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DynamicSystems[ParallelConnect] - create the equivalent system representation of two or more system objects connected in parallel

Calling Sequence

ParallelConnect(systems, opts)

ParallelConnect(systems, inputconnections, opts)

ParallelConnect(systems, inputconnections, outputconnections, opts)

Parameters

systems

-

list(System); list of system objects

inputconnections

-

(optional) listlist or all or none; list of lists of indexes specifying input connections

outputconnections

-

(optional) listlist or all or none; list of lists of indexes specifying output connections

opts

-

(optional) equation(s) of the form option = value; specify options for the ParallelConnect command

Description

• 

The ParallelConnect command creates the equivalent system representation of two or more system objects connected in parallel.

• 

Unless inputconnections or outputconnections are specified, all input vectors of each system object are connected together and all output vectors are summed. The returned system has the same number of inputs as each system object and the same number of outputs as each system object. For this reason, when no inputconnections or no outputconnections are specified, each system object must have the same number of inputs or outputs, respectively.

• 

If inputconnections are provided, specific inputs of each system object are connected . For k system objects, each index list contains k indexes. The kth index in a list corresponds to an input in the kth system object. The number of input index lists must not exceed the size of the input vector of the system object with the least number of inputs. If all is specified, all input vectors of each system object are connected together. If none is specified, no inputs are connected together, therefore, the returned system has a number of inputs equal to the sum of all system object inputs.

• 

If outputconnections are provided, specific outputs of each system object are summed. For k system objects, each index list contains k indexes. The kth index in a list corresponds to an output in the kth system object. The number of output index lists must not exceed the size of the output vector of the system object with the least number of outputs. If all is specified, all output vectors of each system object are summed. If none is specified, no outputs are summed, therefore, the returned system has a number of outputs equal to the sum of all system object outputs.

• 

The system objects must be either all continuous or all discrete with the same sampling times.

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The returned system type is the same as the input system type, unless the outputtype option is used, or the input is an ae system type.

• 

In the specific case when the system parameter is an algebraic equation (ae) and no option is specified, the ParallelConnect command returns a system object in state space form by default. If the algebraic equation system does not have a state space representation, an error is returned. For details on algebraic equation object support by the DynamicSystems package, see DynamicSystems[AlgEquation].

Examples

withDynamicSystems:

Example 1: Connect 2 MIMO systems in parallel

n:=2:m:=2:p:=2:

sys1:=StateSpace'usesymbols','numinputs'=m,'numoutputs'=p,'numstates'=n:

sys2:=StateSpace'symbols'=e,f,g,h,'usesymbols','numinputs'=m,'numoutputs'=p,'numstates'=n:

parallel1:=ParallelConnectsys1,sys2:

PrintSystemparallel1

State Spacecontinuous2 output(s); 2 input(s); 4 state(s)inputvariable=u1t,u2toutputvariable=y1t,y2tstatevariable=x1t,x2t,x3t,x4ta=a1,1a1,200a2,1a2,20000e1,1e1,200e2,1e2,2b=b1,1b1,2b2,1b2,2f1,1f1,2f2,1f2,2c=c1,1c1,2g1,1g1,2c2,1c2,2g2,1g2,2d=d1,1+h1,1d1,2+h1,2d2,1+h2,1d2,2+h2,2

(1)

Now, using sys1 and sys2, merge all inputs, but do not sum the outputs.

parallel1b:=ParallelConnectsys1,sys2,'all','none':

PrintSystemparallel1b

State Spacecontinuous4 output(s); 2 input(s); 4 state(s)inputvariable=u1t,u2toutputvariable=y1t,y2t,y3t,y4tstatevariable=x1t,x2t,x3t,x4ta=a1,1a1,200a2,1a2,20000e1,1e1,200e2,1e2,2b=b1,1b1,2b2,1b2,2f1,1f1,2f2,1f2,2c=c1,1c1,200c2,1c2,20000g1,1g1,200g2,1g2,2d=d1,1d1,2d2,1d2,2h1,1h1,2h2,1h2,2

(2)

Again, using sys1 and sys2, sum all outputs, but do not merge the inputs.

parallel1c:=ParallelConnectsys1,sys2,'none','all':

PrintSystemparallel1c

State Spacecontinuous2 output(s); 4 input(s); 4 state(s)inputvariable=u1t,u2t,u3t,u4toutputvariable=y1t,y2tstatevariable=x1t,x2t,x3t,x4ta=a1,1a1,200a2,1a2,20000e1,1e1,200e2,1e2,2b=b1,1b1,200b2,1b2,20000f1,1f1,200f2,1f2,2c=c1,1c1,2g1,1g1,2c2,1c2,2g2,1g2,2d=d1,1d1,2h1,1h1,2d2,1d2,2h2,1h2,2

(3)

Example 2: Connect 2 MIMO systems in parallel with the 2nd input of sys1 connected to the 2nd input of sys2, and the 1st output of sys1 summed to the only output of sys2.

sys2b:=StateSpace'symbols'=q,r,s,t,'usesymbols','numinputs'=m,'numoutputs'=p1,'numstates'=n:

parallel2:=ParallelConnectsys1,sys2b,2,2,1,1,outputtype=de:

