Lecture 13 Flashcards
What are compensators
Compensation is the alteration or adjustment of a control system to provide a suitable performance
How does cascade compensation compare to feedback compensation
Cascade compensation is easier and simpler to design/analyse, but does not offer as fast a response as feedback compensation
What is an ideal compensator
Compensators that involve pure integration or pure differentiation
Ideal integral compensation can be used to
Improve steady state error
Ideal derivative compensation can be used
To improve transient response
Give an example of an ideal derivative compensator
K(s+z), where K is the derivative gain and Kz is the proportional gain
How can the derivative gain and proportional gain term be choose for a compensator
Using the magnitude condition for K (derivative gain) and angle condition for z
What are the transfer function poles
-p1, …, -pn (n for denominator) start points on the root locus
What are the transfer function zeroes
-z1, …, -zm (m for numerator|) end points on the root locus
What are angle (s - zi) and angle (s-pj)
Arguments of the vectors measured relative to the positive real axis
What is ideal derivative cascade compensation
Proportional plus derivative control
For an open loop unstable system with transfer function =1/s^2, design a suitable ideal cascade compensator to achieve zeta = 0.707, Ts = 1 second
compensator of form K(s+z)
Characteristic equation
1+ K(s+z)/s^2 = 0
Two start point at origin, end point at -z
Performance specification => Im(-1/(1/4)) On line cos(theta) = 0.707 theta=45deg
Angle condition
Beta - (alpha + alpha) = 180
B - 135 -135 = 180, B = 90
z lies on the real axis directly beneath the desired root location z = 4, magnitude K - 8, derivative gain 8, proportional gain = 32
