Tracking control method for a plant with continuous time unstable zeros: Finite preactuation based on state trajectory regeneration by using redundant order polynomial

摘要

A plant with unstable zeros is considered to be difficult to control because of initial undershoot of step response and unstable poles of its inversion system. A plant may have unstable zeros in discrete time domain because of following reasons: 1) non-collocation of actuators and sensors and 2) discretization by zero-order hold. We proposed a solution for these problems by using a multirate feedforward control with state trajectory generation based on time axis reversal. However, this method requires preactuation for negative infinite time. This paper proposes a state trajectory regeneration method via redundant order polynomial for the negative finite time. Although this method abandons perfect tracking during preactuation, it guarantees perfect tracking for a positive time domain. Moreover, the tracking error during finite time preactuation is reduced by the regenerated state trajectory obtained by the optimized redundant order polynomial. The validity of the proposed method is demonstrated through simulations.