Robust control

The final values of the Kalman Gain matrix K and eovarianee matrix P were 

The robust eontrol problem is to find a eontrol law whieh maintains system response and error signals within preseribed toleranees despite the effeets of uneertainty on the system. Forms of uneertainty inelude 

If the forward velocity of the ship is the state variable u, a best estimate of which is given by the Kalman filter, the gain scheduling controller can be expressed as 

Equation set (9.104) approximates to an inverse square law, and increases the controller gains at low speeds, where the control surfaces are at their most insensitive. 

In general, however, robust control system design uses an idealized, or nominal model of the plant Uncertainty in the nominal model is taken into account by 

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The canonical robust control problem is shown in Figure 9.29. 

The results in this example were obtained using the MATLAB Robust Control Toolbox. 

A1.9 Tutorial 8 Optimal and robust control system design... 

This tutorial uses the MATLAB Control System Toolbox for linear quadratie regulator, linear quadratie estimator (Kalman filter) and linear quadratie Gaussian eontrol system design. The tutorial also employs the Robust Control Toolbox for multivariable robust eontrol system design. Problems in Chapter 9 are used as design examples. 

Multivartable robust control using H infinity %Singular value loop shaping using the weighted mixed %sensitivity approach nug=200 ... 

Chiang, R.Y. (1988) Modern Robust Control Theory, PhD Dissertation, USC. 

Chiang, R.Y. and Safonov, M.G. (1992) Robust Control Toolbox for Use with MATLAB. Users Guide, MathWorks. 

Dorato, P. (ed.) (1987) Robust Control, IEEE Press, New York. 

New research advances in control theory that are bringing it closer to practical problems are promising dramatic new developments and attracting widespread industrial interest. One of these advances is the development of "robust" systems. A robust control system is a stable, closed-loop system that can operate successfully even if the model on which it is based does not adequately describe the plant. A second advance is the use of powerful semiempirical formalisms in control problems, particularly where the range of possible process variables is constrained. 

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