Abstract
This study presents proportional-integral-derivative (PID) and adaptive neuro fuzzy inference system (ANFIS) control strategy to stabilize of highly nonlinear triple inverted pendulum system. A nonlinear dynamic representation of the system has been proposed and simulated in MATLAB/Simulink platform. The result indicates better performance of ANFIS controller compared to PID controller. Both ANFIS and PID controllers were able to stabilize complete system with desirable overshoot and steady state response. In order to minimize if–then fuzzy rules, the ANFIS controller has been designed using only three membership functions of triangular shape. The proposed ANFIS controller aided in solving the problem of fuzzy rule explosion commonly associated with fuzzy controllers.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Ananevskii IM (2018) The control of a three-link inverted pendulum near the equilibrium point. Mech Solids 53:16–21. https://doi.org/10.3103/S0025654418030020
Furut K, Ochiai T, Ono N (1984) Attitude control of a triple inverted pendulum. Int J Control 39(6):1351–1365. https://doi.org/10.1080/00207178408933251
Chen W, Theodomile N (2016) Simulation of a Triple inverted pendulum based on fuzzy controller. World J Eng Technol 4(2):267–272. https://doi.org/10.4236/wjet.2016.42026
Huang X, Wen F, Wei Z (2018) Optimization of triple inverted pendulum control process based on motion vision. EURASIP J Image Video Process 73:1–8. https://doi.org/10.1186/s13640-018-0294-6
Arkhipova IM (2019) On stabilization of a triple inverted pendulum via vibration of a support with an arbitrary frequency. Vestnik St. Petersburg University, Mathematics 52:194–198. https://doi.org/10.1134/S1063454119020031
Jahn B, Watermann L, Reger J (2021) On the design of stable periodic orbits of a triple pendulum on a cart with experimental validation. Automatica 125:1–7. https://doi.org/10.1016/j.automatica.2020.109403
Masrom MF, Ghani NMA, Tokhi MO (2021) Particle swarm optimization and spiral dynamic algorithm based interval type-2 fuzzy logic control of triple link inverted pendulum system: a comparative assessment. J Low Freq Noise Vib Control 40(1):367–382. https://doi.org/10.1177/1461348419873780
Hussain K, Salleh M (2015) Analysis of techniques for ANFIS rule-base minimization and accuracy maximization. ARPN J Eng Appl Sci 10(20):9739–9746
Su H, Woodham CA (2003) On the uncontrollable damped triple inverted pendulum. J Comput Appl Math 151(2):425–443. https://doi.org/10.1016/S0377-0427(02)00663-5
Medrano-Cerda GA (1997) Robust stabilization of a triple inverted pendulum cart. Int J Control 68(4):849–866. https://doi.org/10.1080/002071797223361
Pant S, Kumar A, Ram M (2019) Solution of nonlinear systems of equations via metaheuristics. Int J Math Eng Manage Sci 4(5):1108–1126
Kim MH, Lee SU (2021) PID with a switching action controller for nonlinear systems of second order controller canonical form. Int J Control Autom Syst 19:2343–2356. https://doi.org/10.1007/s12555-020-0346-4
Kouba NEY, Menaa M, Hasni M, Boudour M (2019) A new robust fuzzy-PID controller design using gravitational search algorithm. Int J Comput Aided Eng Technol 11(3):331–360. https://doi.org/10.1504/IJCAET.2019.099327
Tsai CC, Tai FC, Chang YL, Tsai CT (2017) Adaptive predictive PID control using fuzzy wavelet neural networks for nonlinear discrete-time time-delay systems. Int J Fuzzy Syst 19:1718–1730. https://doi.org/10.1007/s40815-017-0405-z
Malik P, Nautiyal L, Ram M (2019) A method for considering error propagation in reliability estimation of component-based software systems. Int J Math Eng Manage Sci 4(3):635–653
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Kharola, A., Rahul, Pokhriyal, V. (2023). Adaptive Neuro Fuzzy Control of Triple Inverted Pendulum System. In: Rani, A., Kumar, B., Shrivastava, V., Bansal, R.C. (eds) Signals, Machines and Automation. SIGMA 2022. Lecture Notes in Electrical Engineering, vol 1023. Springer, Singapore. https://doi.org/10.1007/978-981-99-0969-8_28
Download citation
DOI: https://doi.org/10.1007/978-981-99-0969-8_28
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-99-0968-1
Online ISBN: 978-981-99-0969-8
eBook Packages: EnergyEnergy (R0)