Abstract
In this chapter we investigate the regulator problem with internal stability (RPIS) discussed in Chapter 7, from the viewpoint of well-posedness and genericity in the sense of Section 0.15, and of structurally stable implementation. Subject to mild restrictions it is shown that, if and only if RPIS is well-posed, a controller can be synthesized which preserves output regulation and loop stability in the presence of small parameter variations, of a specified type, in controller and plant. Synthesis is achieved by means of a feedback configuration which in general incorporates an invariant, and suitably redundant, copy of the dynamic model adopted for the exogenous reference and disturbance signals which the system is required to process.
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Notes and References
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B.A. FRANCIS, O.A. SEBAKHY, W.M. WONHAM, Synthesis of multivariable regulators: the internal model principle. J. Appl. Maths, and Optimization 1 (1), 1974.
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Wonham, W.M. (1974). Tracking and Regulation III: Structurally Stable Synthesis. In: Linear Multivariable Control. Lecture Notes in Economics and Mathematical Systems, vol 101. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-22673-5_9
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DOI: https://doi.org/10.1007/978-3-662-22673-5_9
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