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Dr. Uri Mahlab transmitterReceiver Channel 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

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Dr. Uri Mahlab In the time domain we get :

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Dr. Uri Mahlab Simulation goals sourcescope H(z) InOut 1 - Drawing the icon picture Definitions before we start to build the model: X(t)Y(t) R C F cut-off = [Hz]

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Dr. Uri Mahlab 3 -Look under mask 2 – User guide window T-sample R C T-sample In R C 4 – S function

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Dr. Uri Mahlab METHOD 1

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Dr. Uri Mahlab Step – 1 -Setup the working environment 1) Define the relevant path 2) Building the block model by: File new model

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Dr. Uri Mahlab system in out S-function Step – 2 -input ports Build input ports

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Dr. Uri Mahlab Step - 3 - Operation with Mask editor called “Edit Mask ” Icon on the Block Click right mouth This is the frame where you build the windows guide ICONPARAMETERS Init..Documentation Mask type Mask description Prompt Variable Type Tsample edit R edit C edit Connecting the block constant to the real parameters

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Dr. Uri Mahlab 0111 00 10 Units “Normalized R C 0.2 0.5 0.85 0.80 0.75 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

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Dr. Uri Mahlab Step – 3-2 - Operation with Mask editor called “Edit Mask ”

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Dr. Uri Mahlab

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The model should look like :

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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

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Dr. Uri Mahlab Function(sys, xo, str, ts)=s_function_name(t,x,u,flag,parameters) s_function_name Model_name <> S-Function name returnsinputs Gets: t- running time x – state variable u- input signal flag – s_function status flag Returns sys – model parament array x0 – initial state conditions str – state ordering string ts – sampling time Step – 4-1: S-function function [sys,x0,str,ts] = sfunc_DiffequLPF(t,x,u,flag,Tsample,R,C)

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Dr. Uri Mahlab The model should look like : Double click

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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 iir sizes.NumOutputs = 1; dynamic size allocation sizes.NumInputs = -1; dynamic size allocation sizes.DirFeedthrough = 1; input dependency sizes.NumSampleTimes = 1; % at least one sample time is needed sys = simsizes(sizes);

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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 changes sys = []; % end mdlDerivatives

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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].

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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

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Dr. Uri Mahlab METHOD 2

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Dr. Uri Mahlab Step – 1 -Setup the working environment 1) Define the relevant path 2) 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 library 3)Select “output port” from the sink sub library 4)Drag each to the model frame work and you may get:

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Dr. Uri Mahlab 1 1 1 system inout S-function constant S – function may contains the program to be executed Untitled window

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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 click 3)Select 4 inputs 4)The connections order should be according – -Input - should port one -Other - constants

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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

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Dr. Uri Mahlab Step - 6 - Operation with Mask editor called “Edit Mask ” Icon on the Block Click right mouth This is the frame where you build the windows guide ICONPARAMETERS Init..Documentation Mask type Mask description Prompt Variable Type Tsample edit R edit C edit Connecting the block constant to the real parameters

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Dr. Uri Mahlab 0111 00 10 Units “Normalized R C 0.2 0.5 0.85 0.80 0.75 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

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Dr. Uri Mahlab Step - 6 - Operation with Mask editor called “Edit Mask ”

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Dr. Uri Mahlab

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The model should look like :

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Dr. Uri Mahlab Function(sys, xo, str, ts)=s_function_name(t,x,u,flag) s_function_name Model_name <> S-Function name returnsinputs Gets: t- running time x – state variable u- input signal flag – s_function status flag Returns sys – model parament array x0 – initial state conditions str – state ordering string ts – sampling time Step - 7 – s-function

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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 iir sizes.NumOutputs = 1; dynamic size allocation sizes.NumInputs = -1; dynamic size allocation sizes.DirFeedthrough = 1; input dependency sizes.NumSampleTimes = 1; % at least one sample time is needed sys = simsizes(sizes);

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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 changes sys = []; % end mdlDerivatives

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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

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