Optimal control: Basis for performance comparison of passive and semiactive isolation systems

Passive damping in shock and vibration isolation systems reduces the deformation of the isolation system but can increase the acceleration sustained by the isolated object. Semiactive (i.e., controllable) damping systems offer a solution to the problem of increased vibration transmissibility at high frequencies. Semiactive damping is especially relevant to protecting acceleration-sensitive components to the effects of large impulsive earthquakes. In this paper, we compare three semiactive control policies, i.e., pseudonegative-stiffness control, continuous pseudoskyhook-damping control, and bang-bang pseudoskyhook-damping control, in terms of their effectiveness in addressing the deficiencies of passive isolation damping. In order to establish a performance goal for these suboptimal semiactive control rules, we present a method for true optimization of the response of dynamically excited, semiactively controlled structures subjected to constraints imposed by the dynamics of a particular semiactive device. The optimization procedure involves solving Euler-Lagrange equations. The closed-loop dynamics of structures with semiactive control systems are nonlinear due to the parametric nature of the control actions. These nonlinearities preclude an analytical evaluation of Laplace transforms. In this paper, frequency response functions for semiactively controlled structural systems are compiled from the computed time history responses to sinusoidal and pulse-like base excitations. For control devices with no saturation forces, the closed-loop frequency response functions are independent of the excitation amplitude. We make use of this homogeneity of the solution of semiactive control systems and present results in dimensionless form.