Transient Response Shaping, Model Based Cheap Control, Saturation Indices and MPC

This paper focusses on the time-response performance aspects and control-signal magnitude aspects of controller design. The problem is stated in the context of the servomechanism problem for a class of extended constant tracking/disturbance signals, which includes constant signals as a special case. In particular, the paper proposes a new cheap-control performance index called “model-based cheap control”, which explicitly includes a desired transient model within it; for example, minimizing the performance index with a first-order desired error model results in smooth nonoscillatory transients with almost no cross-channel interaction (subject to standard performance limitations). Assuming the control input signals have a limited operating range, the notion of a “saturation index” (SI) for a closed-loop system is then introduced. The SI gives a measure of the closed-loop operating range that a given controller requires; an SI of one implies that the controller “makes optimal use” of the control signal constraints, while a larger SI implies that the controller's operating range may be highly restricted. The paper then proposes the use of model predictive control (MPC) using the previously introduced model based cheap-control index. In this case, the resulting MPC closed-loop system always has an SI of one, and owing to the special cheap-control performance index used, the system has a transient response that tends to be smooth and non-oscillatory with little cross-channel interaction. Finally, the paper evaluates the performance of a new “non-feasible active set” algorithm to solve the MPC problem; examples are used to show that, in terms of CPU calculation time, the new algorithm can be up to 40 times faster than standard algorithms.