Block diagram interconnections of dynamic systems
sysc = connect(sys1,...,sysN,inputs,outputs)
sysc = connect(blksys,connections,inputs,outputs)
sysc = connect(___,opts)
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 you create using sumblk. The connect command interconnects the block diagram elements by matching the input and output signals 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(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 is not recommended.
Dynamic system models corresponding to the elements of your block diagram. For example, the elements of your block diagram can include one or more tf or ss model representing plant dynamics. Block diagram elements can also include a pid or ltiblock.pid model representing a controller. You can also include one or more summing junction you create using sumblk. Provide multiple arguments sys1,...,sysN to represent all of the block diagram elements and summing junctions.
For name-based interconnection, a string or cell array of strings specifying the inputs of the aggregate model sysc. The strings in inputs must correspond to entries in the InputName or OutputName property of one or more of the block diagram elements sys1,...,sysN.
For name-based interconnection, a string or cell array of strings specifying the outputs of the aggregate model sysc. The strings in outputs must correspond to entries in the OutputName property of one or more of the block diagram elements sys1,...,sysN.
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)
Matrix specifying 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.
Additional options for interconnection, specified as an options set you create with connectOptions.
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:
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);
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.
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.
ans = 'r(1)' 'r(2)'
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. 1 specifies that the external input connects to u(1). The last argument, 2, specifies that the external output connects from w(2).