Control of a building system with sudden nonlinearity using the sliding mode technique

In civil engineering application such as the seismic resistant structural design, a building system often enters into its nonlinear range to minimize the force transfer to the superstructure. An ideal control design should enhance the usefulness of the nonlinear behavior by diminishing its adverse effects at a minimal control input. This study developed a unified feedback mechanism based on the sliding mode control approach that fostered the multiple selected modal control of a structural system undergoing linear and nonlinear stages of hysteretic deformations. The ideal sliding surface for controlling a specific mode was designed based on the interaction characteristics between two modes at two different stages of deformation. An ′ S ′ type functional form of the control force was developed on either side of the sliding surface based on the velocity feedback of the system by ensuring reachability to the ideal sliding surface. To demonstrate the effectiveness of the adopted control, a five-story shear building with uniform mass and initial stiffness distribution with concentrated nonlinearity at the base column was considered under 10 earthquake excitations. The system was studied under the proposed control along with the uncontrolled system. In addition to the adopted control, a popular and existing LQG control technique was also implemented based on the equivalent linearized structural system for comparison. The adopted control provided the desired performance of the structural system while keeping the effectiveness of the system’s nonlinearity under earthquake excitations. Considering the system’s responses and the input control force, the efficiency of the adopted mechanism outperformed the LQG control, which was found to amplify the unfavorable effects of the system’s nonlinearity.