1. H(s) Transfer Function: f(t): input x(t): response f(t) fz(t)
f(t)=est => x(t)= H(s)est
H(s)
f(t)
x(t)
ms2H(s)est+csH(s)est+H(s)est=est
(ms2+cs+k)H(s)=1
z(t)
fz(t)
f(t)
x(t)

2. z(t) input, x(t) response. Fd: disturbance.
z(t) is controlled by the voltage Va
x(t) is measured by a sensor as a output voltage Vs.
Va voltage of 1 V produces z output of 3 cm.
x displacement of 1 cm produces a sensor voltage of 1 V.
Closed loop control will be applied by Vr reference voltage.
Mathematical model of the system is given below. Draw the closed loop block diagram. e V
Vr:Control input fd:Disturbance Vs:Response

3. Example
Fc: Control Force
Ft: Disturbance (External force)

4. Block diagram of closed loop system:V
P, PI, PD, PID kontrol
Block diagram of open loop system:

5. Block diagram of open loop system:

6. Block diagram of closed loop system: Kapalı sistemin blok diyagramı:V
P, PI, PD, PID kontrol
MATLAB / M File
MATLAB/SIMULINK

7. Solution by SIMULINK
Open loop system:

9. Closed loop system:

10. Steady state error

11. Steady-state error

13. a=0.6, b=0.3, d1=0.45,
ρ=7800, r1=1.4 (10-2)
m2=67
k= , c=
block diagram of the closed loop system
f1:control input f2:Disturbance y:Response

14. Lagrange Eq.: L=E1-E2
a=0.6, b=0.3, d1=0.45,
ρ=7800, r1=1.4 (10-2)
m2=67
k= , c=

15. Va:Control input f2:Disturbance V2:Response
Açık sistem:
Va:Control input f2:Disturbance V2:Response
Kapalı sistem: e V
P, PI, PD, PID kontrol
Vr:Kontrol girdisi f2:Dış etki V2:Cevap

16. Blok Diagrams:
A(s)
G1(s) Kt + - K
G2(s)
C(s)
R(s)