# sumblk

Summing junction for name-based interconnections

## Description

creates
the summing junction described by `S`

= sumblk(`formula`

)`formula`

in the form of a transfer
function (`tf`

) model, `S`

. The string
`formula`

specifies an equation that relates the scalar input and
output signals of `S`

, such as `"e = r - y"`

. The
function sets the `InputName`

and `OutputName`

properties
of `S`

based on `formula`

. Use `S`

in
conjunction with `connect`

to interconnect dynamic system
models and derive aggregate models for block diagrams.

returns a vector-valued summing junction. The input and output signals are vectors with
`S`

= sumblk(`formula`

,`signalsize`

)`signalsize`

elements. `sumblk`

sets the
`InputName`

and `OutputName`

properties by vector
expansion of the signal names in `formula`

.

replaces placeholders in `S`

= sumblk(`formula`

,`signames`

1,...,`signames`

N)`formula`

by the signal names
`signames`

. Indicate a placeholder in `formula`

by
using a signal name beginning with `%`

. The number of
`signames`

arguments must match the number of placeholders in
`formula`

. The first placeholder in `formula`

is
replaced by `signames`

1, the second by `signames`

2,
and so on.

## Examples

### Summing Junction with Scalar-Valued Signals

Create the summing junction of the following illustration. All signals are scalar-valued.

This summing junction has the formula `u = u1 + u2 + u3`

. Use this formula with `sumblk`

to create the summing junction.

`S = sumblk('u = u1 + u2 + u3');`

`S`

is the transfer function (`tf`

) representation of the sum `u = u1 + u2 + u3`

. That is, `S`

is a static-gain `tf`

with three inputs and one output, which is equal to the sum of the inputs. The transfer function `S`

gets its input and output names from the formula.

S.OutputName

`ans = `*1x1 cell array*
{'u'}

S.InputName

`ans = `*3x1 cell*
{'u1'}
{'u2'}
{'u3'}

Therefore, you can use `S`

with the name-based syntax of the `connect`

command to build aggregate models such as the system of the following block diagram.

To do so, create LTI models for `H1`

, `H2`

, and `H3`

, and name their inputs and outputs according to the diagram. For this example, use transfer functions.

H1 = tf(1,[1 2],"InputName","z1","OutputName","u1"); H2 = tf([1 -2],[1 1],"InputName","z2","OutputName","u2"); H3 = tf(2,[2 1],"InputName","u","OutputName","u3");

Connect the models and the summing junction to create an aggregate model with inputs `z1`

and `z2`

and output `u`

. The `connect`

command automatically connects the outputs of the components to inputs with matching names.

T = connect(H1,H2,H3,S,{"z1","z2"},{"u"}); T.InputName

`ans = `*2x1 cell*
{'z1'}
{'z2'}

T.OutputName

`ans = `*1x1 cell array*
{'u'}

### Summing Junction with Vector-Valued Signals

Create the summing junction `v = u - d`

where `u`

, `d`

, `v`

are vector-valued signals of length 2. This summing junction is shown in the following diagram, where each arrow represents two signals.

This summing junction outputs `v(1) = u(1) - d(1)`

and `v(2) = u(2) - d(2)`

. To create this junction using `sumblk`

, specify both the formula and the signal length.

```
S = sumblk('v = u - d',2);
size(S)
```

Transfer function with 2 outputs and 4 inputs.

The result is a transfer function with four inputs and two outputs: two inputs each for `d`

and `u`

, and two outputs for `v`

. `sumblk`

automatically performs vector expansion of the signal names and assigns them to `S.InputName`

and `S.OutputName`

.

S.InputName

`ans = `*4x1 cell*
{'u(1)'}
{'u(2)'}
{'d(1)'}
{'d(2)'}

S.OutputName

`ans = `*2x1 cell*
{'v(1)'}
{'v(2)'}

You can connect `S`

to other dynamic system models to build aggregate models, as you would use any other MIMO transfer function. For instance, suppose that you want to create a model representing the following two-channel feedback loop, that is, a feedback loop in which each line in the diagram represents two signals.

