User Tools

Site Tools


ballandbeam_modelling

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revisionPrevious revision
Last revisionBoth sides next revision
ballandbeam_modelling [2016/07/13 14:46] joaomatosballandbeam_modelling [2016/07/13 14:59] joaomatos
Line 1: Line 1:
-===== Ball and Beam Modelling =====+===== Ball and Beam Modelling using PID Control =====
  
  
Line 82: Line 82:
  
  {{::simulink_and_real.jpg?direct|}}  {{::simulink_and_real.jpg?direct|}}
 +
 +
 +
 +----
 +
 +===== Control using LQR =====
 +
 + {{::1_lqr.jpg?direct|}}
 + {{::2_lqr.jpg?direct|}}
 + {{::4_lqr.jpg?direct|}}
 + {{::5_lqr.jpg?direct|}}
 + {{::6_lqr.jpg?direct|}}
 + {{::7_lqr.jpg?direct|}}
 + {{::8_lqr.jpg?direct|}}
 + {{::9_lqr.jpg?direct|}}
 + {{::10_lqr.jpg?direct|}}
 + {{::11_lqr.jpg?direct|}}
 + {{::12_lqr.jpg?direct|}}
 + {{::13_lqr.jpg?direct|}}
 + {{::14_lqr.jpg?direct|}}
 + {{::15_lqr.jpg?direct|}}
 + {{::16_lqr.jpg?direct|}}
 + {{::17_lqr.jpg?direct|}}
 + {{::18_lqr.jpg?direct|}}
 +
 +
 +
 +----
 +
 +===== PID VS LQR =====
 +
 + Analyzing a 176mm disturbance rejection , we have (PID first LQR second): 
 + 
 +*note here that both methods can show pretty similar results , hand-tuning the gains after the initial guess. The PID version of the controler was intended to stop the ball fast , the LQR version of the controller was intended to stop the ball without overshooting too much. Again , both methods can be adjusted to control the overshoot or the rise time.
 + 
 + {{::comparison.jpg?direct|}}
 + 
 + It's difficult to make a comparison between the PID and LQR control methods , both can be adjusted by hand after the initial guess and can show satisfactory results.However , the main advantage of using LQR on this case is that the energy input can be controlled (at the [R] matrix ). Both methods requires a hand tuning after the initial guess to achieve the desired response.
 +
 + 
 +
ballandbeam_modelling.txt · Last modified: 2016/07/13 15:02 by joaomatos