Time-Optimal Output Transition for Minimum-Phase Systems

Abstract

The time-optimal output transition control problem for stable or marginally stable systems with minimum-phase zeros is discussed in this paper. A double integrator system with a real left-half plane zero is used to illustrate the development of the time-optimal output transition controller. It is shown that an exponentially decaying postactuation control profile is necessary to maintain the output at the desired final location. It is shown that the resulting solution to the output transition time-optimal control profile can be generated by a time-delay filter whose zeros and poles cancels the poles and zeros of the system to be controlled. The design of the time-optimal output transition problem is generalized and illustrated on the benchmark floating oscillator problem.