Optimal self-tuning algorithm

Abstract

The open-loop model for the single-input single-output plant under consideration is described in Section 4.1. The plant output which is to be controlled is affected by two disturbance signals, one of which is assumed measurable.

In Section 4.2 the two-degrees-of freedom (2DF) controller structure employed is introduced. In addition, a feedforward compensator is used to reject the measurable disturbance signal. The optimal controller consists of three parts (feedback, reference and feedforward) which process the system output, reference and measurable disturbance signals separately. Three possible design strategies are proposed in Section 4.2:

(i) The complete general solution of the optimal control problem (Section 4.2.1).

(ii) The optimal solution using the ‘implied’ polynomial equations. The conditions under which the implied equations yield the unique optimal controller are stated (Section 4.2.2).

(ii) A computationally simpler design where the feedback part is calculated optimally, and the reference and feedforward parts of the controller are calculated to give correct steady state performance (Section 4.2.3).

The robustness properties of the LQG self-tuner are discussed in Section 4.4 by summarising the important features of the control design and various techniques which have been used to achieve robust parameter estimation. The main results of a recent convergence analysis are presented in Section 4.5.

The chapter concludes in Section 4.6 with a discussion of practical issues relating to control law implementation, cost-function weight selection and computational issues.