Structural control technologies have been widely accepted as effective ways to protect structures against seismic and wind hazards. Sliding mode control (SMC) is among the popular approaches for control of systems, especially for unknown linear and nonlinear civil structures. Compared with other control approaches, sliding mode control is invariant to disturbance such as wind and earthquake, and to system parameters such as the mass, stiffness, and damping ratio matrices if the uncertainties can be represented the linear combination of the control input, which is generally satisfied for most civil structures.
For known linear civil structures subjected to wind excitation, a filtered sliding mode control approach is presented in order to reduce the response of civil structures. Rather than using a Lyapunov-function based control design, an alternative way is provided to find the control force based on the equivalent control force. A low pass filter is properly selected to remove the high-frequency components of the control force while remaining the structural stability. Simulation results of a 76-story wind-excited high-rising building show that this filtered sliding mode control method has better performance over Linear-quadratic-Gaussian (LQG), unfiltered SMC, and some other approaches with respect to maximum and root-mean-square (RMS) values of structural response.
For unknown nonlinear civil structures, an adaptive and robust control algorithm for nonlinear vibration control of large structures subjected to dynamic loading is presented through integration of a self-constructing wavelet neural network with an adaptive fuzzy sliding mode control approach. It is particularly suitable when structural properties are unknown or change during the dynamic event which is the case for civil structures subjected to dynamic loading. In other words, the proposed control model has the advantages of not requiring accurate mathematical model of the controlled structure and good adaptive ability to the changes of structural parameters and external dynamic loading. The robustness of the proposed algorithm is achieved by deriving a set of adaptive laws for determining the unknown parameters of wavelet neural networks using two Lyapunov functions. Because of these advantages, the proposed adaptive control algorithm is especially effective and implementable for vibration control of large civil structures.
The chattering in SMC is generally a problem that needs to be resolved for better control. To solve this issue, two tuning algorithms are developed for determining the sliding gain function in the SMC. The first algorithm is for systems with no noise and disturbance but with unmodeled dynamics. The second algorithm is for systems with noise, disturbance, unmodeled dynamics, or their combination. Compared with the state-dependent, equivalent-control-dependent, and hysteresis loop methods, the proposed algorithms are more straightforward and easy to implement. The performance of the algorithms is evaluated for six different cases. A 90% to 95% reduction of chattering is achieved for the first algorithm used for systems with sensor dynamics only. By using the second algorithm, the chattering is reduced by 70% to 90% for systems with noise and/or disturbance, and by nearly 25% to 50% for systems with combination of unmodeled dynamics, noise, and disturbance.