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

Calling Sequence

SeriesConnect(systems, indexes, opts)

Parameters

systems

-

list(System); list of system objects

indexes

-

(optional) list(list); list of lists specifying the indexes of the outputs and inputs to be connected in two consecutive systems in series, i.e. [[outputs sys 1], [inputs sys 2], [outputs sys 2],..., [inputs sys n]].

opts

-

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

Description

• 

The SeriesConnect command creates the equivalent system representation of two or more system objects connected in series.

• 

The systems are connected in series in the order specified, matching the outputs of the previous system to the inputs of the next system unless index lists are specified.

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If indexes is provided, specific outputs of the previous system are connected to specific inputs of the next system in the order given by the indexes in the lists.

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When two systems are specified, the first list contains the indexes of the outputs of the first system, and the second list contains the indexes of the inputs of the second system. For subsequent series connections, the same rule applies. For n systems, the necessary number of index lists is (2n - 2).

• 

The returned system has the same number of inputs as the first system specified, and the same number of outputs as the last system specified.

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

• 

The returned system type is determined by the type of the input systems, unless the outputtype option is used. If different types of system objects are passed, the returned system type is determined based on a precedence list defined as tf < coeff < zpk < ss < de. For example, if a ss and tf system are supplied, the output will be an ss system.

Examples

withDynamicSystems&colon;

Example 1: SISO series connection

n:=2&colon;m:=1&colon;p:=1&colon;

sys1:=StateSpace&apos;usesymbols&apos;&comma;&apos;numinputs&apos;&equals;m&comma;&apos;numoutputs&apos;&equals;p&comma;&apos;numstates&apos;&equals;n&colon;

sys2:=StateSpace&apos;symbols&apos;&equals;e&comma;f&comma;g&comma;h&comma;&apos;usesymbols&apos;&comma;&apos;numinputs&apos;&equals;m&comma;&apos;numoutputs&apos;&equals;p&comma;&apos;numstates&apos;&equals;n&colon;

series1:=SeriesConnectsys1&comma;sys2&colon;

PrintSystemseries1

State Spacecontinuous1 output(s); 1 input(s); 4 state(s)inputvariable&equals;u1toutputvariable&equals;y1tstatevariable&equals;x1t&comma;x2t&comma;x3t&comma;x4ta&equals;a1,1a1,200a2,1a2,200f1,1c1,1f1,1c1,2e1,1e1,2f2,1c1,1f2,1c1,2e2,1e2,2b&equals;b1,1b2,1f1,1d1,1f2,1d1,1c&equals;h1,1c1,1h1,1c1,2g1,1g1,2d&equals;h1,1d1,1

(1)

Connect three transfer functions in series

series1tf:=SeriesConnectTransferFunctionss3&plus;bs2&plus;cs&plus;d&comma;TransferFunction1&tau;s&plus;a&comma;TransferFunctionKs2&colon;

PrintSystemseries1tf

Transfer Functioncontinuous1 output(s); 1 input(s)inputvariable&equals;u1soutputvariable&equals;y1stf1,1&equals;Kτs5+τb+as4+ab+τcs3+ac+τds2+ads

(2)

Example 2: MIMO series connection

sys1b:=StateSpace&apos;symbols&apos;&equals;i&comma;j&comma;k&comma;l&comma;&apos;usesymbols&apos;&comma;&apos;numinputs&apos;&equals;m&comma;&apos;numoutputs&apos;&equals;p&plus;1&comma;&apos;numstates&apos;&equals;n&colon;

sys2b:=StateSpace&apos;symbols&apos;&equals;o&comma;q&comma;r&comma;s&comma;&apos;usesymbols&apos;&comma;&apos;numinputs&apos;&equals;m&plus;1&comma;&apos;numoutputs&apos;&equals;p&comma;&apos;numstates&apos;&equals;n&colon;

series2:=SeriesConnectsys1b&comma;sys2b&comma;1&comma;2&comma;1&comma;2&colon;

