Stabilization and Tracking Control of X-Z Inverted Pendulum Using Flatness Based Active Disturbance Rejection Control

A flatness based robust active disturbance rejection control technique scheme with tracking differentiator is proposed for the problem of stabilization and tracking control of the X-Z inverted pendulum known as a special underactuated, non-feedback linearizable mechanical system. The differential parameterization on the basis of linearizing the system around an arbitrary equilibrium decouples the underactuated system into two lower order systems, resulting in two lower-order extended state observers. Using a tracking differentiator to arrange the transient process utilizes the problem of stabilization and tracking control and gives a relatively small initial estimation error, which enlarges the range of the controller parameters. The convincing analysis of the proposed modified linear extended state observer is presented to show its high effectiveness on estimating the states and the extended states known as the total disturbances consisting of the unknown external disturbances and the nonlinearities neglected by the linearization. Simulation results on the stabilization and tracking control of the X-Z inverted pendulum, including a comparative simulation with an all-state-feedback sliding mode controller are presented to show the advantages of the combination of flatness and active disturbance rejection control techniques.