Lecture 10 Flashcards
What is the routh stability criterion
Method of determining whether a system was stable
What are the four steps to the Routh Stability Criterion
- Write down the characteristic equation in the from ans^n + … + a4s^4 + a3*s^3 etc
- Are all coefficients a0 a1 non zero? (No unstable)
- Are all the coefficients a0 a1 the same sign (No
unstable) - Form the Routh Array’
What can you determine from the Routh Array
Number of sign changes in the first column of the array is equal to the number of roots with positive real parts ie system is unstable if there are sign changes in the first column
Draw up the Routh Array for s^3 + s^2 + 2s + 8 = 0
1 2
1 8
-6
8
Routh Array Method
Using two rows above, on new row start 2x2 matrix directly above, doing the -ve of the determinant all divided by the bottom left element on the row above, for the second new element repeat process but skip the row directly above
If there’s no values for use on the routh array what should you treat it as
A zero
What are the caveats of the routh array
Method only works if there are no zeros in the first column (some procedures for overcoming but not in this module)
How can a stable value for controller gain be chosen
Routh method with a variable
Settling time TSS
4* the time constant = 4* tau
How can the natural frequency of a system be determined from a plot of the s plane
Natural frequency is equal to the magnitude of the root
What is the Re(s) equal to
- zeta * natural frequency = -1/tau
What is the Im(s)
The damped natural frequency
What is zeta
Cos(alpha) = zeta
Where alpha is the angle from the -ve real axis to s
What are the properties you can get from the
Natural freq = magnitude of s
Damping ratio = cos(alpha)
-1/tau = Re(s_
Damped natural freq = Im(s)
What can we use the s plane to do
Design systems based upon the standard engineering parameters
