Design of modified fractional order PID controller for cart inverted pendulum system

In recent times, the use of fractional order PID (FOPID) controllers has become quite common due to their superiority over conventional controllers like PID, LQR, and pole placement. However, the biggest challenge in designing a FOPID controller lies in obtaining its optimal parameters. A FOPID controller has five parameters whose tuning requires significant computational effort. Also, the presence of two fractional order parameters makes systems more complex. In this paper, a controller has been designed that performs similarly to FOPID controllers but requires less computational cost to obtain its parameters and is also less complex. The teaching learning-based optimization (TLBO) algorithm has been used for obtaining the controller parameters. The designed controller has been tested on linear systems of various orders. It is then implemented on a nonlinear Simulink and physical model of a Cart-Inverted pendulum (CIP) system. The closed-loop system was found to be stable and robust. Stability analysis was done using the Riemann Surface. Multiplicative gain and parametric variations were utilized for robustness verification.