| With the advent of smart materials, the concept of semi-active control or dynamic control of stiffness and/or damping for vibration control of structures has become practical and has seen limited use. Semi-active control has advantages over active and passive control methods, since it provides almost as much capability as active control while requiring much less power. Its main disadvantage is its inherent nonlinearity, greatly complicating engineering design. The purpose of this research is to extend semi-active control vibration isolation tools and methods, considering applications for space launch and on-orbit systems.; After surveying the literature, variable stiffness using a general on-off control law with constant damping is examined in several contexts. First, the single degree of freedom problem is solved in exact form and approximated for the initial value problem. Results include development of an optimal control policy for all possible variable stiffness settings and a large range of viscous damping settings, guaranteed stability regions, and new possibilities for fast settling time even with an overdamped system. Second, the sinusoidally forced problem was approximated and a near optimal control policy was formulated. Third, the results of the initial value problem were extended to two multi-degree of freedom problems. The problems examined are representative of a cross section of a simple space telescope structure and of a variable stiffness beam. Besides providing new engineering design tools and insight into the nonlinear behavior of variable stiffness concepts, the results open several future research possibilities. |
