An application of dynamic inversion to stabilization of a triple inverted pendulum on a cart

In this research the nonlinear dynamic inversion technique with multiple time-scale approximation is applied to stabilize a triple inverted pendulum on a cart around its unstable equilibrium point by using a single control variable. A linear quadratic regulator controller for the linearized model is designed and utilized to obtain the gains of the desired dynamics for the dynamic inversion control law. A worst case initial condition set, the largest initial condition set for which the system is stable and other requirements are satisfied, is determined through simulations and the system configuration for this set resembles a buckle