Singular kernel and Exponential Kernel Numerical method for FOPID Controller

Abstract

Appropriate numerical method for solving the fractional domain problems is essential in order to find out solutions of various problems. Proportional Integral Derivative controller has the drawbacks of load dynamics and non-linearity hence the fractional order PID controller is introduced to overcome these problems but no appropriate numerical method is available for fractional type controller as in the case of traditional PID controller. The traditional PID controller could be implemented using any of numerical methods. Present work is carried out for investigating appropriate numerical method that have application in fractional order PID controller. Unfortunately, there is no unique definition of fractional derivative. In this work, two type of Caputo definition is used and numerical method is suggested for singular and exponential kernel of Caputo type definition. Results of Proposed numerical method is compared with analytical solution and also compared with Euler and ABC method. It is found that the singular type kernel numerical method shows minimum mean square error and also found suitable for fractional order PID controller. The fractional order PID is used to control the first kind of system G(S) with optimum FOPID parameters and sampling time is 2.56 ms. Response of the control strategy does not have oscillations and does not have underdamping response. Control loop settled down and achieved the set point in 128 ms.