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connect

Block diagram interconnections of dynamic systems

Syntax

sysc = connect(sys1,...,sysN,inputs,outputs)
sysc = connect(sys1,...,sysN,inputs,outputs,APs)
sysc = connect(blksys,connections,inputs,outputs)
sysc = connect(___,opts)

Description

sysc = connect(sys1,...,sysN,inputs,outputs) connects the block diagram elements sys1,...,sysN based on signal names. The block diagram elements sys1,...,sysN are dynamic system models. These models can include summing junctions that you create using sumblk. The connect command interconnects the block diagram elements by matching the input and output signals that you specify in the InputName and OutputName properties of sys1,...,sysN. The aggregate model sysc is a dynamic system model having inputs and outputs specified by inputs and outputs respectively.

sysc = connect(sys1,...,sysN,inputs,outputs,APs) inserts an AnalysisPoint at every signal location specified in APs. Use analysis points to mark locations of interest which are internal signals in the aggregate model. For instance, a location at which you want to extract a loop transfer function or measure the stability margins is a location of interest.

sysc = connect(blksys,connections,inputs,outputs) uses index-based interconnection to build sysc out of an aggregate, unconnected model blksys. The matrix connections specifies how the outputs and inputs of blksys interconnect. For index-based interconnections, inputs and outputs are index vectors that specify which inputs and outputs of blksys are the external inputs and outputs of sysc. This syntax can be convenient when you do not want to assign names to all inputs and outputs of all models to connect. However, in general, it is easier to keep track of named signals.

sysc = connect(___,opts) builds the interconnected model using additional options. You can use opts with the input arguments of any of the previous syntaxes.

Input Arguments

sys1,...,sysN

Dynamic system models that correspond to the elements of your block diagram. For example, the elements of your block diagram can include one or more tf or ss models that represent plant dynamics. Block diagram elements can also include a pid or tunablePID model representing a controller. You can also include one or more summing junction that you create using sumblk. Provide multiple arguments sys1,...,sysN to represent all of the block diagram elements and summing junctions.

inputs

For name-based interconnection, a character vector or cell array of character vectors that specify the inputs of the aggregate model sysc. The inputs in inputs must correspond to entries in the InputName or OutputName property of one or more of the block diagram elements sys1,...,sysN.

outputs

For name-based interconnection, a character vector or cell array of character vectors that specify the outputs of the aggregate model sysc. The outputs in outputs must correspond to entries in the OutputName property of one or more of the block diagram elements sys1,...,sysN.

APs

Locations (internal signals) of interest in the aggregate model, specified as a character vector or cell array of character vectors, such as 'X' or {'AP1','AP2'}. The resulting model contains an analysis point at each such location. (See AnalysisPoint). Each location in APs must correspond to an entry in the InputName or OutputName property of one or more of the block diagram elements sys1,...,sysN.

blksys

Unconnected aggregate model. To obtain blksys, use append to join dynamic system models of the elements of your block diagram. For example, if your block diagram contains dynamic system models C, G, and S, create blksys with the following command:

blksys = append(C,G,S)

connections

Matrix that specifies the connections and summing junctions of the block diagram. Each row of connections specifies one connection or summing junction in terms of the input vector u and output vector y of the unconnected aggregate model blksys. For example, the row:

[3 2 0 0]

specifies that y(2) connects into u(3). The row 

[7 2 -15 6]

indicates that y(2)-y(15)+y(6) feeds into u(7).

If you do not specify any connection for a particular input or output, connect omits that input or output from the aggregate model.

opts

Additional options for interconnection, specified as an options set that you create with connectOptions.

Output Arguments

sysc

Interconnected system, returned as either a state-space model or frequency-response model. The type of model returned depends on the input models. For example:

  • Interconnecting numeric LTI models (other than frd models) returns an ss model.

  • Interconnecting a numeric LTI model with a Control Design Block returns a generalized LTI model. For instance, interconnecting a tf model with a tunablePID Control Design Block returns a genss.

  • Interconnecting any model with frequency-response data model returns a frequency response data model.

By default, connect automatically discards states that do not contribute to the I/O transfer function from the specified inputs to the specified outputs of the interconnected model. To retain the unconnected states, set the Simplify option of connectOptions to false. For example:

opt = connectOptions('Simplify',false);
sysc = connect(sys1,sys2,sys3,'r','y',opt);

Examples

SISO Feedback Loop

Create an aggregate model of the following block diagram from r to y.

