A fixed end-point problem for an electrical drive system

Abstract

The paper presents an optimal control problem for an electrical drive system with a DC motor. The formulated problem is a linear-quadratic one, with fixed end-point. The optimization criterion and a convenient form for the system mathematical model are formulated and discussed. The computing relations for the open loop control and for the feedback optimal control are established using the classical procedures for the optimal control problem. The feedback optimal control is difficult to apply for real-time control because it involves the computation of the inverse time-variant matrices. On the basis of some previous results, the authors propose a method that leads to a more convenient formula for the computing of the feedback optimal control variable. This formula emphasises a feedback component of the optimal control and a corrective component, depending on the initial state, the disturbance torque and the desired values. The real-time computing effort is not very large because the variable matrices and vectors can be computed at each sample moment by multiplying with a constant increment. The simulation results with the overall control system obtained by numerical simulation with MATLAB show the correct functioning of the controller and the effectiveness of the proposed control method.