Control theory
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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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Control Theory

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Control theory

ControlTheory

Session 5 – Transfer Functions


Transfer function of

Transfer function of

  • A

  • B

  • C

  • None of the above

A

B

[Default]

[MC Any]

[MC All]

C


Step response of

Step response of

z(t)

A

t

B

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


A b on previous graph

A, B on previous graph?

  • 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

Standard form of first order TF

Step response:


Second order processes

Second order processes

Typicalexample: mass-spring-damper

z(t)

u(t)

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


The step response of the m c k

The step response of the m-c-k

  • Will oscillate

  • Will not oscillate

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

[Default]

[MC Any]

[MC All]


The step response will oscillate if

The step response will oscillate if

  • Thatdoesn’tdependon

[Default]

[MC Any]

[MC All]


Standard form of second order tf

Standard form of second order TF


Step respones of 2 nd order processes

Step respones of 2nd order processes

>1: Overdamped

=1: Critically damped = fastest without oscillations

<1: Underdamped: Oscillations!

+


The step response of an underdamped 2 nd order system

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 2 nd order systems

Overshoot in 2nd order systems


Overshoot in 2 nd order systems1

Overshoot in 2nd order systems


Group task

Group Task

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]


Group task 2

Group Task 2

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?)


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