Undefined function 'dksyn' for input arguments of type 'ss'. Error in Report8 (line 41) [k, cl, bnd] = dksyn ( G, 1, 1)

R1=2;R2=1;L1=2;L2=1;
C1= ureal('C1',1,'percent',20)

Uncertain real parameter "C1" with nominal value 1 and variability [-20,20]%.

A=[-R1/L1 0 -1/L1 ; 0 -R2/L2 1/L2 ;1/C1 -1/C1 0]

Uncertain matrix with 3 rows and 3 columns.
The uncertainty consists of the following blocks:
  C1: Uncertain real, nominal = 1, variability = [-20,20]%, 1 occurrences

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

B=[1/L1;0;0]

B = 3×1

0.5000 0 0

C=[0 R2 0 ]

C = 1×3

0 1 0

D=[0]

D = 0

P=ss(A,B,C,D)

Uncertain continuous-time state-space model with 1 outputs, 1 inputs, 3 states.
The model uncertainty consists of the following blocks:
  C1: Uncertain real, nominal = 1, variability = [-20,20]%, 1 occurrences

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

s = tf('s');
Wt=(s)/((s)+2)

Wt =
 
    s
  -----
  s + 2
 
Continuous-time transfer function.

w1 = logspace(-10,3,100)

w1 = 1×100

1.0e+03 * 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

P_g = ufrd(P,w1)

Uncertain continuous-time FRD model with 1 outputs, 1 inputs, 100 frequency points.
  C1: Uncertain real, nominal = 1, variability = [-20,20]%, 1 occurrences

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

Dm_g = (P_g - P_g.nominal)/P_g.nominal;

%% Gain plot
MS=2 ; WS=0.38               

WS = 0.3800

Ws=(((s)/MS)+WS)/(s+(WS*.007))

Ws =
 
    s + 0.76
  -------------
  2 s + 0.00532
 
Continuous-time transfer function.

Weps = 5e-4;
figure(1);
w=logspace(-2,3,20);
bodemag(Ws,Wt,'--',w);grid on
legend('Ws','Wt');

figure(2);
w2=logspace(-10,3,100);
bodemag(Dm_g,'--',Wt,'r-',w2);grid on;
legend('\Deltam','Wt');

%% Building of generalized plant
Pn = P.nominal;
systemnames = 'Pn Ws Wt  ';
inputvar = '[w1; w2; u]';
outputvar = '[Ws; Wt; Pn]';
input_to_Pn = '[w1 - u]';
input_to_Ws = '[w1 - u]';
input_to_Wt = '[ u ]';
G = sysic;
whos G

  Name      Size            Bytes  Class    Attributes

  G         3x3              2190  ss                 

[k, cl, bnd] = dksyn ( G, 1, 1)

Incorrect number or types of inputs or outputs for function dksyn.

bnd

[Walter Roberson]

I note that dksyn expects a uss (uncertain space state), but you are passing it a ss (space state)

[shahin]

What would you suggest that I design a MU controller for this system?

Answer 1

[Paul]

According to the doc page dksyn, the first input to the dksyn has to be a uss model, not an ss model. Mabye G should be built using P, not P.Nominal? That's just a guess.

Also, I don't know what release your're using, but, as of 2021b. sysic and dksyn are both not recommended.

R1=2;R2=1;L1=2;L2=1;
C1= ureal('C1',1,'percent',20);
A=[-R1/L1 0 -1/L1 ; 0 -R2/L2 1/L2 ;1/C1 -1/C1 0];
B=[1/L1;0;0];
C=[0 R2 0 ];
D=[0];
D = 0;
P=ss(A,B,C,D);
s = tf('s');
Wt=(s)/((s)+2);
w1 = logspace(-10,3,100);
P_g = ufrd(P,w1);
Dm_g = (P_g - P_g.nominal)/P_g.nominal;
%% Gain plot
MS=2 ; WS=0.38;               
WS = 0.3800;
Ws=(((s)/MS)+WS)/(s+(WS*.007));
Weps = 5e-4;
figure(1);
w=logspace(-2,3,20);
bodemag(Ws,Wt,'--',w);grid on
legend('Ws','Wt');

figure(2);
w2=logspace(-10,3,100);
bodemag(Dm_g,'--',Wt,'r-',w2);grid on;
legend('\Deltam','Wt');

%% Building of generalized plant
Pn = P.nominal;
systemnames = 'Pn Ws Wt  ';
inputvar = '[w1; w2; u]';
outputvar = '[Ws; Wt; Pn]';
input_to_Pn = '[w1 - u]';
input_to_Ws = '[w1 - u]';
input_to_Wt = '[ u ]';
G = sysic;
whos G P Pn

  Name      Size            Bytes  Class    Attributes

  G         3x3              2190  ss                 
  P         1x1              1708  uss                
  Pn        1x1              1450  ss                 

[shahin]

What would you suggest that I design a MU controller for this system?

[Paul]

I don't understand this question. Perhaps the Robust Control Toolbox offers an example that you could work through for the recommended musyn command.

Answer 2

[Sam Chak]

Hi @shahin,

I'm unfamiliar with the MU controller. Perhaps you are referring to the μ synthesis technique used to determine the parameters in tunable components, such as PID controllers, state-space models, or even static gains that minimize a parameter called μ (mu) to ensure robust stability.

The code below uses a basic PID controller to improve tracking but does not minimize the μ parameter. If you have designed a robust controller according to μ synthesis, you can later compare its robust performance with the PID controller.

%% Parameters
R1  = 2;
R2  = 1;
L1  = 2;
L2  = 1;
C1  = ureal('C1', 1, 'percent', 20);    % uncertain parameter

%% Uncompensated system
A   = [-R1/L1 0 -1/L1; 0 -R2/L2 1/L2; 1/C1 -1/C1 0];
B   = [1/L1; 0; 0];
C   = [0 R2 0];
D   =  0*C*B;
sys = ss(A, B, C, D);   % Plant that contains parametric uncertainty
step(sys), grid on
title('Step Response of Uncompensated Plant')

%% PID controller (preliminary design)
kp  = 1;
ki  = 1.5;
kd  = 1;
Gc  = pid(kp, ki, kd)

Gc =
 
             1          
  Kp + Ki * --- + Kd * s
             s          

  with Kp = 1, Ki = 1.5, Kd = 1
 
Continuous-time PID controller in parallel form.

%% Uncertain closed-loop system
figure
subplot(211)
uGcl = feedback(Gc*sys, 1);
step(uGcl, 20), grid on
title('Step Plot: Reference tracking')

subplot(212)
uGcd = feedback(sys, Gc);
step(uGcd, 20), grid on
title('Step Plot: Disturbance Rejection')

%% Evaluate robust performance
figure
S   = feedback(1, Gc*sys);      % closed-loop sensitivity function
bodemag(S, S.NominalValue), grid on

opts = robOptions('Sensitivity', 'On');
[perfmarg, wcu, info] = robgain(S, 1.5, opts)

perfmarg = struct with fields:
           LowerBound: 1.8960
           UpperBound: 1.8999
    CriticalFrequency: 0.7618

wcu = struct with fields:
    C1: 1.3800

info = struct with fields:
                Model: 1
            Frequency: 0.7618
               Bounds: [1.8960 1.8999]
    WorstPerturbation: [1×1 struct]
          Sensitivity: [1×1 struct]

info.Sensitivity

ans = struct with fields:
    C1: 100

Smax = usubs(S, wcu);
getPeakGain(Smax, 1e-6)

ans = 1.5001

step(S.NominalValue, Smax), grid on
legend('Nominal', 'Peak Gain = 1.5')