Proportional integral derivative controller tuning via Kronecker summation and modified particle swarm optimization with experimental validation

This article aims to extend the use of the Kronecker summation method to draw the stability boundary locus for computation of the parameters of a proportional integral (PI) and proportional integral derivative (PID) controller involving a linear time invariant (LTI) plant. The article also tries to elucidate the mathematics that lead into the application of the Kronecker summation method, for the construction of a stability boundary locus (SBL), the problems encountered and a technique to obviate the problems, to allow a systemized application of the technique. The article further gives a method to tune a PI/PID controller using a combination of Kronecker summation and an iterative technique and compares the performance of the controller with the existing classical and modern control techniques. Lastly, the article uses the proposed technique to tune a controller and validate it on a QUBE 2 DC Servo motor setup.