extract the subsystem from a system by specifying a set of inputs, outputs, and/or states - Maple Help

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DynamicSystems[Subsystem] - extract the subsystem from a system by specifying a set of inputs, outputs, and/or states

Calling Sequence

Subsystem(system, opts)

Subsystem(system, inputs, opts)

Subsystem(system, inputs, outputs, opts)

Subsystem(system, inputs, outputs, states, opts)

Parameters

system

-

System; system object

inputs

-

set(posint), all, none; set of indexes of selected inputs to extract from system (the default is all)

outputs

-

set(posint), all, none; set of indexes of selected outputs to extract from system (the default is all)

states

-

set(posint), all, none; set of indexes of selected states to extract from system (the default is all)

opts

-

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

Description

• 

The Subsystem command extracts a subsystem from a system object given a set of selected inputs, outputs and/or states. The input, output, and state variables in the new subsystem are chosen based on the index of their corresponding sets as they appear in the original system object.

• 

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 Subsystem 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:

Define a state-space system with n states, m inputs, and p outputs.

n:=6:m:=4:p:=3:

A1:=Matrixn,n,symbol=a:

B1:=Matrixn,m,symbol=b:

C1:=Matrixp,n,symbol=c:

D1:=Matrixp,m,symbol=d:

sys:=StateSpaceA1,B1,C1,D1:PrintSystemsys

State Spacecontinuous3 output(s); 4 input(s); 6 state(s)inputvariable=u1t,u2t,u3t,u4toutputvariable=y1t,y2t,y3tstatevariable=x1t,x2t,x3t,x4t,x5t,x6ta=a1,1a1,2a1,3a1,4a1,5a1,6a2,1a2,2a2,3a2,4a2,5a2,6a3,1a3,2a3,3a3,4a3,5a3,6a4,1a4,2a4,3a4,4a4,5a4,6a5,1a5,2a5,3a5,4a5,5a5,6a6,1a6,2a6,3a6,4a6,5a6,6b=b1,1b1,2b1,3b1,4b2,1b2,2b2,3b2,4b3,1b3,2b3,3b3,4b4,1b4,2b4,3b4,4b5,1b5,2b5,3b5,4b6,1b6,2b6,3b6,4c=c1,1c1,2c1,3c1,4c1,5c1,6c2,1c2,2c2,3c2,4c2,5c2,6c3,1c3,2c3,3c3,4c3,5c3,6d=d1,1d1,2d1,3d1,4d2,1d2,2d2,3d2,4d3,1d3,2d3,3d3,4

(1)

Extract a subsystem with three inputs (u1(t), u2(t), and u4(t)), one output (y2(t)), and three states (x1(t), x3(t), and x6(t)).

ex_in:=1,2,4:

ex_out:=2:

ex_states:=1,3,6:

subsys:=Subsystemsys,ex_in,ex_out,ex_states:PrintSystemsubsys

State Spacecontinuous1 output(s); 3 input(s); 3 state(s)inputvariable=u1t,u2t,u4toutputvariable=y2tstatevariable=x1t,x3t,x6ta=a1,1a1,3a1,6a3,1a3,3a3,6a6,1a6,3a6,6b=b1,1b1,2b1,4b3,1b3,2b3,4b6,1b6,2b6,4c=c2,1c2,3c2,6d=d2,1d2,2d2,4

(2)

Extract a subsystem in differential equation form  with all of the inputs, two outputs (y1(t) and y2(t)), and the first state.

allinputs:=Subsystemsys,all,1,2,1,outputtype=de:PrintSystemallinputs

Diff. Equationcontinuous2 output(s); 4 input(s)inputvariable=u1t,u2t,u3t,u4toutputvariable=y1t,y2tde={[x1.t=a1,1x1t+b1,1u1t+b1,2u2t+b1,3u3t+b1,4u4t, y1t=c1,1x1t+d1,1u1t+d1,2u2t+d1,3u3t+d1,4u4t, y2t=c2,1x1t+d2,1u1t+d2,2u2t+d2,3u3t+d2,4u4t]

(3)

Extract a subsystem with  three inputs (u1(t), u2(t), and u4(t)), output y2(t), and no states.

nostates:=Subsystemsys,ex_in,ex_out,none:PrintSystemnostates

State Spacecontinuous1 output(s); 3 input(s); 0 state(s)inputvariable=u1t,u2t,u4toutputvariable=y2tstatevariable=a=b=c=d=d2,1d2,2d2,4

(4)

When the inputs, outputs, and states arguments are omitted or incorrect, the Subsystem command returns the original system.

