Robust motion control of flexible systems using feedforward forcing functions

Forcing functions are developed to produce vibration-free motions in flexible systems. These forcing functions are constructed from ramped sinusoid basis functions so as to minimize excitation in a range of frequencies surrounding the system natural frequency. Frequency domain attributes of a particular ramped sinusoid forcing function are compared with corresponding attributes of a minimum-energy optimal input and an impulse-filtered ramp signal. A closed-loop control system is developed that utilizes each of these forcing functions to generate a reference profile, and also feeds the particular forcing function forward directly to the system to enhance closed-loop bandwidth. The use of a direct feedforward signal in the closed-loop implementation results in significantly faster response times when the closed-loop bandwidth is otherwise constrained to be very low. Simulation results indicate that residual vibration has been nearly eliminated for all three forcing functions, even when some error in natural frequency exists. However, the ramped sinusoid input provides the most control over spectral energy near resonance and uses the least amount of energy to achieve vibration-free motions