Title: Modified augmented fractional order control schemes for cart inverted pendulum using constrained Luus-Jaakola optimisation

Authors: Deep Mukherjee; G. Lloyds Raja; Palash Kundu; Apurba Ghosh

Addresses: School of Electronics Engineering, Kalinga Institute of Industrial Technology (DU), Bhubaneswar, 751024, India ' Department of Electrical Engineering, National Institute of Technology Patna, Patna, 800005, India ' Department of Electrical Engineering, Jadavpur University, Kolkata, 700032, India ' Department of Electronics and Instrumentation Engineering, Burdwan University, Burdwan, 713101, India

Abstract: Since the upright position of an inverted pendulum system is an unstable equilibrium, it is extremely challenging to control. Fractional order based control schemes are becoming increasingly popular in stabilising an unstable system and achieving satisfactory closed-loop performance. Therefore, a novel combination of fractional order Lyapunov (FOLyapunov) rule and fractional order proportional integral (FOPI)/two-degree of freedom FOPI (2DOF-FOPI) controller is proposed to tackle this problem. Parameters of FOPI/2DOF-FOPI controllers are obtained using multi-objective constrained Luus-Jaakola multipass optimisation method. Comparative simulation studies are carried out with direct synthesis based PID control scheme, combination of fractional order Massachusetts Institute of Technology (FOMIT) rule augmented with either FOPI/2DOF-FOPI controllers using a mathematical model of inverted pendulum. It is evident that the proposed combination of FOLyapunov method and FOPI/2DOF-FOPI controllers outperforms the other schemes.

Keywords: inverted pendulum; MRAC; fractional calculus; MIT rule; FOMIT rule; FOPI; 2DOF-FOPI; luus-jaakola algorithm; FOLyapunov stability rule.

DOI: 10.1504/IJMIC.2021.123361

International Journal of Modelling, Identification and Control, 2021 Vol.38 No.3/4, pp.367 - 379

Received: 19 Sep 2020
Accepted: 26 Nov 2020
Published online: 13 Jun 2022 *

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