Design of a Finite Time Settling Controller for a System with Input Saturation

Weighting matrix of quadratic performance index and design method of optimal deadbeat control system

“…(27), and by substituting this u k into y Gu k of Eq. (4) and rearranging the result using with D k be 0, D k which will minimize the performance index P can be determined by solving For simplification of explanation, when the case of the preceding example of n = 2, N = 4 (k = 2) is considered, the optimal deadbeat manipulated variables u 2 where Here, the extra poles \ i will be arranged on the z-plane depending on the values of the weighting matrices Q, R of the performance index; however, let us consider the three domains of inside the unit circle, on the unit circle, and outside the unit circle. In the case of a system without self-regulation, since K may be considered infinitely large, all extra poles will be inside the unit circle and always holds; in the case of fixing the weighting matrix q, the extra poles will approach the unit circle as the weight r is made larger.…”

“…In the design of optimal deadbeat control systems, which can cope with the improvement of response waveforms and the limitation of manipulated variables, the method of Nishimura and colleagues, which uses softening filters inside the main loop and state local feedback [1,2], and the method of Urikura and Nagata, which performs local compensation based on state feedback by adding a precompensator to the controlled system [3,4], are well known. Each is a method of design of the state feedback control system which minimizes the quadratic performance index on the manipulated variable and deviation by increasing the number of degrees of freedom with the optimal number of control steps N as N = n k k !…”

A design method for continuous deadbeat control systems

“…All of these papers describe the design of deadbeat digital controllers as sampled-date control systems in which deadbeat control is realized in the form of linear feedback, increasing the number of degrees of freedom by using precompensators [1,2] and smoothing filters [35], which allow the implementation of deadbeat control in the form of a linear feedback evaluating the quadratic integral of the control input and the deviation. The present authors have proposed methods of designing a deadbeat controller with a configuration similar to those described by Urikura [1,2] and Nishimura and colleagues [3,4]. In the method of design of deadbeat control systems proposed herein, the deadbeat control input u k minimizing the performance function is determined by computation of a simple matrix from the sample value of the plant step response, and the response of the controlled object with respect to this u k is used as the reference response of a closed loop system [810].…”