Create C and G, and name the inputs and outputs.

C = pid(2,1); 
C.u = 'e';  
C.y = 'u';
G = zpk([],[-1,-1],1);
G.u = 'u';  
G.y = 'y';

The notations C.u and C.y are shorthand expressions equivalent to C.InputName and C.OutputName, respectively. For example, entering C.u = 'e' is equivalent to entering C.InputName = 'e'. The command sets the InputName property of C to the value 'e'.

Create the summing junction. 

Sum = sumblk('e = r - y');

Combine C, G, and the summing junction to create the aggregate model from r to y.

T = connect(G,C,Sum,'r','y');

connect automatically joins inputs and outputs with matching names.

MIMO Feedback Loop

Create the control system of the previous example where G and C are both 2-input, 2-output models. 

C = [pid(2,1),0;0,pid(5,6)];
C.InputName = 'e';  
C.OutputName = 'u';
G = ss(-1,[1,2],[1;-1],0);
G.InputName = 'u';  
G.OutputName = 'y';

When you specify single names for vector-valued signals, the software automatically performs vector expansion of the signal names. For example, examine the names of the inputs to C.

C.InputName
ans = 

    'e(1)'
    'e(2)'

Create a 2-input, 2-output summing junction.

Sum = sumblk('e = r-y',2);

sumblk also performs vector expansion of the signal names.

Interconnect the models to obtain the closed-loop system.

T = connect(G,C,Sum,'r','y');

The block diagram elements G, C, and Sum are all 2-input, 2-output models. Therefore, connect performs the same vector expansion. connect selects all entries of the two-input signals 'r' and 'y' as inputs and outputs to T, respectively. For example, examine the input names of T.

T.InputName
ans = 

    'r(1)'
    'r(2)'

Feedback Loop With Analysis Point Inserted by connect

Create a model of the following block diagram from r to y. Insert an analysis point at an internal location, u.

Create C and G, and name the inputs and outputs.

C = pid(2,1); 
C.InputName = 'e';  
C.OutputName = 'u';
G = zpk([],[-1,-1],1);
G.InputName = 'u';  
G.OutputName = 'y';

Create the summing junction. 

Sum = sumblk('e = r - y');

Combine C, G, and the summing junction to create the aggregate model, with an analysis point at u.

T = connect(G,C,Sum,'r','y','u')
Generalized continuous-time state-space model with 1 outputs, 1 inputs, 3 states, and the following blocks:
  AnalysisPoints_: Analysis point, 1 channels, 1 occurrences.

Type "ss(T)" to see the current value and "T.Blocks" to interact with the blocks.

The resulting T is a genss model. The connect command creates the AnalysisPoint block, AnalysisPoints_, and inserts it into T. To see the name of the analysis point channel in AnalysisPoints_, use getPoints.

getPoints(T)
ans = 1x1 cell array
    {'u'}

The analysis point channel is named 'u'. You can use this analysis point to extract system responses. For example, the following commands extract the open-loop transfer at u and the closed-loop response at y to a disturbance injected at u.

L = getLoopTransfer(T,'u',-1);
Tuy = getIOTransfer(T,'u','y');

T is equivalent to the following block diagram, where AP_u designates the AnalysisPoint block AnalysisPoints_ with channel name u.

Index-Based Interconnection

Create an aggregate model of the following block diagram from r to y using index-based interconnection.

Create C, G, and the unconnected aggregate model blksys.

C = pid(2,1); 
G = zpk([],[-1,-1],1);
blksys = append(C,G);

The inputs u(1),u(2) of blksys correspond to the inputs of C and G, respectively. The outputs w(1),w(2) of blksys correspond to the outputs of C and G, respectively.

Create the matrix connections, which specifies which outputs of blksys connect to which inputs of blksys. 

connections = [2 1; 1 -2];

The first row indicates that w(1) connects to u(2); in other words, that the output of C connects to the input of G. The second row indicates that -w(2) connects to u(1); in other words, that the negative of the output of G connects to the input of C.

Create the connected aggregate model from r to y.

T = connect(blksys,connections,1,2)

The last two arguments specify the external inputs and outputs in terms of the indices of blksys. The argument 1 specifies that the external input connects to u(1). The last argument, 2, specifies that the external output connects from w(2).

Version History

Introduced before R2006a

See Also

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