Discrete time transfer matrix method for dynamics of multibody system with real-time control

By taking the control and feedback parameters into account in state vectors, defining new state vectors and deducing new transfer equations and transfer matrices for actuator, controlled element and feedback element, a new method named as the discrete time transfer matrix method for controlled multibody system (CMS) is developed to study dynamics of CMS with real-time control in this paper. This method does not need the global dynamics equations of system. It has the modeling flexibility, low order of system matrix, high computational efficiency, and is efficient for general CMS. Compared with the ordinary dynamics methods, the proposed method has more advantages for dynamics design and real-time control of a complex CMS. Adopting the PID adaptive controller and modal velocity feedback control on PZT actuators, and applying the proposed method and ordinary dynamics method, respectively, the tip trajectory tracking for a flexible manipulator is carried out. Formulations of the method as well as numerical simulation are given to validate the proposed method.