Active–passive vibration absorber of beam–cart–seesaw system with piezoelectric transducers

In contrast with fully controllable systems, a super articulated mechanical system (SAMS) is a controlled underactuated mechanical system in which the dimensions of the configuration space exceed the dimensions of the control input space. The objectives of the research are to develop a novel SAMS model which is called beam–cart–seesaw system, and renovate a novel approach for achieving a high performance active–passive piezoelectric vibration absorber for such system. The system consists of two mobile carts, which are coupled via rack and pinion mechanics to two parallel tracks mounted on pneumatic rodless cylinders. One cart carries an elastic beam, and the other cart acts as a counterbalance. One adjustable counterweight mass is also installed underneath the seesaw to serve as a passive damping mechanism to absorb impact and shock energy. The motion and control of a Bernoulli–Euler beam subjected to the modified cart/seesaw system are analyzed first. Moreover, gray relational grade is utilized to investigate the sensitivity of tuning the active proportional-integral-derivative (PID) controller to achieve desired vibration suppression performance. Consequently, it is shown that the active–passive vibration absorber can not only provide passive damping, but can also enhance the active action authority. The proposed software/hardware platform can also be profitable for the standardization of laboratory equipment, as well as for the development of entertainment tools.