Recently, there are growing demands in the robot industry for light structures in order to increase the speed of motion and thus the productivity. As a slender structure gets lighter, it tends to be flexible, leading to severe operational vibration particularly at its free end. In the design of a vibration controller, the robust stability should be checked first since the dynamics of the cantilever beam, which simulates a flexible multi-axis robot arm or a flexible manipulator with varying length, also changes during operation.
In this study, $H_∞$ control theory is adopted as the design technique for a robust controller, which robustly stabilizes the system and satisfies the desired performance, since it has two advantages: One is the fact that variations in system parameters can be considered as the uncertainty in a mathematical model, requiring, not an accurate model of uncertainty, but only its upper bound. The other is that the desired performance of the system is defined as the maximal magnitude of the closed-loop transfer function which can be easily understood.
The cantilever beam with varying natural frequency has the matrix-fraction uncertainty. In order to effectively describe the system with the matrix-fraction uncertainty, an $H_∞$ controller design scheme based on the matrix fraction stability condition is proposed. The matrix fraction stability condition gives a good robust stability by separating the uncertainty of a nominal plant into the variations in the numerator and denominator. The proposed controller is then applied to the cantilever beam with a piezoelectric-type servo-damper such that the vibration at the free end of the beam is effectively suppressed, while its effective length slowly changes. Vibration control experiments are performed to investigate the performance and robust stablity of the proposed controller when the cantilever beam is in rest and moves.
Though the piezoelectric-type servo-damper has a good damping effect, the ...