离散控制4-2.ppt

4-5 Design based on the root-locus method 4-5 Design based on the root-locus method 4-5 Design based on the root-locus method 4-5 Design based on the root-locus method 7. Comments It is important to note that the poles of the closed-loop transfer function determine the natural modes of the system. The transient response and frequency response behaviors, however, are strongly influenced by the zeros of the closed-loop pulse transfer function. In the s plane, adding a zero on the negative real axis near the origin increases the maximum overshoot in response to a step input. In the z plane, adding a zero on the positive real axis between 0 and 1 increases the maximum overshoot. In fact, moving a zero toward point z=1 greatly increase the maximum overshoot. Similarly, in the s plane a closed-loop pole on the negative real axis near the origin increases the settling time. A closed-loop pole in the z plane between 0 and 1 (in particular, near point z=1) increases the settling time. * * 1. Smith predictor (1) The problem of the control of the systems with time delay In 1950s, Smith proposed a compensation model for the systems with time delay, which is difficult to be realized with analog controller The controller system with time delay _ 4-6 Design controllers for system with time delay * (2) Traditional methods and its characteristic equation is 4-6 Design controllers for system with time delay * (3) Smith predictor Block diagram of a Smith-predictor Smith predictor 4-6 Design controllers for system with time delay * and its characteristic equation is 4-6 Design controllers for system with time delay [If the zeros at infinity are included in the count, F(z) has the same number of zeros as poles) * The angle of departure (or angle of arrival) of the root locus from a complex pole (or at a complex zero) can be found by subtracting from 180°the sum of all the angles of lines (complex quantities) from all other poles and zeros to the complex pole (or compl