Suppachai Howimanporn and Manukid Parnichkun
X–Y planar inverted pendulum, particle swarm optimization (PSO), sliding mode control (SMC)
An X–Y planar inverted pendulum is a system which is nonlinear, multi-variable, and unstable. Such a nonlinear system requires appropriate controllers as well as good strategy to determine their optimal control parameters. In this paper, the authors propose an offline approach to balance the X–Y planar inverted pendulum using a robust sliding mode controller with particle swarm optimization (PSO) algorithm to optimize key parameters of the SMC. Particularly, the cost function in SMC parameter optimization is defined as finite time of integration of square of states and control signal, and therefore, we can directly identify the limit of the integration as time duration for each experiment. Our proposed control algorithm is evaluated through both simulation and experiment. The optimal gain matrix is determined offline and consequently applied to the actual model of X–Y planar inverted pendulum to verify the performance of the proposed technique. The experimental results of balancing angle from this proposed technique show that the PSO-based SMC can efficiently balance the X–Y planar inverted pendulum compared to the traditional SMC approach.
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