Robust Adaptive Optimal Control of a DC Motor System Based on Policy Iteration

In this paper, robust optimal control method is used to deal with the speed regulation of a DC motor. Considering the parameter uncertainty, a state space model of the DC motor system is established. To enable the DC motor to track a predetermined speed, the integral variable of tracking error is augmented to the state variable. The tracking problem is transformed into the robust control problem of augmented uncertain linear systems. Then the robust control problem is converted into solving an optimal control with appropriate performance index. Moreover, a policy iteration algorithm in reinforcement learning is proposed to obtain a robust control law for the uncertain motor system, which enables the system output to asymptotically track an ideal signal. And the convergence of the proposed algorithm for the robust optimal control of uncertain linear systems is proved. The advantage of designing controllers through online policy iteration in reinforcement learning is without knowing the nominal system matrix. Finally, the effectiveness of the algorithm is verified by a numerical simulation example.