Research On Stabilization And Tracking Control Of A Kind Of Underactuated Mechanical System

Underactuated system is a kind of system whose control input dimension is less than the degree of freedom, and its essence is a nonlinear system. Inverted pendulum system, as a kind of typical underactuated system, has a wide range of engineering and physical background.The research of the inverted pendulum system has important theoretical and practical significance because of many validations of control algorithms in real systems, such as the stability, controllability, system convergence speed and the ability of anti disturbance of the control system, can be checked and directly displayed by the inverted pendulum system model. Many domestic and foreign scholars have been trying hard to expand their control methods by means of continuous efforts and obtained a lot of research results.According to these theoretical results, this paper focus on the special form of the inverted pendulum Rotary Inverted Pendulum and Rotary Parallel Inverted Pendulum, specific tasks of this paper are as follows:1. Qualitative analysis of inverted pendulum systemAs a kind of inverted pendulum system, the rotational inverted pendulum has many similar characteristics and control methods with other kinds of inverted pendulum. So in this part, in order to lay the foundation for introducing the next research questions, we will carry on the qualitative analysis to the inverted pendulum system.2. Disturbance rejection control of single stage rotary inverted pendulumThe main contribution of this part is that a adaptive control method which doesn’t need the accurate physical parameters is be put forward, when the system has unmodeled dynamics or unknown disturbances. The method gets rid of the dependence on the precise model of the system, so that the proposed control method is more practical and worthy to be spread.By introducing partial feedback linearization and nonsingular coordinate transformation to the system model, the error dynamics are derived. And then, this paper designs a nonlinear integral sliding mode controller.According to the convergence analysis of system error dynamics, it is proved that the method can not only make the swing rod to reach and stable no the target position, but also can make the arm to return to the initial state. Meanwhile,the closed-loop system signals are bounded in the whole process. The simulation results are presented showing effective and feasible of the proposed methods.3. Energy-based swing up control of rotary parallel inverted pendulumThe main contribution of this part is when the double pendulum of rotary parallel inverted pendulum has different inherent properties, this paper use the energy method to design the controller. In order to design the controller so that the rotation parallel double pendulum reaching and stabilizing in the vertical direction, this paper implement partial feedback linearization to the system model firstly.Then we use the energy function of the double pendulum to construct the Lyapunov function.In addition, the designed controller takes a simpler structure and therefore is convenient for implementing and calibrating control parameters.By analyzing the motion of the double pendulum, it is proved that no matter from which initial state both energy of them converge to zero. Finally, the result of simulation shows that the controller can make the system to achieve better control effect in a short time.