Mult&T: [Gt]=mtf(op) - File Exchange

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Highlights from
Mult&T

creditos()
multitool(varargin) MULTITOOL MULTI Design Tool
questimp(varargin)
[A B C D T]=hoform(Gt,W) HOFORM Finds the Ho canonical form of a LTI MIMO SYS model.
[A B C D]=gauthierform(P,Q) GAUTHIERFORM Gauthier minimal algoritm of a MPF model.
[A B C D]=gilbertform(Gt) GILBERTFORM Finds the Gilbert form of a LTI MIMO SYS model.
[A B C D]=lcfform(Gt) LCFFORM Finds the minimal realization by method fraction left coprime.
[A B C D]=lmpf2ss(D1,N) LMPF2SS Finds the realization by method fraction coprime of a LTI
[A B C D]=minhoform(sys) MINHOFORM Finds the Minimal realization by method Ho.
[A B C D]=rcfform(Gt) RCFFORM Finds the minimal realization by method right fraction coprime.
[A B C D]=rmpf2ss(D1,N) RMPF2SS Find the realization by method fraction coprime of a MPF.
[A B C D]=silvermanform(Gt) SILVERMANFORM Finds the minimal realization by method Silverman.
[A B C D]=state(op) STATE state 45 examples in space-state.
[A B C D]=wolovichform(Gt) WOLOVICHFORM Realization by method Wolovich of a LTI MIMO SYS model.
[A B C P]=cx2rJ(A,B,C) CX2RJ Complex to real Jordan format.
[Aj,Bj,Cj,Dj]=exjordanform(Gt... EXJORDANFORM Finds the extended Jordan form of a LTI MIMO SYS model.
[Aj,Bj,Cj,Dj]=jordanform(Gt) JORDANFORM Finds the Jordan form of a LTI MIMO SYS model.
[D N]=mtf2lcf(G) MTF2LCF Matrix Transfer Function to Left Coprime Fraction.
[D N]=mtf2lmpf(Gt) MTF2LMPF Matrix Transfer Function to Left Matrix Fraction Description.
[D N]=mtf2rcf(G) MTF2RCF Matrix Transfer Function to Right Coprime Fraction.
[D N]=mtf2rmpf(Gt) MTF2RMPF Matrix Transfer Function to Right Matrix Polynomial Fraction.
[Dhc Dlc]=uplowM(D) UPLOWM Find the matrices with the hight and low coeficients.
[G]=ss2mtf(A,B,C,D) SS2MTF Convert state-space filter parameters to Matrix Transfer Function.
[Gsp Ginf]=mtfsp(G) MTFSP Strictly Proper Matrix Transfer Function.
[Gt]=lcf2mtf(D,N,Ginf) LCF2MTF Left Coprime Fraction to Matrix Transfer Function.
[Gt]=mtf(op)
[Gt]=rcf2mtf(D,N,Ginf) RCF2MTF Right Coprime Fraction to Matrix Transfer Function.
[M]=normcell(M,op) NORMCELL Normalize cell.
[P Q]=lmpf(op) LMPF 23 Examples in Left MPF Format cell.
[P Q]=ss2lmpf(sys) SS2LMPF State-space to Left Matrix Polynomial Fraction.
[P Q]=ss2rmpf(sys) SS2RMPF State-space to Right Matrix Polynomial Fraction.
[Pm Qm]=mpfred(P,Q) MPFRED Finds the minimal reduction of MPF.
[S dep lidep]=mSilvester(D,N,... MSILVESTER Find the Matrix Silvester.
[ar br cr dr]=minjordanform(s... MINJORDANFORM Finds the Minimal realization by method irreducible Jordan.
[i pnc]=islmpfc(P,Q) ISLMPFC Determine if the left MPF is controlable.
[i pnc]=isrmpfo(P,Q) ISRMPFO Determine if the Right MPF is observable.
[polo n ni]=polindex(Aj) POLINDEX Finds the index of Polynomial characteristic and the minimal.
[rp k]=mresidue(Gt) MRESIDUE Partial fraction expansion of Matrix Transfer Function.
[v Q Af Bf Cf]=canonform(A,B,... CANONFORM Find a observability and controlability canonical form.
[varargout]=cell2sym(varargin... CELL2SYM Cell format to sym format in operator differential.
