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Case studies on non-linear control theory of the inverted pendulum

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The Inverted Pendulum in Control Theory and Robotics: From theory to new innovations — Recommend this title to your library

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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.

Chapter Contents:

• Abstract
• 10.1 Introduction
• 10.2 Modelling of the cart-pendulum systems
• 10.3 Control analysis
• 10.3.1 Linear control analysis
• 10.3.2 Non-linear control analysis
• 10.4 Simulations for single and double pendulum control
• 10.5 Case study 1 - LEGO EV3-based inverted pendulum
• 10.5.1 Introduction
• 10.5.2 LEGO Mindstorms EV3
• 10.5.3 Construction of LEGO inverted pendulum
• 10.5.4 Controller design and Simulink model
• 10.5.5 Experimental results
• 10.6 Case study 2 - a parallel manipulator as the cart
• 10.7 Conclusions
• Appendix A Solving and implementing control solutions using MATLAB
• Appendix A.1 Non-linear control of a single pendulum and cart system
• Acknowledgement
• References

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