Anna University Coimbatore 2009 B.E Electrical and Electronics Engineering Control system - Question Paper

A linear relaxed system is stated to have BIBO stability if every bounded input outcomes in a bounded output.
2.) What is impulse response ?
The impulse response of a system is the inverse Laplace transform of the system transfer function.
3.) What is characteristic formula ?
The denominator polynomial C(s)/R(s) is the characteristic formula of the system.
4.) How the roots of characteristic formula are related to stability ?
If the roots of characteristic formula has positive real part then the impulse response of the system is not bounded,Hence the system will be unstable .If the roots has negative real parts then the impulse response is bounded.Hence the system will be stable.
5.) What is the necessary condition for stability?
The necessary condition for stability is that all the coefficients of characteristic polynomial are positive.
6.) What is the relation ranging from stability and coefficient of characteristic polynomial?
If the coefficients of characteristic polynomial are negative or 0,then a few of roots lies on half of s-plane.Hence the system is unstable.If the coefficients of characteristic polynomial are positive and if no coefficient is 0 the there is a possibility of the system to be stable given all the roots lie on left half os s-plane.
7.) What will be the nature of impulse response when the roots of characteristic formula are lying on imaginary axis?
The nature of impulse is oscillatory.
8.) What will be the nature of impulse response if the roots of characteristic formula are lying on right half s-plane?
When roots are lying on real axis on the right half of s-plane.The response is exponentially increasing.When the roots are complex conjugate and lying on the right half of s-plane,the response is oscillatory with exponentially,increasing amplitude.
9.) What is principle of argument?
The principle of argument states that let F(s) be an analytic function and if an arbitary closed contour in the clockwise direction is chosen in the s-plane so that F(s) is analytic at every point on the contour.Then the corresponding F(s) plane contour mapped in
the F(s) plane will encircle the origin N times in the anticlockwise direction ,where N is the difference ranging from number of poles and zeros of F(s) that are encircled by the chosen closed contour in the s-plane.
10.) What is the necessary and sufficient condition for stability?
The necessary and sufficient condition is that all of the elements in the 1st column of the routh array should be positive.
11.) What is routh stability condition?

Earning:   Approval pending.