Optimal Control Methods for On-Off Sampling Systems

Abstract

This paper considers the problem of optimal (minimum-time) on-off regulation of a dynamic plant whose state is known only at periodic instants of time. It is shown that on-off control inputs which change value only at the sampling instants inherently lack the capability of providing accurate (dead-beat) control. If, however, the on-off controller is modified to include pulse width control, it not only has the capability for accurate control, but also has the capability for optimal control comparable to that of a saturating amplifier controller. In addition, the optimal pulse width control inputs can be specified as a function of the state of the plant at each sampling instant. The application of this method is discussed in detail for the cases of pure inertial and second-order underdamped plants.