Systune reports uncertain system to control as improper, even though isProper returns true

I have an uncertain state-space model for which I want to tune a continuous PID controller.

The model, called my_uss_model, has order 21 and is strictly proper, with a transfer function with 1 zero and 5 poles.

The function

isProper(my_uss_model)

Unrecognized function or variable 'my_uss_model'.

confirms it by returning true.

Each uncertain root has an uncertainty percentage of 50%, and the nominal transfer function looks like the following:

7.1155e09 (s+10)

----------------------------------------------------

(s+2.907e04) (s+1917) (s+38.31) (s+10.24) (s-0.1253)

However, when I try to run the systune function with the goals and the system interconnection as defined below, I get an error:

Error using DynamicSystem/systune

Tuning of improper plants or controllers is not supported.

Error in script (line 41)

Gcl = systune(T, [Rstep Rtrack], [Rov Rmargin Rreject], tuneopts);

This is very unexpected, since all the properties of my system seem in order. Any ideas?

Here is the code I used, I'm attaching the model in a .mat with the script.

% define reqs
Ts = 1e-3;          % sec
responsetime = 1; % sec
dcerror = 0.1;      % perc
peakerror = 1.0;    % fract relative
peak = 0.07;        % abs deg
tSettle = 0.3;      % sec
maxOvershoot = 0;  % perc
phase_margin = 75;
gain_margin = 3;
Rtrack = TuningGoal.Tracking('r', 'y', responsetime, dcerror, peakerror);
Rreject = TuningGoal.StepRejection('u', 'y', peak, tSettle);
Rstep = TuningGoal.StepTracking('r', 'y', 0.3, maxOvershoot);
Rov = TuningGoal.Overshoot('r', 'y', maxOvershoot);
Rmargin = TuningGoal.Margins('y', gain_margin, phase_margin);

% define pid
C = tunablePID('C', 'PID');
C.Kp.Minimum = 0;    C.Kp.Maximum = inf;
C.Ki.Minimum = 0;    C.Ki.Maximum = inf;
C.Kd.Minimum = 0;    C.Kd.Maximum = inf;
C.Tf.Minimum = 10 * Ts;   C.Tf.Maximum = 100 * Ts;    % N = 1/Tf
C.TimeUnit = 'seconds';
C.InputName = 'e';
C.OutputName = 'u';

my_uss_model.InputName = 'u';
my_uss_model.OutputName = 'y';
sumblkstring = append('e = r - ', 'y');
Sum = sumblk(sumblkstring);
T = connect(my_uss_model, C, Sum,'r', 'y', {'u', 'y'});
tuneopts = systuneOptions('RandomStart', 10, 'UseParallel', false);
% Tune up
Gcl = systune(T, [Rstep Rtrack], [Rov Rmargin Rreject], tuneopts);

Answer 1

[Pascal Gahinet]

my_uss_model is the interconnection of an improper model with the uncertain blocks:

[H,B,S] = getLFTModel(my_uss_model)
isproper(H)
ans =
0

This is probably the result of using expressions like (s+u1)/(s+u2) too casually. Try specifying each factor in state space form or as shown below to avoid this.

a = ureal('a',1);
b = ureal('b',2);
fact = tf([1 a],[1 b])

[Mattia Fussi]

Thanks! I'll make sure to follow your guidelines for further development.