Robust control
Encyclopedia
Robust control is a branch of control theory
that explicitly deals with uncertainty in its approach to controller design. Robust control methods are designed to function properly so long as uncertain parameters or disturbances are within some (typically compact) set. Robust methods aim to achieve robust performance and/or stability
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
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, for example,
bounded.
s and emitter-degenerated bipolar transistors to be used in a variety of different settings. This idea was already well understood by Bode
and Black
in 1927.
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; 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.
Another example is LQG/LTR, which was developed to overcome the robustness problems of LQG
control.
Control theory
Control theory is an interdisciplinary branch of engineering and mathematics that deals with the behavior of dynamical systems. The desired output of a system is called the reference...
that explicitly deals with uncertainty in its approach to controller design. Robust control methods are designed to function properly so long as uncertain parameters or disturbances are within some (typically compact) set. Robust methods aim to achieve robust performance and/or stability
Stability theory
In mathematics, stability theory addresses the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions...
in the presence of bounded modelling errors.
The early methods of Bode
Hendrik Wade Bode
Hendrik Wade Bode , was an American engineer, researcher, inventor, author and scientist], of Dutch ancestry. As a pioneer of modern control theory and electronic telecommunications he revolutionized both the content and methodology of his chosen fields of research.He made important contributions...
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
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 consumption; a control law is needed that adapts itself...
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, for example,
bounded.
When is a control method said to be robust?
Informally, a controller designed for a particular set of parameters is said to be robust if it would also work 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. High-gain feedback is the principle that allows simplified models of operational amplifierOperational amplifier
An operational amplifier is a DC-coupled high-gain electronic voltage amplifier with a differential input and, usually, a single-ended output...
s and emitter-degenerated bipolar transistors to be used in a variety of different settings. This idea was already well understood by Bode
Hendrik Wade Bode
Hendrik Wade Bode , was an American engineer, researcher, inventor, author and scientist], of Dutch ancestry. As a pioneer of modern control theory and electronic telecommunications he revolutionized both the content and methodology of his chosen fields of research.He made important contributions...
and Black
Harold Stephen Black
Harold Stephen Black was an American electrical engineer, who revolutionized the field of applied electronics by inventing the negative feedback amplifier in 1927. To some, his invention is considered the most important breakthrough of the twentieth century in the field of electronics, since it...
in 1927.
The modern theory of robust control
The theory of robust control 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
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 optimization techniques to achieve controllers whose stability and performance properties hold good in...
, which was developed by Duncan McFarlane and Keith Glover of Cambridge University; this method minimizes the sensitivity
Sensitivity (control systems)
The controller parameters are typically matched to the process characteristics and since the process may change it is important that the controller parameters are chosen in such a way that the closed loop system is not sensitive to variations in process dynamics...
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.
Another example is LQG/LTR, which was developed to overcome the robustness problems of LQG
Linear-quadratic-Gaussian control
In control theory, the linear-quadratic-Gaussian control problem is one of the most fundamental optimal control problems. It concerns uncertain linear systems disturbed by additive white Gaussian noise, having incomplete state information and undergoing control subject to quadratic costs...
control.
See also
- Control theoryControl theoryControl theory is an interdisciplinary branch of engineering and mathematics that deals with the behavior of dynamical systems. The desired output of a system is called the reference...
- Control engineeringControl engineeringControl engineering or Control systems engineering is the engineering discipline that applies control theory to design systems with predictable behaviors...
- Fractional order controlFractional order controlFractional order control or is a field of control theory that uses the fractional order integrator as part of the control system design toolkit....
- H-infinity control
- H-infinity loop-shapingH-infinity loop-shapingH-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 optimization techniques to achieve controllers whose stability and performance properties hold good in...
- Intelligent controlIntelligent controlIntelligent control is a class of control techniques, that use various AI computing approaches like neural networks, Bayesian probability, fuzzy logic, machine learning, evolutionary computation and genetic algorithms.- Overview :...
- Process controlProcess controlProcess control is a statistics and engineering discipline that deals with architectures, mechanisms and algorithms for maintaining the output of a specific process within a desired range...
- Robust decision makingRobust decision makingRobust decision making is an iterative decision analytic framework that helps identify potential robust strategies, characterize the vulnerabilities of such strategies, and evaluate the tradeoffs among them...
- Root locusRoot locusRoot locus analysis is a graphical method for examining how the roots of a system change with variation of a certain system parameter, commonly the gain of a feedback system. This is a technique used in the field of control systems developed by Walter R...
- ServomechanismServomechanismthumb|right|200px|Industrial servomotorThe grey/green cylinder is the [[Brush |brush-type]] [[DC motor]]. The black section at the bottom contains the [[Epicyclic gearing|planetary]] [[Reduction drive|reduction gear]], and the black object on top of the motor is the optical [[rotary encoder]] for...
- Sliding mode controlSliding mode controlIn control theory, sliding mode control, or SMC, is a nonlinear control method that alters the dynamics of a nonlinear system by application of a discontinuous control signal that forces the system to "slide" along a cross-section of the system's normal behavior. The state-feedback control law is...
- Stable polynomialStable polynomialA 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 first condition defines Hurwitz stability and the second one Schur stability. Stable polynomials arise in various mathematical fields, for example in...
- State space (controls)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...
- System identificationSystem identificationIn control engineering, the field of system identification uses statistical methods to build mathematical models of dynamical systems from measured data...
- Stability radiusStability radiusThe stability radius of an object at a given nominal point is the radius of the largest ball, centered at the nominal point, all whose elements satisfy pre-determined stability conditions...
- Iso-damping