An Approach to the Vibration Control of a Pendulum System Based on the Movement of the Center of Gravity Using a VSS Control Technique

For a pendulum system whose weight is moved up and down along the member, a vibration control technique is presented in view of a VSS control scheme including both a linear observer and a non-linear one, by introducing two different Lyapunov-type functions concerning the pendulum state(θ, θ)and the weight stete(y, y). As for the design condition for the higher damping capacity, it is needed that the parameter s1 in the switching function σp=s1θ+θ is not only made larger, but also the parameter s3 in the switching function σc=s3y+y sets up an appropriate value, and furthermore that from the viewpoint of the Coriolis force effect, the weight speed y is elivated as highly as possible. From the simulation aspect, the highest active damping capacity Q-1max〓0.116 is achieved in the maximum vibration amplitude under the condition of the weight stroke ye=0.4[m], while in the real system, Q-1max〓0.066 is obtained in case of ye=0.287[m]. The robust damping effect is also confirmed by attaching appropriate mass to the movable weight.