by Neil E. Cotter

Research Assistant Professor

Last Updated: 7/16/06

 

 

Linear Systems

Frequency response

Magnitude = 1/product distances to poles

Phase = sum angles to poles

Differential equations altered

Mason's loop rule

Steady state error

Stability

Homogenous solution unstable

Denominator = 0

Routh's method

Root-locus method

overview

phase G = 180˚

real axis left of odd # x's and o's

angle departure sensitive to x

poles approach o's or ∞

large K locus on spoke roots of -1

large K centroid formula

K at imaginary axis crossing

root breakaways from derivative

root breakaways from x and o distance

K from s

Nyquist criteria

Gain margin

Phase margin

Proportional control

Derivative control

Acceleration control

Integral control

Compensation control

Step-Function response