Case studies on nonlinear control theory of the inverted pendulum

This chapter deals with the control of inverted pendulums through nonlinear control theory. Simulations of the proposed control method are carried out in MATLAB environment with satisfactory results in controlling systems of single and double-link inverted pendulum installed in a cart, for a range of starting positions. The proposed control technique can be extended to the control of many other nonlinear systems. Examples are proposed as referring to design and teaching applications. In particular, a single inverted pendulum system constructed using Lego bricks and controlled by Lego Mindstorms EV3 is used to prove the user-friendliness of the proposed control method as implemented by Master students at Sheffield Hallam University. Moreover, a three degrees of freedom parallel manipulator CAPAMAN (Cassino Parallel Manipulator) is investigated for replacing a cart and providing three dimensional motions to an inverted pendulum while minimizing dynamics effects at design stage.