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DynamicSystems[ScaleOutputs] - compute the system resulting from multiplying each output of a system object by a coefficient

Calling Sequence

ScaleOutputs(sys, coefficients, opts)

Parameters

sys

-

System; system object

coefficients

-

list; list of numeric or symbolic coefficients

opts

-

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

Description

• 

The ScaleOutputs command  creates a system that scales the outputs of sys by the coefficients in the coefficients list.

• 

The type of the system object ScaleOutputs returns is determined by the type of the system object specified in the sys parameter unless an option is specified.

• 

If the sys parameter is an algebraic equation (ae) and no option is specified, the ScaleOutputs 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:

Continuous single-input single-output (SISO) system example

sys1:=StateSpacess3+5s2+7s+6:

PrintSystemsys1

State Spacecontinuous1 output(s); 1 input(s); 3 state(s)inputvariable=u1toutputvariable=y1tstatevariable=x1t,x2t,x3ta=010001−6−7−5b=001c=010d=0

(1)

In this example, the list of coefficients contains a symbolic coefficient to be multiplied by the single output of sys1:

co:=k1

co:=k1

(2)

Create the new system, assigning a default value for the symbolic coefficient.

sys1a:=ScaleOutputssys1,co,parameters=k1=1:

PrintSystemsys1a

State Spacecontinuous1 output(s); 1 input(s); 3 state(s)inputvariable=u1toutputvariable=y1tstatevariable=x1t,x2t,x3ta=010001−6−7−5b=001c=01k10d=0

(3)

sys1b:=ScaleOutputssys1,co,outputtype=de:

PrintSystemsys1b

Diff. Equationcontinuous1 output(s); 1 input(s)inputvariable=u1toutputvariable=y1tde={[x1.t=x2t, x2.t=x3t, x3.t=6x1t7x2t5x3t+u1t, y1t=x2tk1]

(4)

Discrete multiple-input multiple-output (MIMO) system example

ss_a:=Matrix1,2,0,4:

ss_b:=Matrix3,7,9,6:

ss_c:=Matrix5,6,5,2:

ss_d:=Matrix0,1,0,0:

sys2:=StateSpacess_a,ss_b,ss_c,ss_d,discrete,sampletime=0.001:

PrintSystemsys2

State Spacediscrete; sampletime = .1e-22 output(s); 2 input(s); 2 state(s)inputvariable=u1q,u2qoutputvariable=y1q,y2qstatevariable=x1q,x2qa=1204b=3796c=5652d=0100

(5)

PrintSystemTransferFunctionsys2

Transfer Functiondiscrete; sampletime = .1e-22 output(s); 2 input(s)inputvariable=u1z,u2zoutputvariable=y1z,y2ztf1,1=69z24z25z+4tf2,1=33z+12z25z+4tf1,2=z2+66z112z25z+4tf2,2=47z92z25z+4

(6)

The list of coefficients for this example contains a symbolic coefficient and a numeric coefficient to be multiplied by sys2 inputs u1 and u2 respectively:

cf:=a,12

cf:=a,12

(7)

sys2a:=ScaleOutputssys2,cf,outputtype=tf:

PrintSystemsys2a

Transfer Functiondiscrete; sampletime = .1e-22 output(s); 2 input(s)inputvariable=u1z,u2zoutputvariable=y1z,y2ztf1,1=69z24az25az+4atf2,1=66z+24z25z+4tf1,2=z2+66z112az25az+4atf2,2=94z184z25z+4

(8)

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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