Optimal Tracking for linear Discrete-time Systems with Sinusoidal Disturbances

The optimal tracking and disturbance rejection problem for a class of linear systems affected by external sinusoidal disturbances in the discrete-time domain is considered. Optimal tracking and disturbance rejection can be designed separately. The original system is first transformed into an augmented system without disturbances, thus the rejection of disturbances can be treated by using the internal model principle (IMP) to secure asymptotic decay to zero of steady-state error. The optimal output tracking control problem is then solved by a reduced optimal control method and an optimal feedback control law with zero steady-state error is obtained. A simulation is conducted to illustrate the effectiveness of the tracking controller