gridureal samples does not match the sampled system.

Hi all

the following code has a nominal and perturbed plant with 2 parametric uncertainties, when you type ''sysp'', you dont see ''JLp'' changing in matrix E, only ''kp'' is changing in matrix A, even though the ''samples'' have perturbed values for both. how can I make ''JLp'' change with ''kp''?

i.e , run the code and type sysp, and check matrix A and E, kp is changing [1080 , 1200, 1320] which is good, but JLp stays the same = 0.5.

it should change to be [0.45 0.5 0.55].

clc
clear
JM = 0.6; % Motor inertia
JL = 0.5; % Load inertia
k = 1200; % Torsional constant

kp = ureal('kp',k,'Percentage',[-10, 10]); % uncertain Torsional constant
JLp = ureal('JLp',JL,'Percentage',[-10, 10]);% uncertain Load inertia



% nominal system
A = [0 -k 0; 1 0 -1; 0 k 0];
E = diag([JM, 1, JL]); % Descriptor matrix
B = [1; 0; 0]; 
Bd = [0; 0; -1]; 
C = [1 0 0];
D = 0;
sys0 = dss(A, B, C, D, E); % Use dss for descriptor systems

% perturbed system
Ap = [0 -kp 0; 1 0 -1; 0 kp 0];
Ep = diag([JM, 1, JLp]); 
Bp = [1; 0; 0]; 
Bdp = [0; 0; -1]; 
Cp = [1 0 0];
Dp = 0;
sys =  dss(Ap, Bp, Cp, Dp, Ep); 

omega = logspace(1,2,5000);

m=3;
[sysp,samples]=gridureal(sys,m);

bodemag(sysp,'c--',omega)

legend('pertrubed')

Answer 1

[Paul]

Hi Mohammad,

I confess that I can't explain how dss is implementing this uncertain, descriptor system. I'm particularly curious as to why sys has four states. Nevertheless, it does appear that sysp does, in fact, capture the simultaneous variation in k and JL

JM = 0.6; % Motor inertia
JL = 0.5; % Load inertia
k = 1200; % Torsional constant
kp = ureal('kp',k,'Percentage',[-10, 10]); % uncertain Torsional constant
JLp = ureal('JLp',JL,'Percentage',[-10, 10]);% uncertain Load inertia
% nominal system
A = [0 -k 0; 1 0 -1; 0 k 0];
E = diag([JM, 1, JL]); % Descriptor matrix
B = [1; 0; 0]; 
%Bd = [0; 0; -1]; 
C = [1 0 0];
D = 0;
sys0 = dss(A, B, C, D, E); % Use dss for descriptor systems
% perturbed system
Ap = [0 -kp 0; 1 0 -1; 0 kp 0];
Ep = diag([JM, 1, JLp]);
Bp = [1; 0; 0]; 
%Bdp = [0; 0; -1]; 
Cp = [1 0 0];
Dp = 0;
sys =  dss(Ap, Bp, Cp, Dp, Ep)

Uncertain continuous-time state-space model with 1 outputs, 1 inputs, 4 states.
The model uncertainty consists of the following blocks:
  JLp: Uncertain real, nominal = 0.5, variability = [-10,10]%, 1 occurrences
  kp: Uncertain real, nominal = 1.2e+03, variability = [-10,10]%, 1 occurrences

Type "sys.NominalValue" to see the nominal value and "sys.Uncertainty" to interact with the uncertain elements.

omega = logspace(1,2,5000);
m=3;
[sysp,samples]=gridureal(sys,m);
samples.JLp

ans = 0.4500

ans = 0.5000

ans = 0.5500

samples.kp

ans = 1080

ans = 1200

ans = 1320

Here, I'll explicitly form the nominal and perturbed systems

pertvec = [0.9 1 1.1];
for ii = 1:3
    pert = pertvec(ii);
    temp{1,ii} = dss([0 -k*pert 0; 1 0 -1; 0 k*pert 0],B,C,D,diag([JM, 1, JL*pert]));
end

The Bode plots are identical

figure
bode(sysp,temp{:},omega)

figure
bode(sysp,temp{:},omega(omega>40))

[Mohammad]

Thanks