Stabilization of a double inverted rotary pendulum through fractional order integral control scheme

Ibrahim Mustafa Mehedi,Maamar Bettayeb,Ubaid M Al-Saggaf,Rachid Mansouri

doi:10.1177/1729881419846741

Abstract

Rotary double inverted pendulum is a highly nonlinear complex system and requires a high performance controller for its control. Using gain matrix which is obtained through state feedback technique may create complexity while removing the steady-state error for all states. Incorporating an integral action can be an alternative for these errors. Therefore, a state space–based fractional order controller with fractional integral action is designed and tested on a rotary double inverted pendulum in this article. The fractional integral controller is designed based on Bode’s ideal transfer function. Two degree of freedom is considered for tuning purpose as well. The integer order controller based on the state space approach is also shown for comparison. Simulation and experimental results are presented for both controllers of this rotary double inverted pendulum system.

Highlights

A link rotating above its pivot point is called an inverted pendulum
The proposed method described in the third section is implemented to test the stability and check the set point tracking performance of the rotary double inverted pendulum system
The closed-loop reference mode parameters are used for the design of fractional order controller such as, ic 1⁄4 100 and k 1⁄4 0.07

Summary

Introduction

A link rotating above its pivot point is called an inverted pendulum. Controlling issues of this type of inherently unstable systems are considered as a classic problem in dynamics and control theory. The challenge in this article is to use fractional order linear controllers to control the rotary double inverted pendulum system. To stabilize the system, the state feedback gain Ks is used and to impose the transient response of the closed-loop system, the compensator KðsÞ is cascaded after the fractional order integrator (1=sa). The impulse response of KðsÞ is represented by KðtÞ This KðtÞ is added in the control law through the convolution product with Ks. Here, the gain vector of the state feedback, Ks 2 R1Ân, is generated to influence the inner-loop’s characteristic polynomial. The proposed method described in the third section is implemented to test the stability and check the set point tracking performance of the rotary double inverted pendulum system.

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Experimental results

Conclusion