SINTONIZACION DE CONTROLADORES PID

RESUMEN DE ALGUNOS MÉTODOS Y CONSIDERACIONES SOBRE LA ESTRUCTURA

ESTRUCTURA

MÉTODO DE ZIEGLER NICHOLS

ZIEGLER NICHOLS

EJEMPLO: EXAMINEMOS EL SIGUIENTE SISTEMA

G(s)=1

𝑠3+3𝑠2+3𝑠+1

K=1

1= 1 𝜏 = 1,5 ∗ 3,26 − 1,85 = 2, , 115

𝐿 = 𝑡2 − 𝜏 =3,26-2,115=1,145

a=𝐾∗𝐿

𝜏=

1∗1,145

2,115= 0,5414

𝑘𝑝 =1,2

0,5414=2,2165

𝑇𝑖 = 2 ∗ 𝐿 =2,29

𝑇𝑑 = 0,5 ∗ 𝐿 =0,5725

SISTEMA EN LAZO CERRADO

CONTROLADOR P CON DIFERENTES GANANCIAS

PID POR ZIEGLER-NICHOLS

Chien–Hrones–ReswickREGULACIÓN DE SET POINT

Chien–Hrones–ReswickRECHAZO DE PERTURBACIONES

Método de Cohen-Coon

PID TUNING: MINIMUM ERROR INTEGRAL CRITERIA.

Integral of the Absolute Value of the Error (IAE):

0(t)IA e dtE

Integral of the Square of the Error (ISE):

2

0( )eISE dtt

• Penaliza los errores grandes

• Controladores de alta ganancia(respuesta oscilatoria)

Integral of Time-Weighted Absolute Value of the Error (ITAE):

0( )I t eT tE dA t

Integral of Time-Weighted Squared Value of the Error (ITSE):

2

0( )tITSE e dtt

• Penaliza los errores u oscilaciones prolongados

• Time penalty

AHORA SUPONGA QUE VA A IMPLEMENTAR EL CONTROLADOR¿QUÉ ESTRUCTURA TENDRA EL CONTROLADOR QUE USARÁ?

DEPENDERÁ DE EN QUE LO IMPLMENTE, SI USTED LO PROGRAMA O USARÁ UN BLOQUE PRE – DEFINIDO DE UN SISTEMA

ADICION DE FILTRO A LA ACCIÓN DERIVATIVA

𝐾𝑝1 +1

𝑇𝑖𝑠+

𝑠𝑇𝑑

1 + 𝑠𝑇𝑑𝑁

La acción derivativa pura, como hemosvisto, no es muy conveniente enpresencia de ruido.Además genera una acción muy“fuerte” ante un escalón.Es por esto que en aplicacionesprácticas suele implementarse un filtropasa-bajas de primer orden.

PI-DPID CON ACCIÓN DERIVATIVA EN EL BUCLE DE

REALIMENTACIÓN

1 +𝐾𝑝𝑁

𝑇𝑖𝑇𝑠2 ± 𝐾𝑝 𝑇𝑖 +𝑇𝑑𝑁

+ 𝐾𝑝

൰𝐾𝑝(𝑇𝑖𝑠 + 1)(𝑇𝑑𝑠𝑁

+ 1

Se trata de poner la acción derivativa detal forma que actúe en el lazo derealimentación, para una respuesta mássuave.

PI-DPID CON ACCIÓN DERIVATIVA EN EL BUCLE DE

REALIMENTACIÓN

CONTROLADOR PARALELO

PARALELO

“Some academic textbooks discuss the parallel form of PID controller, but it is also used in some

DCSs and PLCs. This algorithm is simple to understand, but not intuitive to tune. The reason is

that it has no controller gain (affecting all three control modes), it has a proportional gain instead

(affecting only the proportional mode). Adjusting the proportional gain should be supplemented by

adjusting the integral and derivative settings at the same time. Try to not use this controller

algorithm if possible (in some DCSs it is an option, so select the alternative).”http://blog.opticontrols.com/

CONTROLADOR SERIE (interactivo)

The oldest controller algorithm is called the Series, Classical, Real or Interactive algorithm.

The original pneumatic and electronic controllers had this algorithm and it is still found it in many

controllers today. The Ziegler-Nichols PID tuning rules were developed for this controlleralgorithm

NO INTERACTIVO

The Noninteractive algorithm is also called the Ideal, Standard or ISA algorithm. The Cohen-Coon

and Lambda PID tuning rules were designed for this algorithm.

Note: If no derivative is used (i.e. Td = 0), the interactive and noninteractive controller algorithms are

identical.

http://blog.opticontrols.com/significance of Different Algorithms

• The biggest difference between the controller algorithms is that the Parallel controllerhas a true Proportional Gain (Kp), while the other two algorithms have a Controller Gain(Kc). Controller Gain affects all three modes (Proportional, Integral and Derivative) ofthe Series and Ideal controllers, while Proportional Gain affects only the Proportionalmode of a Parallel controller.

• This difference has a major impact on the tuning of the controllers. All the populartuning rules (Ziegler-Nichols, Cohen-Coon, Lambda, and others) assume the controllerdoes not have a parallel structure and therefore has a Controller Gain. To tune a Parallelcontroller using any of these rules, the Integral time has to be divided and derivativetime multiplied by the calculated Controller Gain.

• The second difference between the controller algorithms is the interaction between theIntegral and Derivative modes of the Series (Interactive) controller. This, of course, isonly of significance if the Derivative mode is used. In most PID controller applications,Derivative mode is not used. Formulas have been developed for converting tuningsettings between Ideal and Series controller algorithms.

Units of Measure of Tuning Settings

• Another very important difference between controllers lies in the units ofmeasure of the tuning settings. There are three differences.

1. Most controller types (e.g. Honeywell Experion, Emerson DeltaV, ABB Bailey)use Controller Gain, while some (e.g. Foxboro I/A, Yokogawa CS3000) useProportional Band (PB). The conversion between the two is easy once you knowwhich one is being used: PB = 100% / Kc.

2. Many controllers (e.g. Siemens APACS) use minutes as the unit for Integral andDerivative modes, but some controllers (e.g. Emerson DeltaV) use seconds.

3. Some controllers (e.g. ABB Mod 300) use Time for their Integral unit, whileothers (e.g. Allen-Bradley SLC500) use Repeats/Time. These are reciprocals of eachother.

The first controller I ever tried to tune used Proportional Band, but at the time, Ihad never heard of this concept. Needless to say, when I entered my calculated Kcof 1.2 into its PB setting, the loop became wildly unstable. It did not take me longto realize that I should read up on PID controllers before trying to tune one again.

Other Differences

• Beyond the differences mentioned above, controllers also differ in theway the changes on controller output is calculated (positional andvelocity algorithms), in the way Proportional and Derivative modesact on set point changes, in the way the Derivative mode islimited/filtered, as well as a interesting array of other minordifferences. These differences are normally subtle, and should notaffect your tuning.

• When tuning controllers, always find out what structure thecontroller has and what units it is using.