Optimal tracking control with zero steady-state error for time-delay systems with sinusoidal disturbances

The problem of optimal tracking control with zero steady-state error for linear time-delay systems with sinusoidal disturbances is considered. Based on the internal model principle, a disturbance compensator is constructed such that the system with external sinusoidal disturbances is transformed into an augmented system without disturbances. By introducing a sensitivity parameter and expanding power series around it, the optimal tracking control problem can be simplified into the problem of solving an infinite sum of linear optimal control series without time-delay and disturbance. The obtained optimal tracking control law with zero steady-state error consists of accurate linear state feedback terms and a time-delay compensating term, which is an infinite sum of an adjoint vector series. The accurate linear terms can be obtained by solving a Riccati matrix equation and a Sylvester equation, respectively. The compensation term can be approximately obtained through a recursive algorithm. A numerical simulation shows that the algorithm is effective and easily implemented, and the designed tracking controller is robust with respect to the sinusoidal disturbances.