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We present a control strategy for an axially moving string system that achieves vibration regulation along the string and ensures that the string 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 string and a pair of control forces applied to the string via an interstitial mechanical guide. Given the hybrid model of the string 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 velocity tracking error and the string displacement along the entire span. The proposed control law is based on measurements of the string displacement, velocity, slope, and slope rate at the mechanical guide.

In this paper, we present the design of boundary controllers for a two-dimensional, spinning flexible rotor system. Specifically, we develop a model-based boundary controller which exponentially regulates the rotor's displacement and the angular velocity tracking error, and an adaptive boundary controller which asymptotically achieves 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, the proposed control architecture achieves angular velocity tracking with no restrictions on the magnitude of the desired velocity trajectory.

We design a control strategy for a spinning rotor with an unbalanced disk attached to its free end. The control strategy is composed of a boundary torque applied to the clamped end, and two boundary forces and two boundary torques applied to the free-end. At the clamped-end, the boundary torque ensures that the rotor tracks a desired angular velocity trajectory, while at the free-end, the boundary forces and torques ensure that the rotor displacement is regulated at every point along the length of the rotor. Under the assumption of exact model knowledge, we first develop a model-based control law which exponentially achieves the control objectives. We then illustrate how the model-based control law can be redesigned as an adaptive controller which asymptotically achieves the same control objectives while compensating for parametric uncertainty associated with unbalanced operation.

In this paper, we develop a boundary controller to actively cancel acoustic disturbances in an enclosed duct of finite length using a loudspeaker. Given a distributed parameter acoustic model and the actuator electrical dynamics at the boundary, Lyapunov-type arguments are used to design a model-based backstepping boundary control law that asymptotically regulates the noise within the duct. Dynamic simulation results demonstrate the improved performance achieved by the proposed active noise cancellation algorithm.

We study the control of an undamped, nonlinear string model with actuator dynamics at the boundary. Specifically, we develop a boundary controller which asymptotically stabilizes the out-of-plane displacement. The performance of the controller is illustrated via dynamic simulation.

We develop boundary controllers for a flexible cable with actuator dynamics at the boundary. Specifically, we develop an exact model knowledge controller which exponentially stabilizes the position of the cable and an adaptive controller which asymptotically stabilizes the position of the cable while compensating for parametric uncertainty. The performance of the controllers is illustrated via experimental results.