Optimal State Trajectory Regeneration for Nonminimum Phase Systems: No Preactuation Approach

To achieve perfect reference trajectory tracking, a plant with continuous time unstable zeros requires an infinite time preactuation. However, literal infinite preactuation is practically infeasible. Preactuation as short as possible is desirable for high-precision motion systems. This paper, thus, proposes an optimal state trajectory regeneration method without preactuation. The original state trajectory, which requires the infinite preactuation, is generated by preactuation perfect tracking control (PPTC) method. Then we regenerate the state trajectory between the start and end time of the reference motion trajectory. This method is an extension of the method of a finite preactuation perfect tracking control (FPPTC) method. In the FPPTC method, perfect tracking after preactuation is guaranteed by regenerating the state trajectory during preactuation, whereas the proposed method of this paper guarantees only after the end of the reference motion. The state trajectory during the reference motion is optimized with respect to the control input and plant output constraints. A multirate feedforward scheme, which is a stable inversion for unstable discretization zeros, is subsequently presented to obtain a discretized control input that perfectly tracks the designed optimal continuous state trajectory.