| A systematic approach to the active control of the vibratory response of a high speed flexible system is proposed. It has been known that a lightly damped flexible mechanism experiences an oscillatory response at certain speeds. This behavior causes inaccuracies in position and fatigue failure. The objective of this research is to damp the response of the flexible system by means of an active control system.;Finite element analysis is employed to derive the equations of motion for the system. Modal analysis is used to obtain the most critical modes. A state variable method is applied to establish a feedback control system which takes into account the variations of the system matrix, input matrix, and output matrix. Structural controllability and Kalman's principle of duality are employed to test the properties of controllability and observability. The feedback controller and observer are constructed by way of a Lyapunov function and Luenberger observer. Stability of unmodeled modes is examined. Two numerical algorithms are presented. One is a direct integration, the other a closed-form solution. The closed-form solution is developed by means of discrete approximations and a periodicity condition and then solved by frontal method. A set of experiments is performed to validate the control strategy. A hybrid compensation system is employed to perform signal processing, implement the control law, and model the observer. Computer simulations and experimental results are both presented. |