[varargout]=cellround(varargi... CELLROUND Round to nearest integer in each cell.
[varargout]=sym2cell(varargin... SYM2CELL Sym matrix polynomial format to cell format.
creditos_1(action)
datagrid_cb(action)
i=iscolred(M) ISCOLRED Determine if the MPF is column reduced.
i=isrowred(M) ISROWRED Determine is the MPF is row reduced.
k=coXm(A,B,C) COXM Check the observability and controlability for mode.
mytimer(obj, event, op)
n=mindeg(sys) MINDEG Degree minimal of LTI MIMO SYS model.
polezero(sys) POLEZERO Pole and zeros of LTI MIMO SYS model.
rga(a,b,c,d,w)
smform(a,b,c,d) SMFORM Finds the Smith-McMillan form of a LTI MIMO SYS model**.
ss2sym(a,b,c,d) SS2SYM State Space to Symbolic Transfer Function conversion**.
sym2tf(g) SYM2TF Symbolic Transfer Function to Numerical Transfer Function**.
tf2sym(G) TF2SYM Numerical Transfer Function to Symbolic Transfer Function**.
v=findv(M,op) FINDV Find the blocks in matrix Jordan or the indices of MPF.
Contents.m
report.html
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from Mult&T by Franklin Pineda
Find realizations of multivariable systems. Created for Msc. students at the UANDES and UAC.

[Gt]=mtf(op)

function [Gt]=mtf(op)
%MTF 71 MTF Examples. 
switch op
    case 1
        G1=tf([1 2],[1 2 1]);G2=tf(1,[1 1]);G3=tf(-1,[1 1]);G4=1;Gt=[G1 G2;G3 G4];
    case 2
        G1=tf(1,[1 1]);G2=tf(1,[1 3]);G3=tf(1,[1 4]);G4=tf(1,[1 2]);Gt=[G1 G2;G3 G4];
    case 3
        G1=tf(1,[1 1]);G2=tf(1,[1 3 2]);G3=tf([1 0],[1 1]);G4=0;G5=tf(1,[1 4 3]);G6=tf([1 1],[1 3]);Gt=[G1 G2 G3;G4 G5 G6];
    case 4
        G1=tf([1 0 1],[1 0 0 0]);G2=2;G3=tf([2 1],[1 0 0]);G4=tf([1 3],[1 0 0]);G5=0;G6=tf(2,[1 0]);Gt=[G1 G2 G3;G4 G5 G6];
    case 5
        G1=tf([1 2],[1 2 1]);G2=tf(1,[1 1]);G3=tf([1 0 1],[1 0 0 0]);G4=tf([1 3],[1 0 0]);G5=tf(2,[1 0]);G6=0;Gt=[G1 G2 G3;G4 G5 G6];
    case 6
        G1=tf([1 1 2],[1 1 0]);G2=tf([1 -1],[1 1 0]);G3=tf([1 2],[1 1 0]);G4=tf([1 0],[1 1 0]);G5=tf([1 0 -1],[1 1 0]);G6=0;Gt=[G1 G2;G3 G4;G5 G6];
    case 7
        G1=tf([1 1 2],[1 1 0 0]);G2=tf([1 -1],[1 1 0 0]);G3=tf([1 2],[1 1 0 0]);G4=tf([1 0],[1 1 0 0]);G5=tf([1 0 -1],[1 1 0 0]);G6=0;Gt=[G1 G2;G3 G4;G5 G6];
    case 8
        G1=tf(2,[1 3 2]);G2=tf(0.1,[1 1]);G3=tf(0.1,[1 2 1]);G4=tf(6,[1 5 6]);Gt=[G1 G2;G3 G4];
    case 9
