Motion Control Of A Class Of Two-link Under Actuated Mechanical Manipulator System

The underactuated mechanical systems are a class of nonlinear systems in which the dimension of the generalized coordination is greater than the dimension of the control input. For this kind of systems, the classical smooth feedback control strategy cannot take effect. Because its motion control is difficult than the common full-actuated mechanical systems, it is very challenging to find a common-used and effective control method for such systems. So the control problem of the underactuated mechanical systems has attracted the attention of many scholars and evoked their great interest in this field.The object of this thesis are a class of two-link planar underactuated. manipulator, in which the first link (shoulder joint) has a actuator (motor), and the second link (elbow joint) is uncontrolled, so this class of systems are a typical class of underactuated mechanical systems. This thesis studies the control methods of the underactuated mechanical systems, from the two types of motions:vertical planar and horizontal planar.The main work of the thesis is listed as follows:First, applying Lagrangian kinetics principle, from the point of view in system energy, the thesis builds a kinetics model of the underactuated mechanical manipulator systems. Then the form of the kinetics model is transformed into a matrix expression, which provides a basis of a further research on the position control of the underactuated manipulator.Second, from the point of view in vertical planar motion, the control problem of the underactuated manipulator is discussed, in which the motion is composed of two phases:the swing-up phase and the balance phase. In the swing-up phase partial feedback linearization controller is designed, at same time, in the balance phase an LQR optimal controller is designed, which can guarantee the stability and the performance index.Third, from the point of view in horizontal planar motion, based on sliding mode control theory and layered sliding mode control idea, the system model is separated into two subsystems:the non-driven subsystem and the driven one. Then the sliding function and the underactuated mechanical sliding mode controller of whole systems are designed, which can achieve asymptotic stability in Lyapunov theory.Finally, improving the anti-disturbance ability and the speed of system convergence, the layered sliding mode controller is combined with a back-stepping control strategy to design an adaptive layered back-stepping sliding mode controller. The proposed controller achieves the fast tracking control of the objective position, and eliminates the steady error caused by uncertainties, and thus has a good robustness against disturbance.