Create two-input, two-output models for `H1`

and `H2`

, and set their `InputName`

and `OutputName`

properties as indicated by the diagram. For this example, use random state-space models.

H1 = rss(3,2,2); H1.InputName = 'v'; H1.OutputName = 'w'; H2 = rss(3,2,2); H2.InputName = 'w'; H2.OutputName = 'd';

Note that the signal names in the dynamic system models are automatically expanded, just as `sumblk`

expands the signal names of `S`

. For instance, examine the outputs of `H1`

.

H1.OutputName

`ans = `*2x1 cell*
{'w(1)'}
{'w(2)'}

The `connect`

command also performs this expansion. Thus, you can assemble the aggregate system with the following command.

T = connect(S,H1,H2,'u','w'); size(T)

State-space model with 2 outputs, 2 inputs, and 6 states.

### Specify Individual Names in Summing Junction with Vector-Valued Signals

As shown in the example Summing Junction with Vector-Valued Signals, when you create a summing junction for vector signals, by default `sumblk`

appends an index to the signal names that you provide. If you need to specify distinct signal names instead of this vector expansion, use a placeholder in the summing-junction formula to represent the signals you want to name. Then, use the `signames`

input argument to provide the specific names to substitute for the placeholder in creating the summing junction.

For instance, create a summing junction having the following formula.

$$\begin{array}{l}e\left(1\right)=setpoint\left(1\right)-alpha\\ e\left(2\right)=setpoint\left(2\right)-q\end{array}$$

This formula is the summing junction shown in the following diagram, where `setpoint`

represents two inputs and `e`

represents two outputs.

To create this summing junction, allow `sumblk`

to expand `e`

and `setpoint`

, but use a signal name beginning with `%`

as a placeholder for the specific signal names you provide in the `signames`

argument.

formula = 'e = setpoint - %y'; signames = ["alpha","q"]; S = sumblk(formula,signames);

`sumblk`

replaces the placeholder `%y`

with the signal names `alpha`

and `q`

and expands the other signal names. Note that `sumblk`

takes the size of the vector signals from the number of signals in `signames`

. Thus, the `setpoint`

input and `e`

output of `S`

each contain two signals.

S.InputName

`ans = `*4x1 cell*
{'setpoint(1)'}
{'setpoint(2)'}
{'alpha' }
{'q' }

S.OutputName

`ans = `*2x1 cell*
{'e(1)'}
{'e(2)'}

This syntax is particularly useful when you want to create a summing junction to connect existing models whose `InputName`

or `OutputName`

properties are already set. For instance, consider the following two-input, two-output state-space model.

A = [-0.004 0.03; 0.03 -0.19]; B = [0.3 0.2; -0.06 0]; C = [0.99 0.5; 0 0]; D = 0; G = ss(A,B,C,D); G.InputName = {'angle','rate'}; G.OutputName = {'current','temp'};

Create a summing junction that subtracts the outputs of `G`

from a pair of reference inputs, such that

$$\begin{array}{l}e\left(1\right)=ref\left(1\right)-current\\ e\left(2\right)=ref\left(2\right)-temp\end{array}$$

To do so, use a placeholder for these signals in the formula. Then, use `G.OutputName`

as the `signames`

input.

```
S = sumblk('e = ref - %outputs',G.OutputName);
S.InputName
```

`ans = `*4x1 cell*
{'ref(1)' }
{'ref(2)' }
{'current'}
{'temp' }

You can use multiple placeholders to replace multiple elements of the formula. `sumblk`

replaces the placeholders in the order you provide them. For instance, give the reference signals specific names instead of `ref(1)`

and `ref(2)`

.

refnames = ["refcur","reftemp"]; S = sumblk('e = %refs - %outputs',refnames,G.OutputName); S.InputName

`ans = `*4x1 cell*
{'refcur' }
{'reftemp'}
{'current'}
{'temp' }

## Input Arguments

`formula`

— Equation relating input and output signals of summing junction

string | character vector

Equation that relates the input and output signals of the summing junction transfer
function `S`

, specified as a string or character vector. For example,
consider the summing junction of the following diagram.

