Stabilization of a Flexible Inverted Pendulum via Hysteresis Control: The Bouc-Wen Approach

In this chapter we consider stabilization of a flexible inverted pendulum via the hysteresis control modelled within the Bouc-Wen approach. To implement the numerical analysis of the dynamics of this system an explicit difference scheme were built. Numerical results for stability domains and phase portraits of the system are obtain and presented together with the results for optimal control coefficients. Numerical results showed that inclusion of the hysteresis component to the control circuit leads to increase of the stability domain for the system. Particularly, the hysteresis nonlinearity in the control circuit reduces the stabilization time for the pendulum. Spectral characteristics of the system under consideration are also obtained. Analysis of spectral characteristics showed that the hysteresis component can be considered as a low-pass filter for the considered oscillatory system.