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

Abstract

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.

Improved Decentralized Fractional-Order Control of Higher-Order Systems Using Modified Flower Pollination Optimization

“…Despite s 0 being necessary, s 0 can actually be as low as 0.1. It is challenging to produce pseudorandom step sizes that accurately match the Levy distribution though [48]. As a result, the Mantegna method [49], a useful algorithm that has been documented in the literature, is utilized in the FPA to generate these random values.…”

Interval Type-3 Fuzzy Inference System Design for Medical Classification Using Genetic Algorithms

“…An illustration of a Type-3 Trapezoidal MF with a vertical cut is shown in Figure 2. This Interval Type-3 membership function is defined with the Equation (6). The vertical cuts A (x) (u) identify the FOU(A), these are Interval Type-2 FS with Gaussian Interval Type-2 MF, µ A(x) (u) with parameters [σ u , ⇕(x)] for the UMF, and for LMF: λ (LowerScale) and ↕ (LowerLag).…”

“…An illustration of a Type-3 Trapezoidal MF with a vertical cut is shown in Figure 2. This Interval Type-3 membership function is defined with the Equation (6). The function 𝜇(𝑥) and the parameter 𝜆 are multiplicated to create the LMF of the domain of uncertainty, 𝜇(𝑥), is described as the following: 𝜇(𝑥) = 𝜆 𝜇(𝑥).…”

“…But another area within AI is fuzzy logic (FL), which, since its creation, has had many areas of application where it has demonstrated its effectiveness in solving highly complex problems. Its applications range from the classification of foods based on their characteristics [5], fuzzy control problems where the inputs of the FIS play an important role in obtaining important output values that allow the stability of the models [6], to responses combination for pattern recognition applied to time series prediction [7] or human recognition [8], and classification problems [9] to mention a few applications. A significant contribution that FL has had is in medical applications, where, either alone or in combination with other techniques, it has allowed it to be an excellent support tool in medical diagnosis [10,11].…”

“…In Ref. [6], The advantages of Interval Type-2 FIS are shown over Type-1 FIS, applied to a modification of Flower Pollination Optimization for Rotary Inverted Pendulum System. The application of noise effects and load disturbance mainly demonstrates the robustness and effectiveness of the method.…”