MODEL PREDICTIVE CONTROLLER DESIGN AND COMPARATIVE STUDY WITH TUNED FUZZY PID CONTROLLER FOR THE MAGNETIC LEVITATION SYSTEM

Abstract

The study of control of Magnetic levitation system has been broached with PID controller. The response of properly tuned PID controller shows good response however values of parameters (Kp , Kd Ki ) cannot be determined so easily, and also readjustment of these parameters are difficult in case of variation in system parameters or presence of external disturbance at system input and output, So another algorithm has been introduced which is based on human experience. This is known as Fuzzy logic. In fuzzy logic two inputs are chosen I) change in error 2) error. PID controller parameters can be optimized using fuzzy logic. A Fuzzy PID controller contains the characteristics of both controllers that are specific modeling characteristic of PID controller and flexibility behavior of fuzzy logic. PID control requires very precise model structure, however most of the practical processes are not having the precise model i.e. there are various external disturbance, environment changes and uncertainty in model parameters that make the system non ideal. Thus using convectional PID controller, the precise control can be achieved. Fuzzy control does not dependent on mathematical model of the system so it is not required any precise modeling of the plant. The use of Fuzzy logic leads to high robustness of the controller. To include the fuzzy characteristic into PID controller, PID parameters are tuned using fuzzy logic. The simulation result in MATLAB shows that Fuzzy PID response is much better than PID controller. Since tuning of PID controller with fuzzy logic Fuzzy gives satisfactory response; however for this purpose an expertise is required to develop if then rules which are base on manual observation. The response can also be improved more using Model Predictive Controller. Model Predictive Controller completely depends on the prediction of future output. For this future output control signal is optimized over a particular number of intervals (control horizon). This optimization is done at each sampling instants. In each step first optimized value is applied to controller and remaining values are dropped out. The same procedure is recurring for next step. Further this control theory is dealt with stability of Model Predictive Controller under varying constraints applied on its input and output. The stability of the system is analyzed using state estimation technique. This controller is based on prediction theory according to which, input signal is computed at each sampling instants and output states are estimated and parameter are chosen in such way that it ensures the stability of the system. The first optimal value - is implemented over a specified control horizon and rest values are ignored. This process gets repeated iv 4 -ì in the next step. The conventional controller like PID and improved Fuzzy PID controller are not able to control the system effectively under wide constraints variation, so the complexity of algorithm design and model constraints lead to design a Model Prediction Controller which provide the systematic design structure to accommodate the stability and constraints variation effectively. The analysis of simulation results of PID, Fuzzy PID and Model Predictive Controller shows that performance of Fuzzy PID controller is better than PID and performance of Model Predictive Controller is better than Fuzzy PID controller.