Feedback control systems with low-frequency stochastic disturbances

Abstract

Optimal controllers are investigated for linear feedback systems with low-frequency stochastic disturbances, measurement noise and power constraint on the control signal. By adoption of simplified models closed-form expressions are obtained for the optimal controller. These expressions facilitate the study of the controller structure and of the stability margin of the optimal system. It is found that if measurement noise is neglected, the resulting optimal system has a very poor stability margin. If the power constraint on the control signal is neglected, the resulting system is usually again impractical because it. requires excessive control power. On the other hand, if both measurement noise and power constraint are taken into account in the design, the system has a good stability margin, at least in low-order cases. Furthermore, the optimal controller approximates a conventional type such as proportional plus integral.

It is concluded that in most cases it is essential to take into account (a) low-frequency disturbances, (b) measurement noise and (c) control power constraint when designing optimal linear feedback systems. If this is done, good agreement with contemporary design practice is obtained; the gap between control theory and control practice is thus bridged.