Control
Valiollah Ghaffari
Abstract
Employing discrete-time techniques, the min-time control of continuous-time dynamical systems is mainly studied through an analytical framework. To this aim, the exact discrete-time model of the linear time-invariant systems is specified through a zero-order hold. The optimal solution could be directly ...
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Employing discrete-time techniques, the min-time control of continuous-time dynamical systems is mainly studied through an analytical framework. To this aim, the exact discrete-time model of the linear time-invariant systems is specified through a zero-order hold. The optimal solution could be directly determined from some necessary conditions. However, the structure of the optimum control sequences is derived by utilizing the well-known Pontryagin principle. Employing the state transition matrix, the states of the control system are computed at the switching times. The switching times of the control signal would be found from a set of nonlinear algebraic equations. Accordingly, the transformation of the system’s states, from a known initial point to a specific value, would be accomplished in the minimum possible time. Applying the proposed scheme, the exact (integer) values of the switching times and the final time are numerically determined from the solution of an algebraic equation. Several discrete-time and continuous-time examples are discussed and simulated to show the feasibility and effectiveness of the suggested procedure in the dynamical systems. The simulation results confirm the method’s advantages over the existing ones.
Control
Valiollah Ghaffari
Abstract
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 ...
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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.