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LMI-based control design for balancing and attitude stabilization of inverted pendulums

LMI-based control design for balancing and attitude stabilization of inverted pendulums

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This chapter explores the dynamic modeling and feedback stabilization of different types of inverted pendulums (IPs). It contains a theoretical analysis of the system dynamics and control methods, as well as a summary of MATLAB®/Simulink® simulation results. There are two primary objectives of this chapter: 1. To provide technical results pertaining to robust control-design approaches using convex optimization methods over linear-matrix inequalities. The design approaches include linear quadratic regulator (LQR), linear quadratic regulator with integral gain (LQRI), model-predictive control, H2 control, H control and multiobjective state feedback. 2. To demonstrate the application of these approaches to the balancing and attitude stabilization of IP systems including pendulums on cart, double and triple link systems on pivot, rotational double IP and IP-type assistant robot.

Chapter Contents:

  • Abstract
  • 14.1 Introduction
  • 14.2 Dynamic modeling
  • 14.3 Pendulums on cart
  • 14.3.1 Single pendulum on cart
  • 14.3.2 Double pendulums on cart
  • 14.3.3 State-space representation
  • 14.4 Inverted pendulum on pivot
  • 14.4.1 DIP on pivot
  • 14.4.2 TIP on pivot
  • 14.5 Rotational double inverted pendulum
  • 14.6 Inverted pendulum-type assistant robot
  • 14.7 LMI-based control-design methods
  • 14.7.1 LQR: proportional gain
  • 14.7.2 LQRI: proportional-integral gain
  • 14.7.3 LQR+: proportional gain with disturbance rejection
  • 14.7.4 LQRI+: proportional-integral gain with disturbance rejection
  • 14.7.5 Model-predictive control
  • 14.8 Multiobjective state feedback
  • 14.8.1 ℋ2 performance
  • 14.8.2 ℋ∞ performance
  • 14.8.3 Mixed ℋ2/ℋ∞ performance
  • 14.9 Simulation results
  • 14.9.1 SIP-DIP open-loop response
  • 14.9.2 SIP LQR response
  • 14.9.3 DIP on cart
  • 14.9.4 Triple IP
  • 14.9.5 RDIP simulation
  • 14.9.6 I-PENTAR simulation
  • 14.10 Conclusions
  • Acknowledgment
  • References

Inspec keywords: linear quadratic control; H2 control; predictive control; nonlinear control systems; convex programming; control system synthesis; H∞ control; state feedback; robots; robust control; pendulums

Other keywords: LQRI; MATLAB/Simulink simulation; model-predictive control; H∞ control; rotational double IP; system dynamics; convex optimization methods; linear quadratic regulator with integral gain; control methods; feedback stabilization; attitude stabilization; cart; multiobjective state feedback; IP system balancing; inverted pendulums; dynamic modeling; IP-type assistant robot; double link systems; triple link systems; H2 control; robust control-design approaches; linear-matrix inequalities

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

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