compute properties of a step response - Maple Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Science and Engineering : Dynamic Systems : System Manipulation Tools : DynamicSystems/StepProperties

DynamicSystems[StepProperties] - compute properties of a step response

Calling Sequence

StepProperties( sys, opts )

Parameters

sys

-

System; a system object

opts

-

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

Description

• 

The StepProperties command calculates the unit-step response properties of a system object, sys, where this object must be linear and stable. Both continuous and discrete objects are accepted.

• 

It returns an expression sequence: (final-value, 10%-point, 33%-point, 67%-point, 90%-point, peak-point, settling-point).

• 

The first element in the sequence (final-value) is a single value. Each of the remaining elements is a list of two values, the time or index of the point and the associated value of the step response.

Returned Properties

This list describes each of the properties returned.

• 

Final-value: the steady-state value of the step response.

• 

10%-point: where response first reaches 1/10 to the final value.

• 

33%-point: where response first reaches 1/3 to the final value.

• 

67%-point: where response first reaches 2/3 to the final value.

• 

90%-point: where response first reaches 9/10 to the final value.

• 

peak-point: where response first reaches the peak value. If the peak does not occur, [undefined, undefined] is returned.

• 

settling-point: the settling point of the step response. If the settling time is not found within the given interval, [undefined, undefined] is returned.

Examples

withDynamicSystems:

Sampling frequency

Ts:=0.05

Ts:=0.05

(1)

Duration of simulation

dur:=10

dur:=10

(2)

Number of samples

Ns:=rounddurTs

Ns:=200

(3)

Continuous System

sys:=TransferFunction1s2+s+10

sys:=Transfer Functioncontinuous1 output(s); 1 input(s)inputvariable=u1soutputvariable=y1s

(4)

prop:=StepPropertiessys

prop:=0.100000000000000,0.146150201098349,0.0100000000000000,0.278988775168172,0.0333333333333333,0.419998798778775,0.0666666666666667,0.512928287463024,0.0900000000000000,1.00611486305525,0.160467906604390,7.31709090935268,0.102000000000000

(5)

Final value

prop1

0.100000000000000

(6)

10% to the final value

prop2

0.146150201098349,0.0100000000000000

(7)

33% to the final value

prop3

0.278988775168172,0.0333333333333333

(8)

67% to the final value

prop4

0.419998798778775,0.0666666666666667

(9)

90% to the final value

prop5

0.512928287463024,0.0900000000000000

(10)

peak value

prop6

1.00611486305525,0.160467906604390

(11)

settling value

prop7

7.31709090935268,0.102000000000000

(12)

plots[display]plotprop2..7,style=point,symbol=cross,color=black,symbolsize=30,plot0,prop1,dur,prop1,color=gray,ResponsePlotsys,Step,duration=dur,numpoints=200

Discrete System

sysz:=ToDiscretesys,Ts

sysz:=Transfer Functiondiscrete; sampletime = .5e-11 output(s); 1 input(s)inputvariable=u1zoutputvariable=y1z

(13)

propz:=StepPropertiessysz

propz:=0.0999999989357504,3,0.00760283829914389,6,0.0324850042198717,9,0.0677171304079914,11,0.0926758273948584,21,0.160324379799413,148,0.101735627624127

(14)

Final value

propz1

0.0999999989357504

(15)

10% to the final value

propz2

3,0.00760283829914389

(16)

33% to the final value

propz3

6,0.0324850042198717

(17)

67% to the final value

propz4

9,0.0677171304079914

(18)

90% to the final value

propz5

11,0.0926758273948584

(19)

peak value

propz6

21,0.160324379799413

(20)

settling value

propz7

148,0.101735627624127

(21)

tfs:=subsTs_=Ts,x→x11Ts_,x2

tfs:=x→0.05x10.05,x2

(22)

plots[display]plotmaptfs,propz2..7,style=point,symbol=cross,color=black,symbolsize=30,plot0,prop1,dur,prop1,color=gray,ResponsePlotsysz,Stepsampletime=Ts,samplecount=Ns,discrete=true

See Also

DynamicSystems, DynamicSystems[Step]


Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam