This paper presents an approximate analytical solution for the weakly nonlinear closed-loop dynamics of the sliding phase of a sliding mode controlled rotary inverted pendulum based on the multiple scale method. A locally stable nonlinear sliding mode control law with starting configurations above the horizontal line is presented for the rotary inverted pendulum. The analytical expressions derived from the nonlinear solution of the reduced-order closed-loop dynamics provide both qualitative and quantitative insight into the closed-loop response leading to proper selection of parameters that guarantee stabilization and improve controller performance. The approximate analytical solution is verified through comparison with the exact numerical solution. The control performance predicted by the analytical solution is experimentally demo.

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