Finite Time Optimal Preactuation for Non-Minimum Phase Systems Considering Control Input and Tracking Error Constraints

Abstract

To achieve perfect reference trajectory tracking, a plant with continuous time unstable zeros requires an infinite time preactuation. Albeit, this is practically infeasible, as typical high-precision motion systems target a short time finite preactuation. Truncating the control input to a limited time preactuation leads to undesirable tracking errors. This paper, thus, proposes a finite time preactuation method with an optimized state trajectory considering control input and tracking error constraints. The proposed method generates an optimal state trajectory for a given reference and finite time while explicitly considering the actuator, i.e. peak force, and stroke, i.e. maximum undershoot, limitations of the system. A multirate feedforward scheme is subsequently presented to obtain a discretized control input that perfectly tracks the designed optimal state trajectory. In comparison to conventional finite preactuation methods, the proposed approach reaches an order of magnitude lower tracking error bounds. Additionally, this finite time procedure attains, in contrast to conventional optimization approaches, through a multirate feedforward formulation, perfect tracking during the main motion after preactuation.