PrintSystemseries2

State Spacecontinuous1 output(s); 1 input(s); 4 state(s)inputvariable&equals;u1toutputvariable&equals;y1tstatevariable&equals;x1t&comma;x2t&comma;x3t&comma;x4ta&equals;i1,1i1,200i2,1i2,200q1,1k1,1+q1,2k2,1q1,1k1,2+q1,2k2,2o1,1o1,2q2,1k1,1+q2,2k2,1q2,1k1,2+q2,2k2,2o2,1o2,2b&equals;j1,1j2,1q1,1l1,1+q1,2l2,1q2,1l1,1+q2,2l2,1c&equals;s1,1k1,1+s1,2k2,1s1,1k1,2+s1,2k2,2r1,1r1,2d&equals;s1,1l1,1+s1,2l2,1

(3)

Example 3: Series connection of two systems with 2nd output of 1st system to 1st input of 2nd system

sys1c:=StateSpace&apos;symbols&apos;&equals;t&comma;v&comma;w&comma;z&comma;&apos;usesymbols&apos;&comma;&apos;numinputs&apos;&equals;m&plus;1&comma;&apos;numoutputs&apos;&equals;p&plus;1&comma;&apos;numstates&apos;&equals;n&colon;

series3:=SeriesConnectsys1c&comma;sys2b&comma;2&comma;1&comma;&apos;outputtype&apos;&equals;de&colon;

PrintSystemseries3

Diff. Equationcontinuous1 output(s); 2 input(s)inputvariable&equals;u1t&comma;u2toutputvariable&equals;y1tde&equals;&lcub;&lsqb;x1.t&equals;t1,1x1t+t1,2x2t+v1,1u1t+v1,2u2t, x2.t&equals;t2,1x1t+t2,2x2t+v2,1u1t+v2,2u2t, x3.t&equals;&lcub;q1,1w2,1x1t+q1,1w2,2x2t+o1,1x3t+o1,2x4t +q1,1z2,1u1t+q1,1z2,2u2t, x4.t&equals;&lcub;q2,1w2,1x1t+q2,1w2,2x2t+o2,1x3t+o2,2x4t +q2,1z2,1u1t+q2,1z2,2u2t, y1t&equals;&lcub;s1,1w2,1x1t+s1,1w2,2x2t+r1,1x3t+r1,2x4t +s1,1z2,1u1t+s1,1z2,2u2t&rsqb;

(4)

Example 4: Series connection of two systems with 1st output of 1st system to 2nd input of 2nd system and 2nd output of 1st system to 1st input of 2nd system

series4:=SeriesConnectsys1c&comma;sys2b&comma;1&comma;2&comma;2&comma;1&colon;

PrintSystemseries4

State Spacecontinuous1 output(s); 2 input(s); 4 state(s)inputvariable&equals;u1t&comma;u2toutputvariable&equals;y1tstatevariable&equals;x1t&comma;x2t&comma;x3t&comma;x4ta&equals;t1,1t1,200t2,1t2,200q1,1w2,1+q1,2w1,1q1,1w2,2+q1,2w1,2o1,1o1,2q2,1w2,1+q2,2w1,1q2,1w2,2+q2,2w1,2o2,1o2,2b&equals;v1,1v1,2v2,1v2,2q1,1z2,1+q1,2z1,1q1,1z2,2+q1,2z1,2q2,1z2,1+q2,2z1,1q2,1z2,2+q2,2z1,2c&equals;s1,1w2,1+s1,2w1,1s1,1w2,2+s1,2w1,2r1,1r1,2d&equals;s1,1z2,1+s1,2z1,1s1,1z2,2+s1,2z1,2

(5)

Example 5: Series connection of three systems as shown in the figure.

series5:=SeriesConnectsys1c&comma;sys2b&comma;sys1b&comma;1&comma;2&comma;2&comma;1&comma;1&comma;1&colon;

