29 Questions
What is the difference between absolute and relative stability?
Absolute stability refers to whether a system is stable or unstable, while relative stability refers to the degree of stability.
What is the necessary and sufficient condition for a feedback system to be stable?
All poles of the system transfer function have negative real parts.
What is the effect of pole locations on the unit step response of a 2nd-order system?
The system is stable if all poles have negative real parts.
What is the condition for a system to be BIBO stable?
The system has a bounded response to a bounded input.
What is the form of the poles of the standard transfer function of a 2nd-order system?
s1, 2 = -ζωn ± j1 - ζ2
Is the system G(s) = 10(s+2)/(s+1)(s-3)(s+4) stable?
No, the system is unstable.
What is the Routh array used for?
To determine the stability of a system
What is the form of the response transform X1(s)?
X1(s) = bn s^n + bn-1 s^n-1 +... + b1s + b0
What is the characteristic equation of the system?
Q(s) = bn s^n + bn-1 s^n-1 +... + b1s + b0 = 0
How are the constants c1, c2, c3, etc. evaluated in the Routh array?
By using the coefficients of the characteristic equation
What is the condition for stability of a system according to Routh's criterion?
All terms in the first column have the same sign
What is the number of roots of the characteristic equation with positive real parts equal to?
The number of changes of sign of the coefficients in the first column
What does the presence of imaginary roots in the characteristic equation indicate about the output of the system?
The output includes a sinusoidally oscillating component
What is the next step after finding the characteristic equation of a system?
Form the auxiliary equation from the preceding row
What is the condition for a system to be stable according to the Routhian array method?
There are no changes of sign in the first column
What is the purpose of differentiating the auxiliary equation in the Routhian array method?
To complete the Routhian array
What is the condition for the numerator of the first term in the s1 row to be positive for a stable system?
–K2 – 43K + 2000 > 0
What is the range of K for which the system is stable in the given example?
K < 80 and K > 0
What is the necessary condition for a stable system?
All the coefficients of the characteristic equation have the same sign
What is the Routh-Hurwitz stability criterion used for?
To determine the number of roots of q(s) with positive real parts
What is the first step in the Routh-Hurwitz stability test?
To construct the Routh array from the system characteristic equation
What is the characteristic equation of a system?
The equation q(s) = 0
What is the purpose of the Routh-Hurwitz stability test?
To determine the stability of a SISO-LTI system
What is the necessary and sufficient condition for a stable system?
The Routh-Hurwitz test is satisfied
What is the condition for all roots of the 1st Order polynomial Q(s) = a1s + a0 to be in the Left Half Plane (LHP)?
a1 and a0 have the same sign
What is the condition for all roots of the 2nd Order polynomial Q(s) = a2s^2 + a1s + a0 to be in the LHP?
a2, a1, and a0 have the same sign
What is the condition for all roots of the Higher Order polynomial Q(s) = an s^n + an-1s^n-1 +... + a1s + a0 to be in the LHP?
All coefficients ak have the same sign
What is the limitation of the Routh-Hurwitz criterion?
It is only applicable to polynomials
What is the value of K for which the system is stable in the given example?
0 < K < 28.1
Test your understanding of the stability criteria for polynomials of different orders, including 1st, 2nd, and higher orders. Learn about the conditions for all roots to be in the Left Half Plane (LHP).
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