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# Control Theory - PowerPoint PPT Presentation

Control Theory. Session 5 – Transfer Functions. Transfer function of . A B C None of the above. A. B. [Default] [MC Any] [MC All]. C. Step response of. z(t). A. t. B. Definition of step response: Δ z(t) if Δ u(t) is a step of size 1. A, B on previous graph?. A=2, B=3

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### ControlTheory

Session 5 – Transfer Functions

• A

• B

• C

• None of the above

A

B

[Default]

[MC Any]

[MC All]

C

z(t)

A

t

B

Definition of step response: Δz(t) ifΔu(t) is a step of size 1

• A=2, B=3

• A=2, B=6

• A=4, B=6

• None of the above

[Default]

[MC Any]

[MC All]

Standard form of first order TF

Step response:

Second order processes

Typicalexample: mass-spring-damper

z(t)

u(t)

(set-up in a horizontal plane, spring in rest positionwhen x=0)

• Will oscillate

• Will not oscillate

• Might oscillate, depending on the values of m,cand k

[Default]

[MC Any]

[MC All]

• Thatdoesn’tdependon

[Default]

[MC Any]

[MC All]

Standard form of second order TF

Step respones of 2nd order processes

>1: Overdamped

=1: Critically damped = fastest without oscillations

<1: Underdamped: Oscillations!

+

The step response of anunderdamped 2nd order system

• Shows no overshoot

• Shows overshoot of which the sizedependsonnbutnoton

• Shows overshoot of which the sizedependson butnoton n

• Shows overshoot of which the sizedependson and n

[Default]

[MC Any]

[MC All]

Overshoot in 2nd order systems

Overshoot in 2nd order systems

m=1 [kg]

k=1 [N/m]

Find the TF and

plot the step response for

c= 4 [Ns/m]

c=2 [Ns/m]

c=1 [Ns/m]