Swing-up Control Method Study Of A Class Of Underactuated Mechanical Systems

The underactuated mechanical system is a kind of nonlinear system, the number of control input variables is less than the degrees of the system freedom. It has strong nonlinearity and strong coupling. Because the underactuated part can not be controlled directly, so the smooth feedback control method is invalid for such system. It widely exists in the robot system, spacecraft system, navigation system, flexible system and locomotive system. In recent years, due to the need of practical application, the control problem of the underactuated mechanical system has gradually become one of the research hotspot in the nonlinear control field. Although there are many types of underactuated mechanical systems, but for the planar underactuated robot Pendubot with two degree of freedom, due to complex mechanical structure, strong nonlinearity and coupling, difficult to control, and it has better reference for the other underactuated mechanical systems to realize the control of the Pendubot. Therefore, it has been chosen as the research object by this thesis to study the related control algorithms.Pendubot is an underactuated planar robot, which has an input vector and two outp-ut vectors. The Pendubot has some additional rotational coupling, which is not found in either the linear inverted pendulum or the rotational inverted pendulum. For example, in both the linear inverted pendulum and the rotational inverted pendulum, the Taylor series linearization computed around any operating point results in a same and controll-able linear system. With the Pendubot, the linearization is operating point dependent; in other words, the linearization changes at each configuration and there are even special configurations where the linearization is uncontrollable. The control of Pendubot mainly divided into the swing-up control and the balance control. Especially, the swing-up control is a difficult point of the control of Pendubot. Now the existed control methods of Pendubot mainly have several problems:(1)When the controller is designed, it don’t consider the disturbance of friction, so most of the existed swing-up control algorithms need to repeatedly swing the drive arm; (2) Dependenting on the accurate dynamic model of Pendubot, the control algorithms are more complex, and most of them stay in the simulation.In view of the above questions, selecting the Pendubot actual system as the object, the swing-up control method study of a class of underactuated mechanical systems is lauched, and the obtained main results are as follows:(1) When the control target of Pendubot is the uppermost unstable equilibrium position, in order to eliminate the disturbance caused by friction, the neural network compensator is designed by this thesis; in order to avoid the singularity of energy based controller, by constructing appropriate energy evaluation function, the singularity avoid-ance energy based controller is proposed. On this basis, the neural-network friction compensation based energy swing-up controller is given by this thesis, which also offers the stability and convergence analysis of the closed loop system. The simulation results show that the Pendubot is once swung up to the control target within a shorter time compared with other control laws of underactuated mechanical system.(2) When the control target of Pendubot is the non-equilibrium position, due to the influence of gravity, the friction characteristics of system becomes more complex. In order to eliminate the disturbance caused by friction, the fuzzy neural network compensator is designed by this thesis. Incorporating with the singularity avoidance energy based controller, the fuzzy neural network friction compensation based energy swing-up controller is proposed, the thesis also gives the stability and convergence analysis of the closed loop system. The simulation results show that the controller provided in this thesis has better control performance compared with the neural network friction compensation based energy controller.(3) Building an underactuated planar robot dynamic model with three degree of freedom, when the control target is uppermost unstable equilibrium position, this thesis designs the fuzzy neural network friction compensator and the singularity avoidance energy based controller. On the basis, the fuzzy neural network friction compensation based energy swing-up controller is proposed, which also gives the stability and convergence analysis of the closed loop system. The simulation results confirm that the underactuated planar robot with three degree of freedom is once swung up to the control target within a shorter time.(4) By using actual Pendubot system, the proposed control algorithms experiment study is launched. When the control target of Pendubot is the uppermost unstable equilibrium position, the experimental results show that the controller proposed by this thesis can make Pendubot have higher swing-up control success rate compared with the controllers of other underactuated mechanical system; When the control target of Pend-ubot is the non-equilibrium position, the experimental results show that the fuzzy neural network friction compensation based energy controller has better control performance compared with the neural network friction compensation based energy controller.