How to reduce order model within simulink (matlab fcn) block without using coder.extrinsic

Hi,

I am currently working on a control system for an over-actuated aircraft with adaptive on-board actuator dynamics model. This actuator dynamics model is used within the control allocation optimizer. To estimate the actuator dynamics online, I use a recursive least squares (RLS) algorithm with adaptive forgetting factor, based on the information that is available in the input signal (to omit persistence of excitation requirements).

My control allocation optimizer can only take first order actuator dynamics, because my control effectiveness continuity is limited and I want to omit the need for higher order output within the control scheme. The RLS estimator however, estimates the parameters of a second order actuator dynamics model. To use this information within my control allocator, I need to find the best fitting first order lag (gain+time constant) for the second order dynamics estimate (estimating the parameters of a first order lag directly won't work, as it gets really confused about overshoot and stuff).

Currently, my actuator dynamics parameter update model code looks like this, with pk the parameter estimates and Pk the covariance at timestep k. In the second for loop, I translate the parameter estimates of the second order difference equation into a discrete state space model, after which I try to reduce the model to a first order lag. For this I use Task-Based Model Order Reduction Workflow - MATLAB & Simulink - MathWorks Benelux. However, because this code is within my Simulink Matlab fcn block, I need to call coder.extrinsic, which makes my simulation rather slow.

Is there anybody who can help me to make the simulation go a bit faster again. Either by omitting the task-based model reduction for some other method, or any other way?

Regards,

Noah

function [Pk, pk] = fcn(P0,hk,sig,yk,lam_min,d_on,p0)

% Function to estimate the parameters a, b, c, d of

% d_k+1 = a*d_k + b*d_k-1 + c*u_k + d*u_k-1

% Define persistent variables

persistent p P

if isempty(p)

p=p0;

end

if isempty(P)

P=P0;

end

% dimensions hk [4x13], yk [13x4], pk [4x13], Pk [4x13x4]

for i = d_on' % for each actuator

Pi = squeeze(P(:,i,:)); % [4x4]

hi = hk(i,:)'; % [4x1]

yi = yk(i); % [1]

pi = p(:,i); % [4x1]

% Compute least squares gain L and adaptive forgetting factor lambda

err = yi-hi'*pi; % [1]

L = Pi*hi*inv(hi'*Pi*hi+1); % [4x1]

lam = 1-(1-hi'*L)*err^2/sig;

if lam < lam_min

lam = lam_min;

end

% Determine new parameter estimates for i-th actuator

p(:,i) = pi+L*err; % [4x1]

% Determine new covariance matrix for i-th actuator

P(:,i,:) = (eye(4)-L*hi')*Pi/lam; % [4x4]

end

% Put into control canonical state space form and reduce to first order lag

pk=zeros(2,13);

coder.extrinsic('ss', 'reducespec', 'getrom', 'ssdata', 'process')

for i = d_on'

% Extract parameter estimates

a = p(1,i);

b = p(2,i);

c = p(3,i);

d = p(4,i);

% Define state space model (control canonicle form)

PHI = [a, b; 1, 0];

GAM = [1; 0];

PSI = [c, d];

sys = ss(PHI,GAM,PSI,0,0.01);

% Simplify to first order actuator dynamics model estimates

R = reducespec(sys,"balanced");

R = process(R);

rsys = getrom(R,Order=1);

[p1,p2,p3,~] = ssdata(rsys);

pk(1,i) = p1;

pk(2,i) = p3*p2;

end

Pk = P;

Answer 1

[Ashutosh Thakur]

Hi Noah,

I understand that you are facing issues with simulation running very slow as compared to desired speed.

Kindly follow the following suggestions which may help you to improve the simulation performance:

• If the simulation does not rely on the real time data, a certain functions can be calculated offline and can use these precompiled imformation as a MATLAB function block in the model.This can reduce certain computation overhead during simulation.
• MATLAB profiliing tools can be used to identify the sections of code which is responsible for the computation costs and can be investigated to improve the performance.
• You can replace the usage of "code.extrinsic" by creating a S-Function block for the similar operation if possible as "coder.extrinsic" slows down the performance.
• Try to use Parallel Computing Toolbox which can execute the code as well as Simulation parallely to improve the performance.

Please follow the documentation links below which can be helpful in implementing above suggestions:

• https://in.mathworks.com/help/matlab/matlab_prog/profiling-for-improving-performance.html
• https://in.mathworks.com/help/control/ug/model-reduction.html
• https://in.mathworks.com/help/parallel-computing/
• https://in.mathworks.com/help/simulink/sfg/what-is-an-s-function.html

I hope above suggestions helps you in improving the performance of the simulation.