Uppsala universitet

LQ Controller Design and Self-tuning Control

M Sternad and A Ahlén

Chapter 3 in K Hunt, ed: Polynomial Methods in Optimal Control and Filtering,
pp 56-92, Control Engineering Series, Peter Peregrinus, London, 1993.

The chapter contributes on some aspects of infinite-horizon LQG control for discrete time systems. The discussion relates to four themes:
  1. A variational technique for deriving polynomial equations for LQG controller design is presented in Section 3.2. It is illustrated on MIMO feedforward design in Section 3.3.

  2. Rejection of nonstationary disturbances, described by marginally stable and non-stabilizable models, is another topic. A control law discussed in Section 3.4 achieves this by utilising the internal model principle (generalised integration) combined with disturbance measurement feedforward.

  3. The suitability of polynomial LQG design as a candidate for self-tuning control is highlighted, and an algorithm is presented in Sections 3.5.

  4. We investigate some of the user choices in LQG control, which influence the robustness of both self-tuning and fixed control laws. In particular, the roles of feedforward control and of different choices of observer polynomials are discussed. See Section 3.6.
3.1. Introduction
3.2. Outline of a variational procedure for deriving LQG control laws in polynomial form
3.3. Feedforward control and Disturbance decoupling
3.4. A scalar feedback-feedforward LQG design
3.5. An LQG self-tuner
5.6. User choices affecting the robustness

Related publications:
PhD Thesis by L-J Brännmark, Jan. 2011, using MIMO feedforward design for robust sound field control for audio reproduction.
Paper in IEEE Trans. AC 1995, on a probabilistic approach to multivariable robust filtering and open-loop control.
Paper in IEEE Trans. AC 1993, variational technique applied to multivariable LQG feedback.
Paper in Automatica 1988 on scalar LQG disturbance measurement feedforward design.
Paper in IJC 1991 on LQG self-tuners, on whicn Sect. 5.3-5.6 are based.
Paper in IJC 1993 on the duality between deconvolution and feedforward control.
Book Chapter 5 , which discusses Wiener filter desing.

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