        denp=[1 6 13 12 4];G1=tf([1 0],denp);G2=tf([1 2 1 0],denp);G3=tf(-[1 2 1 0],denp);G4=tf(-[1 2 1 0],denp);Gt=[G1 G2;G3 G4];
    case 10
        G1 = tf([1 -1],[1 1]);G2 = tf([1 2],[1 4 4]);Gt=[G1;G2];
    case 11
        G1 = tf([1 1],[1 0 0]);G2 = tf(1,[1 0]);G3=tf(2,[1 0]);G4=tf(1,[1 0]);Gt=[G1 G2;G3 G4];
    case 12
        G1 = tf([1 0],[1 -2 1]);G2 = tf(1,[1 -1]);G3=tf(-6,[1 2 -3]);G4=tf(1,[1 3]);Gt=[G1 G2;G3 G4];
    case 13
        G1 = tf([1 0],[1 2 1]);G2 = tf(1,[1 -1]);G3=tf(-6,[1 2 -3]);G4=tf(1,[1 3]);Gt=[G1 G2;G3 G4];
    case 14
        Gt = [tf(10,[1 2 -3]) , tf(1,[1 1])];
    case 15
        G1=tf([1 2],[1 1]);G2=tf(1,[1 3]);G3=tf([1 0],[1 1]);G4=tf(1,[1 2]);Gt=[G1 G2;G3 G4];
    case 16
        denp=1.25*conv([1 1],[1 2]);G1=tf([1 -1],denp);G2=tf([1 0],denp);G3=tf(-6,denp);G4=tf([1 -2],denp);Gt=[G1 G2;G3 G4];
    case 17
        G1=tf(1,[1 1]);G2=tf(1,[1 2]);G3=tf([1 5],[1 2 1]);G4=tf(1,[1 3]);Gt=[G1 G2;G3 G4];
    case 18
        G1=tf(0.071,[1 0.19]);G2=tf(0.007,[1 0.46 0.0529]);G3=tf(0.24,[1 0.46 0.0529]);G4=tf(0.027,[1 0.6 0.09]);Gt=[G1 G2;G3 G4];
    case 19
        G1=tf([-1 0],[1 1]);G2=tf(1,[1 1]);G3=tf([2 1],[1 1 0]);G4=tf(1,[1 1]);Gt=[G1 G2;G3 G4];
    case 20
        G1=tf([1 1],[1 3]);G2=0;G3=0;G4=tf([1 2],[1 4]);G5=tf([1 2],[1 5]);G6=tf([1 1],[1 5]);Gt=[G1 G2;G3 G4;G5 G6];
    case 21
        denp=[1 4 5];G1=tf(2,denp);G2=tf([1 2 1],denp);G3=tf([1 2 1],denp);G4=tf(-2,denp);Gt=[G1 G2;G3 G4];
    case 22
        denp=[1 0.9 -2.2];G1=tf([1 -1],denp);G2=tf(1,denp);G3=0;G4=tf([10 -10],denp);Gt=[G1 G2;G3 G4];
    case 23
        denp=[1 2 1];G1=tf([1 1],denp);G2=tf([1 3],denp);G3=tf([1 6],denp);G4=tf(1,denp);G5=tf(2,denp);G6=tf(3,denp);Gt=[G1 G2 G3;G4 G5 G6];
    case 24
        denp=[1 2 1];G1=tf([1 1],denp);G2=tf([1 3],denp);G3=tf(1,denp);G4=tf(2,denp);Gt=[G1 G2;G3 G4];
    case 25
        G1=tf(1,[1 1]);G2=tf(2,[1 1]);G3=tf(2,[1 2]);G4=tf(4,[1 2]);Gt=[G1 G2;G3 G4];
    case 26
        denp=[0.2 1.2 1];G1=tf(1,denp);G2=tf(1,denp);G3=tf([2 1],denp);G4=tf(2,denp);Gt=[G1 G2;G3 G4];
    case 27
        G1=tf([11 -18 -70 -50],[1 6 -45 -50 0]);G2=tf([1 2],[1 -4 -5]);G3=tf([5 10],[1 -4 -5]);G4=tf([5 10],[1 -4 -5]);Gt=[G1 G2;G3 G4];
    case 28
        G1=tf([1 -1],[1 1]);G2=tf([1 -2],[1 2]);Gt=[G1 G2];
    case 29
        %G1=tf([4 -10],[2 1]);G2=tf([3],[1 2]);G3=tf([1],[2 5 2]);G4=tf([1 1],[1 4 4]);Gt=[G1 G2;G3 G4];
