Jaspreet System Type and Steady State errors from Bode Plots

Question 1

What is the type number?

Answer 1

It is equal to the number of poles at the origin

Question 2

What is the equation for the Position error constant and when does it occur?

Answer 2

It occurs for a type 0 system and is Lim(s->0) G(s)

Question 3

What is the equation for the velocity error constant and when does it occur?

Answer 3

It occurs for a type 1 system and is Lim(s->0) s * G(s)

Question 4

What is the equation for the acceleration error constant and when does it occur?

Answer 4

It occurs for a type 2 system and is lim(s->0) s^2 * G(s)

Question 5

What is the relative degree?

Answer 5

It is denoted by K and is the number of poles - the number of zeros:
n-m

Question 6

What do the low frequency characteristics of a system depend on?

Answer 6

The type number. The gradient will be the type number * -20db. The phase angle will be type number * -90

Question 7

What do high frequency characteristics depend on?

Answer 7

The relative degree of the system K.
Gradient = k * -20
Phase = k * -90

Question 8

How can we use the Bode Plot to determine steady state error?

Answer 8

By projecting the low frequency asymptote which is a straight line until it hits the 0db Gain line.
Kp = G(0)
Kv = wr - the point where the line crosses the frequency axis
Ka = wa^2

Question 9

What is the slope of low frequency asymptote for a type 1 or type 2 system?

Answer 9

For type 1 = -20

For type 2 = -40