PID tuning based on Ziegler-Nichols time domain (open-loop) methods - MapleSim Help

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ControlDesign[ZNTimeModified] - PID tuning based on Ziegler-Nichols time domain (open-loop) methods

Calling Sequence

ZNTimeModified(Kt, T, L, opts)

Parameters

Kt

-

algebraic or non-zero realcons; gain of the FOTD (First order with Time Delay) model

T

-

algebraic or positive realcons; time constant of the FOTD model

L

-

algebraic or positive realcons; time delay of the FOTD model

opts

-

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

Description

• 

The ZNTimeModified command calculates the controller gains based on the Ziegler-Nichols time domain (open-loop) tuning methods as specified in the options, using the given  first order time delay model parameters.

• 

The ZNTimeModified command returns a list of controller gains Kp, Ki and Kd according to the selected controller type P, PI or PID, respectively, where Kp is the proportional gain, Ki is the integral gain, and Kd is the derivative gain.

• 

The controller transfer function is then obtained as:

– 

P: Cs=Kp 

– 

PI: Cs=Kp+Kis

– 

PID: Cs=Kp+Kis+Kds

Examples

withControlDesign:

withDynamicSystems:

sysNewSystem2.5s2+3s+5:

Identify the parameters [Kt, T, L] of sys

ParamsParameterIdentify:-TimeDomainsys

Params:=0.5000000000,0.2000000000,0.3645751311

(1)

Calculate the controller parameters using the MZN method

ZNTimeModifiedParams1,Params2,Params3,'method'=MZN,'controller'=P

1.097167540

(2)

ZNTimeModifiedParams1,Params2,Params3,'method'=MZN,'controller'=Π

0.9874507860,0.9028324590

(3)

pidZNTimeModifiedParams1,Params2,Params3,'method'=MZN,'controller'=PID,'factored'=true,'returntype'=record

pid:=RecordpackedK=1.316601048,Ti=0.7291502622,Td=0.1822875656

(4)

pidsysZNTimeModifiedParams1,Params2,Params3,'method'=MZN,'controller'=PID,'returntype'=system:

Warning, improper transfer-function, degree(num) > degree(den)

PrintSystempidsys

Transfer Functioncontinuous1 output(s); 1 input(s)inputvariable=u1soutputvariable=y1stf1,1=0.2399999999s2+1.316601048s+1.805664917s

(5)

Calculate the controller parameters using the AMIGO method

The AMIGO method does not apply to the P controller

ZNTimeModifiedParams1,Params2,Params3,'method'=AMIGO,'controller'=P

Error, (in ControlDesign:-ZNTimeModified) invalid controller type; the AMIGO method does not apply to the 'P' controller

PIparsZNTimeModifiedParams1,Params2,Params3,'method'=AMIGO,'controller'=Π,'returntype'=record

PIpars:=RecordpackedKp=0.4330243721,Ki=1.879995098

(6)

PIsysZNTimeModifiedParams1,Params2,Params3,'method'=AMIGO,'controller'=Π,'returntype'=system:

PrintSystemPIsys

Transfer Functioncontinuous1 output(s); 1 input(s)inputvariable=u1soutputvariable=y1stf1,1=0.4330243721s+1.879995098s

(7)

ZNTimeModifiedParams1,Params2,Params3,'method'=AMIGO,'controller'=PID

0.8937253934,3.082606536,0.1053196425

(8)

See Also

ControlDesign, ControlDesign[CohenCoon], ControlDesign[ParameterIdentify][TimeDomain], ControlDesign[ZNFreq]

References

  

[1] K. J. Astrom and T. Hagglund, Advanced PID Control, ISA, 2006.


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