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bloc2exp
Conversion of a block-diagram to its symbolic expression
Calling Sequence
[str]=bloc2exp(blocd) [str,names]=bloc2exp(blocd)
Arguments
- blocd
list
- str
string
- names
string
Description
given a block-diagram representation of a linear system
bloc2exp
returns its symbolic evaluation. The first
element of the list blocd
must be the string
'blocd'
. Each other element of this list
(blocd(2),blocd(3),...)
is itself a list of one the
following types :
list('transfer','name_of_linear_system')
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], ...)
The strings 'transfer'
and
'link'
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
(syslin
list) or in transfer form (matrix of
rationals).
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 [number_of_upstream_box,upstream_box_port]
,
to different inputs of other blocks. Each such input is represented by the
pair
[downstream_box_i,downstream_box_i_portnumber]
.
The different elements of a block-diagram can be defined in an arbitrary order.
For example
[1] S1*S2
with unit feedback.
There are 3 transfers S1
(number
n_s1=2
) , S2
(number
n_s2=3
) and an adder (number
n_add=4
) with symbolic transfer function
['1','1']
.
There are 4 links. The first one (named 'U'
)
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 S1
, and (output)port 1
of S1
to (input)port 1 of S2
. The
fourth link (named 'Y'
) links (output) port 1 of
S2
to the output (port 0 of fictitious block -1,
omitted) and to (input)port 2 of the adder.
Examples
//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);
The result is the character string:
w=-(s2*s1-eye())\s2*s1
.
Note that invoked with two output arguments, [str,names]=
blocd(syst)
returns in names
the list of
symbolic names of named links. This is useful to set names to inputs and
outputs.
//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);
In this case the result is a formula equivalent to the usual one:
P11+P12*invr(eye()-K*P22)*K*P21;
See Also
- bloc2ss — block-diagram to state-space conversion
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