Stability of MIMO controllers for floor vibration control

Abstract

There are many research studies in the literature that have been devoted to active control of human-induced vibrations in civil engineering structures. This technology has been implemented in floors and footbridges in order to improve their vibration serviceability performance. Most of these works have focused on single-input single-output (SISO) controller schemes, i.e. comprising of a single sensor and actuator pair. Their closed-loop stability properties expressed in terms of the gain margin (GM) and phase margin (PM) can easily be evaluated from techniques such as root locus studies of the closed-loop systems and Nyquist contour plots. For multiple-input multiple-output (MIMO) controller schemes, i.e. systems with multiple sets of actuators and sensors, evaluation of their stability properties is not so obvious and most past researches hardly show this although it is taken into account in one way or another. This is the focus of this work. It presents a study of MIMO stability of a control set-up comprising of two sensors and actuators and further reviews what might be regarded as the appropriate controller gains for velocity based controllers. The approaches used to evaluate the stability properties of this control scheme comprise of comparative studies covering the generalized Nyquist criterion, plots of eigenvalues of the closed-loop system and relative gain arrays (RGA). A limiter on the actuator displacement to disturbance loop both for SISO and MIMO studies is introduced to reduce potential stroke saturation.