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By Yung-Kai Lai, C.-C. Jay Kuo, Jin Li

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21. 15). The denominator of the output sensitivity function defines the 22 Digital Control Systems poles of the closed-loop transfer function. The stability properties of the system are determined by the denominator of the transfer function. In order that the closedloop system be asymptotically stable, all the poles of S yp (s ) must lie in the halfplane Re s < 0 . If the plot of the open-loop transfer function HOL(s) passes through the point [1, j0], for a value s = jω, the denominator of the closed-loop system transfer function will be null at this frequency.

J. of Adaptive Control and Signal Processing, vol. 9, no. 5, pp. 395-422 as well as in (Takahashi et al. 1970) and (Ogata 1990). 2 Computer Control Systems In this chapter we present the elements and the basic concepts of computercontrolled systems. The discretization and choice of sampling frequency will be first examined, followed by a study of discrete-time models in the time and frequency domains, discrete-time systems in closed loop and basic principles for designing digital controllers. 1.

062 An oscillatory damped response is observed with a period equal to two sampling periods. This type of phenomenon cannot result from the discretization of a continuous-time first order system, since this latter is always a-periodic. It may thus be concluded that the first order discrete-time model corresponds to the discretization of a first order continuous-time system only if a1 is negative1. 11. 5) We now go back to the method used to describe discrete-time models. The delay operator q-1 is used to obtain a more compact writing of the recursive (difference) equations which describe discrete-time models in the time domain (it has the same function as the operator p = d/dt for continuous-time systems).

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