Sensitivity Analysis on Optimal PID Controller for Nonlinear Smart Base-Isolated Structures

This paper presents a sensitivity analysis on the performance of optimal proportional–integral–derivative (PID) controller for use in nonlinear smart base-isolated structures with uncertainties. A set of nine performance indices is defined to evaluate the performance of the controller in the presence of uncertainties in the superstructure, lead rubber bearing (LRB) seismic isolation system, and applied loads. The time delay effect on the stability and performance of the PID controller is also examined. The results show that the PID controller is robust against the uncertainties up to [Formula: see text]% in the damping and stiffness coefficients of the superstructure, the yield force of the LRB and the artificial earthquake. In the case with [Formula: see text]% of uncertainty, the input energy entering into the structure is increased with respect to the nominal model. However, the changes of the performance indices related to the damage energies are negligible. An uncertainty of [Formula: see text]20% in the stiffness coefficient and stiffness ratio of the LRB gives an increase of 15% in the maximum and root mean square (RMS) of the structural responses. In the case with [Formula: see text]20% of uncertainty, the damage and damping energies do not change in comparison with the case of the nominal model, but a significant decay in the performance index related to the input energy response is obtained in this case. Not all performance indices are sensitive to time delay. For large time delays, the performance index for the seismic input energy increases significantly, while the maximum damage and damping energies increase up to 5% and 10%, respectively.