Merge pull request #2 from tamaskis/normalization

added normalization + better input checking, updated examples

Author: tamaskis

.gitignore

@@ -1,2 +1 @@
-.DS_Store
-local/
+.DS_Store

Continuous_to_Discrete_Transfer_Function_Transformation_Using_the_Euler_Methods.pdf

@@ -3,18 +3,23 @@
 Transforms a continuous transfer function to a discrete transfer function using the forward and backward Euler methods.
 
 
-
 ## Syntax
 
-`Hz = c2d_euler(Hs,T,'forward')` \
-`Hz = c2d_euler(Hs,T,'backward')`
+`Hz = c2d_euler(Hs,T,type)` \
+`Hz = c2d_euler(Hs,T,type,output,normalize)`
+
 
+## Inputs
 
-## Description
+- `Hs` (1×1 `'tf'` or `'zpk'`): continuous transfer function
+- `T` (1×1 double): sampling period
+- `type` (`char` array): `'forward'` or `'backward`
+- `output` (OPTIONAL) (`char` array): specifies output type (`'tf'` or `'zpk'`) (defaults to `'tf'`)
+- `normalize` (OPTIONAL) (1×1 `logical`) `true` if transfer function should be normalized, `false` otherwise (defaults to `false`)
 
-`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.
+## Outputs
 
-`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.
+- `Hz` (1×1 `tf` or `zpk`): discrete transfer function
 
 
 ## Examples and Additional Documentation

EXAMPLES.mlx

@@ -3,13 +3,13 @@
 % 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')
-%   Hz = c2d_euler(Hs,T,'backward')
+%   Hz = c2d_euler(Hs,T,type)
+%   Hz = c2d_euler(Hs,T,type,output,normalize)
 %
 % See also c2d.
 %
 % Copyright © 2021 Tamas Kis
-% Last Update: 2022-09-26
+% Last Update: 2023-09-17
 % Website: https://tamaskis.github.io
 % Contact: tamas.a.kis@outlook.com
 %
@@ -25,32 +25,42 @@
 % ------
 % INPUT:
 % ------
-%   Hs      - (1×1 tf or zpk) continous transfer function
-%   T       - (1×1 double) sampling period
-%   type    - (char) 'forward' or 'backward'
-%   output  - (OPTIONAL) (char) specifies output type ('tf' or 'zpk')
+%   Hs          - (1×1 tf or zpk) continous transfer function
+%   T           - (1×1 double) sampling period
+%   type        - (char array) 'forward' or 'backward'
+%   output      - (OPTIONAL) (char array) specifies output type ('tf' or 
+%                 'zpk') (defaults to 'tf')
+%   normalize   - (OPTIONAL) (1×1 logical) true if transfer function should
+%                 be normalized, false otherwise (defaults to false)
 %
 % -------
 % OUTPUT:
 % -------
 %   Hz      - (1×1 tf or zpk) discrete transfer function
 %
 %==========================================================================
-function Hz = c2d_euler(Hs,T,type,output)
+function Hz = c2d_euler(Hs,T,type,output,normalize)
 
     % defaults "output" to 'tf' if not input
     if (nargin < 4) || isempty(output)
         output = 'tf';
     end
 
+    % defaults "normalize" to false if not input
+    if (nargin < 5) || isempty(normalize)
+        normalize = false;
+    end
+    
     % symbolic variable for z;
     z = sym('z');
 
     % specified Euler approximation of s
     if strcmpi(type,'backward')
         s = (z-1)/(T*z);
-    else
+    elseif strcmpi(type,'forward')
         s = (z-1)/T;
+    else
+        error("'type' must be input as 'backward' or 'forward'")
     end
 
     % converts transfer function object to symbolic function object
@@ -66,6 +76,13 @@
     num = sym2poly(sym_num);
     den = sym2poly(sym_den);
 
+    % normalizes coefficients w.r.t. coefficient on largest power of z in
+    % denominator
+    if normalize
+        num = num/den(1);
+        den = den/den(1);
+    end
+    
     % creates discrete transfer function model
     Hz = tf(num,den,T);