Multi-rate Ripple-Free Deadbeat Control for Nonlinear Systems Using Diophantine Equations

The response able to track the reference signal after small finite time with SSE equal zero.

The proposed control can be divided into two sub-controllers: one uses state feedback and the other uses the Diophantine equations. The complete nonlinear design guarantees the convergence to a neighborhood of origin from any initial state in finite time; thus, providing a stable deadbeat performance. Results shows that the ripple-free deadbeat controller is able to track the input signal and the error decays to zero in a finite number of sampling times.