Analytical design of Proportional Derivative Controller for Interval System: Experimental Validation on Servo System

Abstract

It is observed that classical controller design techniques, i.e., particularly fixed type of PI/PD/PID analytical control approach, fails for the parametric uncertainty issues. However, the graphical approach for PID tuning and advanced control techniques such as H infinity, Quantitative feedback technique (QFT) have already been developed for handling parametric uncertainty, but these approaches are complex. Because of this, instead of using advanced controller techniques and graphical PID tuning approach, a variant of PID, i.e., a fixed type proportional derivative (PD) controller design is proposed for a single input single output plant (SISO) interval system with no zeros using Krishnamurthy's approach based on Routh criterion, Kharitonov's theorem and model order reduction approach based on Routh criterion. The beauty of the proposed approach is that the direct formulae is proposed for the tuning of the PD controller for an interval system. The proposed controller design gives the necessary and sufficient condition of stability and also the desired performance. The proposed approach is validated through simulation, and further experimental validation is carried out on the Servo system.