ROBUST FINITE-TIME SETTLING CONTROL OF DISTRIBUTED PARAMETER-SYSTEMS

Rapid finite time settling control of a distributed parameter system (DPS), utilizing a single point force actuator with bounded input, is considered. A control strategy combining feedforward and feedback is proposed to reduce the effect of uncertainties on the desired finite time settling system response. The feedforward which plays a key role in the finite time settling of the DPS is based on minimizing the control energy while the feedback is designed separately to satisfy a set of prescribed performance specifications in the time domain. It is assumed that the system is initially excited by a disturbance, and that the initial energy is distributed among a finite set of known vibratory modes. The control strategy is first developed for a simple harmonic oscillator which is then extended to multimode systems. The robustness of the proposed strategy with respect to uncertainties in the initial state, system parameters, external disturbances, and the time delay are also studied. Furthermore, it is shown that these novel strategies lead to at least comparable, if not better, results to those obtained by conventional control strategies employing only feedback, under the realistic constraint that control inputs must be bounded due to actuator limitations. It is shown that, for a finite set of controlled modes, the feed forward control consists of a combination of exponentially growing sinusoidal functions; they are at the natural frequencies of the modes being controlled. The feedback portion of the controller is based on state feedback. © 1990 Taylor and Francis Group, LLC.