Dr. Uri Mahlab

transmitter ReceiverChannel

Lets assume we would like to represent a channel by using SIMULINK.

Lets define a channel as a low-pass filter.

SIMULINK EXAMPLE

X(t) Y(t)R

C

Dr. Uri Mahlab

s

ss

TRC

T

zsT

zs

ZzX

zY

SRCsHzH

/1

11

)1(

1

)(

)(

1

1)()(

11

)(1

1))1((

1)(

)()1()( 1

nTxTnynTy

or

zXZzY

In the time domain we get :

Dr. Uri Mahlab

Simulation goals

source scopeH(z)In Out

1 - Drawing the icon picture

Definitions before we start to build the model:

X(t) Y(t)R

C

F cut-off = [Hz]

Dr. Uri Mahlab

3 -Look under mask

2 – User guide window

T-sampleRC

T-sample

In

R C

4 – S function

Dr. Uri Mahlab

METHOD

1

Dr. Uri Mahlab

Step – 1 -Setup the working environment

1) Define the relevant path2) Building the block model by:

File new model

Dr. Uri Mahlab

systemin out

S-function

Step – 2 -input ports

Build input ports

Dr. Uri Mahlab

Step - 3 - Operation with Mask editor called “Edit Mask ”

Icon on the BlockClick right mouthThis is the frame where you build the windows guide

ICON PARAMETERS Init.. Documentation

Mask typeMask description

Prompt Variable Type Tsample edit R edit C edit

Connecting the block constant to the real parameters

Dr. Uri Mahlab

01 11

00 10

Units “Normalized

R

C

0.2 0.5

0.850.800.75

fprintf(‘Fcutoff=%1.2f’,1/RC)%plot([x],[y])plot([0,0.2],[0.8,0.8])plot ([0.2, 0.2, 0.5, 0.5, 0.2],[0.75,0.85,0.85,0.75,0.75])Plot([0.5,1],[0.8,0.8])

Step – 3-1 – draw icon

Dr. Uri Mahlab

Step – 3-2 - Operation with Mask editor called “Edit Mask ”

Dr. Uri Mahlab

Dr. Uri Mahlab

Dr. Uri Mahlab

The model should look like :

Dr. Uri Mahlab

S – function contains the name of the program and users parameters

Step – 4 -Start with S - function

Choose the S-Function from the “User Define function” library

S-function name should be the same as the name of the file.m

Dr. Uri Mahlab

Function(sys, xo, str, ts)=s_function_name(t,x,u,flag,parameters)

s_function_name

Model_name <> S-Function name

returns inputs

Gets:t- running time x – state variableu- input signalflag – s_function status flag

Returnssys – model parament array x0 – initial state conditionsstr – state ordering stringts – sampling time

Step – 4-1: S-function

function [sys,x0,str,ts] = sfunc_DiffequLPF(t,x,u,flag,Tsample,R,C)

Dr. Uri Mahlab

The model should look like :

Double

click

Dr. Uri Mahlab

Step – 4:1 – Defining the S-function

a) Initialization – setup number of input and outputs

function [sys,x0,str,ts]=mdlInitializeSizes

% call simsizes for a sizes structure, fill it in and convert it to a% sizes array.% Note that in this example, the values are hard coded. This is not a% recommended practice as the characteristics of the block are typically% defined by the S-function parameters.

sizes = simsizes;

sizes.NumContStates = 0;sizes.NumDiscStates = 1; represent the Number of delay units in the iirsizes.NumOutputs = 1; dynamic size allocationsizes.NumInputs = -1; dynamic size allocationsizes.DirFeedthrough = 1; input dependencysizes.NumSampleTimes = 1; % at least one sample time is needed

sys = simsizes(sizes);

)())1(()( nTxTnynTy

Dr. Uri Mahlab

% initialize the initial conditions

x0 = []; x0 = [0]; Initial conditions

% str is always an empty matrix

str = [];

% initialize the array of sample times

ts = [0 0];

function sys=mdlDerivatives(t,x,u) Stay without changessys = [];

% end mdlDerivatives

Dr. Uri Mahlab

TS = An m-by-2 matrix containing the sample time

% (period, offset) information. Where m = number of sample times. The ordering of the sample times must be:

% TS = [0 0, : Continuous sample time.

% 0 1, : Continuous, but fixed in minor step sample time.

% PERIOD OFFSET, : Discrete sample time where PERIOD > 0 & OFFSET < PERIOD.

% -2 0]; : Variable step discrete sample time where FLAG=4 is used to get time of next hit.

% There can be more than one sample time providing they are ordered such that they are monotonically increasing. Only the needed sample times should be specified in TS. When specifying than one sample time, you must check for sample hits explicitly by eeing if

abs(round((T-OFFSET)/PERIOD) - (T-OFFSET)/PERIOD)

is within a specified tolerance, generally 1e-8. This tolerance is dependent upon your model's sampling times and simulation time.

You can also specify that the sample time of the S-function is inherited from the driving block. For functions which change during minor steps, this is done by specifying SYS(7) = 1 and TS = [-1 0]. For functions which

are held during minor steps, this is done by specifying SYS(7) = 1 and TS = [-1 1].

