Wavelet-Based Algorithms for Control of Smart Civil Structures

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AbstractEven though classical feedback control algorithms such as the Linear Quadratic Regulator (LQR) and Linear Quadratic Gaussian (LQG) algorithms can be used to reduce vibrations, they suffer from a number of fundamental shortcomings. They achieve a significant level of attenuation in the vicinity of the natural frequencies of the structure, but fail to suppress the vibrations when frequency of the external disturbance differs even slightly from the natural frequencies of the structure. A limitation of classical optimal control algorithms is due to the fact that the input excitation must be known a priori which is not the case for civil structures subjected to earthquake or wind loading. Intellectual Merits: The primary objective of the proposed research is to explore wavelet-based algorithms for creation of a new control model for active, semi-active, and hybrid control of civil structures subjected to dynamic forces such as earthquakes and winds overcoming some of the shortcomings of the existing feedback control algorithms. The new control model will a) have the ability to suppress vibrations over a range of input frequencies, b) be less susceptible to structural modeling approximations and errors, and c) include the external excitation term. This is achieved through adroit integration of a feedback control algorithm such as the LQR or LQG algorithm, the filtered-x Least Mean Square (LMS) algorithm, and wavelets. The goal is to achieve optimum control under external dynamic disturbances in real time. A focus of the proposed research will be development of optimal control strategies utilizing the filtering and transformation characteristics of wavelets and wavelet-based algorithms. A secondary objective of the proposed research is to explore the development of a hybrid control system through judicious integration of a passive supplementary damping system with a semi-active tuned liquid column damper (TLCD) system. The new model utilizes the advantages of both passive and semi-active control systems, thereby improving the overall performance, reliability, and operability of the control system during normal operations as well as a power or computer failure. The robust wavelet-hybrid feedback LMS control algorithm will be used to find optimal values of the control parameters. The proposed hybrid control system eliminates the need for a large power requirement, unlike other proposed hybrid control systems where active and passive systems are combined. Broader Impacts: The potential benefits of the proposed research to society at large will be creation of a new generation of smart civil structures with improved safety and reliability against natural hazards such as earthquakes and strong winds encountered in most of the country. The proposed research will a) lead to new control techniques for hazard mitigation of structures subjected to dynamic seismic and wind loading, b) be of value to the general domain of vibration control including control of mechanical and aerospace structures, and c) result in new insights in the use of wavelets for solution of other intelligent civil infrastructure systems.