Transfer function of DC motor in discrete transfer function

Objective
To convert continuous transfer function to discrete transfer function.

Activity
Use the MATLAB applications to convert continuous transfer function to discrete transfer function.

Analysis
The program to convert continuous to discrete are as below:


The first step in designing the discrete control system is to convert the continuous transfer function to a discrete transfer function. The MATLAB command c2d will do this for you. The c2d command requires the following three arguments: system, the sampling time (Ts) and method for conversion. In this example, we will use the zero-order hold ('zoh') method.

From the design requirement, let the sampling time, Ts equal 0.12 seconds, which is 1/10 the time constant of a system with a settling time of 2 seconds. Let's create a new m-file and enter the following commands:

R = 1;
L = 0.5;
Kt = 0.01;
J = 0.01;
b = 0.1;

num = Kt;
den = [(J*L) (J*R)+(L*b) (R*b)+(Kt^2)];

motor = tf(num,den)

Ts = 0.12;
motor_d= c2d(motor,Ts,'zoh')

Running this m-file should return the following:

 
Transfer function:
0.009201 z + 0.005709
----------------------
z^2 - 1.088 z + 0.2369
 
Sampling time: 0.12