Control Systems
Stability
Practice questions from Stability.
3
Total0
Attempted0
Correct0
IncorrectConsider the polynomial
. Let be defined as follows.
is the number of roots of with negative real parts.
is the number of roots of that are purely imaginary.
is the number of roots of with positive real parts.
Which one of the following options is correct?
, and
, and
, and
, and
Routh Hurwitz criteria,
No. of sign change in column of RH table .
Auxiliary equation:
Imaginary Poles
and
Hence, option (a) is correct.
In the feedback control system shown in the figure below .
R(s), Y(s) and E(s) are the Laplace transforms of r(t), y(t), and e(t), respectively. If the input r(t) is a unit step function, then ________.
does not exist, e(t) is oscillatory
Here,
i.e inner product outer product
System is marginally stable.
oscillatory system
doesn't exist
Consider a unity negative feedback control system with forward path gain as shown.
The impulse response of the closed-loop system decays faster than if
Impulse response
To decay faster than , poles must lie to the left of
Replace
If poles lie to the left of imaginary axis after transformation then poles will lie to the left of s=-1
For stability inner producer outer product
Option (a) satisfies