1 Apply Lyaponove function to design the observer Advisor: Ming-Shyan Wang Presenter: Hanh Nguyen Thi

2 Contents  Principle of method  Apply for servo motor  Simulation results

3 Principle of method  Theorem : Lyaponove function If (2) is satisfied, then (1) is asymtotically stable system (1) (2)

4 Principle of method  The system is affected by the unknown disturbance. Unknown disturbance Given value Canonical control form

5 Principle of method State feedback controller is the unknown disturbance Is the known disturbance State feedback controller for canonical control form Block diagram of State feedback controller

6 Principle of method Method: Lyaponove function:

7 Principle of method

8 Choose : Satisfy:

9 Apply for servo motor :angular position :speed of motor. :disturbance torque :motor torque. :moment of inertia. :the friction coefficient. :unmodelled uncertainty :parameter variations Canonical control form Mechanical model:

10 Apply for servo motor Observer Controller:

11 Apply for servo motor  Determine A matrix: use pole placement method.  Determine controller parameter:

12 Apply for servo motor  Determine Q matrix: dV/dt the larger, the better. Choose q2=0 and q1,q4, H big enough

13 Apply for servo motor  Determine P matrix:

14 Simulation Block diagram for the disturbance observer

15 Simulation  Parametter for simulation: Bm=8e-5; Jm=6.45e-5; h=500; s1=-50; %the pole s2=-400; %the pole q1=0.5; %the element of Q matrix q4=2; %the element of Q matrix Kp=100; % Kp,Ki,Kd of PID (disturbance) Ki=1500; Kd=2

16 Simulation Disturbance profile

17 Simulation Speed response at 2 rpm

18 Thank you for your attention !

19 Model of canonical control form :