Optimal Fractional Order PID Controller Design for Fractional Order Systems by Stochastic Multi Parameter Divergence Optimization Method with Different Random Distribution Functions

This paper modifies Stochastic Multi Parameter Divergence Optimization Method (SMDO) by using some types of random distribution functions in order to show effects of different random distribution functions on optimization performance. SMDO is a parameter wise random search algorithm in random walk class. A prominent feature of SMDO method lies in using random number with standard uniform distribution while diverging a parameter of solution point in backward and forward directions to reach an optimal solution. SMDO method benefits from the success of random backward and forward divergences. This study investigates effects of four types of random distribution functions on performance of SMDO algorithm for controller tuning problem. These distributions are Chi-Square Distribution (CSD), Rayleigh Distribution (RD), Log Normal Distribution (LND) and Uniform random (UD) distribution. To illustrate effects of these random distribution functions, SMDO is employed to fractional order PID (FOPID) controller tuning problems for fractional order model (FOM) and results obtained for different distribution functions are demonstrated.