Time-Delayed Control of Nondispersive Continuous Systems

by Firdaus E. Udwadia, Univ of Southern California, Los Angeles, United States,



Document Type: Proceeding Paper

Part of: Mechanics Computing in 1990's and Beyond

Abstract: This paper deals with the noncollocated, time-delayed active point control of continuous systems. It considers systems of finite spatial extent which can be modelled by the undamped wave equation. The paper presents a method of control of continuous systems 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 response at (at most) three different locations in the system. This result is then used to motivate a closed-loop control design which is capable of stabilizing the system and dampening the vibrations in all its modes, while using dislocated sensor and actuator locations, thereby eliminating any spillover effects. Simple finite-dimensional controllers, commonly used in control design, are found to suffice. The results are valid for rather general conditions at the boundaries of the continuum. Explicit conditions are provided to obtain the bounds on the controller gains (in terms of the locations of the sensors and the actuators) to ensure stability of the closed loop control design.

Subject Headings: Control systems | Probe instruments | Wave equations | Vibration | Active control | Physical properties | Motivation | Damping

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