Control of relative vibration between flexible appendages using passive and semi-active isolation

•Relative vibration can be controlled through individual vibrations or directly.•Necessary conditions for the feasibility of the direct control method are found.•Body-hook-body is a generalization of ground-hook and sky-hook semi-active control laws.•Direct method is implemented with semi-active isolators using body-hook-body.•Direct method is as effective as the indirect, but with lower cost and complexity. Relative vibration between two flexible subsystems can be detrimental to the performance of many engineering applications, such as optics-based instruments, machine tools, or adjacent industrial structures sharing piping. For the purpose of controlling this particular vibration, this paper presents two control approaches based on the passive and semi-active isolation at each subsystem: the indirect control method, consisting in the reduction of the individual vibration of each subsystem, and the direct control method, which aims to reduce the relative vibration between both subsystems. Necessary conditions for the feasibility of the direct control method are found, thereby reducing the universe of possible design configurations. From the traditional ground-hook and sky-hook control laws, which simulate, respectively, a damper between the body to be controlled and the support or the reference framework, it is generalized a control law called body-hook-body, which simulates a damper between both bodies to be controlled. Taking into account the performance and cost/complexity of the whole system, different alternatives for each vibration control method are numerically and experimentally studied. From the results, it is inferred that the proposed direct control method, using body-hook-body, is as effective as the traditional indirect control method, using ground-hook or sky-hook, but with lower cost and complexity.