The Design Of Observers For One-sided Lipschitz And Use The Observer Design Method In The Single-link Flexible Robotic System Control

With the development of science and technology, lightweight and flexible components have been widely used in mechanism. Meanwhile, the requirements on operating speed and precision of mechanism become higher and higher. Research in this area comes to the so-called flexible multibody dynamic system or rigid-flexible coupling dynamic system. The flexible manipulator is atypical application in this area. For a single-link flexible joint robot, we need select the motor angular rotation,motor angular velocity, link angular position and link angular velocity. All state variables are rarely available due to physically factors.So we need to recontruct the state variables of the system and to use it to replace the actual state variables of the system to satisfy the requirement of the state feedback. State observer is both a theoretical and a applied subject developed under the background mentioned above. In the field of observer design of nonlinear systems, however, the design of observers is much more challenging than linear systems. If we assume that the system of Nonlinear part satisfies the Lipschitz condition, a major defect will appear that the results only in the case of Lipschitz constant is smaller. The one-sided Lipschitz non-linear system is a generalisation of its well-known Lipschitz counterpart and possesses inherent advantages with respect to conservativeness.In this study,We will use one-sided Lipschitz condition to replace well-known Lipschitz to apply in state estimation.To carry out the following research:(1) The LMI-based method to design observers for One-sided Lipschitz nonlinear systems.(2) For a class of one-sided Lipschitz nonlinear systems in continuous time case, a unified framework has been established for both full-order and reduced-order state observers. It is shown that the sufficient conditions that ensuring the existence of a full-order state observer also guarantee the existence of a reduced-order state observers for one-sided Lipschitz nonlinear systems. In this sence, the classical design theory of Lipschitz nonlinear observers was sucessfully extended to the case of one-sided Lipschitz nonlinearsystems.(3) We design the observers for one-sided Lipschitz nonlinear systems.And use the observer design method in the Single-link flexible robotic system control. Finally, The simulation proved the feasibility of the design method.