More Efficient Batch Linearization Varying Parameters

This example shows how to speed up the batch linearization of a model when a set of model parameters are varied.

The decrease the linearization time, you pass the varying parameter values to the linearize function. linearize avoids recompiling the model when the varied parameters are tunable parameters. The best improvements in the overall linearization time are for models with large model update times. To run this example, you need Aerospace Blockset™ software.

Plant Model

In this example, you linearize a lightweight airplane model. For more information on this model, see Lightweight Airplane Design (Aerospace Blockset).

Open the model.

mdl = 'scdskyhogg';
open_system(mdl)
io = getlinio(mdl);
op = operpoint(mdl);

Linearize Model By Calling linearize Multiple Times

For this example, you vary the gains of the altitude and pitch controllers by +/- 10%.

Initialize the gains of the controllers to vary with MATLAB® workspace variables k1 and k2.

open_system('scdskyhogg/Vehicle System Model/Avionics/Autopilot')
blks = {'scdskyhogg/Vehicle System Model/Avionics/Autopilot/Alt Controller';...
        'scdskyhogg/Vehicle System Model/Avionics/Autopilot/Theta Controller'};
set_param(blks{1},'Gain','0.0337283240400683*k1')
set_param(blks{2},'Gain','-261.8699347622*k2')

Vary the values of k1 and k2 and linearize the model 20 times.

t = cputime;
for ct = 20:-1:1
    k1 = 1+(ct-10)/100;
    k2 = 1+(ct-10)/100;
    sys_forloop(:,:,ct) = linearize(mdl,op,io);
end

View the total time to compute the 20 linearizations in seconds.

dt_for = cputime - t
dt_for =

   84.6300

A factor that impacts this time is the total time it takes to compile and evaluate block masks and resolve workspace parameters. To identify bottlenecks in your model compilation, use the MATLAB Profiler.

Linearize Model By Passing Parameter Values to linearize

To pass the parameter values to linearize, specify the parameter names and values using a structure.

ct = 1:20;
k1val = 1+(ct-10)/100;
k2val = 1+(ct-10)/100;

params(1).Name = 'k1';
params(1).Value = k1val;
params(2).Name = 'k2';
params(2).Value = k2val;

t = cputime;
sys_params = linearize(mdl,op,io,params);

View the total time to compute the 20 linearizations with one call to the linearize command. In this case, the model is compiled only once when varying the specified parameters.

dt_params = cputime - t
dt_params =

   20.8800

Compare Results

In this example, the varying parameters do not impact the operating point of the Simulink model. The linearizations using both approaches are equivalent.

bode(sys_forloop(:,:,1),sys_params(:,:,1))
legend('Linearization in FOR loop','Linearization using parameter structure')

Calculate the resulting time improvement ratio.

ratio = dt_for/dt_params
ratio =

    4.0532

Close the model.

bdclose(mdl)