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

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

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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

Inspec keywords: pendulums; human computer interaction; nonlinear control systems; control engineering computing; control system synthesis; manipulator dynamics

Other keywords: teaching applications; dynamics effects; simulations; user-friendliness; MATLAB environment; double-link inverted pendulum; inverted pendulums; 3 degrees of freedom parallel manipulator; nonlinear systems; Sheffield Hallam University; Lego Mindstorms EV3; design applications; nonlinear control theory; Master students; Cassino Parallel Manipulator; single double-link inverted pendulum; design stage; Lego bricks

Subjects: Control system analysis and synthesis methods; Robot and manipulator mechanics; Manipulators; Control engineering computing; Nonlinear control systems

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