Sliding Mode Control for an Inverted-Double Pendulum System Consisting of an Elastic Link Mounted on a Rigid One by Using the H.INF. Control Theory.

Abstract

The stabilizing control techniques for an inverted-double pendulum system consisting of an elastic link mounted on a rigid one have been investigated by employing a distributed-parameter modeling method taking the 2nd and 3rd vibration modes of the elastic beam as the residual modes, and by using both a sliding mode controller (SMC) designed on the basis of the H∞ control theory and a conventional H∞ servo controller to compare the robust performance. By applying the loop-shaped H∞ control scheme to the design of the switching plane of SMC, the robust hyper-plane with both frequency characteristics and integral ones can be easily realized even to a multi-mode of flexible structure system having the jω poles such as the double pendulum system discussed here, and the effectiveness of the design is verified from the real system-experimental results that the H∞ control based frequency-shaped SMC has not only the simultaneous suppression effect against the chattering and the spillover components, but also the cart positioning control without static error. Furthermore, it is found that the designed SMC system exhibits considerably robust performance against impulsively applied disturbances, and that the SMC system is robust as compared with the conventionally designed H∞ controller system.