Advanced Discrete-Time Control by Khalid Abidi & Jian-Xin Xu

Author:Khalid Abidi & Jian-Xin Xu
Language: eng
Format: epub
Publisher: Springer Singapore, Singapore

(5.21)

Note that a general solution of (5.18) is given by

(5.22)

where is the error in control at the 0th iteration. If we use the approximation of to compute we get

(5.23)

where

(5.24)

The binomial coefficient is plotted for a constant as a function of in Fig. 5.1. It can be seen that the coefficient attains a very large value before converging to unity and if the convergence due to and is slower than that of the initial divergence of then would also follow the characteristic of . This overshooting phenomenon will be illustrated in later examples. From the above results it is obvious that we need to guarantee monotonic convergence. Two conditions exist that guarantee monotonic convergence. The first one is time domain based while the other is frequency domain based and will be investigated later on. According to [119], if then the monotonic convergence is guaranteed if the following condition is satisfied

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.