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Control Theory

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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]

Step response:

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]

>1: Overdamped

=1: Critically damped = fastest without oscillations

<1: Underdamped: Oscillations!

+

- Shows no overshoot
- Shows overshoot of which the sizedependsonnbutnoton
- Shows overshoot of which the sizedependson butnoton n
- Shows overshoot of which the sizedependson and n

[Default]

[MC Any]

[MC All]

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]

m=1 [kg]

k=1 [N/m]

Can we nowadd a P controller and calculate the

Transfer function of the closed loop?

(by the way, what’s the transfer function of a P controller?)