We deal with LTI nonminimum phase (NMP) systems which are difficult to control with conventional methods because of their inherent characteristics of undershoot. In such systems, reducing the undesirable undershoot phenomenon makes the response time of the systems much longer. Moreover, it is impossible to control the magnitude of undershoot in a direct way and to predict the response time. In this paper, we propose a novel two sliding mode control scheme which is capable of stably determining the magnitude of undershoot and thus the response time of NMP systems a priori. To do this, we introduce two sliding lines which are in charge of control in turn. One is used to stabilize the system and achieve asymptotic regulation eventually like the conventional sliding mode methods and the other to stably control the magnitude of undershoot from the beginning of control until the state meets the first sliding line. This control scheme will be proved to have an asymptotic regulation property. The computer simulation shows that the proposed control scheme is very effective and suitable for controlling the NMP systems compared with the conventional ones.

Nonminimum phase systems are difficult to be controlled with a conventional PID-type controller because of their inherent characteristics of undershooting. A neuro-controller combined with a PID-type controller has been shown to improve the control performance of the nonminimum phase systems while maintaining stability. In this paper, we apply a multiobjective evolutionary optimization method for training the neuro-controller to reduce the undershooting of the nonminimum phase system. The computer simulation shows that the proposed multiobjective approach is very effective and suitable because it can minimize the control error as well as reduce undershooting and chattering. This method can be applied to many industrial nonminimum phase problems with ease.

This paper presents a new blind identification method of nonminimum phase FIR systems and an adaptive blind equalization for PAM/QAM inputs without employing higher-order statistics. They are based on the observation that the absolute mean of a second-order white sequence can measure whether the sequence is higher-order white or not. The proposed methods are new alternatives to many higher-order statistics approaches. Some computer simulations show that the absolute mean is exactly estimated and the proposed methods can overcome the disadvantages of the higher-order statistics approaches.