A Case Study on Designing a Sliding Mode Controller to Stabilize the Stochastic Effect of Noise on Mechanical Structures: Residential Buildings Equipped with ATMD

Abstract

This study aims to stabilize the unwanted fluctuation of buildings as mechanical structures subjected to earth excitation as the noise. In this study, the ground motion is considered as a Wiener process, in which the governing stochastic differential equations have been presented in the form of Ito equation. To stabilize the vibration of the system, the ATMD system is considered and located on the upmost story of the building. A sliding mode controller has been utilized to control the ATMD system, which is a robust controller in the presence of uncertainty. For this purpose, the design of a sliding mode controller for the general dynamic system with Lipschitz nonlinearity and considering the Ito relations has been accomplished. The mentioned design has been implemented considering the presence of the Weiner process and existence of uncertainty in the structure and actuator. Then, the obtained general control law has been generalized to control the ATMD system. The results show that the designed controller is effective to reduce the effect of the unwanted impused vibrations on the building.

Suspension System Control Based on Type‐2 Fuzzy Sliding Mode Technique

“…(1) Propose a new recurrent type-2 fuzzy system to update the SMC coe cients for use in the suspension system. Figure 1 (page 6) shows a new structure of the type-2 fuzzy neural network, which is carefully observed in (13) that weights are also type-2 fuzzy sets (in addition to membership functions. )…”

“…Robustness means to achieve an optimal outcome in the worst conditions, and invariance means to achieve the optimal outcome without influencing the system with noise, disturbances, and indeterminacy. In the face of noise, disturbance, and uncertainty, a robust system may malfunction, while invariance means robustness with strong performance [12,13]. Chattering is one of the bad properties of sliding phase; therefore, the arrival time to the sliding surface and arrival phase should be limited in a nonlinear system.…”

Kinematic Modelling and Position Control of A 3-DOF Parallel Stabilizing Robot Manipulator

“…Modeling of the structural and feedback sensor noises and application of the noise handling techniques play a critical role in the robot manipulator accuracy improvement [37][38][39]. Azizi et al [39] have investigated the effect of the noise on mechanical structures and designed PID and Sliding mode controllers to eliminate the unwanted applied noise to the system. The results show that the controller designs are effective.…”

Chaotic vibration control of a composite cantilever beam

“…Among those control strategies, one strategy, namely the sliding mode control (SMC), was proposed in 1992 by Utkin 22 , and has been wildly applied in engineering vibration control along with other SMC based strategies. In 2019, Mobki et al 23 applied the SMC in a closed-loop control of a one-dimensional nonlinear dynamic system of a capacitive micro structure subjected to electrostatic forces; in 2020, Azizi 24 used the SMC to reduce the unwanted vibrations of buildings subjected to earthquakes; in the next year, Azizi and Mobki 25 employed the SMC for active control of car suspension systems. Based on the existing SMC, Mobki et al 26 designed an adaptive control scheme to control the vibration of a one-dimensional nonlinear dynamic system of a micro capacitor in 2020; in 2022, Azizi et al 27 also developed a nonsingular terminal SMC strategy to control the vibration of a one-dimensional nonlinear dynamic system of a micro structure.…”