Structured Robust Stability Analysis Of An Inverted Pendulum System With A Fixedfeedback

Year 2005, Volume: 18 Issue: 2, 55 - 70, 31.12.2005

Ahmet Yazıcı , Abdurrahman Karamancıoğlu

Abstract

Robust stability analysis of inverted pendulum system with a fixed linear quadratic feedback is carried out using μ analysis tools. A mathematical model of inverted pendulum system is presented and linearized about the desired equilibrium point. A linear quadratic control feedback matrix is used in the configuration of the nominal inverted pendulum system for its stabilization. After this, uncertainties in the inverted pendulum with a fixed feedback, is modeled in linear fractional transformation form , which is suitable for structured singular value computation. Both parametric and modeling uncertainties are considered in the inverted pendulum system. After deriving out uncertain system model, mixed μ analysis method which is a structured uncertainty analysis method, is used to compute the uncertainty bound that does not cause instability of the inverted pendulum under feedback. A simulation test for validity of the results is provided.

Keywords

Structured singular value, Uncertainty, Robustness, Inverted pendulum

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