Viscoelastic (VE) dampers are sensitive to temperature, excitation frequency, and strain level. As they dissipate the kinetic energy from earthquake or wind‐induced structural vibrations, their temperature increases from the heat generated, consequently softening their VE materials and lowering their dynamic mechanical properties. Temperature increase can be significant for long‐duration loading, but can be limited by heat conduction and convection which depend on damper configuration. The writers analytically explored such effect on the six different dampers by using their previously proposed three‐dimensional finite‐element analysis method. Results provided better understanding of how heat is generated within the VE material, conducted and stored in different damper parts, and dispersed to the surrounding air. These results also led to characterization of both local (e.g., temperatures, properties, and strain energy density) and global (e.g., hysteresis loops, and stiffness) behavior of VE dampers, and provided a framework for a new simplified one‐dimensional (1D) modeling approach for time‐history analysis. This new proposed 1D method greatly improves the computation time of the previously proposed long‐duration method coupling fractional time‐derivatives VE constitutive rule with 1D heat transfer analysis. Unlike the previous method, it idealizes uniform shear strain and VE material property distributions for computational efficiency, but still simulating non‐uniform temperature distribution along the thickness direction of the VE material. Despite the approximations, it accurately predicts VE damper global responses.

This article carries out an inside observation of a disturbance-compensation error in the equivalent-input-disturbance (EID) approach and divides the causes of the compensation error into two types: disturbance- and state-estimation errors. A modified EID (MEID) approach precisely deals with each type separately. Considering that the disturbance-estimation error cannot be measured, we use a high-gain observer to ensure the rapid convergence of the disturbance-estimation error. Unlike the conventional EID approach, the MEID approach newly introduces a weighted output-estimation error, which is produced by a state observer, to compensate for the state-estimation error in a prescribed frequency range. A stability condition is devised for an MEID-based control system. The parameters of a filter and an observer are optimized simultaneously based on a time-domain performance index with a constraint in the frequency domain. An experimental comparison with other EID approaches demonstrates the superiority of the MEID approach.