Modeling and control of flexible manipulators

The modeling and control of flexible manipulators are investigated in this research. It contributes to three areas: (1) the tracking control of nonminimum phase systems; (2) modeling and control of flexible one-link manipulators; (3) modeling and control of flexible multi-link manipulators. In this research, the characteristics of the discrete-time nonminimum phase zeros are first analyzed, and a precision tracking control method for nonminimum phase systems is proposed. The proposed precision tracking controller cancels all the phase shift of the nonminimum phase zeros and minimizes their gain errors within the concerned frequency range. The second part of the research is the modeling and control of flexible one-link manipulators. A reduced order finite element model is presented, and the system transfer functions are constructed. A real time end-point tracking control scheme is developed by applying the proposed precision tracking control method. A payload adaptation algorithm is proposed to identify the payload variation, and an adaptive tracking control algorithm is formulated. Based on the understanding from the study of flexible one-link manipulators, the modeling and control of flexible multi-link manipulators are investigated. An accurate system model, which includes the mutual dependence of the rigid and the elastic motion as well as the effects of the elastic deformation on the transformation matrix, is proposed for general planar flexible manipulators. To reduce the amount of computations in the dynamic analysis, a model reduction technique is developed, in which the dominant modes of the system as well as the time variant nature of the mode shape functions remain. Consequently, the required computation for dynamic analysis is greatly reduced while the accuracy of the system response is maintained. The end-point tracking control of a flexible manipulator is also investigated in this paper. A time-varying estimator is designed to estimate the system elastic deformation. Using the desired end-point motion and the estimated system elastic motion, a tracking control scheme, which consists of a feedback controller, a command feedforward controller, and an elastic motion estimator, is proposed. The proposed tracking control algorithm is very efficient and can be implemented for real time control.