method that alters the dynamics of a nonlinear system by applying a discontinuous control signal (or more rigorously, a set-valued control signal) that forces the system to "sl ...
(SMC), which is a variation of
variable structure control Variable structure control (VSC) is a form of discontinuous nonlinear control. The method alters the dynamics of a nonlinear system by application of a high-frequency ''switching control''. The state- feedback control law is ''not'' a continuou ...
(VSC). The robustness properties of SMC with respect to matched uncertainty as well as the simplicity in design attracted a variety of applications. While robust control has been traditionally dealt with along deterministic approaches, in the last two decades this approach has been criticized on the basis that it is too rigid to describe real uncertainty, while it often also leads to over conservative solutions. Probabilistic robust control has been introduced as an alternative, see e.g. that interprets robust control within the so-called
scenario optimization The scenario approach or scenario optimization approach is a technique for obtaining solutions to robust optimization and chance-constrained optimization problems based on a sample of the constraints. It also relates to inductive reasoning in mod ...
theory. Another example is loop transfer recovery (LQG/LTR),http://www.nt.ntnu.no/users/skoge/book.html Multivariable Feedback Control Analysis and Design (2nd Edition) which was developed to overcome the robustness problems of linear-quadratic-Gaussian control (LQG) control. Other robust techniques includes
quantitative feedback theory In control theory, quantitative feedback theory (QFT), developed by Isaac Horowitz (Horowitz, 1963; Horowitz and Sidi, 1972), is a frequency domain technique utilising the Nichols chart (NC) in order to achieve a desired robust design over a specif ...
(QFT), passivity based control, Lyapunov based control, etc. When system behavior varies considerably in normal operation, multiple control laws may have to be devised. Each distinct control law addresses a specific system behavior mode. An example is a computer hard disk drive. Separate robust control system modes are designed in order to address the rapid magnetic head traversal operation, known as the seek, a transitional settle operation as the magnetic head approaches its destination, and a track following mode during which the disk drive performs its data access operation. One of the challenges is to design a control system that addresses these diverse system operating modes and enables smooth transition from one mode to the next as quickly as possible. Such
state machine A finite-state machine (FSM) or finite-state automaton (FSA, plural: ''automata''), finite automaton, or simply a state machine, is a mathematical model of computation. It is an abstract machine that can be in exactly one of a finite number o ...
-driven composite control system is an extension of the gain scheduling idea where the entire control strategy changes based upon changes in system behavior.


See also

*
Control theory Control theory is a field of mathematics that deals with the control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a ...
*
Control engineering Control engineering or control systems engineering is an engineering discipline that deals with control systems, applying control theory to design equipment and systems with desired behaviors in control environments. The discipline of controls o ...
*
Fractional-order control Fractional-order control (FOC) is a field of control theory that uses the fractional-order integrator as part of the control system design toolkit. The use of fractional calculus (FC) can improve and generalize well-established control methods a ...
* H-infinity control *
H-infinity loop-shaping H-infinity loop-shaping is a design methodology in modern control theory. It combines the traditional intuition of classical control methods, such as Bode's sensitivity integral, with H infinity, H-infinity optimization techniques to achieve contro ...
*
Sliding mode control In control systems, sliding mode control (SMC) is a nonlinear control method that alters the dynamics of a nonlinear system by applying a discontinuous control signal (or more rigorously, a set-valued control signal) that forces the system to "sl ...
*
Intelligent control Intelligent control is a class of control techniques that use various artificial intelligence computing approaches like neural networks, Bayesian probability, fuzzy logic, machine learning, reinforcement learning, evolutionary computation and genet ...
*
Process control An industrial process control in continuous production processes is a discipline that uses industrial control systems to achieve a production level of consistency, economy and safety which could not be achieved purely by human manual control. I ...
*
Robust decision making Robust decision-making (RDM) is an iterative decision analytics framework that aims to help identify potential robust strategies, characterize the vulnerabilities of such strategies, and evaluate the tradeoffs among them. RDM focuses on informing ...
*
Root locus In control theory and stability theory, root locus analysis is a graphical method for examining how the roots of a system change with variation of a certain system parameter, commonly a gain within a feedback system. This is a technique used as a ...
*
Servomechanism In control engineering a servomechanism, usually shortened to servo, is an automatic device that uses error-sensing negative feedback to correct the action of a mechanism. On displacement-controlled applications, it usually includes a built-in ...
*
Stable polynomial In the context of the characteristic polynomial of a differential equation or difference equation, a polynomial is said to be stable if either: * all its roots lie in the open left half-plane, or * all its roots lie in the open unit disk. The ...
*
State space (controls) In control engineering, a state-space representation is a mathematical model of a physical system as a set of input, output and state variables related by first-order differential equations or difference equations. State variables are variables w ...
*
System identification The field of system identification uses statistical methods to build mathematical models of dynamical systems from measured data. System identification also includes the optimal design of experiments for efficiently generating informative data f ...
*
Stability radius In mathematics, the stability radius of an object (system, function, matrix, parameter) at a given nominal point is the radius of the largest ball, centered at the nominal point, all of whose elements satisfy pre-determined stability conditions ...
* Iso-damping * Active disturbance rejection control *
Quantitative feedback theory In control theory, quantitative feedback theory (QFT), developed by Isaac Horowitz (Horowitz, 1963; Horowitz and Sidi, 1972), is a frequency domain technique utilising the Nichols chart (NC) in order to achieve a desired robust design over a specif ...


References


Further reading

* * * * * * * * {{DEFAULTSORT:Robust Control Control theory Stochastic control