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 (TMS) is presented. The control scheme considers constraints in the stator voltage and currents of the driving machine: a permanent magnet synchronous motor (PMSM). Its design is based on results of the more general framework of optimal control and its implementation constitutes an ad hoc adaption of a numerical method, formulated to solve a more general class of time-optimal control problems. This method leverages the assumption of a bang-bang structure for the actuation and the proposed algorithm exploits the geometrical properties displayed by the system state trajectories in the state space, when steered under this regime, to render its implementation feasible. Once the state reaches a region near its target, the control task is taken over by a classical linear quadratic regulator, to avoid spurious chattering. The algorithm outputs a reference for the electrical torque to be developed by the PMSM, which is controlled with a finite-set model predictive torque controller, modified to make use of a voltage modulation scheme. The performance of the proposed controller is validated with experimental results, which consider an external proportional-integral controller for the load speed, tunned for relatively high bandwidth.