Simultaneous Design of Active Vibration Control and Passive Viscous Damping

Abstract

Structural engineers have found that passive damping can reduce the amount of active damping required to control structural vibration. Conversely, improperly designed passive damping can inadvertently increase system reaction times, reducing control effectiveness. This paper presents several techniques for blending active vibration control and passive viscous damping. A closed-form optimal solution for minimizing a quadratic cost functional is derived, but it is shown to be dependent on the initial conditions and produces time-varying damping coefficients. To eliminate the dependence on initial conditions, solution techniques for suboptimal, state independent solutions are developed. The suboptimal solutions require less computation effort, but still give good estimates of the optimal solution. The advantages and disadvantages of the different solution techniques are discussed with respect to computation requirements and robustness. Methods of comparing competing designs are also discussed. Several numerical examples illustrate the similarities and differences of the various techniques. More importantly, the examples demonstrate the significant improvements achievable by simultaneously designing passive and active damping.