A NEW APPROACH TO FEEDFORWARD CONTROL DESIGN UNDER OUTPUT CONSTRAINTS APPLIED TO THE SIDE–STEPPING OF THE TRIPLE INVERTED PENDULUM

The side–stepping maneuver of the triple inverted pendulum serves as a benchmark problem for the presentation of a new feedforward control design approach for finite–time transition problems under consideration of output constraints. The inversion–based design treats the transition task as a two–point boundary value problem (BVP) defined in the input–output coordinates of the pendulum model. The new approach allows to directly incorporate constraints of the output and its time derivatives within the BVP, which is solved by a standard Matlab function. A linear LQR controller is used to stabilize the pendulum along the feedforward side–stepping trajectories. Simulation and experimental results for the triple inverted pendulum illustrate the accuracy and robustness of the proposed feedforward/feedback control scheme.