Smoothened Quasi-Time-Optimal Control for the Torsional Torque in a Two-Mass System

In this work, a quasi-time-optimal, nonlinear state-feedback control for the torsional torque of a two-mass system is proposed. The scheme considers constraints in the stator voltage and currents of the driving machine: a permanent-magnet synchronous motor. Its design is based on results of the general framework of optimal control and leverages the assumption of a bangbang structure for the actuation. In order to render its implementation feasible, the proposed algorithm exploits the geometrical properties displayed by the system state trajectories in the state space, when steered under a time-optimal regime. Spurious chattering is avoided switching to a smoother linear quadratic regulator, once the state reaches the vicinity of the target. The performance of the proposed controller is validated with experimental results, which consider an external proportional-integral controller for the load speed, tuned for relatively high bandwidth.