A fractional-order controller for vibration suppression of uncertain structures

Area of Science:

• Structural Engineering
• Control Theory
• Applied Mathematics

Background:

• Active vibration control is crucial for protecting structures from external disturbances like earthquakes.
• Existing methods face challenges with system uncertainties and external disturbances.

Purpose of the Study:

• To introduce a novel fractional-order sliding mode control (FOSMC) for attenuating structural vibrations.
• To address uncertainties and external disturbances in vibration systems.
• To analytically prove the stability and robustness of the proposed control strategy.

Main Methods:

• Development of a stable fractional sliding surface.
• Design of a sliding mode control law based on the fractional surface.
• Analytical proof of global asymptotic stability using the fractional Lyapunov stability theorem.
• Validation through simulations on a three-degree-of-freedom structure and a two-story shear building.

Main Results:

• Successful attenuation of structural vibrations under uncertainties and disturbances.
• Demonstration of global asymptotic stability for the closed-loop system.
• Verification of the robustness and practical applicability of the FOSMC technique.

Conclusions:

• The proposed fractional-order sliding mode control is an effective method for vibration suppression in structures.
• The FOSMC strategy offers enhanced stability and robustness compared to conventional methods.
• This approach holds significant promise for seismic vibration control and structural protection.