Lecture 5 Flashcards
What is a unity feedback system?
A system with a feedback term with a transfer function of 1
What happens as controller gain increases?
The response gets closer to the desired value and the
What is the steady state error?
The difference between ‘what we asked for’ and ‘what we got’
Do 1st and 2nd order responses exhibit a steady state error?
1st: yes
2nd: no
Why is integral control used?
The controller provides better performance if the system were second order, which is achieved by integral control
What is the equation for proportional control in the t and s domains?
t: Kpe(t)
s: KpE(s)
What is the equation for integral control in the t and s domains?
t: Ki * Int e(t)dt
s: Ki(1/s)E(s)
What is the transfer function for when K is replaced by a combination of integral and proportional control?
Kp + Ki/s
What is the final value theorem?
lim f(t) = lim SF(s)
t -> infinity s -> 0
What happens when controller gain is increased
The response gets closer to the desired value of 1 and the response speed is faster, reduce steady state error but it will never become zero
How do we change a first order system to a second order system
Adding integral control;
Change controller gain from K to Kp + Ki * 1/s
In the Laplace domain what does multiplying and dividing by s do
If you multiply by s same as differentiating, if you divide by s same as integrating
What is the final value theorem
Way of exploring the steady state response of a system without taking inverse Laplace transform and setting t = infinity
How does the final value theorem work
Multiply the transfer function by s and then find the value when s tends towards zero