        G1=tf([2 -5],[1 1/2]);G2=tf(3,[1 2]);G3=tf(1/2,[1 2.5 1]);G4=tf([1 1],[1 4 4]);Gt=[G1 G2;G3 G4];
    case 30
        denp=[1 2 -1 -2];G1=tf([1 1 -2],denp);G2=0;G3=tf([1 -2 1],denp);G4=tf(-[1 3 2],denp);G5=tf([1 0 -1],denp);G6=tf([1 0 -1],denp);Gt=[G1 G2 G3;G4 G5 G6];
    case 31
        G1=tf([1 0],[1 1]);G2=tf(1,[1 3 2]);G3=tf(1,[1 3]);G4=tf(-1,[1 1]);G5=tf(1,[1 3 2]);G6=tf(1,[1 0]);Gt=[G1 G2 G3;G4 G5 G6];
    case 32
        G1=tf(2,[1 1]);G2=tf([2 -3],[1 3 2]);G3=tf([1 -2],[1 1]);G4=tf([1 0],[1 2]);Gt=[G1 G2;G3 G4];
    case 33
        G1=tf([-12 -6],[3 24]);G2=tf([12 23],[3 24]);Gt=[G1 G2];
    case 34
        Gt = [tf(10,[1 2 10]) , tf(1,[1 1])];
    case 35
        G1=tf([1 0],[1 1]);G2=tf([1 -1],[1 0]);G3=0;G4=tf(1,[1 0]);
        Gt=[G1 G2; G3 G4];
    case 36
        G1=tf([1 1],[1 1 1]);G2=tf([1 2],[1 2 0 1]);Gt=[G1 G2];
    case 37
        G1=tf(2,[1 3]);G2=0;G3=0;G4=tf(2,[1 4]);G5=tf(3,[1 5]);G6=tf(4,[1 5]);Gt=[G1 G2;G3 G4;G5 G6];
    case 38
        G1=tf([1 0 1],[1 0 0 0]);G2=tf([2 1],[1 0 0]);G3=tf([1 2],[1 0 0]);G4=tf(2,[1 0]);Gt=[G1 G2;G3 G4];
    case 39
        G1=tf(1,[1 2 1]);G2=tf([1 3],[1 2]);G3=tf(1,[1 5]);G4=tf(1,[1 2 1]);G5=tf([1 1],[1 4]);G6=tf(1,[1 0]);Gt=[G1 G2 G3;G4 G5 G6];
    case 40
        G1=tf([1 2],[1 1]);G2=tf(1,[1 3]);G3=tf([1 0],[1 1]);G4=tf([1 1],[1 2]);Gt=[G1 G2;G3 G4];
    case 41
        G1=tf(1,[1 2 1]);G2=tf(1,[1 3 2]);G3=tf(1,[1 2]);G4=tf(1,[1 3 2]);Gt=[G1 G2;G3 G4];
    case 42
        G1=tf(1,[1 0]);G2=tf([1 3],[1 1]);G3=tf(1,[1 3]);G4=tf([1 0],[1 1]);Gt=[G1 G2;G3 G4];
    case 43
        G1=tf([1 0 1],[1 0 0 0]);G2=tf([2 1],[1 0 0]);G3=tf([1 3],[1 0 0]);G4=tf(2,[1 0]);Gt=[G1 G2;G3 G4];
    case 44
        den=conv([1 1],[1 2]);
        G1=tf([-47 2],den);G2=tf([56 0],den);G3=tf([-42 0],den);G4=tf([50 2],den);Gt=[G1 G2;G3 G4];
    case 45
        G1=tf(1,[1 1]);G2=tf(1,[1 2]);G3=0;G4=tf([1 1],[1 2]);Gt=[G1 G2;G3 G4];
    case 46
        G1=tf(1,[1 3]);G2=tf(1,[1 4]);G4=0;G3=tf(1,[1 1]);Gt=[G1 G2;G3 G4];
    case 47
        G1=tf([1 -1],[1 1]);G2=tf([1 0 0],[1 0 0 1]);G3=tf([1 -1],[1 0 1]);G4=tf(1,[1 0]);Gt=[G1 G2;G3 G4];
    case 48
        G1=tf(1,[1 1]);G2=tf([1 0 0],[1 0 0 1]);G3=tf([1 -1],[1 0 1]);G4=tf(1,[1 0]);Gt=[G1 G2;G3 G4];
    case 49
