Control Theory

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# Control Theory - PowerPoint PPT Presentation

Control Theory. Session 6 – Transfer Functions. Standard form of first order TF. We will consider changes w ith respect to a given initial equilibrium . Step response:. Step response of. Δ z (t). A. t. B.

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## PowerPoint Slideshow about ' Control Theory' - waylon

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Presentation Transcript

### ControlTheory

Session6 – Transfer Functions

Standard form of first order TF

We willconsider changes

with respect to a giveninitial

equilibrium

Step response:

Step response of

Δz(t)

A

t

B

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

Second order processes

Typicalexample: mass-spring-damper

z(t)

u(t)

(set-up in a horizontal plane, spring in rest positionwhen x=0, initialvelocity v=0: equilibrium!)

Step respones of 2nd order processes

>1: Overdamped

=1: Critically damped = fastest without oscillations

<1: Underdamped: Oscillations!

+

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]