Stabilization of Inverted Cart-Pendulum System Using Controller: A Frequency-Domain Approach

Abstract

This paper focuses on the angular stabilization of inverted cart-pendulum system using PI D controller. The tuning of PI D controller is formulated as a nonlinear optimization problem, in which the objective function is composed of five design conditions in frequency domain. Particle swarm optimization technique has been used for optimizing PI D parameters. Also a PID controller has been designed based on same specifications, and a comparative study has been carried out. All the responses have been calculated using FOMCON toolbox of Matlab/Simulink.

Design of State Feedback LQR Based Dual Mode Fractional-Order PID Controller using Inertia Weighted PSO Algorithm: For Control of an Underactuated System

“…The search space is D dimensional, then the i th particle of the swarm can be denoted by a D-dimensional vector X i ðtÞ ¼ x i1 ðtÞ; x i2 ðtÞ; Á Á Á ; x iD ðtÞ ð Þ , and the velocity of the particle can be represented as V i ðtÞ ¼ v i1 ðtÞ; v i2 ðtÞ; Á Á Á ; v iD ðtÞ ð Þ [60]. The best previously explored location of i th particle is denoted as P best i ðtÞ ¼ p best i 1 ðtÞ; p best i 2 ðtÞ; Á Á Á ; p best i D ðtÞ ð Þ .…”

“…The best previously explored location of i th particle is denoted as P best i ðtÞ ¼ p best i 1 ðtÞ; p best i 2 ðtÞ; Á Á Á ; p best i D ðtÞ ð Þ . The optimal value among those P best i is called G best and it is denoted as G best ðtÞ ¼ g best1 ðtÞ; g best2 ðtÞ; Á Á Á ; g bestD ðtÞ ð Þ [60]. The PSO algorithm can be implemented using the following equations:…”

Design and implementation of adaptive control logic for cart-inverted pendulum system

“…The approximations done in equations (21) and (22) incur no problem in the stabilization of the system as the feedback consists of both position and angle for the stabilization and the states got cancelled get included in both the transfer functions. 42 Similarly, using the same approximation for angle control (u(s)=F(s)), we get the transfer function as given in equation (24).…”

“…13,21 To improve the performance using PID, fractional order calculus is introduced to design fractional order proportional integral derivative (FOPID) for stabilizing CIPS efficiently. 22,23 Although promising improvement in performance is achieved, determination of the fractional orders by heuristic search algorithms makes the controller design a computationally intensive as well as sluggish process, hence delimiting the applicability. A Fuzzy state-feedback modelling control is proposed by Teixeira and Zak 24 in two parts.…”

Stabilization and Tracking Control of Inverted Pendulum Using Fractional Order PID Controllers

“…In some recent studies [20][21][22][23][24], the PI D controller gives better outcomes than PID controller. Though there are some applications of PI D controller for IP system [25,26], PI D controller has not received considerable attention for unstable systems similar to IP system. Hence, in the present work, fractional order PID controller is designed in time domain to control pendulum angle as well as cart position.…”