Noncollocated control of distributed-parameter nondispersive systems with tip inertias using time delays

摘要

This paper deals with the noncollocated, time-delayed active point control of a spatially finite system which has a tip inertia and which is modeled by the one-dimensional wave equation. The paper presents a new method of control of the system using noncollocated sensors and actuators. By using the physical properties of the mode shapes of vibration of the system it is shown that the modal response at a given location in the system can be reconstructed from the time-delayed modal responses at (at most) three different locations in the system. Based on this observation, a closed-loop control design is provided which is capable of stabilizing the system and dampening the vibrations in all its modes, while using dislocated sensor and actuator locations. Simple dinite-dimensional controllers are used in the control design. Explicit conditions are provided to obtain the bounds on the controller gains to ensure stability of the closed-loop control design. These bounds are obtained in terms of the locations of the sensors and the actuators. Simulation results, which validate the control methodology and the theoretical bounds on the gain, are also presented.