Steady state

Question 1

Why do we use feedback?

Answer 1

It accounts for uncertainty in our models
-regardless of disturbances, the system can be designed to follow the input with zero ss error

Question 2

Thinking of the system as a differential equation, what is the system output?

Answer 2

Solution of free response + solution of forced response
(complimentary function + particular integral)

Question 3

When the reference signal settles, what is it called?

Answer 3

Steady state

Question 4

How can we find the steady state of a system?

Answer 4

Apply unity feedback and find the output without the error signal
Using Final value therorem with Laplace
lim f(t) = lim {sF(s)}

Question 5

When does final value theorem not work?

Answer 5

When the system is unstable

Question 6

What is the steady state value for a system G(s) with a unit step input?

Answer 6

yss = lim{sF(s)} = lim{sU(s)G(s)}
= G(0)

Question 7

How do we define system type?

Answer 7

a system is type n if it has NO steady state error to an input of form 1/sn

e.g
type 1 - no ss error to a unit step
type 2 - has no ss error to a unit ramp

Question 8

How can we find steady state error of a system?

Answer 8

Using a unity feedback system, define the error signal without the output.
apply FVT

Question 9

How can we find steady state error due to disturbance?

Answer 9

using a unity loop. Find output in terms of forward loop.
use output = input - error
find error signal and apply fvt to both part of the equation
apply input signal to fvt of e_disturbance

Question 10

When given a requirement for error, how do we find the value of K for a second order system?

Answer 10

ess_max = dss / K

so K > dss / ess_max

dss is the disturbance steady state

Question 11

When given a requirement for error, how do we find the value of K for a first order system?

Answer 11

ess = 1/ 1+KG(o) x rss

where rss is reference signal steady state