Modeling and structural control of a building with holonomic constraints

ABSTRACT In this study, we propose to evaluate structural control systems in terms of mechanical impedance and the peak of energy stored by the structure. Our main hypothesis is that the higher the mechanical impedance, the lower the peak of energy reached by the structure. This peak is calculated as the maximum of the difference between the energy injected by the seism and the energy dissipated as heat by viscous dampers. To support our claim, we performed numerical simulations on a three-story planar building comprising 12 revolute and four prismatic joints. Instead of using a linear mass-spring-damper model, we simulated a set of nonlinear equations given by the Newton-Euler (NE) algorithm, which has been widely used in robotics, but rarely in structural control. For energy dissipation, we compared a proportional derivative (PD) with a computed torque control (CTC). Simulation results for the CTC indicate that when all parameters of the structure are perfectly known, the deviations of the revolute and prismatic joints with respect to their nominal values are close to zero. This feature leads to almost null energy dissipation, but also reduces the energy transferred by the seism to the structure.