PID Controller Design for Non-Minimum Phase Time-Delay Systems Using Optimization Methods

Author Name(s): B.Amarendra Reddy, M.Anil Kumar, K.Anusha, G.Ananda Rao
Author Email: bamarendrareddy@yahoo.com

Abstract

Non-minimum phase systems are difficult to control with conventional methods because of their inherent characteristics of undershoot. The complexity in control of such systems increases when time delay is added. These systems will exhibit undershoot in time-response and oscillations in the high frequency region in magnitude frequency response. This paper focuses on design of PID controller for non-minimum phase time-delay systems under the disturbance and noise conditions. The PID controllers for these systems are designed by using Magnitude-Optimum Multiple Integration and numerical optimization methods. Mathematical analysis is developed using numerical optimization technique for non-minimum phase time delay systems. By using these methods the PID controllers are obtained mathematically. The effectiveness of PID controllers resulted using these methods compared in MATLAB environment by considering NMP time-delay systems.

Introduction

There have been great amount of research work on the tuning of PID controllers. In this paper, two approaches are given for the controller design of non-minimum phase systems. PID controllers have been used for a long time. Taylor developed the first PID controller [12]. But the problem is occurred how to tune a PID controller. At that time Ziegler and Nichols discover the famous Ziegler and Nichols tuning rules. These rules are still widely used. This is why so many different tuning rules have been developed which are based on the same tuning procedure. In this paper discussed about the controller design of the non-minimum phase systems by using magnitude optimum and multiple integration and numerical optimization approach.In this paper the procedural steps for design of a controller for Non-minimum phase time-delay systems using MOMI are discussed in section II. Design of controllers using Numerical optimization is discussed in section III. To validate these concepts simulation results are presented in section VI.

Conclusion

In this paper mathematical analysis is developed using numerical optimization technique for non-minimum phase time delay systems. The PID controllers are designed for Non-minimum phase time-delay systems using the magnitude optimum multiple integration. These both methods are effectively rejecting disturbances. The effectiveness of these controllers in rejecting disturbances are shown in time-domain and also in frequency domain  in the MATLAB environment. It is observed from these simulation results that MOMI method is more accurate compared to Numerical optimization. Magnitude sensitivity frequency responses using these controllers are shown for these systems. It is observed that these controllers are capable to reject disturbances and also attenuate the noice effectively.

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