Universal Journal of Mechanical Engineering Vol. 5(5), pp. 150 - 169
DOI: 10.13189/ujme.2017.050503
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Unstable Mechanical Objects: Motion Control, Stabilization

A. M. Formalskii ^*
Institute of Mechanics, Lomonosov Moscow State University, Russia

ABSTRACT

We consider here mechanical objects that have desired operating regime unstable without additional control signal. The resources of control are assumed limited. First of all the motion equations of a multi-link pendulum mounted on a moving base – wheel are designed. Equations that describe only the pendulum motion are separated. The problem of controlling a single inverted pendulum on a wheel is studied. Control law that ensures large basin of attraction of the top unstable equilibrium is developed. The 'inverse' system – the inertia wheel pendulum with fixed suspension point is investigated. For this system the control algorithm is developed to stabilize globally the top equilibrium of the pendulum. This control law is tested successfully in simulation and experiments. The double pendulum with fixed suspension point is considered. The limited in absolute value control torque is applied in the inter-link joint. The control algorithm to ensure global stabilization of the inverted pendulum is designed. For maximizing basin of attraction of unstable system, we use all control resources to suppress the unstable modes. At the end of the paper, the problem of gyroscopic stabilizing of the upright unstable position of a robot-bicycle is studied.

KEYWORDS
Unstable Object, Limited Control Resources, Control Algorithm, Controllability Domain, Asymptotical Stability, Basin of Attraction

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] A. M. Formalskii , "Unstable Mechanical Objects: Motion Control, Stabilization," Universal Journal of Mechanical Engineering, Vol. 5, No. 5, pp. 150 - 169, 2017. DOI: 10.13189/ujme.2017.050503.

(b). APA Format:
A. M. Formalskii (2017). Unstable Mechanical Objects: Motion Control, Stabilization. Universal Journal of Mechanical Engineering, 5(5), 150 - 169. DOI: 10.13189/ujme.2017.050503.