Approximate optimal rejection to sinusoidal disturbance for nonlinear systems

The problem of approximate optimal rejection to sinusoidal disturbances with zero steady-state error (ZSSE) for nonlinear systems is considered. Based on the internal model principle, a disturbance compensator is constructed through which the plant model with external disturbances is transformed into an augmented nonlinear system without disturbances. Introducing a sensitivity parameter and expanding power series around it, the original optimal control problem is transformed into a series of linear two-point boundary value (TPBV) problems. The obtained optimal control law consists of a linear analytic term which is obtained by solving a Riccati matrix equation and a nonlinear compensatory term in form of series which is obtained by a recursive algorithm. By intercepting a finite sum of the compensation series, an approximate optimal control law is obtained. A numerical simulation shows that the algorithm is easily implemented and has a fast convergence rate. The designed controller has more robustness.