BUILT-IN MATHEMATICA SYMBOL

SystemsModelSeriesConnect

connects TransferFunctionModel or StateSpaceModel objects

and

in series.

connects only output y of

to input u of

.

SystemsModelSeriesConnect

connects outputs

of

to inputs

of

.

MORE INFORMATION

The inputs and outputs of the system produced by SystemsModelSeriesConnect are the inputs of and the outputs of , respectively.

The arguments y, u, , and are integers specifying the positions of the input or output channels.

They can also be specified using the appropriate values of SystemsModelLabels.

If or is in state-space form, the result is given in state-space form.

EXAMPLES

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Basic Examples (4)

Connect two systems in series:

Connect three discrete-time systems in series:

Connect the second output of a two-output system to a single-input system:

Connect two state-space models in series:

Connect the second output of the first system to the first input of the second system:

Connect the inputs to the outputs in reverse order:

Connect two systems in series:

In[1]:=

Out[1]=

Connect three discrete-time systems in series:

In[1]:=

Out[1]=

Connect the second output of a two-output system to a single-input system:

In[1]:=

Out[1]=

Connect two state-space models in series:

In[1]:=

Out[1]=

Connect the second output of the first system to the first input of the second system:

In[2]:=

Out[2]=

Connect the inputs to the outputs in reverse order:

In[3]:=

Out[3]=

Scope (3)

Connect two single-input, single-output systems in series:

Connect a system with two outputs to a system with two inputs:

Connect the first output to the second input:

Connect the first and second outputs of the first system to the second and first inputs of the second system:

Connect the two outputs of the first system to the first two inputs of the second system:

Connect the second output to the fourth input:

Connect the first output to the first and third inputs:

Applications (4)

A function that connects any number of matching systems in series:

Connect a family of first-order systems in series:

Connect several multiple-input, multiple-output systems:

The cascade of four abstract systems:

The tree structure of the cascade:

Obtain the open-loop transfer function of an azimuth-positioning system having a power amplifier, motor-load, and angular rate sensor in series:

Visualize the open-loop step response:

Integrate the last output of a three-output system:

Use SystemsModelSeriesConnect in multi-loop reduction:

Properties & Relations (8)

SystemsModelSeriesConnect yields a system that has the inputs of the first system and the outputs of the second system:

SystemsModelSeriesConnect does not cancel poles and zeros:

The poles of the reduced system containing only series and parallel connections are the poles of the individual subsystems:

The order of the reduced system is the sum of the orders of the subsystems:

SystemsModelSeriesConnect is essentially a flat function:

SystemsModelSeriesConnect

is essentially equivalent to TransferFunctionModel

without any pole-zero cancellation:

For continuous-time systems, SystemsModelSeriesConnect is essentially the Laplace transform of the convolution of the impulse responses:

If any one of the subsystems is a StateSpaceModel object, so is the result: