Implementation of 12 Transition Controls for Rotary Double Inverted Pendulum Using Direct Collocation

초록

The rotary double inverted pendulum system has one stable and three unstable equilibrium points due to its kinematic properties. This paper extends the traditional swing-up control problem by defining a novel transition control problem among these points. We formulate the system’s dynamic equations and boundary conditions for different equilibrium points to minimize energy consumption during transitions, resulting in a two-point boundary value optimal control problem. This problem is solved offline to calculate the feedforward trajectory for feedforward control. To convert the continuous optimal control problem with constraints into a nonlinear optimization problem, we employ the direct collocation method. A time-varying Linear Quadratic controller is used as the feedback controller to accurately track the generated feedforward path during real-time control, compensating for uncertainties. Previous studies on rotary double inverted pendulums have focused on the swing-up problem, with no research addressing transition control between the four equilibrium points. This paper defines the transition control problem for the rotary double inverted pendulum and proposes a control strategy. The method’s effectiveness and practicality were validated through the design and implementation of 12 transition trajectories in experimental settings, successfully demonstrating its feasibility and utility. © 2024 by SCITEPRESS– Science and Technology Publications, Lda.

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