The document discusses pulse transfer functions for sampled data systems. A pulse transfer function relates the z-transform of the pulsed output to the z-transform of the pulsed input. It is defined as the ratio of the z-transforms of the output and input with zero initial conditions. The pulse transfer function can be derived by first obtaining the continuous transfer function using conventional techniques, modeling the input as a zero-order hold, and then taking the inverse z-transform to obtain the transfer function in the z-domain. Examples are provided on deriving pulse transfer functions from given continuous transfer functions.

1. UNIT – II (SYSTEM MODELLING AND
IDENTIFICATION)
Lesson 01 – Pulse Transfer Function
COMPUTER CONTROL OF
PROCESS

2. Pulse Transfer Function
 In sampled data system we must relate the
pulsed output. The Z-Transform of pulsed input
can be related to the Z-transform of pulsed output
according to expression
G(z)=Y(z)/X(z) or H(z) = C(z)/R(z)
The term G(z) & H(z) is called Pulse Transfer
Function, also called Linear Discrete-Time
System (LDS).
we can define that, it is the transfer function of LDS
system as ratio of Z-transforms of output to input
to system with zero initial conditions.

3. Pulse transfer function relates z-transform of the
output at the sampling instants to the Ztransform of
the sampled input. When the same system is subject
to a sampled data or digital signal r ∗ (t), the
corresponding block diagram is given in Figure 1.
Sometimes it is also referred to as the starred
transfer function. If we now substitute z = e T s in the
previous expression we will directly get the z transfer
function

4. Procedure
 Step by step procedure for developing Pulse
Transfer Function:
1.Derive transfer function G(s) of system by
conventional techniques.
2.Take Zero order Hold system for pulse function
3. Find inverse Z transform for the given transform
4.Thus G(z) can be obtained from Y(z) and R(z) for
evaluating sum of series.

5. Example Problems
1. Find the pulse transfer function in Z-domain for a
system with transfer function in Laplace domain
given below (Assume Zero order hold)
Gp(s) = 2 / {(0.1s+1)(5s+1)(s+1)}
Solution:

8. 2. Find the pulse transfer function in Z-domain for a
system with transfer function in Laplace domain
given below (Assume Zero order hold)

12. Practice problem
1.