Parametric control for structural applications

Developments in materials and structural design techniques have created much interest in structural vibration suppression. While recent advances in control have resulted in a great many high-performance control design methods, most require actuators capable of producing large forces, with high degrees of reliability and fidelity to their modeled behavior. Thus, these high-power control laws have limited utility in space structures, where low power and weight are the main constraints, or in civil applications, where very large input forces are usually required due to large inertial forces that ground motion creates.; In this dissertation, a semi-active parametric control framework is developed to manipulate the stiffness of the structure, which can result in large effective reacting forces. Mathematical models of systems with variable stiffness are developed to study the effects of the changing stiffness of the system. Different control laws are developed for two different hardware configurations: stiffness resetting and stiffness switching. The resetting configuration includes actuators acting as active stiffness elements. Valves can be opened to allow hydraulic flow across the actuators' chambers, thus releasing the energy stored in the devices. The switching configuration includes truss elements that can be locked or unlocked. These control algorithms are decentralized and force the system onto sliding surfaces, which can be designed by placement of the active elements. These control laws do not require the exact model of the system and are therefore robust with respect to parameter uncertainty, and they do not require either full state feedback or an explicit observer.; A complete proof of stability of the system is provided, and it is shown that with adequate numbers of actuators, asymptotic stability can be guaranteed for an undamped system. In addition, the control laws can be used in disturbance rejection. An extension of the control laws for earthquake application is developed. Closed-form solutions of the controlled system are derived for a single mass-spring system (single degree of freedom) for both resetting and switching control laws. The effectiveness of each control law is evaluated and compared directly to one another. Numerical simulations are also provided. Earthquake application and space structure application simulations are also provided to show the effectiveness of the controllers for multi-degree-of-freedom systems.; Hybrid control is a semi-active control law implemented in conjunction with an active control law. A framework of hybrid control laws is developed and investigated. For the full state feedback method, the active control law is designed first, assuming full state feedback, and then a semi-active control law is designed. The {dollar}Hsb{lcub}infty{rcub}{dollar} approach considers the semi-active control as a random structural uncertainty or disturbance. In this case, the active control law works even if the semi-active device malfunctions. A special form of active control law is also designed to work with the proposed semi-active or active variable stiffness control laws.