Added matlab code samples.

All of these code samples currently are mis-identified in my repositories. I'm
donating them to the cause.

samples/Matlab/bicycle_state_space.m

@@ -0,0 +1,168 @@
+function bicycle = bicycle_state_space(bicycle, speed, varargin)
+% function bicycle = bicycle_state_space(bicycle, speed, varargin)
+%
+% Returns the state space system of the Whipple model linearized about the
+% nominal configuration and the supplied speed.
+%
+% Parameters
+% ----------
+% bicycle : char
+%   The name of a bicycle in the parameters directory.
+% speed : double
+%   The forward speed at which to linearize the model about.
+% varargin : char/cell array pairs, optional
+%   Specify a subset of states, inputs or outputs by setting one of the
+%   following: `states`, `inputs`, `outputs` as a cell array of
+%   chars which include the subset variable names. Beaware that not all
+%   state, input and output combinations are necessarily possible.
+%   Valid state names: 'xP', 'yP', 'psi', 'phi', 'thetaB', 'thetaR', 'delta',
+%       'thetaF', 'phiDot', 'thetaRDot', 'deltaDot'
+%   Valid input names: 'tPhi', 'tDelta', 'fB'
+%   Valid output names: 'xP', 'yP', 'psi', 'phi', 'thetaB', 'thetaR', 'delta',
+%       'thetaF', 'xPDot', 'yPDot', 'psiDot', 'phiDot', 'thetaBDot',
+%       'thetaRDot', 'deltaDot', 'thetaFDot', 'xQ', 'yQ'
+%
+% Returns
+% -------
+% bicycle : ss
+%   The state space model of the bicycle.
+%
+% Notes
+% -----
+% The variable names are defined as in Meijaard2007.
+%
+% Examples
+% --------
+% bicycle = bicycle_state_space('Benchmark', 5.0, ...
+%   'states', {'phi', 'phiDot', 'delta', 'deltaDot'}, ...
+%   'inputs', {'tDelta'}, ...
+%   'outputs', {'delta', 'phi'})
+
+% get the directory which this m-file is in
+S = dbstack('-completenames');
+[CURRENT_DIRECTORY, ~, ~] = fileparts(S(1).file);
+
+% load the paramaters
+par = par_text_to_struct([CURRENT_DIRECTORY filesep 'parameters' ...
+    filesep bicycle 'Par.txt']);
+
+% generate the state space matrices
+[A, B, C, D] = whipple_pull_force_abcd(par, speed);
+
+% name the states, outputs and inputs
+states = {'xP',
+          'yP',
+          'psi',
+          'phi',
+          'thetaB',
+          'thetaR',
+          'delta',
+          'thetaF',
+          'phiDot',
+          'thetaRDot',
+          'deltaDot'};
+
+outputs = {'xP',
+           'yP',
+           'psi',
+           'phi',
+           'thetaB',
+           'thetaR',
+           'delta',
+           'thetaF',
+           'xPDot',
+           'yPDot',
+           'psiDot',
+           'phiDot',
+           'thetaBDot',
+           'thetaRDot',
+           'deltaDot',
+           'thetaFDot',
+           'xQ',
+           'yQ'};
+
+inputs = {'tPhi',
+          'tDelta',
+          'fB'};
+
+defaultSettings.states = states;
+defaultSettings.inputs = inputs;
+defaultSettings.outputs = outputs;
+% load in user supplied settings
+if size(varargin, 2) >= 1
+    userSettings = varargin_to_structure(varargin);
+else
+    userSettings = struct();
+end
+% combine the defaults with the user settings
+settings = overwrite_settings(defaultSettings, userSettings);
+
+% Will the system have the bare minimum states?
+minStates = {'phi', 'delta', 'phiDot', 'deltaDot'};
+if sum(ismember(settings.states, minStates)) < 4
+    error(['You have not specified the minimum set of states. Please ' ...
+        'include at least phi, delta, phiDot, and deltaDot'])
+end
+
+% Have state derivatives been specified that can't be computed with the
+% specified states?
+keepStates = find(ismember(states, settings.states));
+removeStates = find(~ismember(states, settings.states));
+for row = keepStates'
+    for col = removeStates'
+        if abs(A(row, col)) > 1e-10
+            s = sprintf(['It is not possible to compute the derivative ' ...
+                'of state %s because it depends on state %s'], ...
+                states{row}, states{col});
+            error(s)
+        end
+    end
+end
+
+removeInputs = find(~ismember(inputs, settings.inputs));
+
+% Have outputs been specified that can't be computed with the specified
+% states and inputs?
+keepOutputs = find(ismember(outputs, settings.outputs));
+for row = keepOutputs'
+    for col = removeStates'
+        if abs(C(row, col)) > 1e-10
+            s = sprintf(['It is not possible to keep output %s because ' ...
+                'it depends on state %s'], outputs{row}, ...
+                states{col});
+            error(s)
+        end
+    end
+    for col = removeInputs'
+        if abs(D(row, col)) > 1e-10
+            s = sprintf(['It is not possible to keep output %s because ' ...
+                'it depends on input %s'], outputs{row}, ...
+                inputs{col});
+            error(s)
+        end
+    end
+end
+
+removeOutputs = find(~ismember(outputs, settings.outputs));
+
+A(removeStates, :) = [];
+A(:, removeStates) = [];
+
+B(removeStates, :) = [];
+B(:, removeInputs) = [];
+
+C(removeOutputs, :) = [];
+C(:, removeStates) = [];
+
+D(removeOutputs, :) = [];
+D(:, removeInputs) = [];
+
+states(removeStates) = [];
+inputs(removeInputs) = [];
+outputs(removeOutputs) = [];
+
+% build the ss structure
+bicycle = ss(A, B, C, D, ...
+             'StateName', states, ...
+             'OutputName', outputs, ...
+             'InputName', inputs);