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iconnect

Create empty iconnect (interconnection) objects

Syntax

H = iconnect

Description

Interconnection objects (class iconnect) are an alternative to sysic, and are used to build complex interconnections of uncertain matrices and systems.

An iconnect object has 3 fields to be set by the user, Input, Output and Equation. Input and Output are icsignal objects, while Equation.is a cell-array of equality constraints (using equate) on icsignal objects. Once these are specified, then the System property is the input/output model, implied by the constraints in Equation. relating the variables defined in Input and Output.

Examples

iconnect can be used to create the transfer matrix M as described in the following figure.

Create three scalar icsignal: r, e and y. Create an empty iconnect object, M. Define the output of the interconnection to be [e; y], and the input to be r. Define two constraints among the variables: e = r-y, and y = (2/s) e. Get the transfer function representation of the relationship between the input (r) and the output [e; y].

r = icsignal(1); 
e = icsignal(1); 
y = icsignal(1); 
M = iconnect; 
M.Input = r; 
M.Output = [e;y]; 
M.Equation{1} = equate(e,r-y); 
M.Equation{2} = equate(y,tf(2,[1 0])*e); 
tf(M.System) 

The transfer functions from input to outputs are

        s 
 #1:  ----- 
      s + 2 

        2 
 #2:  ----- 
      s + 2 

By not explicitly introducing e, this can be done more concisely with only one equality constraint.

r = icsignal(1); 
y = icsignal(1); 
N = iconnect; 
N.Input = r; 
N.Output = [r-y;y]; 
N.Equation{1} = equate(y,tf(2,[1 0])*(r-y)); 
tf(N.System) 

You have created the same transfer functions from input to outputs.

        s 
 #1:  ----- 
      s + 2 

        2 
 #2:  ----- 
      s + 2 

You can also specify uncertain, multivariable interconnections using iconnect. Consider two uncertain motor/generator constraints among 4 variables [V;I;T;W], V-R*I-K*W=0, and T=K*I. Find the uncertain 2x2 matrix B so that [V;T] = B*[W;I].

R = ureal('R',1,'Percentage',[-10 40]); 
K = ureal('K',2e-3,'Percentage',[-30 30]); 
V = icsignal(1); 
I = icsignal(1); 
T = icsignal(1); 
W = icsignal(1); 
M = iconnect; 
M.Input = [W;I]; 
M.Output = [V;T]; 
M.Equation{1} = equate(V-R*I-K*W,iczero(1)); 
M.Equation{2} = equate(T,K*I); 
B = M.System 
UMAT: 2 Rows, 2 Columns 
  K: real, nominal = 0.002, variability = [-30  30]%, 2 occurrences 
  R: real, nominal = 1, variability = [-10  40]%, 1 occurrence     
B.NominalValue 
ans = 
    0.0020    1.0000 
         0    0.0020 

A simple system interconnection, identical to the system illustrated in the sysic reference pages. Consider a three-input, two-output state-space matrix T,

which has internal structure

P = rss(3,2,2); 
K = rss(1,1,2); 
A = rss(1,1,1); 
W = rss(1,1,1); 
M = iconnect; 
noise = icsignal(1); 
deltemp = icsignal(1); 
setpoint = icsignal(1); 
yp = icsignal(2); 
rad2deg = 57.3 
rad2deg = 
   57.3000 
M.Equation{1} = equate(yp,P*[W*deltemp;A*K*[noise+yp(2);setpoint]]); 
M.Input = [noise;deltemp;setpoint]; 
M.Output = [rad2deg*yp(1);setpoint-yp(2)]; 
T = M.System; 
size(T) 
State-space model with 2 outputs, 3 inputs, and 6 states. 

Limitations

The syntax for iconnect objects and icsignals is very flexible. Without care, you can build inefficient (i.e., nonminimal) representations where the state dimension of the interconnection is greater than the sum of the state dimensions of the components. This is in contrast to sysic. In sysic, the syntax used to specify inputs to systems (the input_to_ListedSubSystemName variable) forces you to include each subsystem of the interconnection only once in the equations. Hence, interconnections formed with sysic are componentwise minimal. That is, the state dimension of the interconnection equals the sum of the state dimensions of the components.

More About

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Algorithms

Each equation represents an equality constraint among the variables. You choose the input and output variables, and the imp2exp function makes the implicit relationship between them explicit.

See Also

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