The LQG controller can be used to avoid some of the problems with existing self-tuning schemes for complex industrial problems. It is shown in reference that LQG controller gives a better performance than PID controllers for open loop unstable large tankers. It is, very difficult, if not impossible, to adequately control such systems using a simple three term PID controller. The polynomial system approach has been used by Grimble to derive the control law for the general case of coloured measurement noise, dynamical cost function weights and stochastic reference signal. The optimal controller can be computed from two spectral factor equations and three diophantine equations. In the adaptive version described here only one spectral factorisation must be performed. The LQG Optimal control design method can be used to derive an explicit adaptive scheme by adding the identification of the plant and disturbance models. The identification scheme differs from the usual methods employed in self-tuning systems which normally involve a common denominator polynomial. This paper is concerned with the implementation aspects of the above adaptive schemes. The optimal controller is described in Section 2. The adaptation procedure is explained in Section 3. The diophantine equation solution is discussed in Section 4, and two algorithms are proposed to solve the coupled and the single diophantine equations.
LQG self-tuning control with applications to ship steering systems
LQG, selbstabstimmende Regelung zur Anwendung fuer Schiffslenkeinrichtungen
1985
15 Seiten, 3 Bilder, 11 Quellen
Conference paper
English