A journal of IEEE and CAA , publishes high-quality papers in English on original theoretical/experimental research and development in all areas of automation
Volume 7 Issue 3
Apr.  2020

IEEE/CAA Journal of Automatica Sinica

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Article Contents
Jia-Jun Wang and Tufan 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. doi: 10.1109/JAS.2018.7511267
Citation: Jia-Jun Wang and Tufan 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. doi: 10.1109/JAS.2018.7511267

Optimal PID Control of Spatial Inverted Pendulum With Big Bang – Big Crunch Optimization

doi: 10.1109/JAS.2018.7511267

the National Natural Science Foundation of China 61873079

More Information
  • 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.


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    • A novel spatial inverted pendulum (SIP) is proposed for the first time.
    • Five PID controllers are designed for the SIP to realize the tracking control.
    • The parameters of the PID controllers are optimized with Big Bang-Big Crunch (BBBC).
    • The optimization performance of the BBBC is compared with that of the PSO.


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