Abstract
The optimalβdistributed control of a transversely vibrating cantilever beam is studied with the objective of minimizing the deflection and velocity in a given period of time with the minimum possible expenditure of force. The beam undergoes transient vibrations and is subject to given displacement and velocity initial conditions. The control is exercised by means of a transversely distributed force referred to as the control force. In the present study, a multiβinterval optimal control method is developed with the application of a maximum principle. The method consists of dividing the control duration into several intervals and using the maximum principle to obtain the optimality conditions at each interval. The explicit solutions for a cantilever beam are obtained by a recursive algorithm that takes the final conditions of the last interval as the initial conditions of the next interval. The formulation and the method of solution are suitable and convenient for digital computation. Numerical results are given, which compare the deflections, velocities and the control force under the optimal multiβinterval control with those under the optimal singleβinterval control. Copyright Β© 2008 John Wiley & Sons, Ltd.