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Stabilization and tracking control of the inverted pendulum on a cart via a modified PSO fractional order PID controller

Stabilization and tracking control of the inverted pendulum on a cart via a modified PSO fractional order PID controller

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In this chapter, a fractional-order proportional integral derivative controller, PIλDμ, based super-twisting observer for the cart inverted pendulum system is proposed. The mathematical model of the underactuated robotic system is derived using Lagrange equation and Grunwald-Letnikov fractional calculus with the physical parameters of a commercial device, the Googol Technology experimental Laboratory. PIλDμ parameters are optimized using a modified Particle Swarm intelligence optimization approach with the help of a multiobjective fitness function. A comparative analysis with the classical Particle Swarm Optimization algorithm shows the superiority of the proposed approach.

Chapter Contents:

  • Abstract
  • 4.1 Introduction
  • 4.2 The cart-inverted pendulum system
  • 4.2.1 System presentation
  • 4.2.2 Dynamic modeling
  • 4.3 Control system
  • 4.3.1 Super-twisting observer
  • 4.3.2 Fractional controller
  • 4.3.2.1 Fractional order calculus
  • 4.3.2.2 Fractional order PID (FOPID) controller
  • 4.3.3 Tuning parameters of fractional-order controller
  • 4.3.3.1 Particle swarm optimization
  • 4.3.3.2 Modified particle swarm optimization
  • 4.3.3.3 Fitness function
  • 4.4 Simulation results
  • 4.4.1 Simulation results and performance analysis: case study 1
  • 4.4.2 Simulation results and performance analysis: case study 2
  • 4.5 Conclusion
  • References

Inspec keywords: stability; three-term control; pendulums; nonlinear control systems; particle swarm optimisation; tracking; robots

Other keywords: modified PSO fractional order PID controller; particle swarm optimization algorithm; Googol Technology experimental laboratory; stabilization control; Grunwald-Letnikov fractional calculus; Lagrange equation; tracking control; inverted pendulum; cart inverted pendulum system; multiobjective fitness function; underactuated robotic system; super-twisting observer; fractional-order proportional integral derivative controller

Subjects: Nonlinear control systems; Robotics; Optimisation techniques; Stability in control theory

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