Gain margin improvement using generalized sampled-data hold function based multirate output compensator

Abstract

For a SISO, strictly proper, nonminimum-phase, continuous-time, linear time-invariant (LTI) plant, it was shown in Yan, W., B. D. O. Anderson and R. R. Bitmead (1993). IEEE Trans. Automat. Contr., that the closed-loop gain margin obtained via a generalized sampled-data hold function (GSHF) based dynamic compensator is significantly improved over that achieved via a conventional periodic controller used in Francis, B. A. and T. T. Georgiou (1988). IEEE Trans. Automat. Contr., AC-33, 820–832. Nevertheless, the compensator so designed is not necessarily strictly proper. It is well-known that it is practically difficult and sometimes impossible to implement a nonstrictly proper compensator due to the requirement of zero computation time. Further, as has been shown in Vidyasagar, M. (1985). Systems and Control Letters, 5, 413–418, stabilization by a nonstrictly proper controller is never robust against singular perturbations. In this paper, we propose a new type of GSHF based compensator which employs multirate sampling of the plant output. Using the proposed compensator, not only the same level of gain margin as in Yan, W., B. D. O. Anderson and R. R. Bitmead (1993). IEEE Trans. Automat. Contr., can be achieved, but also, more importantly, the compensator is strictly proper.