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## PowerPoint Slideshow about ' Control Theory' - abrial

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### ControlTheory

Session 5 – Transfer Functions

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)

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]

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 sizedependsonnbutnoton
- 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

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

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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