Trade-offs in linear control system design: a practical example

In this paper two modern control techniques, the H2 and H∞ control design methods, are presented. After a brief theoretical explanation they are applied to a practical example: the control of the air flow rate through an axial ventilator. Modern control techniques are model-based. In the first part of the paper it is explained how a model can be obtained both of the process and of the disturbances acting on it. On the basis of the model, several controllers can be designed. The example clearly illustrates some of the trade-offs of modern control design. The H2 and H∞ controllers are also compared with a classical PI controller.

[1]  Edmond A. Jonckheere,et al.  A new set of invariants for linear systems--Application to reduced order compensator design , 1983 .

[2]  B. Francis,et al.  A Course in H Control Theory , 1987 .

[3]  P. Khargonekar,et al.  State-space solutions to standard H/sub 2/ and H/sub infinity / control problems , 1989 .

[4]  Stephen Boyd,et al.  A new CAD method and associated architectures for linear controllers , 1988 .

[5]  K. Glover All optimal Hankel-norm approximations of linear multivariable systems and their L, ∞ -error bounds† , 1984 .

[6]  B. Moor,et al.  Stepped sine system identification, errors-in-variables and the quotient singular value decomposition , 1990 .

[7]  S. Boyd,et al.  Example of exact trade-offs in linear controller design , 1989, IEEE Control Systems Magazine.

[8]  B. Moore Principal component analysis in linear systems: Controllability, observability, and model reduction , 1981 .

[9]  K. Glover,et al.  A characterization of all solutions to the four block general distance problem , 1991 .

[10]  D. Naidu,et al.  Optimal Control Systems , 2018 .

[11]  G. Zames Feedback and optimal sensitivity: Model reference transformations, multiplicative seminorms, and approximate inverses , 1981 .

[12]  Stephen P. Boyd,et al.  Subharmonic functions and performance bounds on linear time-invariant feedback systems , 1984, IEEE Conference on Decision and Control.

[13]  K. Glover,et al.  State-space formulae for all stabilizing controllers that satisfy and H ∞ norm bound and relations to risk sensitivity , 1988 .