compute the system resulting from multiplying each input of a system object by a coefficient - Maple Help

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

Calling Sequence

ScaleInputs(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 ScaleInputs command

Description

• 

The ScaleInputs command creates a system that scales the inputs of sys by the coefficients in the coefficients list.

• 

The type of the system object ScaleInputs 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 ScaleInputs 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 input of sys1:

ci:=k1

ci:=k1

(2)

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

sys1a:=ScaleInputssys1,ci,parameters=k1=1:

PrintSystemsys1a

State Spacecontinuous1 output(s); 1 input(s); 3 state(s)inputvariable=u1toutputvariable=y1tstatevariable=x1t,x2t,x3ta=010001−6−7−5b=00k1c=010d=0

(3)

sys1b:=ScaleInputssys1,ci,outputtype=coeff:

PrintSystemsys1b

Coefficientscontinuous1 output(s); 1 input(s)inputvariable=u1soutputvariable=y1snum1,1=k1,0den1,1=1,5,7,6

(4)

Discrete multiple-input multiple-output (MIMO) case 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 the inputs of sys2:

cf:=a,0.5

cf:=a,0.5

(7)

sys2a:=ScaleInputssys2,cf,outputtype=tf:

PrintSystemsys2a

Transfer Functiondiscrete; sampletime = .1e-22 output(s); 2 input(s)inputvariable=u1z,u2zoutputvariable=y1z,y2ztf1,1=69az24az25z+4tf2,1=33az+12az25z+4tf1,2=0.5000000000z2+33.z56.z25.z+4.tf2,2=23.50000000z46.z25.z+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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