System definitions

This file loads in basic definitions of the system and of the energy balance relations which various connections of the systems satisfy.

     

	=	F[x,W,U]
out1	=	G [x,W,U]
Y	=	G [x,W,U]
	=	f[z,Y]
U	=	g[z,Y]

(* An Input Affine (IA) one port system is *)                       

                   SetNonCommutative[f,g,a,b,c,dd,z]

                       f[z_,Y_]:=a[z]+b[z]**Y
                       g[z_,Y_]:=c[z]+dd[z]**Y

(* An Input Affine (IA) two port system is *)

                   SetNonCommutative[W,U,Y,DW,DU,DY]
                   SetNonCommutative[A,x,B1,B2,C1,C2,G1,G2] 
                   SetNonCommutative[D11,D22,D12,D21]
                     D11[x_]:=0  
                     D22[x_]:=0                         
                     D12[x_]:=1                         
                     D21[x_]:=1                         
                        
                   F[x_,W_,U_]:=A[x]+B1[x]**W+B2[x]**U
                   G1[x_,W_,U_]:=C1[x]+D11[x]**W+D12[x]**U;
                            out1=G1[x,W,U];
                   G2[x_,W_,U_]:=C2[x]+D21[x]**W+D22[x]**U;
                            out2=G2[x,W,U];
                            G2I[x_,Y_,U_]:=inv[D21[x]]**Y-inv[D21[x]]**C2[x];