Dr. Uri Mahlab

function sys=mdlUpdate(t,x,u,Tsample,R,C)% This is where the discrete state is updated

% Yo(n+1) = Yo(n)*(1-a) + a*Yi(n).

% The state x corresponds to the state at the previous time step,

% which is Yo(n-1)

% uri

tau = R*C;

alpha = tau/Tsample;

sys = x*alpha/(1 + alpha) + u/(alpha+1);

% end mdlUpdate

=========================================

% mdlOutputs

% Return the block outputs.

function sys=mdlOutputs(t,x,u,Tsample)sys = x; % The x state now is Yo(n), which is the same as sys from

% the mdlUpdate function

% end mdlOutputs

)(1

1))1((

1)( nTxTnynTy

Dr. Uri Mahlab

METHOD 2

Dr. Uri Mahlab

Step – 1 -Setup the working environment

1) Define the relevant path2) Building the block model by:

File new model

Step – 2 -Start with the lowest hierarchy

1) Choose the “constant” block from the source simulink library as the number of the parameter needed to be installed

2) Select “input port” from the sources sub library3) Select “output port” from the sink sub library4) Drag each to the model frame work and you may get:

Dr. Uri Mahlab

1

1

1

system

in out

S-function

constant

S – function may contains the program to be executed

Untitled window

Dr. Uri Mahlab

Step – 3 - S Function

Choose the S-Function from the “User Define function” library

Step – 4 -Combining the MUX

1) Choose the “MUX” block from the signal routing library

2) Press double click3) Select 4 inputs4) The connections order should be according – - Input - should port one- Other - constants

Dr. Uri Mahlab

Step – 5 : connecting the following and getting the picture

Tsample

R

C

sfunc_DiffequLPF

In**

Out^^

S-function

Constant 1

Constant 2

Constant 3

In** Out^^

Create sub-system

Dr. Uri Mahlab

Step - 6 - Operation with Mask editor called “Edit Mask ”

Icon on the BlockClick right mouthThis is the frame where you build the windows guide

ICON PARAMETERS Init.. Documentation

Mask typeMask description

Prompt Variable Type Tsample edit R edit C edit

Connecting the block constant to the real parameters

Dr. Uri Mahlab

01 11

00 10

Units “Normalized

R

C

0.2 0.5

0.850.800.75

fprintf(‘Fcutoff=%1.2f’,1/RC)%plot([x],[y])plot([0,0.2],[0.8,0.8])plot ([0.2, 0.2, 0.5, 0.5, 0.2],[0.75,0.85,0.85,0.75,0.75])Plot([0.5,1],[0.8,0.8])

Step – 6-1 – draw icon

Dr. Uri Mahlab

Step - 6 - Operation with Mask editor called “Edit Mask ”

Dr. Uri Mahlab

Dr. Uri Mahlab

Dr. Uri Mahlab

The model should look like :

Dr. Uri Mahlab

Function(sys, xo, str, ts)=s_function_name(t,x,u,flag)

s_function_name

Model_name <> S-Function name

returns inputs

Gets:t- running time x – state variableu- input signalflag – s_function status flag

Returnssys – model parament array x0 – initial state conditionsstr – state ordering stringts – sampling time

Step - 7 – s-function

Dr. Uri Mahlab

Step – 7:1 – Defining the S-function

a) Initialization – setup number of input and outputs

function [sys,x0,str,ts]=mdlInitializeSizes

% call simsizes for a sizes structure, fill it in and convert it to a% sizes array.% Note that in this example, the values are hard coded. This is not a% recommended practice as the characteristics of the block are typically% defined by the S-function parameters.

sizes = simsizes;

sizes.NumContStates = 0;sizes.NumDiscStates = 1; represent the Number of delay units in the iirsizes.NumOutputs = 1; dynamic size allocationsizes.NumInputs = -1; dynamic size allocationsizes.DirFeedthrough = 1; input dependencysizes.NumSampleTimes = 1; % at least one sample time is needed

sys = simsizes(sizes);

)())1(()( nTxTnynTy

Dr. Uri Mahlab

% initialize the initial conditions

x0 = []; x0 = [0]; Initial conditions

% str is always an empty matrix

str = [];

% initialize the array of sample times

ts = [0 0];

function sys=mdlDerivatives(t,x,u) Stay without changessys = [];

% end mdlDerivatives

Dr. Uri Mahlab

function sys=mdlUpdate(t,x,u)% This is where the discrete state is updated

% Yo(n+1) = Yo(n)*(1-a) + a*Yi(n).

% The state x corresponds to the state at the previous time step,

% which is Yo(n-1)

% uri

Tsample = u(2); R = u(3); C = u(4);

tau = R*C;

alpha = tau/Tsample;

sys = x*alpha/(1 + alpha) + u(1)/(alpha+1);% end mdlUpdate

=========================================

% mdlOutputs

% Return the block outputs.

function sys=mdlOutputs(t,x,u)sys = x; % The x state now is Yo(n), which is the same as sys from

% the mdlUpdate function

% end mdlOutputs

)(1

1))1((

1)( nTxTnynTy