H(s) Transfer Function: f(t): input x(t): response f(t) fz(t)

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Presentation transcript:

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)

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

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

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

Block diagram of open loop system:

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

Solution by SIMULINK Open loop system:

Closed loop system:

Steady state error

Steady-state error

a=0.6, b=0.3, d1=0.45, ρ=7800, r1=1.4 (10-2) m2=67 k=106011.29, c=1099.89 block diagram of the closed loop system f1:control input f2:Disturbance y:Response

Lagrange Eq.: L=E1-E2 a=0.6, b=0.3, d1=0.45, ρ=7800, r1=1.4 (10-2) m2=67 k=106011.29, c=1099.89

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

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