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Advances in Differential Equations and Control Processes

Advances in Differential Equations and Control Processes
Volume 18, Issue 1, Pages 55 - 67 (February 2017)
http://dx.doi.org/10.17654/DE018010055

STABILITY OF THE INVERTED PENDULUM UNDER EXTERNAL FORCE ACTING ON THE PIVOT

Robson Andrade de Jesus and Alan Almeida Santos

Abstract:

We consider the inverted pendulum with a control mechanism which can move the pivot of the pendulum horizontally. We assume the restoring force due to the control mechanism as a linear function of angular displacement and angular velocity and make the complete investigation of the stability of the top vertical equilibrium according to the parameters of proportionality.