Robust control theory is a method to measure the performance changes of a control system with changing system parameters. The goal is to allow exploration of the design space for alternatives that are insensitive to changes in the system and can maintain their stability and performance.Robust Control Definition · Effects of Uncertainty · Modeling. Mathematics > Optimization and Control of complex systems, the use of robust control theory remains limited, partly because the mathematics. Jump to The modern theory of robust control - In control theory, 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) set.

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Robust control theory studies the effect of noise, disturbances, and other uncertainty on system performance. Despite growing recognition across science and engineering that robustness and efficiency tradeoffs dominate the evolution and design of complex systems, the use of robust control theory remains limited, partly because the mathematics involved is relatively inaccessible to nonexperts, robust control theory the important concepts have been inexplicable without a fairly rich robust control theory background.

This paper aims to begin changing that by presenting the most essential concepts in robust control using human stick balancing, a simple case study popular in both the sensorimotor control literature and extremely familiar to engineers.

Modern control covers the techniques from to the present. Each of these is examined in this introduction. Conventional control became interesting with the development of feedback theory.

### Robust control

Feedback was used in order to stabilize the control system. One early use of feedback control was the development of the flyball governor for stabilizing steam engines in locomotives.

Another example was the use of feedback robust control theory telephone signals in the s. The problem robust control theory the transmission of signals over long lines.

There was a limit to the number of repeaters that could be added in series to a telephone line due to distortion. Harold Stephen Black proposed a feedback system that would use feedback to limit the distortion.

## Robust Control Theory

Even though the added feedback sacrificed some gain in the repeater, it enhanced the overall performance. Refer to [ Bennet96 ] for more historical treatment of robust control theory theory. Conventional control relies upon developing a model of the control system using differential equations.

LaPlace transforms are then used to express the system equations in the frequency domain where they can be manipulated algebraically. Robust control theory 1 shows a typical control loop. The input to the system is some reference signal, which represents the desired control value.

This reference is fed through a forward transfer function G s to determine the plant output, y. The output is fed back through a feedback transfer function, H s.

The feedback signal is subtracted from robust control theory reference to determine the error signal, e. Further control is based on the error signal.

Therefore, the system serves to bring the output as close as possible to the desired reference input.

Refer to [ Oppenheim97 ] for an introduction to conventional control techniques. Typical Control Loop One development that was key to robust control theory developments in robust control was the root-locus method. In the frequency domain, G s and H s were expressed as ratios of polynomials in the complex frequency variable, s.

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Nyquist, Robust control theory and others realized that the roots of the denominator polynomial determined the stability of the control system. These roots were referred to as "poles" of the transfer functions. The location of these poles had to be in the left half-plane of the complex frequency plot robust control theory guarantee stability.

Root locus was developed as a method to graphically show the movements of poles in the frequency domain as the coefficients of the s-polynomial were changed.

### Robust Control: Theory and Applications

Movement into the right half plane robust control theory an unstable system. Thus systems could be judged by their sensitivity to small changes in the denominator coefficients.

Modern control methods were developed with a realization that robust control theory system equations could be structured in such a way that computers could efficiently solve them. It was shown that any nth order differential equation describing a control system could be reduced to n 1st order equations.

These equations could be arranged in the form of matrix equations.