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Author: tamaskis

DOCUMENTATION.pdf

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+%% Copyright (c) 2021 Tamas Kis
+
+% Examples for using the c2d_euler function.
+
+
+
+%% SCRIPT SETUP
+
+% clears variables and command window, closes all figures
+clear;
+clc;
+close all;
+
+
+
+%% EXAMPLES
+
+% continuous transfer function
+s = tf('s');
+Hs = (s+1)/(0.1*s+1);
+
+% sampling period
+T = 0.25;
+
+% discrete transfer function obtained via Euler transformations
+Hz_forward = c2d_euler(Hs,T,'forward')
+Hz_backward = c2d_euler(Hs,T,'backward')

EXAMPLES.m

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+% c2d_euler  Transforms a continuous transfer function to a discrete 
+% transfer function using the forward and backward Euler methods.
+%
+%   Hz = c2d_euler(Hs,T,'forward') returns the discrete transfer function
+%   "Hz" obtained by applying the forward Euler (i.e. forward difference)
+%   transformation to a continuous transfer function "Hs", where "T" is the
+%   sampling period.
+%
+%   Hz = c2d_euler(Hs,T,'backward') returns the discrete transfer function
+%   "Hz" obtained by applying the backward Euler (i.e. backward difference)
+%   transformation to a continuous transfer function "Hs", where "T" is the
+%   sampling period.
+%
+% See also c2d
+%
+% MATLAB Central File Exchange: 
+% GitHub: https://github.com/tamaskis/c2d_euler-MATLAB
+%
+% See "DOCUMENTATION.pdf" for additional documentation and examples. 
+% Examples can also be found in EXAMPLES.m. Both of these files are 
+% included with the download.
+%
+% Copyright (c) 2021 Tamas Kis
+% Last Update: 2021-04-10
+
+
+
+%% FUNCTION
+
+% INPUT: Hs - continuous transfer function
+%        T - sampling period
+%        type - 'forward' or 'backward'
+% OUTPUT: Hz - discrete transfer function
+function Hz = c2d_euler(Hs,T,type)
+    
+    % symbolic variable for z;
+    z = sym('z');
+    
+    % specified Euler approximation of s
+    if strcmp(type,'backward')
+        s = (z-1)/(T*z);
+    else
+        s = (z-1)/T;
+    end
+    
+    % converts transfer function object to symbolic function object
+    [num,den] = tfdata(Hs);
+    Hz = poly2sym(cell2mat(num),z)/poly2sym(cell2mat(den),z);
+    
+    % performs Euler transformation
+    Hz = simplify(subs(Hz,s));
+    
+    % obtains numerator and denominator of symbolic expression in MATLAB's
+    % "polynomial form"
+    [sym_num,sym_den] = numden(Hz);
+    num = sym2poly(sym_num);
+    den = sym2poly(sym_den);
+
+    % creates discrete transfer function object
+    Hz = tf(num,den,T);
+    
+end