Gain Scheduled PID Control for Electromagnetic Vibration Absorbers

Electromagnetic vibration absorbers (EMA's) are mechanical bandpass filters attached to a structure, and tuned to attenuate the structures forced response over a limited bandwidth. In the presence of large applied forces, EMA effectiveness is dominated by the effective actuator stroke and by saturation effects. Under conventional PID control, assuming operation below saturation, the effective stroke is limited by the validity of the linear approximation to the actuator force-displacement relationship. In this paper, equations are presented for an extended linearization of this relationship about a series of linearizing points throughout the air gap. Expressions are derived for PID gains that optimally attenuate the forced response at each of the linearizing points and that can be switched into use according to a position variable inequality. Experimental frequency response plots are presented which demonstrate attenuation within each gain scheduled region and show the potential to increase the test rig actuator stroke by a factor of 1.7 over conventional PID control.