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System stability - Coggle Diagram
System stability
Root locus diagram
How high can k be before the system becomes unstable
instead of plotting a single point or a pair
, its a series of different solutions
corresponding to different values of k
Step 1 : search the real axis for the existence of a root
create trial points and test
Step 2 : Asymptotes of loci
S-plane plots
Show the imaginary and real parts of a sytem
Imaginary parts come in complex conjugate pairs
defined by solution to characteristic equation
Stability types
Unstable
divergent
Marginally stable
Stable
all roots must have negative real parts
apply a unit impluse - stability defined by index on e
Gives an output that is bounded provided that the input to the system is also bounded