Control of flexible systems is effected by design requirements and also manufacturing aspects. The dynamics and control of such systems are challenging, especially in the case of an inverted flexible pendulum system. The experimental study of the dynamical behavior of this kind of system showing jumping phenomenon between three equilibria is not considered in detail in literatures so far. The paper focuses on studying the effects of some parameters to the dynamics of the flexible pendulum. By varying the excitation parameters, control parameters, as well as other distinguished mechanical parameters, different phenomena are observed in experiments discussed in this contribution. In this study, a custom built inverted flexible pendulum on cart system under PID-controlled harmonic excitation is considered. Data are collected from both cart excitation signal and displacement of the pendulum, also to observe their correlation towards jumping behavior. Effects of the variation of the parameters leading to changes in chaotic jumping patterns. Multiple equilibria are observed and analyzed. It can be concluded that depending on the excitation amplitudes, frequencies, and controller parameters, the minimum of two equilibria with an unstable third equilibrium can be detected while jumping phenomena between the equilibria are observed. Questions about the stimulation of the jumping by impulses resulting from imperfect sinusoidal excitation due to control limitations are discussed.
Robot control parameters auto-tuning in trajectory tracking applications
