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Modern Optimal Control Methods Applied in Active Control of a Cantilever Beam in Bending Vibration

机译：现代最优控制方法在悬臂梁弯曲振动主动控制中的应用

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The equations of motion for a cantilever beam in bending vibration are developed in state vector form using a normal mode approximation. A linear optimal control system generates a feedback control proportional to the state which is represented by modal amplitudes and velocities determined using position information from sensors. The observer gain matrix and the feedback control gain matrix are both determined from a steady state optimal regulator which minimizes the related quadratic performance index. Control is applied through point force actuators. System response is shown to be very sensitive to actuator location. Singular perturbation provided a method through which control spillover could be minimized for the actuator locations chosen, however, it did not provide the means by which the actuators could be positioned such that the spillover effect could be eliminated. Robustness of system response to modal amplitude errors was very good, and the unstable controllers tested did not appear to seriously affect this robustness.

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