Case studies on non-linear control theory of the inverted pendulum
This chapter deals with the control of inverted pendulums through non-linear 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 non-linear 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, 3 degrees of freedom parallel manipulator Cassino Parallel Manipulator is investigated for replacing a cart and providing three dimensional motions to an inverted pendulum while minimising dynamics effects at design stage.
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