PrintSystemseries5

State Spacecontinuous2 output(s); 2 input(s); 6 state(s)inputvariable&equals;u1t&comma;u2toutputvariable&equals;y1t&comma;y2tstatevariable&equals;x1t&comma;x2t&comma;x3t&comma;x4t&comma;x5t&comma;x6ta&equals;t1,1t1,20000t2,1t2,20000q1,1w2,1+q1,2w1,1q1,1w2,2+q1,2w1,2o1,1o1,200q2,1w2,1+q2,2w1,1q2,1w2,2+q2,2w1,2o2,1o2,200j1,1s1,1w2,1+j1,1s1,2w1,1j1,1s1,1w2,2+j1,1s1,2w1,2j1,1r1,1j1,1r1,2i1,1i1,2j2,1s1,1w2,1+j2,1s1,2w1,1j2,1s1,1w2,2+j2,1s1,2w1,2j2,1r1,1j2,1r1,2i2,1i2,2b&equals;v1,1v1,2v2,1v2,2q1,1z2,1+q1,2z1,1q1,1z2,2+q1,2z1,2q2,1z2,1+q2,2z1,1q2,1z2,2+q2,2z1,2j1,1s1,1z2,1+j1,1s1,2z1,1j1,1s1,1z2,2+j1,1s1,2z1,2j2,1s1,1z2,1+j2,1s1,2z1,1j2,1s1,1z2,2+j2,1s1,2z1,2c&equals;s1,1l1,1w2,1+l1,1s1,2w1,1s1,1l1,1w2,2+l1,1s1,2w1,2l1,1r1,1l1,1r1,2k1,1k1,2l2,1s1,1w2,1+s1,2l2,1w1,1l2,1s1,1w2,2+s1,2l2,1w1,2l2,1r1,1l2,1r1,2k2,1k2,2d&equals;s1,1l1,1z2,1+l1,1s1,2z1,1s1,1l1,1z2,2+l1,1s1,2z1,2l2,1s1,1z2,1+s1,2l2,1z1,1l2,1s1,1z2,2+s1,2l2,1z1,2

(6)

Alternately, using the series4 result:

series5e:=SeriesConnectseries4&comma;sys1b&colon;

PrintSystemseries5e

State Spacecontinuous2 output(s); 2 input(s); 6 state(s)inputvariable&equals;u1t&comma;u2toutputvariable&equals;y1t&comma;y2tstatevariable&equals;x1t&comma;x2t&comma;x3t&comma;x4t&comma;x5t&comma;x6ta&equals;t1,1t1,20000t2,1t2,20000q1,1w2,1+q1,2w1,1q1,1w2,2+q1,2w1,2o1,1o1,200q2,1w2,1+q2,2w1,1q2,1w2,2+q2,2w1,2o2,1o2,200j1,1s1,1w2,1+s1,2w1,1j1,1s1,1w2,2+s1,2w1,2j1,1r1,1j1,1r1,2i1,1i1,2j2,1s1,1w2,1+s1,2w1,1j2,1s1,1w2,2+s1,2w1,2j2,1r1,1j2,1r1,2i2,1i2,2b&equals;v1,1v1,2v2,1v2,2q1,1z2,1+q1,2z1,1q1,1z2,2+q1,2z1,2q2,1z2,1+q2,2z1,1q2,1z2,2+q2,2z1,2j1,1s1,1z2,1+s1,2z1,1j1,1s1,1z2,2+s1,2z1,2j2,1s1,1z2,1+s1,2z1,1j2,1s1,1z2,2+s1,2z1,2c&equals;l1,1s1,1w2,1+s1,2w1,1l1,1s1,1w2,2+s1,2w1,2l1,1r1,1l1,1r1,2k1,1k1,2l2,1s1,1w2,1+s1,2w1,1l2,1s1,1w2,2+s1,2w1,2l2,1r1,1l2,1r1,2k2,1k2,2d&equals;l1,1s1,1z2,1+s1,2z1,1l1,1s1,1z2,2+s1,2z1,2l2,1s1,1z2,1+s1,2z1,1l2,1s1,1z2,2+s1,2z1,2

(7)

See Also

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


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