|M.Sc Student||Buzovski Michael|
|Subject||PID Controller Design for Systems with Time-Delay based on|
Smith Predictor Approximation
|Department||Department of Electrical Engineering||Supervisor||Professor Nahum Shimkin|
|Full Thesis text|
The PID controller is the most commonly used control algorithm today. In spite of its wide-spread use there exist no generally accepted design method. There are several reasons to look for better methods to design PID controllers. One reason is the significant impact it may give because of the wide-spread use of the controllers. Another reason is the significant benefit improved design methods will give emerging auto tuners and tuning devices.
This work examines two novel numerical methods for PID-control design for systems with time delay. Those methods make use of the Generalized Hermite-Biehler Theorem, which defines the set of PID - controllers that can stabilize a given time-delay system. We further implement an H ∞ - related criterion to get a robust stability set of PID parameters.
In the proposed Direct Search method we minimize the ISE (Integrated Square Error) criterion on the robust stability set to get the optimal PID parameters. In addition, we extract from the numerical results a simple tuning rule for PI and PID controllers, that gives us good robust properties on one hand and optimal performance according to ISE criterion on the other. In the second method proposed here, we look for the PID controller parameters from the robust stability set which are the nearest approximation to a control loop operating with a Smith Predictor and optimized controller. Like in the Direct Search method, some simple rules for tuning of PI and PID controllers are introduced. These rules can be used to simplify the tuning problem and can easily be implemented in industrial applications.
The proposed design procedures have been applied to First Order Time Delay System and the results have been compared one to another and to other well-known methods of PID tuning.