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This example shows how to interconnect Numeric LTI Models representing multiple system components to build a single numeric model of a closed-loop system, using model arithmetic and interconnection commands.

Construct a model of the following single-loop control system.

The feedback loop includes a plant *G*(*s*),
a controller *C*(*s*), and a representation
of sensor dynamics, *S*(*s*). The
system also includes a prefilter *F*(*s*).

Create model objects representing each of the components.

G = zpk([],[-1,-1],1); C = pid(2,1.3,0.3,0.5); S = tf(5,[1 4]); F = tf(1,[1 1]);

The plant

*G*is a zero-pole-gain (`zpk`) model with a double pole at*s*= –1. Model object*C*is a PID controller. The models*F*and*S*are transfer functions.Connect the controller and plant models.

H = G*C;

To combine models using the multiplication operator

`*`, enter the models in reverse order compared to the block diagram.**Tip**Alternatively, construct*H*(*s*) using the`series`command:H = series(C,G);

Construct the unfiltered closed-loop response .

T = feedback(H,S);

Construct the entire closed-loop system response from

*r*to*y*.T_ry = T*F;

`T_ry` is a Numeric LTI Model representing
the aggregate closed-loop system. `T_ry` does not keep track of
the coefficients of the components `G`, `C`, `F`,
and `S`.

You can operate on `T_ry` with any Control System Toolbox™ control
design or analysis commands.

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