Design of fractional PID controller based on model reference

Proportional-Integral-Derivative (PID) controller is frequently preferred in automatic control applications due to its easy design and sufficient control performance. It has three basic parameters called Proportional gain (Kp), Integral gain (Ki) and Derivative gain (Kd). The integral and derivative operators in a conventional PID controller are integer order. The researchers proposed a fractional order PID controller by using the integral and derivative operators with a fractional order instead of the integer order integral and derivative operators in the traditional PID controller because it improves the control performance. The fractional order PID controller has an additional fractional integrator order (λ) and fractional derivative order (µ) compared to the traditional PID controller. In this thesis, it is focused on the design of the fractional order PID controller according to a reference model in the time domain. Bode's ideal transfer function is used as the reference model. It is aimed to obtain fractional order PID parameters by minimizing the error between the time domain response of Bode's ideal transfer function model and the output of the system to be controlled. In order to minimize the error, the Genetic Algorithm (GA) optimization method was used in the study. The study was carried out as a simulation study on an inverted pendulum system with a single-input multi-output (SIMO) structure. In the inverted pendulum system, two separate fractional order PID controllers were used for the chart and the pendulum, and the GA optimization was achieved by adjusting the Kp, Ki, Kd, λ and µ parameters of these two controllers to approximate the output response of the inverted pendulum system to the reference model.