Modified Flower Pollination Optimization Based Design of Interval Type-2 Fuzzy PID Controller for Rotary Inverted Pendulum System

The Type 2 Fuzzy Logic System (T2FLS) is an enhanced form of the classical Fuzzy Logic System (FLS). The T2FLS based control technics demonstrated a lot of improvements for the past few decades. This is based on the advantage of its membership function (MF). Many experimental studies indicated the superiority of Type 2 Fuzzy Logic Controller (T2FLC) over the ordinary Type 1 Fuzzy Logic Controller (T1FLC), particularly in the event of non-linearities and complex uncertainties. However, the organized design method of T2FLCs is still an interesting problem in the control engineering community. This is due to the difficulties in computing the parameters associated it. A novel application of the Modified Flower Pollination (MFP) optimization algorithm in the design of T2FL is presented. The optimized Cascade Interval Type 2 Fuzzy PID Controller (IT2FPIDC) structure is proposed in this study. The best values of the parameters of the antecedent MFs and the PID gains of IT2FPIDC are found using the MFP algorithm. The MFP optimization technique was used because of its lower computational effort and high convergence speed, in view of the higher number of variables to be optimized in cascaded IT2FPIDC. The MFP-based Type-1 Fuzzy Proportional Integral Derivative Controller (T1FPIDC) is compared with the proposed MFP-based cascade-optimized IT2FPIDC. The rotary inverted pendulum (RIP) which is a non-minimum phase, non-linear, and unstable system is employed as a benchmark for testing the proposed controller. Balance and trajectory-tracking controls of the RIP are considered. Furthermore, the disturbance rejection ability of the proposed controller is analysed. The presented control methos is evaluated on the RIP manufactured by Quanser over many simulations and real-world experiments. The performance characteristics considered are steady state error (Ess), settling time (ts), maximum overshoot (Mp) and rise time (tr). The improvement of the effectiveness and robustness proposed controller in the presence of load disturbance, noise effects and parameter variation is shown.