Co-ordinate tuning of PID parameters for dynamical systems

Abstract

This paper proposes a co-ordinate tuning strategy for PID control parameters in achieving both the robustness and better transient characteristics. Modified Ziegler-Nichols, BodeIntegrals and Iso-damping are well known methods for tuning of PID parameters in meeting the desirable. In order to achieve the robustness to gain variations and better transient properties, a new control strategy known as co-ordinate control structure is derived by incorporating the important features of Iso-damping and Bode integral methods. In this process a weightage factor μ is obtained optimally by minimizing Integral Time Absolute Error through Genetic Algorithm (GA). The effectiveness of the proposed scheme has been illustrated with typical systems. I. INTRODUCTIONPID Controllers are extensively being used in Industrial applications because of their simplicity and effectiveness. Due to rapid developments in control technology, there have been different tuning methods reported in the literature [1][2][3]. Among these the Modified Ziegler-Nichols (MZN) [1] method has an advantage of simplicity and works well in many situations of process control applications. In this method, for the given specifications of desired Phase Margin and Gain Crossover frequency, the controller parameters can be selected such that the Nyquist plot passes through the desired location on the unit circle. For designing a PID Controller, however, an additional equation should be introduced which specifies the ratio between integral time and derivative time is α. In order to obtain a unique solution in MZN method, α is selected as 4. Recently, the role of α has drawn much attention and new relationships between T i and T d are presented in [4][5][6] instead of T i = 4T d . In [4][5] it has been shown that the slope of the Nyquist curve at crossover frequency can be adjusted. The design of controller is based on Bode's integrals and only requires the knowledge of the frequency of the system at the crossover frequency as well as its static gain without any model. In [6],a robust PID tuning method was proposed to achieve the flat phase property, that is the phase derivative with respect to the frequency is zero at a given frequency called the tangent frequency, so that the closed-loop system is robust to gain variations and the step responses exhibits Iso-damping property. Flat Phase controller is robust to plant gain variations compared to that of other methods mentioned. Some important suggestions have been made for the improvement of Flat phase controller scheme in [7]. Both the Flat phase controller and controller based on Bode's integrals are preferable compared to MZN