Routh-Hurwitz Stability Criterion

[BrianSoddingBoru4]

With the help from people from forum.hr, I have modified the code of my program like this:

Code:

Function obrni_polinom() Which Returns Nothing Is Declared;

Function f(Integer16 i, Integer16 j) Which Returns Integer16 Does
 // Za pretvaranje indeksa dvodimenzionalnog polja u indeks jednodimenzionalnog
 // polja. Kada u svoj AEC compiler još nisam implementirao dvodimenzionalna
 // polja...
 Return 20 * i + j;
EndFunction

Function popuni_matricu() Which Returns Integer16 Does
 Integer16 broj_stupaca :=
             (stupanj_polinoma + 1) / 2 + mod(stupanj_polinoma + 1, 2),
           broj_redaka := stupanj_polinoma + 1;
 Integer16 i := 0;
 //Popunimo matricu prvo not-a-numbersima...
 While i < broj_redaka Loop
   Integer16 j := 0;
   While j < broj_stupaca Loop
     matrica[f(i, j)] := 0. / 0.;
     j += 1;
   EndWhile
   i += 1;
 EndWhile
 //Zatim idemo primjeniti Hurwitzov algoritam...
 i := 0;
 While i < broj_redaka Loop
   Integer16 j := 0;
   While j < broj_stupaca Loop
     If i = 0 Then // Prvi redak
       matrica[f(i, j)] := polinom[j * 2];
     ElseIf i = 1 Then // Drugi redak
       matrica[f(i, j)] := (j * 2 + 1 < stupanj_polinoma + 1) ?
                           polinom[j * 2 + 1] :
                           0;
     Else // Ostali reci...
       If matrica[f(i - 1, 0)] = 0 Then // Posebni slučajevi, kada se u prvom
                                        // stupcu matrice pojavi nula.
         If jesmo_li_obrnuli_polinom Then // Obrtanje polinoma nije "upalilo".
           Return 0;
         Else // Možda obrtanje polinoma "upali"...
           obrni_polinom(); // https://www.forum.hr/showpost.php?p=97955497&postcount=16
           jesmo_li_obrnuli_polinom := 1;
           Return popuni_matricu();
         EndIf
       EndIf
       matrica[f(i, j)] := (matrica[f(i - 1, 0)] *
                           (j + 1 < broj_stupaca ?
                            matrica[f(i - 2, j + 1)] : 0) -
                           (matrica[f(i - 2, 0)] *
                           (j + 1 < broj_stupaca ?
                            matrica[f(i - 1, j + 1)] : 0))) /
                           matrica[f(i - 1 , 0)];
     EndIf
     j += 1;
   EndWhile
   i += 1;
 EndWhile
 If matrica[f(broj_redaka - 1, 0)] = polinom[stupanj_polinoma] Then
   Return 1;
 EndIf
 Return 0;
EndFunction

Function broj_korijena_u_desnoj_poluravnini() Which Returns Integer16 Does
 Integer16 i := 1, brojac := 0;
 While i < stupanj_polinoma + 1 Loop
   brojac += not(signum(matrica[f(i, 0)]) = signum(matrica[f(i - 1, 0)]));
   i += 1;
 EndWhile
 Return brojac;
EndFunction

Function obrni_polinom() Which Returns Nothing Does
 Decimal64 pomocni_polinom[20];
 Integer16 i := 0, j := stupanj_polinoma;
 While i < stupanj_polinoma + 1 Loop
   pomocni_polinom[i] := polinom[j];
   i += 1;
   j -= 1;
 EndWhile
 i := 0;
 While i < stupanj_polinoma + 1 Loop
   polinom[i] := pomocni_polinom[i];
   i += 1;
 EndWhile
EndFunction

It seems to work so far.

So, we can focus on my second question: How can I solve the preparation for the laboratory exercise that is asking to calculate the range (interval) of gain for which the system will be stable using both the Hurwitz'es Criterion and the Bode's Criterion? Neither the Hurwitz'es Criterion nor the Bode's Criterion give us ranges. Hurwitz'es Criterion gives us the number of poles on the right-hand-side of the imaginary axis, which is always zero for stable systems. Bode's Criterion gives us, for stable systems, the Amplitude Security and Phase Security. Can you somehow calculate the range of gain for which the system is stable using Amplitude Security and Phase Security? I don't know.

What’s this ‘we’ stuff? You have a mouse in your pocket or something?

Boru