Implementation and Modeling of a Semi-Active Control System

This paper discusses implementation and modeling details for a simple semi- active control system which uses an electro-rheological (ER) damping wall as an actuator. The ER damping wall follows the principle of viscous damping walls. The control system requires measurements that are available directly from the ER damper itself: namely a relative velocity and an absolute acceleration. An absolute velocity is obtained from the accelerometer via an analog integrator which was designed for this application. The integrator is made from a cascaded low-pass filter and a differentiator, is stable at zero frequency, and has a perfect ninety degree phase lag at the first resonant frequency of the structure. The control rule is implemented with four op-amps, five transistors, and a high-voltage switch. Modeling details for this system are emphasized in the second part of the paper. The ER damping wall is a highly non-linear device, however its behavior can be described via a state-variable model that has only one non-linear term. The structure to be controlled exhibits linear behavior, although linear behavior is not presumed in the control rule synthesis. Natural frequencies, damping ratios, and mode shapes are obtained from a frequency-domain curve-fit. A technique to determine the damping and stiffness matrices from the modal data requires that the mass matrix is known a-priori. This method is used to create a state-variable model in physical coordinates. By comparing simulations of the numerical model to data from the closed-loop control experiment, aspects of the ER device behavior most salient to the performance of the closed-loop system are identified.