The Stability of Linear Feedback Systems

,
5.6 Summary
225
2
"
06
o
o
so 70
100 126 ISO
K
Figure 5.8. The stable region.
ell is equal to 23.8% of A, we require that Ka = 42. This can be satisfied
the selected point in the stable region when K = 70 and a = 0.6, as shown in
5.8. Of course, another acceptable design would be attained when K = 50
G - 0.84. We can calculate a series ofpossible combinations of K and a that
utisfy Ka = 42 that lie within the stable region, and all will be acceptable
solutions. However, not all selected values of K and a will lie within the
region. Note that K cannot exceed 126.
Summary
chapter we have considered the concept ofthe stability ofa feedback cont)'Item.
A definition ofa stable system in terms ofa bounded system response
':'Ottined and related to the location of the poles of the system transfer fune­
In the s-plane.
The Routh-Hurwitz stability criterion was introduced and several examples
~idered. The relative stability ofa feedback control system was also con­
• In terms ofthe location ofthe poles and zeros ofthe system transfer func­
~ the s-plane. Finally, the determination of the roots of the c-haracteristie
on was considered and the Newton-Raphson method was illustrated.
• A sYStem has a characteristic equation 5 l + 3Ks l
ofK for a stable system.
K :> 0.53
+ (2 + K)s + 4 = O. Determine