HOME

TheInfoList



OR:

In
control theory Control theory is a field of control engineering and applied mathematics that deals with the control system, control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the applic ...
, 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, a type of agreement used by U.S. states * Blood compact, an ancient ritual of the Philippines * Compact government, a t ...
) 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 ** Exponential stability ** Linear stability **Lyapunov stability ** Marginal s ...
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 consump ...
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 In control theory, a closed-loop transfer function is a mathematical function describing the net result of the effects of a feedback control loop on the input signal to the plant under control. Overview The closed-loop transfer function is mea ...
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, models the system's output for each possible ...
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 direct coupling, DC-coupled Electronic component, electronic voltage amplifier with a differential input, a (usually) Single-ended signaling, single-ended output, and an extremely high gain ( ...
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 (FET), uses only one kind of charge carrier. A ...
s to be used in a variety of different settings. This idea was already well understood by Bode and
Black Black is a color that results from the absence or complete absorption of visible light. It is an achromatic color, without chroma, like white and grey. It is often used symbolically or figuratively to represent darkness.Eva Heller, ''P ...
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, which was developed by Duncan McFarlane and Keith Glover of
Cambridge University The University of Cambridge is a Public university, public collegiate university, collegiate research university in Cambridge, England. Founded in 1209, the University of Cambridge is the List of oldest universities in continuous operation, wo ...
; 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 dynamic system, dynamics of a nonlinear system by applying a discontinuous control signal (or more rigorously, a set-valued control signal) that forces th ...
(SMC), which is a variation of
variable structure control Variable structure control (VSC) is a form of Classification of discontinuities, discontinuous nonlinear control. The method alters the dynamic system, dynamics of a nonlinear system by application of a high-frequency ''switching control''. The sta ...
(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 constraint (mathematics), constraints. It also relates to in ...
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 (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 control engineering and applied mathematics that deals with the control system, control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the applic ...
*
Control engineering Control engineering, also known as control systems engineering and, in some European countries, automation engineering, is an engineering discipline that deals with control systems, applying control theory to design equipment and systems with d ...
* Fractional-order control * H-infinity control * H-infinity loop-shaping *
Sliding mode control In control systems, sliding mode control (SMC) is a nonlinear control method that alters the dynamic system, dynamics of a nonlinear system by applying a discontinuous control signal (or more rigorously, a set-valued control signal) that forces th ...
* Robust Integral of the Sign of the Error (RISE) Control *
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 gene ...
*
Process control Industrial process control (IPC) or simply process control is a system used in modern manufacturing which uses the principles of control theory and physical industrial control systems to monitor, control and optimize continuous Industrial processe ...
* Robust decision making * Root locus *
Servomechanism In mechanical and control engineering, a servomechanism (also called servo system, or simply servo) is a control system for the position and its time derivatives, such as velocity, of a mechanical system. It often includes a servomotor, and ...
* Stable polynomial *
State space (controls) In control engineering and system identification, a state-space representation is a mathematical model of a physical system that uses state variables to track how inputs shape system behavior over time through first-order differential equation ...
*
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#System identification and stochastic approximation, optimal de ...
* Stability radius * Iso-damping * Active disturbance rejection control * Quantitative feedback theory


References


Further reading

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