Identification of n-link inverted pendulum on a cart

The identification procedure specially designed for an n-link inverted pendulum on a cart is presented. By the Lagrangian mechanics, the mathematical model of the n-link inverted pendulum is established initially. To fully model the system, the standard dynamic parameters which are some algebraic functions of geometric, inertial, and friction parameters are introduced. Because the dynamic model of the n-link inverted pendulum is linear with respect to these parameters, the ordinary and weighted least squares techniques can be applied to estimation their values and the corresponding standard deviations. Also, the exact algorithms for numerical differentiation used in the formation of the regression model are described in detail. Finally, the results from identification of the real triple inverted pendulum are presented.