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CohenCoon

  

PID tuning based on Cohen-Coon method

 

Calling Sequence

Parameters

Options

Description

Examples

References

Calling Sequence

CohenCoon(Kt, T, L, opts)

Parameters

Kt

-

algebraic or non-zero realcons; gain of the first-order with time-delay (FOTD) 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 CohenCoon command

Options

• 

controller = P, PI, PD, or PID

  

Specifies the controller type. The default value is PID.

• 

factored  = true or false

  

True means return the factored version of the controller gains (K=Kp, Ti=KpKi, Td=KdKp). False means return the controller gains (Kp, Ki, Kd). The default is false.

• 

returntype =  list or record or system

  

Specifies the returned type. If list (or record) is specified, a list (or record) containing the controller parameters is returned. If system is specified, a System (DynamicSystems system object) containing the transfer function of the specified controller type (P, PI, PID) is returned. The default value is list.

Description

• 

The CohenCoon command calculates the controller gains based on the Cohen-Coon tuning method using the given first-order time-delay model parameters.

• 

The CohenCoon command returns a list of controller gains Kp, Ki and Kd according to the selected controller type (P, PI, PD, PID), 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

– 

PD: Cs=Kds+Kp

– 

PID: Cs=Kp+Kis+Kds

Examples

withControlDesign:

withDynamicSystems:

sys1NewSystems+1s2+5s+12:

Params1evalfParameterIdentify:-TimeDomainsys1

Params1:=0.08333333333,0.9965217283,0.9331168468

(1)

Calculate the gains for controller types P, PI, PD, and PID.

PgainCohenCoonParams11,Params12,Params13,'controller'=P

Pgain:=17.01539475

(2)

PIgainsCohenCoonParams11,Params12,Params13,'controller'=Π

PIgains:=12.52745528,11.47249211

(3)

PDgainsCohenCoonParams11,Params12,Params13,'controller'=PD

PDgains:=17.82548949,2.753995614

(4)

PIDgainsCohenCoonParams11,Params12,Params13,'controller'=PID

PIDgains:=20.21678293,11.46866675,5.925668011

(5)

Return a record containing the PID controller gains.

PIDrecCohenCoonParams11,Params12,Params13,'controller'=PID,'returntype'=record

PIDrec:=RecordpackedKp=20.21678293,Ki=11.46866675,Kd=5.925668011

(6)

Return a System (DynamicSystems system object) for the PID controller.

PIDsysCohenCoonParams11,Params12,Params13,'controller'=PID,'returntype'=system:

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

PrintSystemPIDsys

Transfer Functioncontinuous1 output(s); 1 input(s)inputvariable=u1soutputvariable=y1stf1,1=5.925668011s2+20.21678293s+11.46866675s

(7)

sys2NewSystems+as2+5s+12:

Params2ParameterIdentify:-TimeDomainsys2

Params2:=112a,12120736a21144a,124125a+144120736a21144a+124213a2+10368120736a21144+60aa2a144120736a21144a

(8)

Return a record containing the PID controller parameters in factored form.

PIDparamsCohenCoonopParams2,'controller'=PID,'factored'=true,'returntype'=record:

evalfPIDparams:-Ka=1|PIDparams:-Ka=1

20.21678291

(9)

evalfPIDparams:-Tia=1|PIDparams:-Tia=1

1.762784060

(10)

evalfPIDparams:-Tda=1|PIDparams:-Tda=1

0.2931063776

(11)

Return a record containing the PID controller gains.

PIDgainsCohenCoonopParams2,'controller'=PID,'returntype'=record:

evalfPIDgains:-Kpa=1|PIDgains:-Kpa=1

20.21678291

(12)

evalfPIDgains:-Kia=1|PIDgains:-Kia=1

11.46866674

(13)

evalfPIDgains:-Kda=1|PIDgains:-Kda=1

5.925668008

(14)

References

  

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

See Also

ControlDesign

ControlDesign[ParameterIdentify][TimeDomain]

ControlDesign[ZNFreq]

ControlDesign[ZNTimeModified]

 


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