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4. From the knowledge of the transfer function the poles and zeros of a system is found out. Both poles and zeros ofa system ploy a very important role in response of the system.5. From the characteristic equation, system stability can be inferred.Disadvantages1. Transfer function is valid only for Linear Time Invariant systems.2. It does not take Into account the initial conditions. Initial conditions looses it's significance.

3. It does not give any idea about how the present output is progressing. No idea about physical structure of thesystem Is immediately known.

[D]Poles and Zeros of Transfer FunctionPoles: The values of s' for which the transfer function magnitude I G (s) | becomes infinite after substitution in thedenominator of the system are called as poles of transfer function.

Zeros: The values of s' for which the transfer function magnitude I G (s) | becomes zero after substitution in thenumerator of the system are called as Zeros of transfer function.

[E]Characteristic Equation The equation obtained by equating the denominator polynomial of a transfer function to zero is called as thecharacteristic equation.

[F]Block Diagram Fundamentals1 Block Diagram : Block diagram is a pictorial representation of the cause and effect relationship between input and output of the

system.

2 Output :

Output = Gain * InputValue of input is multiplied to value of block gain to get the output.

3 Summing Point : More than one sigal can be added or subtracted at summing point.

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4 Take off Point :

The output signal can be applied to two or more input from a take off point.

5 Forward Path :The direction of flow of signal is from input to output.

6 Feedback Path : The direction of flow of signal is from output to input.

[G]Rules of Block Diagram Reduction:Rule No 1 : Blocks in series or cascade

Any finite number of blocks in series may be algebraically combined by multiplication.

Rule No 2 : Blocks in parallelThe blocks which are connected in parallel get added algebraically (considering the sign or polarity of thesignal )

Rule No 3 : Eliminate feedback loop

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Rule No 4 :Associative law for summoningThe order of summing point can be changed if two or more summing points are in series.

Rule No 5 : Shifting a summoning point before a block

Rule No 6 : Shifting a summoning point after a blockHere the aim is to shift summing point after G as shown by dotted lines.

Rule No 7 : Shifting a Take off point before a blockHere the aim is to shift the take off point before G as shown by dotted lines.

Rule No 8 : Shifting a Take off point after a block

Here the aim is to shift the take off point after G as shown by dotted lines.

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Rule No 9 :Shifting a Take off point after a summoning point

Rule No10 :Shifting a Take off point before a summoning point

[H]Advantages and Disadvantages of Block Diagram Reduction

Advantages:(1) The functional operation of the system observed from block diagram.(2) Block diagram gives the information about system(3) Block diagram is used to analysis and design of control system.(4) It is very simple to construct the block diagram for big and complicated system.Disadvantages :(1) Block diagram for given system are non unique.(2 )Source of energy flow in the system is not shown on the diagram.(3 )In block diagram, it is assumed that inside the block is affected by its inputs and not by other blocks. There is nointeraction between various blocks.(4) In procedure of reduction of block diagram algebra some important functions may be omitted or hidden. There isno check for it.