Design Optimization to Meet Frequency-Domain Requirements (Code)

function Vals = sdoSimpleSuspension_Design(P,Simulator,Requirements,UncVars,UncVars_Values)
%SDOSIMPLESUSPENSION_DESIGN
%
%    The sdoSimpleSuspension_Design function is used to evaluate a simple
%    suspension system design.
%
%    The |P| input argument is the vector of suspension design parameters.
%
%    The |Simulator| input argument is a sdo.SimulinkTest object used to
%    simulate the |sdoSimpleSuspension| model and log simulation signals.
%
%    The |Requirements| input argument contains the design requirements
%    used to evaluate the suspension design.
%
%    The |UncVars| and |UncVars_Values| arguments specify the uncertain
%    variable and uncertain variable values.
%
%    The |Vals| return argument contains information about the design
%    evaluation that can be used by the |sdo.optimize| function to optimize
%    the design.
%
% See also sdoSimpleSuspension_cmddemo

% Copyright 2015 The MathWorks, Inc.

%% Evaluate the suspension reliability 
%
%Get the spring and damper design values
allVarNames = {P.Name}; 
idx         = strcmp(allVarNames,'k');
k           = P(idx).Value;
idx         = strcmp(allVarNames,'b');
b           = P(idx).Value;

%Get the nominal mass from the model workspace
wksp = get_param('sdoSimpleSuspension','ModelWorkspace');
m    = evalin(wksp,'m0');

%The expected failure rate is defined by the Weibull cumulative
%distribution function, 1-exp(-(x/l)^k), where k=3, l is a function of the
%mass, spring and damper values, and x the lifetime.
d        = b/2/sqrt(m*k);
pFailure = 1-exp(-(100e3*d/250e3)^3);

%% Nominal Evaluation
%
% Evaluate the model and requirements with uncertain parameters set to their
% nominal values.

% Simulate the model.
Simulator.Parameters = [P(:);UncVars(:)];
Simulator = sim(Simulator);

% Retrieve logged linearizations.
Sys = find(Simulator.LoggedData,'IOs');

% Evaluate the design requirements.
Cleq_Bandwidth = evalRequirement(Requirements.Bandwidth,Sys.values);
Cleq_DampingRatio = evalRequirement(Requirements.DampingRatio,Sys.values);

%% Uncertain Evaluation
%
% Evaluate the model and requirements for all combinations of uncertain
% parameter values.
for ct=1:size(UncVars_Values,1)
    UncVars(1).Value = UncVars_Values{ct,1};
    
    % Simulate the model.
    Simulator.Parameters = [P(:);UncVars(:)];
    Simulator = sim(Simulator);
    
    % Retrieve logged linearizations.
    Sys = find(Simulator.LoggedData,'IOs');
    
    % Evaluate the design requirements.
    Cleq_Bandwidth_UncVars = evalRequirement(Requirements.Bandwidth,Sys.values);
    Cleq_DampingRatio_UncVars = evalRequirement(Requirements.DampingRatio,Sys.values);
    
    Cleq_Bandwidth = [Cleq_Bandwidth; Cleq_Bandwidth_UncVars]; %#ok<AGROW>
    Cleq_DampingRatio = [Cleq_DampingRatio; Cleq_DampingRatio_UncVars]; %#ok<AGROW>
end

%% Return Values.
%
% Collect the evaluated design requirement values in a structure to
% return to the optimization solver.
Vals.F = pFailure;
Vals.Cleq = [...
    Cleq_Bandwidth(:); ...
    Cleq_DampingRatio(:)];
end

 Optimization started 2024-Sep-05, 19:04:52

                               max                     First-order 
 Iter F-count        f(x)   constraint    Step-size    optimality
    0      5    0.0619897       0.7642
    1     10     0.351266      -0.1277        0.461         1.22
    2     15     0.189345     -0.03881        0.188        0.312
    3     20    0.0829063      0.01312         0.51        0.425
    4     24    0.0365398            0        0.308         1.55
    5     28    0.0294977            0       0.0143        0.733
    6     32    0.0293065     1.57e-16     0.000417      0.00142
Local minimum found that satisfies the constraints.

Optimization completed because the objective function is non-decreasing in 
feasible directions, to within the value of the optimality tolerance,
and constraints are satisfied to within the  value of the constraint tolerance.