Variable structure and singular perturbation control of elastic dynamical systems

This thesis treats the question of control of flexible dynamical systems for space applications. Two elastic dynamical systems are considered; The multibody system developed in Phillips Laboratory, Edwards Air Force Base, CA consists of two elastic links actuated by electric motors at the joints and rotate on a smooth horizontal granite table. An air bearing is used, which allows the whole system to float on the air so that the frictional forces do not exist between the support plate and the granite table. The controlled output is judiciously chosen such that the zero dynamics are stable or almost stable. For the control of the end point, two kinds of parameterizations of end effector position are considered. A variable structure control (VSC) law is derived for the end point trajectory control of each chosen output. Stability of zero dynamics associated with end point control is examined. Although, the VSC law accomplishes precise end point tracking, elastic modes are excited during the maneuver of the arm. A linear stabilizer is designed for the final capture of the terminal state; The second flexible system considered in this thesis is the elastic space vehicle. For the attitude control and vibration stabilization of the elastic space craft (spacecraft-beam-tip body configuration), singular perturbation technique is used. Based on nonlinear inversion, a control law is derived to decouple the attitude angle and the dominant flexible modes from the remaining elastic modes. The inverse control law decomposes the spacecraft dynamics into a slow and a fast subsystem. Based on singular perturbation theory, controllers are designed for each lower-order subsystem. Then a composite state feedback control is obtained by combining the slow and the fast control laws. (Abstract shortened by UMI.)