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Higher order sliding-mode stabilization of inverted cart-pendulum

Higher order sliding-mode stabilization of inverted cart-pendulum

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Stabilization of a cart-pendulum system through a generalized higher order surface-controller design is presented. The singular Linear Quadratic (LQ) method presents a natural relationship between order of singularity of a given performance index and the order of sliding-mode controller. Thus, several arbitrary relative degree optimal sliding surfaces and its corresponding higher order sliding-mode controller can be specified for a given system. Continuous higher order sliding-mode controllers are obtained through a robustification method for arbitrary relative degree nominal controllers based on integral sliding modes and supertwisting algorithm. An agreement between the accuracy/complexity of the Continuous Higher Order Sliding Mode (CHOSM) controller and the limited accuracy offered by the system's sensors and actuators is obtained through several experiments.

Chapter Contents:

  • Abstract
  • 3.1 Introduction
  • 3.2 Singular LQ sliding variable design
  • 3.2.1 MATLAB® function: SSLQ
  • 3.3 Continuous higher order sliding-mode controllers
  • 3.3.1 Integral sliding-mode control
  • 3.3.2 Continuous integral sliding-mode control
  • 3.3.3 Arbitrary order controllers design
  • 3.4 Cart-pendulum system
  • 3.4.1 Mathematical model
  • 3.4.1.1 Nonlinear model
  • 3.4.1.2 Equilibrium points
  • 3.4.1.3 Stability analysis
  • 3.4.2 Linear model
  • 3.4.2.1 Controllability and observability analysis
  • 3.4.2.2 Controllable canonical form
  • 3.5 Continuous higher order sliding-mode controllers: cart-pendulum system realization
  • 3.5.1 Relative degree one SMC
  • 3.5.2 Relative degree two SMC
  • 3.5.3 Relative degree three SMC
  • 3.5.4 Relative degree four SMC
  • 3.6 Results
  • 3.6.1 Accuracy analysis
  • 3.7 Conclusions
  • References

Inspec keywords: actuators; pendulums; optimal control; variable structure systems; robust control; nonlinear control systems; performance index; control system synthesis; sensors; linear quadratic control

Other keywords: performance index; robustification method; sliding-mode controller; continuous higher order sliding-mode controller; integral sliding modes; inverted cart-pendulum system; LQ method; system sensors; higher order sliding-mode stabilization; system actuators; arbitrary relative degree nominal controllers; singular linear quadratic method; natural relationship; arbitrary relative degree optimal sliding surfaces; supertwisting algorithm

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

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