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Model-free control of the inertia wheel inverted pendulum with real-time experiments

Model-free control of the inertia wheel inverted pendulum with real-time experiments

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In this chapter, we propose to design a control scheme based on model-free technique to deal with underactuation in stable limit cycle generation. In order to achieve stable limit cycles on both coordinates of the inertia wheel inverted pendulum, we first design a family of p-parameterized periodic trajectories for the pendulum's angle. Those trajectories are then tracked using the control input thanks to a classical model-free controller. Since the system is underactuated and nonminimum phase, a second controller is needed to update the parameter p of the above trajectories in order to deal with the convergence of the internal dynamics of the system.To achieve this control, we propose a second model-free controller using actuated coordinate (inertia wheel) as output and trajectories' parameter p as control input. Note that this control scheme can be easily applied to the stabilization case by carefully choosing appropriate trajectories. Numerical simulations as well as real-time experiments are presented to show the effectiveness of the proposed control scheme and its ability for external disturbances rejection.

Chapter Contents:

  • 5.1 Introduction
  • 5.2 Description of the system: inertia wheel inverted pendulum
  • 5.2.1 Description of the mechanical part of the system
  • 5.2.2 Description of the electronic part of the system
  • 5.2.3 Description of the control PC and software
  • 5.3 A proposed control solution for underactuated systems
  • 5.3.1 Brief background on model-free control
  • 5.3.1.1 Nonlinear dynamics
  • 5.3.1.2 The control law
  • 5.3.2 Proposed control solution
  • 5.3.2.1 Basic principle of the proposed control scheme
  • 5.3.2.2 Cyclic reference trajectories generation
  • 5.3.2.3 The dual model-free controller
  • 5.4 Application: the inertia wheel inverted pendulum system
  • 5.4.1 Dynamic modeling of the system
  • 5.5 Numerical simulations
  • 5.6 Real-time experiments
  • 5.6.1 Scenario 1: Control in nominal case
  • 5.6.2 Scenario 2: External disturbance rejection
  • 5.7 Conclusion
  • References

Inspec keywords: limit cycles; control system synthesis; pendulums; stability; nonlinear control systems

Other keywords: underactuation; inertia wheel inverted pendulum; model-free controller; stable limit cycle generation; control scheme design; control input; actuated coordinate; convergence; external disturbance rejection; nonminimum phase; pendulum angle; trajectory parameter; p-parameterized periodic trajectories; internal dynamics

Subjects: Control system analysis and synthesis methods; Stability in control theory; Nonlinear control systems

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