Swing-Up Control by BVP Arithmetic for the Rotational Inverted Pendulum
The swing-up control strategy via BVP arithmetic is presented for rotational inverted pendulum. The swing-up control programming from hanging to the upright position can be transformed into the two-point boundary value problem (BVP) of nonlinear systems. According to the boundary conditions of the swing-up process, the control torque function of Fourier series form with free parameters is constructed. The BVP is solved with the bvp4c function in Matlab toolbox, and the control torque sequence is obtained. The swing-up process is open-loop feedforward control essentially. In order to inhibition parameters perturbation, the closed-loop stabilizing control is designed around the upright position for the inverted double pendulum with unstable zero-dynamics. The simulation of swing-up, stabilizing and switching process illustrates the effectivity of the control strategy.
Z. D. Yu and X. F. Wang, "Swing-Up Control by BVP Arithmetic for the Rotational Inverted Pendulum", Advanced Materials Research, Vols. 211-212, pp. 515-519, 2011