Download
rotary inverted pendulum balance control n.
Skip this Video
Loading SlideShow in 5 Seconds..
Rotary Inverted Pendulum Balance Control PowerPoint Presentation
Download Presentation
Rotary Inverted Pendulum Balance Control

Rotary Inverted Pendulum Balance Control

449 Vues Download Presentation
Télécharger la présentation

Rotary Inverted Pendulum Balance Control

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

  1. Rotary Inverted Pendulum Balance Control ChengsenSong Dec. 1, 2010

  2. Model

  3. Non-linear Model Modeling of the inverted pendulum system - Using Free Body Diagram method - Using Lagranian Formulation

  4. State variables representation • Define the state variable x as • Linearizing under the assumption that α ≈ 0, the state space representation of the pendulum is

  5. Numerical solution • A = • 0 0 1.0000 0 • 0 0 0 1.0000 • 0 53.1012 -0.6586 0.6575 • 0 98.3814 -0.6575 1.2182 • B = • 0 • 0 • 274.4012 • 273.9627 • C = • 1 0 0 0 • 0 1 0 0 • D = • 0 • 0 • eig(A)=  • 0 • 10.3650 • -9.5021 • -0.3033

  6. The implementation of the state variable compensator

  7. The state variable presentation of the observer

  8. K • Gain K is decided by the LQR controller design method. • LQR : determine the matrix gain K such that the static, full-state feedback control law u(t) = −Kx(t) satisfies the following criteria • a) the closed-loop system is asymptotically stable • b) the quadratic performance functionalis minimized • x = 10; • y = 500; • Q = [x 0 0 0; • 0 y 0 0; • 0 0 0 0; • 0 0 0 0]; • R = 15; • Klqr = lqr(A,B,Q,R)

  9. L • Matrix Lis decided using the pole placement method. • Given the single- or multi-input system and a vector p of desired self-conjugate closed-loop pole locations, place computes a gain matrix K such that the state feedback u = –Kx places the closed-loop poles at the locations p. • P = [-2 -5 -42 -43]; • L = place(A',C',P)';

  10. N • Gain N is to eliminate the steady-state error. • Cn = [1 0 0 0]; • sys = ss(A,B,Cn,0); • Nbar = rscale(sys,Klqr)

  11. Simulink model

  12. Ref input: 0.1Hz, amplitude 0.2rad.

  13. Network control system

  14. sampling period 10ms (without packet loss)

  15. sampling period 8ms, loss rate 0.1

  16. Future goal • Digital control system. • Varying sampling time. • Delay analysis

  17. Thank you