LOW-DRER $H_\infty$ CONTROLLERS WITH THE MIXWED SENSITIVITY PROBLEMS

This paper presents a simple methodology for reducing the order of H$_{\infty}$ controllers in the mixed sensitivity control problems. The key point of this methodology is to transform the generalized plant expression to new one, where the control object and the weighting functions for the sensitivity function may have some poles on the imaginary axis. So that, this methodology makes it possible to use the standard method to solve the general H$_{\infty}$ design problems about the mixed sensitivity problems, even for a servo system or a oscillatory system. We derive that the order of H$_{\infty}$ controllers designed by this methodology may be reduced to n$_{p}$ where n$_{p}$ is the order of the denominator of the control object. It is clear that n$_{p}$ is lower than n$_{p}$ + n$_{s}$, which is the order of H$_{\infty}$ controllers obtained by the ordinary H$_{\infty}$ design method up to now, where n$_{s}$ is the order of the denominator of the weighting function for sensitivity. Finally, a numerical example is given to illustrate the results..lts.ts..lts.lts.