Distributed control and simulation of a Bernoulli-Euler beam

Abstract

The optima] distributed control of a Bernoulli-Euler beam is studied. A distributed parameter model of the system dynamics is derived, and this model is used to solve the linear quadratic regulator control problem. The exact model avoids the potentially destabilizing effects of control spillover, as it reproduces the beam dynamics at all frequencies, insofar as the mathematical model represents the actual physical structure. Functional Riccati equations are derived, and numerical procedures are developed to iteratively converge on a solution. The solutions represent gain surfaces, which relate the measured state variables to the control forces at arbitrary points along the beam. An efficient procedure for simulating the response of the closed-loop system to initial conditions and disturbance forces is then developed. Simulation results are presented that indicate that the control law successfully suppresses structural vibration. Issues concerning implementation of the distributed control system are addressed. Finally, an extension of the formulation to multiple beam systems, such as space frames, is discussed.