        G1=tf(1,[1 1]);G2=tf([1 3],[1 3 2]);G3=tf(1,[1 1]);G4=tf([1 2],[1 4 3]);Gt=[G1 G2;G3 G4];
    case 50
        G1=tf(1,[1 2]);G2=tf([1 1],[1 2]);Gt=[G1;G2];
    case 51
        G1=tf([1 2],[1 1 1]);G2=tf(1,[1 1 2]);G3=tf(1,[1 2 1]);G4=tf(3,[1 1 4]);Gt=[G1 G2;G3 G4];
    case 52
        den=[1 4 3];
        G1=tf([2 4],den);G2=tf(-2,den);G3=tf([-3 -1],den);G4=tf([-5 -7],den);Gt=[G1 G2;G3 G4];
    case 53
        G1=tf(4,[1 3 2]);G2=tf(-1,[1 1]);G3=tf(2,[1 1]);G4=tf(-0.5,[1 3 2]);Gt=[G1 G2;G3 G4];
    case 54
        den=[1 5 8 4];
        G1=tf(1,den);G2=tf([1 2],den);G3=tf([1 1],den);G4=tf(0.25*[1 2 1],den);G5=tf([-1 2],den);G6=tf(0.25*[1 3 2],den);
        G7=tf(-0.5*[1 4 4],den);G8=0;G9=tf([4 4],den);Gt=[G1 G2 G3;G4 G5 G6;G7 G8 G9];
    case 55
        G1=tf(-2,[1 -1]);G2=tf([1 3],[1 3 2]);G3=tf([1 3],[1 5 8 4]);G4=tf(2,[1 2]);Gt=[G1 G2;G3 G4];
    case 56
        G1=tf([-2 1],[1 2 1]);G2=tf(2,[1 6 8]);G3=tf([1 3],[1 6 8]);G4=tf(2,[1 4]);Gt=[G1 G2;G3 G4];
    case 57
        G1=tf([1 2 3],[1 2 1]);G2=tf([1 6 3],[1 2 1]);G3=tf(1,[1 1]);G4=tf(-1,[1 1]);G5=tf([-1 2],[1 2 1]);G6=tf([7 4],[1 2 1]);Gt=[G1 G2;G3 G4;G5 G6];
    case 58
        G1=tf(1,[1 1]);G2=tf(2,[1 3 2]);G3=tf(1,[1 3 2]);G4=tf(1,[1 3]);Gt=[G1 G2;G3 G4];
    case 59
        G1=tf(1,[1 11  42  68  40]);G2=tf(1,[1 5]);G3=tf(1,[1 2]);G4=0;Gt=[G1 G2;G3 G4];
    case 60
        den=[1 0 0 0 0];
        G1=tf([1 -1 0 1],den);G2=tf(1,den);G3=tf([-1 1 0 -2],den);G4=tf([1.5 1],den);G5=tf([1 1],den);
        G6=tf([-1.5 -2],den);G7=tf([1 -9 -1 1],den);G8=tf([-1 0 1],den);G9=tf([1 0 -1 -2],den);
        Gt=[G1 G2 G3;G4 G5 G6;G7 G8 G9];
    case 61
        G1=tf([-1 0],[1 2 1]);G2=tf(1,[1 1]);G3=tf([2 1],[1 1 0]);G4=tf(1,[1 1]);Gt=[G1 G2;G3 G4];
    case 62
        den=[1 -1];
        G1=tf(1,den);G2=tf(-1,conv([1 0],den));G3=tf(-1,den);G4=tf(1,den);Gt=[G1 G2;G3 G4];
    case 63
        G1=tf([1 0],[1 2 1]);G3=tf([1 0],[1 2 1]);G2=tf([-1 0],[1 5 8 4]);G4=tf([1 2 0 -1 0],[1 7 19 25 16 4]); Gt=[G1 G2;G3 G4];
    case 64
        den=[2 4];
        G1=tf([5 4],den);G2=tf([1 4],den);G3=tf([-1 -4],den);G4=tf([1 0],den);Gt=[G1 G2;G3 G4];
    case 65
        den=[1 3 2];
        G1=tf([2 3],den);G2=tf([6 25 23],[1 6 11 6]);G3=tf(1,[1 1]);G4=tf([3 5],den);Gt=[G1 G2;G3 G4];
    case 66
        G1=tf([1 2],[1 2 1]);G2=tf(1,[1 1.01]);G3=tf(-1,[1 1]);G4=1;Gt=[G1 G2;G3 G4];
