Active Damping with Collocated System

Introduction

The use of collocated (and dual) actuator and sensor pairs, for a lightly damped flexible structure, always leads to alternating poles and zeros near the imaginary axis, Fig.7.1. In this chapter, we use this interlacing property to develop Single Input-Single Output (SISO) active damping schemes with guaranteed stability. By active damping, we mean that the primary objective of the controller is simply to increase the negative real part of the system poles, while maintaining the natural frequencies essentially unchanged. This simply attenuates the resonance peak in the dynamic amplification (Fig 7.2). Recall that the relationship between the damping ratio ξ and the angle φ with respect to the imaginary axis is sinφ = ξ, and that the dynamic amplification at resonance is 1/2ξ. Note that for typical damping values encountered in practice, the values of φ are very close to 0; this is why in most of the root locus plots shown in this chapter, different scales are used for the real and the imaginary axes, leading to a distortion of the angles.