Properties of signal flow graph
1. A branch indicates the functional dependence of one
signal upon another. A
signal passes through only in the direction specified by the
arrow of the branch .
2. A node adds the signals of all incoming branches and
The system is said to be relatively more
stable or unstable on the
basis of settling time. System is said to be
more stable if settling time for that system is
less than that of other system.
The settling time of the root or pair of
Every System, for small amount of time has to pass
through a transient period, whether
the system will reach its steady state after passing through
transients or not. The answer
to this question is whether the system is stable or unstab
If a control system is to be designed or analyzed using
we need a set of specification to describe the system
performance. The following
frequency-domain specifications are often used in practi
Routh Hurwitz Criterion
This represents a method of determining the location of
poles of a characteristics
equation with the respect to the left half & right half of the
s-plane without actually
solving the equation.
The T.F.of any linear closed loop syst
Application of Rouths of criterion :
Relative stability analysis :
If it is required to find relative stability of system about a
line s = - . i.e. how
many roots are located in right half of this line s = - , the
Rouths method can be
Types of feed back control system
The open loop T.F. of a unity feed back system can be
written in two std, forms;
1) Time constant form and 2) Pole Zero form,
G(S) = K(TaS +1) (TbS +1).
Sn(T1 S+1) (T2S + 1).
Where K = open loop gain.
Above Eq:- involves
Standard Test Input Signals
For the analysis point of view, the signals, which are most
commonly used as
reference inputs, are defined as standard test inputs.
The performance of a system can be evaluated with
respect to these test signals.
Based on the
Time response analysis of control
Time is used as an independent variable in most of the
control systems. It is
important to analyse the response given by the system for
the applied excitation, which is
function of time. Analysis of
Importance of auxillary equation :
Auxillary equation is always the part of original
characteristic equation. This means the
roots of the auxillary equation are some of the roots of
original characteristics equation.
Not only this but roots of auxillary e