Control Law Design with Dead-beat Property in Continuous-Time Dynamical Systems

In this paper, an open loop control scheme is developed in order to design a dead-beat control effort in the high order continuous-time systems. The dead-beat control is really a finite-time control law. In this method, the input signal has been manually selected such that the output signal becomes constant in a finite time. In the LTI systems, having known the step response, a control signal could be exactly selected such a way that the control objective would be met in a finite time. For this end, the dead-beat control problem is firstly investigated in a standard first order system. Then a similar problem is studied in the second order systems. Finally a general design framework would be developed to obtain a dead-beat control policy in the high order continuous-time systems. In the proposed method, the control design problem is deliberately converted into the solution of a linear matrix equation. Therefore the control signal would be determined by solving such an algebraic equation. The proposed procedure is applied in some continuous-time LTI systems. The simulation results are shown effectiveness of the suggested methods for designing of a finite-time control law in the continuous-time systems.