.TH bloc2exp 1 "April 1993" "Scilab Group" "Scilab Function"
.so man1/sci.an 
.SH NAME
bloc2exp - block-diagram to symbolic expression
.SH CALLING SEQUENCE
.nf
[str]=bloc2exp(blocd)
[str,names]=bloc2exp(blocd)
.fi
.SH PARAMETERS
.TP 10
blocd
: list
.TP 10
str
: string
.TP 10
names
: string
.SH DESCRIPTION
given a block-diagram representation of a linear system
\fVbloc2exp\fR returns its symbolic evaluation.
The first element of the list \fVblocd\fR must be the string \fV'blocd'\fR.
Each other element of this list \fV(blocd(2),blocd(3),...)\fR
is itself a list of one the following types :

.nf
list('transfer','name_of_linear_system')
.fi

.nf
list('link','name_of_link',
               [number_of_upstream_box,upstream_box_port],
               [downstream_box_1,downstream_box_1_portnumber],
               [downstream_box_2,downstream_box_2_portnumber],
               ...)
.fi

The strings \fV'transfer'\fR and \fV'links'\fR are keywords which
indicate the type of element in the block diagram.

Case 1 :  the second parameter of the list is a character string which 
may refer (for a possible further evaluation) 
to the Scilab name of a linear system given
in state-space representation (\fVsyslin\fR list) or in transfer
form (matrix of rationals).
.LP
To each transfer block is associated an integer.
To each input and output of a transfer block is also
associated its number, an integer (see examples)

Case 2 :  the second kind of element in a block-diagram representation
is a link.
A link links one output of a block represented by the pair
\fV[number_of_upstream_box,upstream_box_port]\fR, to different
inputs of other blocks. Each such input is represented by 
the pair \fV[downstream_box_i,downstream_box_i_portnumber]\fR.
.LP
The different elements of a block-diagram can be defined
in an arbitrary order.

For example
.LP
[1] \fVS1*S2\fR with unit feedback.
.LP
There are 3 transfers \fVS1\fR (number \fVn_s1=2\fR) , \fVS2\fR (number \fVn_s2=3\fR)
and an adder (number \fVn_add=4\fR) with symbolic transfer 
function \fV['1','1']\fR.
.LP
There are 4 links. The first one (named \fV'U'\fR) links the input 
(port 0 of fictitious block -1, omitted) to port 1 of the adder.
The second and third one link respectively (output)port 1 
of the adder to (input)port 1 of system \fVS1\fR, and 
(output)port 1 of \fVS1\fR to (input)port 1 of \fVS2\fR.
The fourth link (named \fV'Y'\fR) links (output)port 1 of \fVS2\fR to 
the output (port 0 of fictitious block -1, omitted) and to 
(input)port 2 of the adder.
.nf
//Initialization
syst=list('blocd'); l=1;
//
//Systems
l=l+1;n_s1=l;syst(l)=list('transfer','S1');  //System 1
l=l+1;n_s2=l;syst(l)=list('transfer','S2');  //System 2
l=l+1;n_adder=l;syst(l)=list('transfer',['1','1']);  //adder
//
//Links
// Inputs  -1 --> input 1
l=l+1;syst(l)=list('link','U',[-1],[n_adder,1]);
// Internal 
l=l+1;syst(l)=list('link',' ',[n_adder,1],[n_s1,1]);
l=l+1;syst(l)=list('link',' ',[n_s1,1],[n_s2,1]);
// Outputs // -1 -> output 1
l=l+1;syst(l)=list('link','Y',[n_s2,1],[-1],[n_adder,2]);
//Evaluation call
w=bloc2exp(syst);
.fi
The result is the character string:
\fVw=-(s2*s1-eye)\s2*s1\fR.
.LP
Note that invoked with two output arguments,
\fV[str,names]= blocd(syst)\fR returns in \fVnames\fR the list
of symbolic names of named links. This is useful to
set names to inputs and outputs.
.HR
[2] second example
.nf
//Initialization
syst=list('blocd'); l=1;
//
//System (2x2 blocks plant)
l=l+1;n_s=l;syst(l)=list('transfer',['P11','P12';'P21','P22']);  
//
//Controller
l=l+1;n_k=l;syst(l)=list('transfer','k'); 
//
//Links
l=l+1;syst(l)=list('link','w',[-1],[n_s,1]);
l=l+1;syst(l)=list('link','z',[n_s,1],[-1]);
l=l+1;syst(l)=list('link','u',[n_k,1],[n_s,2]);
l=l+1;syst(l)=list('link','y',[n_s,2],[n_k,1]);
//Evaluation call
w=bloc2exp(syst);
.fi
In this case the result is a formula equivalent to the usual one:
.LP
\fVP11+P12*invr(eye-K*P22)*K*P21;\fR
.SH SEE ALSO
bloc2ss
.SH AUTHOR 
S. S., F. D. (INRIA)