Using the command hinfsyn(), returns the error "Error using DynamicSystem/hinfsyn Plant P must have an explicit state-space realization".

Here is the code in which I am getting an error

clear all;

clc;

L=500e-6;

C=40e-6;

R=0.01;

Ts=50e-6;

w_lc = 1/(sqrt(L*C));

w_sys = 2*pi*60;

s = tf('s');

Z_inv = (R+ (L*s));

Y_inv = 1/Z_inv;

Z_cap = 1/C*s;

%controller

% define weights and model matching

%W_cmd_i = ss(w_sys^2/(s^2+w_sys^2)*(7.078e11)^-1*1/1.3 );

%for output current

W_cmd_i= ss(0,0,0,1);

W_perf= ss(makeweight(50,1.5*w_lc,0.5));

G11_ss=ss(0,0,0,1);%for E_ref

G13 = minreal((Z_cap*Y_inv)/(1+(Z_cap*Y_inv)));%for Vinv

G13_ss = ss(G13);

G12= -minreal((Z_cap)/(1+(Z_cap*Y_inv)));%for I_o

G12_ss= ss(G12);

%G_gen=[G11 G12];

%G_ss = ss(G_gen);

%%

%interconnection using connect

G13_ss.InputName ='V_inv';

G13_ss.OutputName ='E_ou';

G12_ss.InputName= 'I_o';

G12_ss.OutputName= 'E_od';

G11_ss.InputName='E_ref';

G11_ss.OutputName= 'E_or';

plant_out = sumblk('sys_out = E_or-E_od-E_ou');

W_cmd_i.InputName='E_ref';

W_cmd_i.OutputName='E_odes';

Z= sumblk('match_err= E_odes-sys_out ');

W_perf.InputName = 'match_err';

W_perf.OutputName='weight_match_err';

Plant_gen= connect(G11_ss,G12_ss,G13_ss,W_cmd_i,W_perf,plant_out,Z,{"E_ref","I_o","V_inv"},{"weight_match_err","sys_out"});

ny = 1;

nu= 1;

[K_ff,CLs,GAMs,INFOs] = hinfsyn(Plant_gen,ny,nu);%<- this is where the error occurs

Answer 1

[Paul]

Hi BIJIT,

Running the code ....

L=500e-6;
C=40e-6;
R=0.01;
Ts=50e-6;
w_lc = 1/(sqrt(L*C));
w_sys = 2*pi*60;
s = tf('s');
Z_inv = (R+ (L*s));
Y_inv = 1/Z_inv;
Z_cap = 1/C*s;
%controller 
% define weights and model matching
%W_cmd_i = ss(w_sys^2/(s^2+w_sys^2)*(7.078e11)^-1*1/1.3 );
%for output current
W_cmd_i= ss(0,0,0,1);
W_perf= ss(makeweight(50,1.5*w_lc,0.5));
G11_ss=ss(0,0,0,1);%for E_ref
G13 = minreal((Z_cap*Y_inv)/(1+(Z_cap*Y_inv)));%for Vinv
G13_ss = ss(G13);
G12= -minreal((Z_cap)/(1+(Z_cap*Y_inv)));%for I_o
G12_ss= ss(G12);
%G_gen=[G11 G12];
%G_ss = ss(G_gen);
%%
%interconnection using connect
G13_ss.InputName ='V_inv';
G13_ss.OutputName ='E_ou';
G12_ss.InputName= 'I_o';
G12_ss.OutputName= 'E_od';
G11_ss.InputName='E_ref';
G11_ss.OutputName= 'E_or';
plant_out = sumblk('sys_out = E_or-E_od-E_ou');
W_cmd_i.InputName='E_ref';
W_cmd_i.OutputName='E_odes';
Z= sumblk('match_err= E_odes-sys_out ');
W_perf.InputName = 'match_err';
W_perf.OutputName='weight_match_err';
Plant_gen= connect(G11_ss,G12_ss,G13_ss,W_cmd_i,W_perf,plant_out,Z,{"E_ref","I_o","V_inv"},{"weight_match_err","sys_out"});
ny = 1;
nu= 1;

Plant_gen is in descriptor form, as indicated by the non-zero E martrix.

Plant_gen.E

ans = 5×5

0 0.2500 0 0 0 0 0 1.0000 0 0 0 0 1.0000 0 0 0 0 0 1.0000 0 0 0 0 0 1.0000

It is in descriptor form because some of the transfer functions are improper, i.e., the numerator has higher order than the denominator.

tf(Plant_gen)

ans =
 
  From input "E_ref" to output...
   weight_match_err:  0
 
   sys_out:  1
 
  From input "I_o" to output...
                      -0.00025 s^3 - 4.599 s^2 - 91.87 s + 4.864e-21
   weight_match_err:  ----------------------------------------------
                                 s^2 + 183.7 s + 7.35e-05
 
             0.0005 s^2 + 0.01 s - 5.294e-25
   sys_out:  -------------------------------
                        s + 4e-07
 
  From input "V_inv" to output...
                      0.5 s^2 + 9187 s - 4.877e-19
   weight_match_err:  ----------------------------
                        s^2 + 183.7 s + 7.35e-05
 
                -s
   sys_out:  ---------
             s + 4e-07
 
Continuous-time transfer function.

[K_ff,CLs,GAMs,INFOs] = hinfsyn(Plant_gen,ny,nu);%<- this is where the error occurs

Error using DynamicSystem/hinfsyn
Plant P must have an explicit state-space realization.

Are those improper transfer functions expected? Next steps would depend on the answer to that question.

I didn't take the time to try to figure out what in the model is causing those improper transfer functions.

[BIJIT]

Hey, thanks for your response. I don't know why, the way I wrote G12 and G13, the resulting transfer function was becoming improper. I sorted it out by writing the transfer functions explicitly.