PrintSystemparallel2

Diff. Equationcontinuous2 output(s); 3 input(s)inputvariable=u1t,u2t,u3toutputvariable=y1t,y2tde={[x1.t=a1,1x1t+a1,2x2t+b1,1u1t+b1,2u2t, x2.t=a2,1x1t+a2,2x2t+b2,1u1t+b2,2u2t, x3.t=q1,1x3t+q1,2x4t+r1,2u2t+r1,1u3t, x4.t=q2,1x3t+q2,2x4t+r2,2u2t+r2,1u3t, y1t={c1,1x1t+c1,2x2t+s1,1x3t+s1,2x4t+d1,1u1t +d1,2+t1,2u2t+t1,1u3t, y2t=c2,1x1t+c2,2x2t+d2,1u1t+d2,2u2t]

(4)

Example 3: Connect 3 MIMO systems in parallel with the 2nd, 3rd and 2nd inputs of sys1, sys2 and sys3 respectively connected together, the 3rd, 2nd and 1st inputs of sys1, sys2 and sys3 respectively connected together, and the 1st, 2nd and 3rd outputs of sys1, sys2 and sys3 respectively summed together.

sys1c:=StateSpace'symbols'=a1,b1,c1,d1,'usesymbols','numinputs'=m+1,'numoutputs'=p+1,'numstates'=n:

sys2c:=StateSpace'symbols'=a2,b2,c2,d2,'usesymbols','numinputs'=m+2,'numoutputs'=p+2,'numstates'=n:

sys3c:=StateSpace'symbols'=a3,b3,c3,d3,'usesymbols','numinputs'=m+2,'numoutputs'=p+1,'numstates'=n:

parallel3:=ParallelConnectsys1c,sys2c,sys3c,2,3,2,3,2,1,1,2,3:

PrintSystemparallel3

State Spacecontinuous8 output(s); 7 input(s); 6 state(s)inputvariable=u1t,u2t,u3t,u4t,u5t,u6t,u7toutputvariable=y1t,y2t,y3t,y4t,y5t,y6t,y7t,y8tstatevariable=x1t,x2t,x3t,x4t,x5t,x6ta=a11,1a11,20000a12,1a12,2000000a21,1a21,20000a22,1a22,2000000a31,1a31,20000a32,1a32,2b=b11,1b11,2b11,30000b12,1b12,2b12,300000b21,3b21,2b21,1b21,4000b22,3b22,2b22,1b22,4000b31,2b31,100b31,3b31,40b32,2b32,100b32,3b32,4c=c11,1c11,2c22,1c22,2c33,1c33,2c12,1c12,20000c13,1c13,2000000c21,1c21,20000c23,1c23,20000c24,1c24,2000000c31,1c31,20000c32,1c32,2d=d11,1d11,2+d22,3+d33,2d11,3+d22,2+d33,1d22,1d22,4d33,3d33,4d12,1d12,2d12,30000d13,1d13,2d13,300000d21,3d21,2d21,1d21,4000d23,3d23,2d23,1d23,4000d24,3d24,2d24,1d24,4000d31,2d31,100d31,3d31,40d32,2d32,100d32,3d32,4

(5)

Alternately, connect sys1c and sys2c first, and then connect sys3c to obtain the same result.

parallel3i:=ParallelConnectsys1c,sys2c,2,3,3,2,1,2:

parallel3e:=ParallelConnectparallel3i,sys3c,2,2,3,1,1,3:

PrintSystemparallel3e

State Spacecontinuous8 output(s); 7 input(s); 6 state(s)inputvariable=u1t,u2t,u3t,u4t,u5t,u6t,u7toutputvariable=y1t,y2t,y3t,y4t,y5t,y6t,y7t,y8tstatevariable=x1t,x2t,x3t,x4t,x5t,x6ta=a11,1a11,20000a12,1a12,2000000a21,1a21,20000a22,1a22,2000000a31,1a31,20000a32,1a32,2b=b11,1b11,2b11,30000b12,1b12,2b12,300000b21,3b21,2b21,1b21,4000b22,3b22,2b22,1b22,4000b31,2b31,100b31,3b31,40b32,2b32,100b32,3b32,4c=c11,1c11,2c22,1c22,2c33,1c33,2c12,1c12,20000c13,1c13,2000000c21,1c21,20000c23,1c23,20000c24,1c24,2000000c31,1c31,20000c32,1c32,2d=d11,1d11,2+d22,3+d33,2d11,3+d22,2+d33,1d22,1d22,4d33,3d33,4d12,1d12,2d12,30000d13,1d13,2d13,300000d21,3d21,2d21,1d21,4000d23,3d23,2d23,1d23,4000d24,3d24,2d24,1d24,4000d31,2d31,100d31,3d31,40d32,2d32,100d32,3d32,4

(6)

See Also

Description of the Model of a Linear System Object, DynamicSystems, DynamicSystems[AlgEquation], DynamicSystems[AppendConnect], DynamicSystems[DiffEquation], DynamicSystems[FeedbackConnect], DynamicSystems[PrintSystem], DynamicSystems[SeriesConnect], DynamicSystems[StateSpace], DynamicSystems[SystemConnect]


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