Abdul Radhi Azli bin Ali A137221 Assignment1 KZ4064

1. Find The Differential Equation of Flush System

Block Diagram of Simple Flush System

Rv = resistance of valve

Rp = resistance of pipe

C = area of tank/capacitance

Water Inlet (Valve)

Water Storage (Flush Tank)

Level Sensor (Float Ball)

- H (actual)

H (desired)

Rv R/1+RCs

1

- H (actual)

H (desired)

Radhi AliRectangle

Radhi AliPencil

Transfer Function representation

State Space representation

[X] = [1+

] [X] + [1] [Hdesired]

Output

[Y] = [

] [X]

For this example of flush control system, we used

Capacitance of tank (C) : 0.2 m2

Height of tank (H) : 0.4 m

Width of tank (W) : 0.5 m

Flow rate (Q) : 0.2 m3/s

Resistance of valve (Rv) : 5 s/m3

Resistance of pipe (Rp) : 0.2 s/m2

After we calculate all the value, then we got the transfer function as below:

RvRp

1++

H (desired) H (actual)

10

0.4+11

H (actual) H (desired)

2. Change from S plane to Z plane

Using sys_d = c2d (sys, Tz, zoh) command, the discrete transfer function obtained.

3. Find the input output data.

Using Simulink, create a model based on the plant that have been made, using discrete-time transfer

function.

Input Output

4. Checking the value of input/output data then transfer it into Excel Workbook.

Load the data into Matlab and remove it timestamp

Save input/output variables into Excel file.

Rearrange the input/output variable into table of y(k),y(k-1) and u(k-1).

5. Import back data into Matlab and find the value of a and b.

6. Find the difference equation of the plant and its transfer function using hand calculation.

y(k) = a1y(k-1) + b1u(k-1)

a1=0.06393 ; b1=0.8510

y(k) = 0.06393 y(k-1) + 0.851 u(k-1) difference equation

Y(z) = 0.06393z-1 Y(z) + 0.851z-1 U(z)

Y(z) - 0.06393z-1 Y(z) = 0.851z-1 U(z)

Y(z)/U(z) = 0.851z-1/(1-0.06393z-1)

Y(z)/U(z) = 0.851/(z-0.06393) transfer function