CCPUnit 2
- 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)