Internal Model Control (IMC) and IMC Based PID Controller

Abstract

Internal Model Control (IMC) is a commonly used technique that provides a transparent mode for the design and tuning of various types of control. In this report, we analyze various concepts of IMC design and IMC based PID controller has been designed for a plant transfer function to incorporate the advantages of PID controller in IMC. The IMC-PID controller does good set-point tracking but poor disturbance response mainly for the process which have a small time-delay/time-constant ratio. But, for many process control applications, rejection of disturbance for the unstable processes is more important than set point tracking. Thus, we assume an appropriate IMC filter to design an IMC-PID controller for better set-point tracking in unstable processes. The controller assumed works differently for different values of the filter tuning parameters to achieve the required response As the IMC approach is based on cancellation of pole zero, methods by which IMC is designed result in good set point responses. However, the IMC leads to a long settling time for the load disturbances in lag dominant processes which is not desirable in the control industry. In our study we determined transfer function for the model of the actual process of a chemical reactor plant as we do not know the actual process which incorporates within it the effect of model uncertainties and disturbances entering into the process. As parameters of the physical system may vary with operating conditions and time and so it is essential to design a control system that shows robust performance in every situation. Then we tried to tune our IMC controller for different values of the filter tuning factor using SISO tool.Since all the IMC-PID procedures include some kind of model factorization techniques to convert the IMC controller to the PID controller so approximation error usually occurs. This error becomes problematic for the processes which have time delay. For this we have taken some transfer functions with significant time delay or with non invertible parts i.e. containing RHP poles or the zeroes. Here we have used different techniques like factorization or elimination of RHP to get rid of these error containing stuffs. It is because if these errors are not removed then even if IMC filter gives best IMC performance but it is internally unstable leading to a false PID controller and poor performance. Also, when a controller is designed based on an assumed model and implemented on the actual plant, its close loop performance may be arbitrarily poor depending on the extent of the mismatch between the model and the process. So we studied model uncertainty (model plant mismatch) more carefully and evaluated its impact on the expected performance of the control system. Apart from the objectives stability and performance in designing a control system we also concentrated on a third objective robustness which is the ability of a system to maintain its above properties in the presence of model uncertainty.