Rework the matlab script / add functions

matlab/src/createWeight.m

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+function [W] = createWeight(args)
+% createWeight -
+%
+% Syntax: [in_data] = createWeight(in_data)
+%
+% Inputs:
+%    - n  - Weight Order
+%    - G0 - Low frequency Gain
+%    - G1 - High frequency Gain
+%    - Gc - Gain of W at frequency w0
+%    - w0 - Frequency at which |W(j w0)| = Gc
+%
+% Outputs:
+%    - W - Generated Weight
+
+    arguments
+        args.n  (1,1) double {mustBeInteger, mustBePositive} = 1
+        args.G0 (1,1) double {mustBeNumeric, mustBePositive} = 0.1
+        args.G1 (1,1) double {mustBeNumeric, mustBePositive} = 10
+        args.Gc (1,1) double {mustBeNumeric, mustBePositive} = 1
+        args.w0 (1,1) double {mustBeNumeric, mustBePositive} = 1
+    end
+
+  mustBeBetween(args.G0, args.Gc, args.G1);
+
+  s = tf('s');
+
+  W = (((1/args.w0)*sqrt((1-(args.G0/args.Gc)^(2/args.n))/(1-(args.Gc/args.G1)^(2/args.n)))*s + (args.G0/args.Gc)^(1/args.n))/((1/args.G1)^(1/args.n)*(1/args.w0)*sqrt((1-(args.G0/args.Gc)^(2/args.n))/(1-(args.Gc/args.G1)^(2/args.n)))*s + (1/args.Gc)^(1/args.n)))^args.n;
+
+  end
+
+  % Custom validation function
+  function mustBeBetween(a,b,c)
+      if ~((a > b && b > c) || (c > b && b > a))
+          eid = 'createWeight:inputError';
+          msg = 'Gc should be between G0 and G1.';
+          throwAsCaller(MException(eid,msg))
+      end
+  end

matlab/src/plotMagUncertainty.m

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+function [p] = plotMagUncertainty(W, freqs, args)
+% plotMagUncertainty -
+%
+% Syntax: [p] = plotMagUncertainty(W, freqs, args)
+%
+% Inputs:
+%    - W     - Multiplicative Uncertainty Weight
+%    - freqs - Frequency Vector [Hz]
+%    - args  - Optional Arguments:
+%      - G
+%      - color_i
+%      - opacity
+%
+% Outputs:
+%    - p - Plot Handle
+
+arguments
+    W
+    freqs double {mustBeNumeric, mustBeNonnegative}
+    args.G = tf(1)
+    args.color_i (1,1) double {mustBeInteger, mustBePositive} = 1
+    args.opacity (1,1) double {mustBeNumeric, mustBePositive} = 0.3
+    args.DisplayName char = ''
+end
+
+% Get defaults colors
+colors = get(groot, 'defaultAxesColorOrder');
+
+p = patch([freqs flip(freqs)], ...
+          [abs(squeeze(freqresp(args.G, freqs, 'Hz'))).*(1 + abs(squeeze(freqresp(W, freqs, 'Hz')))); ...
+           flip(abs(squeeze(freqresp(args.G, freqs, 'Hz'))).*max(1 - abs(squeeze(freqresp(W, freqs, 'Hz'))), 1e-6))], 'w', ...
+          'DisplayName', args.DisplayName);
+
+p.FaceColor = colors(args.color_i, :);
+p.EdgeColor = 'none';
+p.FaceAlpha = args.opacity;
+
+end

matlab/src/plotPhaseUncertainty.m

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+function [p] = plotPhaseUncertainty(W, freqs, args)
+% plotPhaseUncertainty -
+%
+% Syntax: [p] = plotPhaseUncertainty(W, freqs, args)
+%
+% Inputs:
+%    - W     - Multiplicative Uncertainty Weight
+%    - freqs - Frequency Vector [Hz]
+%    - args  - Optional Arguments:
+%      - G
+%      - color_i
+%      - opacity
+%
+% Outputs:
+%    - p - Plot Handle
+
+arguments
+    W
+    freqs double {mustBeNumeric, mustBeNonnegative}
+    args.G = tf(1)
+    args.color_i (1,1) double {mustBeInteger, mustBePositive} = 1
+    args.opacity (1,1) double {mustBeNumeric, mustBePositive} = 0.3
+    args.DisplayName char = ''
+end
+
+% Get defaults colors
+colors = get(groot, 'defaultAxesColorOrder');
+
+% Compute Phase Uncertainty
+Dphi = 180/pi*asin(abs(squeeze(freqresp(W, freqs, 'Hz'))));
+Dphi(abs(squeeze(freqresp(W, freqs, 'Hz'))) > 1) = 360;
+
+% Compute Plant Phase
+G_ang = 180/pi*angle(squeeze(freqresp(args.G, freqs, 'Hz')));
+
+p = patch([freqs flip(freqs)], [G_ang+Dphi; flip(G_ang-Dphi)], 'w', ...
+          'DisplayName', args.DisplayName);
+
+p.FaceColor = colors(args.color_i, :);
+p.EdgeColor = 'none';
+p.FaceAlpha = args.opacity;
+
+end