The Dynamic Analysis And Control Of A Species Type Of Two-link Underacutated System

Underactuated system is a species of system which have fewer actuators than degrees-of-freedom. It's widely used in the mechanical system. Due to the merit of less actuators, lighter weight, less cost, the underactuated designation is widely used in the space robot, mobile robot, ROV (Remotely operated underwater vehicles)and so on.Our plant in this paper is a species of two-link underactuated system. It's similar with the common two-link manipulator, but it only has one actuator either in the"elbow"or in the"shoulder". It has complex dynamic and kinematics, because it is a non-linear, underactuated, strong coupling system. This system has become the focus of studying the non-linear control, and more and more researcher pay attention to it.Our main work in this paper is to analyse the dynamic and control the system. Our work is based on the theory of non-linear system, modern control, optimal control and the experiment is done on the Matlab/simulink. Our main purpose is to deeply realize the dynamic and kinetics of the system and the outline of purpose are in the below:(1) Analyse the open-loop properties and equilibrium point of the system;(2) Analyse the energy properties. And design the swing up control strategy for the Acrobot and Pendubot depend on it. Beside that, we should estimate the region of attraction of the asymptotically stable equilibrium point. And an another important work is analysis the dynamic and kinetic of the process of swing up control.(3) We divide the process to two steps, the first step is to swing up the system near the invert position, the second step is to balance the system in the invert position.It's necessary to analyse the open-loop system before we consider it in the closed-loop state. The open-loop analysis is very useful to understand the behavior of the system. For our plant is the very typical model, it's meaningful for us to discuss the open-loop model. The open-loop analysis include: (1) qualitative behavior of the equilibrium (2) the dynamic and kinetic analysis of the open-loop model. The eigenvalue of the Jacobian matrix will be discussed to analyse the different case of the equilibrium. At the same time, the local controllabilitycondition and the dynamic properties of the neighborhood of the equilibrium are discussed in the paper. Moreover, the phase portrait was constructed to analyse the dynamic and kinetic of the system with different initial condition. Through these analysis, we get some basic conclusions about the dynamic and kinetic of the system.In the process of studying the swing up algorithm of the Acrobot, based on the energy control algorithm was designed in this section. Before that, the collocated linearization was given to the Acrobot. And through all this, we get the swing up algorithm of the Acrobot. The simulation show when we choose the suitable parameter, this control algorithm could achieve the control task of the system and at that time, the energy of the system will increase fast. Our paper also investigate the zero dynamic of the system, show it's a non-minimum phase zero dynamic. The dynamic properties of the swing up process was also investigate in our paper. At last, our paper analyse the different kinetic and energy mode of the system, when the reference input change. And through all these analysis, we get some conclusions about the dynamic and kinetic of the swing up process of Acrobot. In the fifth chapter of this paper, because of the different actuator position between the Acrobot and Pendubot we design another type of the energy control for the Pendubot. The strategy is control the state and the energy of Pendubot to a fixed value. And the fixed energy value is equal to the energy value of the invert position. The simulation result show that this control algorithm has the merit of short transit time and smooth control swich process. Moreover, we use the LaSalle theory estimate the region of the attraction. At last, the different experiment result were discussed, when we use the different initial condition.In the sixth chapter of this paper, the balance controller was designed based on the LQR method for Acrobot and Pendubot. We use the control plan of swing-swich-balance to finish the control process. The simulation result prove that the control algorithm.All in all, we study deeply the Acrobot and Pendubot not only in the theory but also in the experiment and basically achieves its given goals. Because of the typification of the Acrobot and Pendubot in its dynamics and kinematics analysis and control issues in the non-linear, underactuated system. The work of this paper will be contributive to the following research on similar dynamic system.