Operating Time Modification by Elliptic Integration in Feedforward Control of One-Time Swing-Up Pendulum Using Finite-Time Settling Functions with Half-Odd-Integer Trigonometric Functions

In this study, feedforward control of the one-time swing of a 1DOF pendulum is performed using a finite-time settling function expressed by half-odd-integer trigonometric functions. The operating time is set to half the natural period of the oscillator, and the periods are half-odd-integer fractions of this operating time. To apply the finite-time settling functions to enable more accurate control of the pendulum, two modifications are proposed to compensate for the nonlinearity of the pendulum. The first method determines the operation time by considering complete elliptic integral of the first kind, which represents the period of half of the target swing-up angle. The second method uses a parameter that modifies the amplitude of the finite-time settling function, derived from the difference in potential energy between the 1DOF pendulum and the linear oscillator. Simulations are performed to evaluate the improvement in the operation of one-time swinging the pendulum up by these modification methods.