Note: This page has been translated by MathWorks. Please click here

To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

This example shows how to build a MIMO control system using `connect`

to interconnect Numeric LTI models and
tunable Control Design Blocks.

Consider the following two-input, two-output control system.

The plant *G* is a distillation column with
two inputs and two outputs. The two inputs are the reflux *L* and
boilup *V*. The two outputs are the concentrations
of two chemicals, represented by the vector signal *y* = [*y*_{1},*y*_{2}].
You can represent this plant model as:

$$G\left(s\right)=\frac{1}{75s+1}\left[\begin{array}{cc}87.8& -86.4\\ 108.2& -109.6\end{array}\right].$$

The vector setpoint signal *r* = [*r*_{1},*r*_{2}] specifies
the desired concentrations of the two chemicals. The vector error
signal *e* represents the input to *D*,
a static 2-by-2 decoupling matrix. *C _{L}* and

To create a two-input, two-output model representing this closed-loop control system:

Create a Numeric LTI model representing the 2-by-2 plant

*G*.s = tf('s','TimeUnit','minutes'); G = [87.8 -86.4 ; 108.2 -109.6]/(75*s+1); G.InputName = {'L','V'}; G.OutputName = 'y';

When you construct the closed-loop model,

`connect`

uses the input and output names to form connections between the block diagram components. Therefore, you must assign names to the inputs and outputs of the transfer function`G`

in either of the following ways: .You can assign input and output names to individual signals by specifying signal names in a cell array, as in

`G.InputName = {'L','V'}`

Alternatively, you can use vector signal naming, which the software automatically expands. For example, the command

`G.OutputName = 'y'`

assigns the names`'y(1)'`

and`'y(2)'`

to the outputs of`G`

.

Create tunable Control Design Blocks representing the decoupling matrix

*D*and the PI controllers*C*and_{L}*C*._{V}D = tunableGain('Decoupler',eye(2)); D.u = 'e'; D.y = {'pL','pV'}; C_L = tunablePID('C_L','pi'); C_L.TimeUnit = 'minutes'; C_L.u = 'pL'; C_L.y = 'L'; C_V = tunablePID('C_V','pi'); C_V.TimeUnit = 'minutes'; C_V.u = 'pV'; C_V.y = 'V';

### Note

`u`

and`y`

are shorthand notations for the`InputName`

and`OutputName`

properties, respectively. Thus, for example, entering:D.u = 'e'; D.y = {'pL','pV'};

is equivalent to entering:

D.InputName = 'e'; D.OutputName = {'pL','pV'};

Create the summing junction.

The summing junction produces the error signals

*e*by taking the difference between*r*and*y*.Sum = sumblk('e = r - y',2);

`Sum`

represents the transfer function for the summing junction described by the formula`'e = r - y'`

. The second argument to`sumblk`

specifies that the inputs and outputs of`Sum`

are each vector signals of length 2. The software therefore automatically assigns the signal names`{'r(1)','r(2)','y(1)','y(2)'}`

to`Sum.InputName`

and`{'e(1)','e(2)'}`

to`Sum.OutputName`

.Join all components to build the closed-loop system from

*r*to*y*.CLry = connect(G,D,C_L,C_V,Sum,'r','y');

The arguments to the

`connect`

function include all the components of the closed-loop system, in any order.`connect`

automatically combines the components using the input and output names to join signals.The last two arguments to

`connect`

specify the output and input signals of the closed-loop model, respectively. The resulting`genss`

model`CLry`

has two-inputs and two outputs.

- Control System Model With Both Numeric and Tunable Components
- Multi-Loop Control System
- MIMO Control System