dsubsys1:=Subsystemsys:PrintSystemdsubsys1

State Spacecontinuous3 output(s); 4 input(s); 6 state(s)inputvariable=u1t,u2t,u3t,u4toutputvariable=y1t,y2t,y3tstatevariable=x1t,x2t,x3t,x4t,x5t,x6ta=a1,1a1,2a1,3a1,4a1,5a1,6a2,1a2,2a2,3a2,4a2,5a2,6a3,1a3,2a3,3a3,4a3,5a3,6a4,1a4,2a4,3a4,4a4,5a4,6a5,1a5,2a5,3a5,4a5,5a5,6a6,1a6,2a6,3a6,4a6,5a6,6b=b1,1b1,2b1,3b1,4b2,1b2,2b2,3b2,4b3,1b3,2b3,3b3,4b4,1b4,2b4,3b4,4b5,1b5,2b5,3b5,4b6,1b6,2b6,3b6,4c=c1,1c1,2c1,3c1,4c1,5c1,6c2,1c2,2c2,3c2,4c2,5c2,6c3,1c3,2c3,3c3,4c3,5c3,6d=d1,1d1,2d1,3d1,4d2,1d2,2d2,3d2,4d3,1d3,2d3,3d3,4

(5)

dsubsys2:=Subsystemsys,no,al,1,2,3:PrintSystemdsubsys2

State Spacecontinuous3 output(s); 4 input(s); 6 state(s)inputvariable=u1t,u2t,u3t,u4toutputvariable=y1t,y2t,y3tstatevariable=x1t,x2t,x3t,x4t,x5t,x6ta=a1,1a1,2a1,3a1,4a1,5a1,6a2,1a2,2a2,3a2,4a2,5a2,6a3,1a3,2a3,3a3,4a3,5a3,6a4,1a4,2a4,3a4,4a4,5a4,6a5,1a5,2a5,3a5,4a5,5a5,6a6,1a6,2a6,3a6,4a6,5a6,6b=b1,1b1,2b1,3b1,4b2,1b2,2b2,3b2,4b3,1b3,2b3,3b3,4b4,1b4,2b4,3b4,4b5,1b5,2b5,3b5,4b6,1b6,2b6,3b6,4c=c1,1c1,2c1,3c1,4c1,5c1,6c2,1c2,2c2,3c2,4c2,5c2,6c3,1c3,2c3,3c3,4c3,5c3,6d=d1,1d1,2d1,3d1,4d2,1d2,2d2,3d2,4d3,1d3,2d3,3d3,4

(6)

Extract a subsystem with no inputs, no outputs, and no states.

nsubsys:=Subsystemsys,none,none,none:PrintSystemnsubsys

State Spacecontinuous0 output(s); 0 input(s); 0 state(s)inputvariable=outputvariable=statevariable=a=b=c=d=

(7)

Extract subsystem with inputs u1(t), u2(t) and u3(t). Observe that index repetition and sorting are not relevant in a set.

subsys1:=Subsystemsys,1,2,3,3,1:PrintSystemsubsys1

State Spacecontinuous3 output(s); 3 input(s); 6 state(s)inputvariable=u1t,u2t,u3toutputvariable=y1t,y2t,y3tstatevariable=x1t,x2t,x3t,x4t,x5t,x6ta=a1,1a1,2a1,3a1,4a1,5a1,6a2,1a2,2a2,3a2,4a2,5a2,6a3,1a3,2a3,3a3,4a3,5a3,6a4,1a4,2a4,3a4,4a4,5a4,6a5,1a5,2a5,3a5,4a5,5a5,6a6,1a6,2a6,3a6,4a6,5a6,6b=b1,1b1,2b1,3b2,1b2,2b2,3b3,1b3,2b3,3b4,1b4,2b4,3b5,1b5,2b5,3b6,1b6,2b6,3c=c1,1c1,2c1,3c1,4c1,5c1,6c2,1c2,2c2,3c2,4c2,5c2,6c3,1c3,2c3,3c3,4c3,5c3,6d=d1,1d1,2d1,3d2,1d2,2d2,3d3,1d3,2d3,3

(8)

Extract subsystem with inputs u1(t) and u3(t) and outputs y1(t) and y2(t).

subsys2:=Subsystemsys,3,1,1,2:PrintSystemsubsys2

State Spacecontinuous2 output(s); 2 input(s); 6 state(s)inputvariable=u1t,u3toutputvariable=y1t,y2tstatevariable=x1t,x2t,x3t,x4t,x5t,x6ta=a1,1a1,2a1,3a1,4a1,5a1,6a2,1a2,2a2,3a2,4a2,5a2,6a3,1a3,2a3,3a3,4a3,5a3,6a4,1a4,2a4,3a4,4a4,5a4,6a5,1a5,2a5,3a5,4a5,5a5,6a6,1a6,2a6,3a6,4a6,5a6,6b=b1,1b1,3b2,1b2,3b3,1b3,3b4,1b4,3b5,1b5,3b6,1b6,3c=c1,1c1,2c1,3c1,4c1,5c1,6c2,1c2,2c2,3c2,4c2,5c2,6d=d1,1d1,3d2,1d2,3

(9)

See Also

Description of the Model of a Linear System Object, DynamicSystems, DynamicSystems[AlgEquation], DynamicSystems[Coefficients], DynamicSystems[DiffEquation], DynamicSystems[PrintSystem], DynamicSystems[StateSpace], DynamicSystems[TransferFunction], DynamicSystems[ZeroPoleGain]


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