Optimal PID control of spatial inverted pendulum with big bang-big crunch optimization

Jia Jun Wang*, Tufan Kumbasar

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

26 Citations (Scopus)


As the extension of the linear inverted pendulum ( LIP ) and planar inverted pendulum ( PIP ) , this paper proposes a novel spatial inverted pendulum ( SIP ). The SIP is the most general inverted pendulum ( IP ) than any existing IP. The model of the SIP is presented for the first time. The SIP inherits all the characteristics of the LIP and the PIP, which is a nonlinear, unstable and underactuated system. The SIP has five degrees of motion freedom and three control forces. Thus, it is a multiple-input and multiple-output ( MIMO ) system with nonlinear dynamics. To realize the spatial trajectory tracking of the SIP, the control structure with five PID controllers will be designed. The parameter tuning of the multiple PIDs is a challenging work for the proposed SIP model. To alleviate the difficulties of the parameter tuning for the multiple PID controllers, optimal PIDs can be achieved with the help of Big Bang-Big Crunch ( BBBC ) optimization. The BBBC algorithm can successfully optimize the parameters of the multiple PID controllers with high convergence speed. The optimization performance index of the BBBC algorithm is compared with that of the particle swarm optimization ( PSO ). Simulation results certify the rightness and effectiveness of the proposed control and optimization methods.

Original languageEnglish
Article number8577040
Pages (from-to)822-832
Number of pages11
JournalIEEE/CAA Journal of Automatica Sinica
Issue number3
Publication statusPublished - May 2020

Bibliographical note

Publisher Copyright:
© 2014 Chinese Association of Automation.


Manuscript received March 18, 2018; accepted July 23, 2018. This work was supported by the National Natural Science Foundation of China (618730 79). Recommended by Associate Editor Hongyi Li. (Corresponding author: Jia-Jun Wang.) Citation: J. J. Wang and T. Kumbasar, “Optimal PID control of spatial inverted pendulum with big bang – big crunch optimization,” IEEE/CAA J. Autom. Sinica, vol. 7, no. 3, pp. 822−832, May 2020.

FundersFunder number
National Natural Science Foundation of China618730 79


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