    case 67
        den=conv(conv(conv([1 1],[1 1]),[1 1]),[1 2]);
        G1=tf(conv(conv(conv([1 2],[1 2]),[1 2]),[1 1]),den);
        G2=tf(conv(conv(conv([1 1],[1 1]),[1 2]),[2 3]),den);
        G3=tf(conv(conv([1 2],[1 2]),[1 2]),den);
        G4=tf(conv(conv([1 1],[1 2]),[2 5 4]),den);
        G5=tf(conv(conv(conv([1 1],[1 1]),[1 2]),[1 2]),den);
        G6=tf(conv(conv([1 2],[1 2]),[1 2 2]),den);
        G7=tf(conv(conv(conv([1 1],[1 1]),[1 2]),[1 2]),den);
        G8=tf(conv(conv(conv([1 1],[1 1]),[1 1]),[1 2]),den);
        G9=tf(conv(conv([1 1],[1 2]),[2 3]),den);
        G10=tf(conv(conv(conv([1 1],[1 1]),[1 2]),[1 2]),den);
        G11=tf(conv(conv([1 1],[1 1]),[1 1]),den);
        G12=tf(conv([1 1],[2 6 5]),den);
        Gt=[G1 G2 G3;G4 G5 G6;G7 G8 G9;G10 G11 G12];
    case 68
        G1=tf(1,conv([1 1],[1 2]));G2=tf([2 1],conv([1 1],[1 2]));G3=tf([1 0],conv([1 1],[1 2]));
        G4=tf(1,conv([1 2],[1 2]));G5=tf([1 5 3],conv([1 1],[1 1]));G6=tf([1 0],conv([1 1],[1 1]));
        G7=tf(1,conv(conv([1 1],[1 1]),[1 2]));G8=tf([2 1],conv(conv([1 1],[1 1]),[1 2]));
        G9=tf([1 0],conv(conv([1 1],[1 1]),[1 2]));
        Gt=[G1 G2 G3;G4 G5 G6;G7 G8 G9];
    case 69
        den=[1 -1 -2 -4 3];
        G1=tf([1 -1 -3 2 0],den);G2=tf([-2 1 5 -3],den);G3=tf([-1 -1 1],den);G4=tf([-2 -1 -2 2],den);
        Gt=[G1 G2;G3 G4];
    case 70
        G1=tf([-0.1 0.1],[1 6/5 1/5]);G2=tf([0.1 -0.05],[1 2.1 0.2]);G3=tf(-0.005,[1 0.1]);
        G4=tf([-1/3 1/9],[1 2/3 1/9]);G5=tf([2/5 -1/5],[1 0.7 0.1]);G6=tf(-0.0014,[1 1/7]);
        G7=tf([15/4 -3/4],[1 13/40 1/40]);G8=tf([-5 1],[1 0.3 0.02]);G9=tf(0.01,[1 0.25 0.01]);
        Gt=[G1 G2 G3;G4 G5 G6;G7 G8 G9];
    case 71
        G1=tf(1,[1 0 0]);G2=tf(1,[1 0]);G4=tf(1,[1 0]);Gt=[G1 G2;0 G4];
    case 72
        G1=tf([1 0],[1 2]);G2=0;G4=tf([1 2],[1 0]);Gt=[G1 G2;0 G4];
    case 73
        G1=tf([1 1 0],[1 0 1]);G2=tf([1 1],[1 2]);G4=tf([1 3 2],[1 2 2]);Gt=[G1 G2;0 G4];
    case 74
        G1=tf([4 7 3],[1 4 5 2]);G2=tf(1,[1 1]);Gt=[G1 G2];
    case 75 
        G1=tf(-33.89,conv([98.02 1],[0.42 1]));G3=tf(-18.85,conv([75.43 1],[0.3 1]));G2=tf(32.63,conv([99.6 1],[0.35 1]));G4=tf(34.84,conv([110.5 1],[0.03 1])); Gt=[G1 G2;G3 G4];
    case 'z'
        Gt=75;
end

Highlights from Mult&T

Highlights from
Mult&T