Closed-Loop Quantification and Compensation of Friction in an Inverted Pendulum
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Closed-Loop Quantification and Compensation of Friction in an Inverted Pendulum Hugo Tanzarella Teixeira · Victor Semedo de Mattos Siqueira · Celso José Munaro
Received: 17 August 2012 / Revised: 25 December 2012 / Accepted: 28 July 2013 / Published online: 5 September 2013 © Brazilian Society for Automatics–SBA 2013
Abstract In this paper, different approaches for friction estimation and compensation in an inverted pendulum are compared. The Coulomb, static, and viscous frictions are estimated using data only from a closed-loop operation. A control law using linear state feedback is designed to stabilize the pendulum, but limit cycles appear due to friction. Methods based on fitting an ellipse to the input–output plot and using least squares with the Karnopp friction model are employed to estimate the friction parameters to be used with the friction models considered. The values are then compared to those obtained in open-loop tests, obtained via application of a ramp of current to the motor of the cart. Friction compensation is carried out using the friction values in two strategies: model based compensation using the Karnopp and LuGre friction models and non-model based compensation using the knocker and constant reinforcement techniques. While model-based methods use the sign of the velocity to change the sign of the compensation, the non-model- based methods use the sign of the control signal for this decision, with an anticipatory action. Both strategies are compared through their application to a simulation model and to a real inverted pendulum, using the IAE and variance of position H. T. Teixeira (B) LCSI, Faculdade de Engenharia Elétrica e de Computação, UNICAMP, Av. Albert Einstein, 400, Sala LE-31, Cidade Universitária Zeferino Vaz, Destrito de Barão Geraldo, Campinas, SP CEP 13083-852, Brazil e-mail: [email protected] V. S. de Mattos Siqueira · C. J. Munaro Departamento de Engenharia Elétrica, Centro Tecnológico, Universidade Federal do Espírito Santo, Av. Fernando Ferrari, 514, Goiabeiras, Vitória, ES CEP 29075-910, Brazil e-mail: [email protected] C. J. Munaro e-mail: [email protected]
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and angle for performance measurement. This comparison and the analysis about the difficulty for estimating the parameters to be used for each compensation indicate the best scheme for estimation and compensation method to be used for this benchmark. Keywords systems
Friction · Inverted pendulum · Nonlinear
1 Introduction The interest in studying the effects of friction in control systems comes from its presence in all control systems involving mechanical systems. The inverted pendulum is an underactuated mechanical system, inherently open-loop unstable and with nonlinear dynamics. These aspects make it a classic problem that is extensively used for the application of control techniques. The presence of friction produces limit cycles that may prevent the stabilization of the inverted pendulum when appropriate friction compensation is not used (Olsson and Åström 2001). The describing function method
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