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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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Control theory

ControlTheory

Session6 – Transfer Functions


Standard form of first order tf
Standard form of first order TF

We willconsider changes

with respect to a giveninitial

equilibrium

Step response:


Step response of
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
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!)


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!

+


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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