
LQ Controller Design and Selftuning Control
M Sternad
and
A Ahlén
Chapter 3 in K Hunt, ed:
Polynomial Methods in Optimal Control and Filtering,
pp 5692, Control Engineering Series,
Peter Peregrinus, London, 1993.
 Abstract:

The chapter contributes on
some aspects of infinitehorizon LQG control for discrete
time systems.
The discussion relates to four themes:
 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.
 Rejection of nonstationary disturbances,
described by marginally stable and nonstabilizable 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.
 The suitability of polynomial LQG design as a candidate for
selftuning control is highlighted, and an
algorithm is presented in Sections 3.5.
 We investigate some of the user choices in LQG control,
which influence the robustness of both selftuning
and fixed control laws.
In particular, the roles of feedforward control and of different choices
of observer polynomials are discussed. See Section 3.6.
 Contents:
 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 feedbackfeedforward LQG design
 3.5. An LQG selftuner
 5.6. User choices affecting the robustness
 Related publications:


PhD Thesis
by LJ 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 openloop 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 selftuners, on whicn Sect. 5.35.6 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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