Research On The Swing-up Of The Inverted Pendulum

Inverted pendulum system is a nonlinear, unstable, high order, multi-arguments, close coupling and underactuated system. Many abstract control concepts can be shown visually by the experiments of the inverted pendulum. The methods and techniques stemming from the study of the inverted pendulum system can be extensively used in many fields, such as robot control technology, artificial intelligence, missile interceptor control systems and so on.This thesis focuses on the swing-up of the inverted pendulum. The following is the work of the thesis.1. The thesis reviews the developments of the inverted pendulum. The model of the n-order inverted pendulum can be derived via the Lagrangian method. In the neighborhood of the equilibrium point, the model is linearized and the state equation of the inverted pendulum is obtained.2. Energy well controller is proposed for swing-up of the single inverted pendulum. Energy well functions are introduced in order to restrict the displacement and velocity of the cart. Stabilization is carried out by the SDRE (State-Dependent Riccati Equation) method. This method can be thought of as the nonlinear counterpart of LQR. Simulation and experimental results reveal the advantages of SDRE over LQR under the same control parameters.3. Swing-up of the double inverted pendulum is achieved by inversion-based trajectory control. From a mathematical point of view, swinging up the pendulums from their pending position to their upright position can be treated as a nonlinear two-point boundary value problem. The reference trajectories are obtained by solving the BVP. The two-degree-of-freedom control combined feedforward and feedback controls is used to track the desired reference trajectories. Simulation and experimental results show that the inversion-based trajectory control can swing up the double inverted pendulum in short time with well stability and strong robustness.4. Hardware configuration of the inverted pendulum is introduced. Real-time control is achieved in the VC++6.0 enviroment. Finally, the further research is presented.