Modeling and H∞ Control for an Inverted-Double Pendulum System Consisting of Elastic Links Connected in Series
Double Elastic Links
Loop Shaping Design
The stabilizing control techniques for an inverted-double pendulum system consisting of elastic links connected in series are investigated by employing a distributed-parameter modeling method taking the 2nd and 3rd vibration modes of the elastic beam as the residual modes, and designing the H∞ controller with both frequency characteristics and integral ones based on the loop-shaped H∞ control scheme. It is found that the present design method is very convenient for such a flexible structure system having the jω poles as a double pendulum system discussed here, and that the frequency-shaped H∞ controller has not only the simultaneous suppression effect against the chattering and the spillover components, but also the precise cart positioning control effect without static error. Furthermore, It is found that although the coupling effect of the different natural frequencies between two flexible beams makes the stabilization problem more difficult, even such a simple feedback controller using only the output signal based on the strain vibration on the upper elastic beam is possible in stabilizing the most unstable system.