Boundary control of flexible mechatronic systems

This doctoral dissertation describes the design and implementation of various Lyapunov-based boundary control strategies for three different flexible mechatronics systems: (i) the flexible rotor system, (ii) an axially moving elastic medium, and (iii) an axially accelerating inelastic web. Experimental results are presented for all of the above systems to illustrate the feasibility of implementing the controllers.; The first chapter presents the design of boundary controllers for a two-dimensional, spinning flexible rotor system. Specifically, a model-based boundary controller is designed to exponentially regulate the rotor's displacement and the angular velocity tracking error. In addition, an adaptive boundary controller is designed to asymptotically achieve the same control objective while compensating for parametric uncertainty. As opposed to previous boundary control work, which focused on the velocity setpoint problem and placed restrictions on the magnitude of the desired angular velocity setpoint, this control architecture achieves angular velocity tracking with no restrictions on the magnitude of the desired velocity trajectory. Experimental results compare the performance of the model-based and adaptive controllers with a standard damper controller.; In the next chapter, control torques applied to rollers at the boundaries of an axially moving system are designed to regulate the material speed and tension using speed and tension sensors for each roller. Given a distributed parameter model, Lyapunov theory is used to develop a model-based boundary control system that exponentially stabilizes the material tension and speed at desired setpoints and stabilizes longitudinal vibration. Experimental results are used to compare the tension and speed setpoint regulation provided by the proposed control strategy with proportional plus integral speed control and proportional tension feedback.; The third chapter presents a control strategy for an axially moving web system that achieves vibration regulation along the web and ensures that the web tracks a desired axial velocity trajectory. The control strategy is implemented by utilizing the roller torque inputs applied at the entry and exit points of the web and a pair of control forces applied to the web via an interstitial mechanical guide. Given the hybrid model of the web system (i.e., the distributed parameter field equation coupled to discrete actuator equations), Lyapunov-type arguments are utilized to design a model-based control law that exponentially regulates the axial speed tracking error and the web displacement along the entire span. The control law is based on measurements of the web speed and displacement, slope, and slope rate at the mechanical guide. Experimental results demonstrate the speed tracking and vibration damping provided by the control strategy.