To represent this summing junction as a three-input, one-output transfer function, use the following commands.

formula = "e = r + d - y"; S = sumblk(formula);

For vector-valued signals, you can optionally use one or more placeholders in
`formula`

to control the names that `sumblk`

assigns to `S.InputName`

and `S.OutputName`

. To put a
placeholder in `formula`

, use a signal name that begins with
`%`

. When assigning signal names to `S`

, the
`sumblk`

command replaces each placeholder with the names you
provide in the `signames`

argument.

Such placeholders are particularly useful for creating summing junctions for
connecting existing models that have named signals. For example, if `C`

and `G`

are dynamic system models with nonempty
`InputName`

and `OutputName`

properties,
respectively, you can create a summing junction using the following expression.

S = sumblk("%e = r - %y",C.InputName,G.OutputName)

`sumblk`

uses the values of `C.InputName`

and
`G.OutputName`

in place of `%e`

and
`%y`

, respectively. The vector dimension of
`C.InputName`

and `G.OutputName`

must match.
`sumblk`

assigns the signal `r`

the same dimension.
For an example, see Specify Individual Names in Summing Junction with Vector-Valued Signals.

`signalsize`

— Number of elements in each signal

1 (default) | positive integer

Number of elements in each input and output signal of `S`

,
specified as a positive integer. Setting `signalsize`

greater than 1
lets you specify a summing junction that operates on vector-valued signals. For
instance, `S = sumblk("e = r - y",2)`

creates a summing junction where
each of the inputs `r`

and `y`

and the output
`e`

is a vector signal with two elements. See Summing Junction with Vector-Valued Signals.

`signames`

— Substitute signal names for a placeholder

string array | cell array of character vectors

Substitute signal names for a placeholder (signal name beginning with
`%`

) in the argument `formula`

, specified as a
string array or a cell array of character vectors. Provide one
`signames`

argument for each placeholder in
`formula`

.

Specify `signames`

as:

A string array, such as

`["alpha","q"]`

.A cell array of signal names, such as

`{'alpha','q'}`

.The

`InputName`

or`OutputName`

property of a model in the MATLAB^{®}workspace. For example:S = sumblk("%e = r - y",C.InputName)

This command creates a summing junction whose outputs have the same name as the inputs of the model

`C`

in the MATLAB workspace. Specify Individual Names in Summing Junction with Vector-Valued Signals.If you use placeholders and the

`signames`

argument, then`sumblk`

sets the vector length of the signals of`S`

. If you use multiple placeholders, than all`signames`

arguments must have the same number of signals.

## Output Arguments

`S`

— Transfer function for summing junction

`tf`

model

Transfer function for the summing junction, returned as a `tf`

model.

`sumblk`

sets the `InputName`

and
`OutputName`

properties of `S`

using the signal
names in `formula`

. For instance, if you enter ```
S = sumblk("e
= r + d - y")
```

, then `sumblk`

creates
`S`

with `S.InputName = {'r';'d';'y'}`

and
`S.OutputName = {'e'}`

. Use these input and output names to
interconnect `S`

with other dynamic system models to build composite
systems. For an example, see Summing Junction with Scalar-Valued Signals.

If `signalsize`

is greater than 1, then `S`

has
`signalsize`

inputs (or outputs) per signal name in
`formula`

. The function sets `S.InputName`

and
`S.OutputName`

by applying vector expansion to the signal name
specified in `formula`

, such as
`{'e(1)','e(2)',...}`

. For an example, see Summing Junction with Vector-Valued Signals.

If you use placeholders in `formula`

, then
`sumblk`

sets the `InputName`

and
`OutputName`

properties of `S`

using the names you
provide in `signames`

. For an example, see Specify Individual Names in Summing Junction with Vector-Valued Signals.

## Version History

**Introduced in R2008a**

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