Intelligent Self-Tuning PID Controller

INTELLIGENT TUNING/CONTROL

Copyright © IFAC Intclligcnt Tuning and Adaptivc Control, Singaporc 1991

INTELLIGENT SELF-TUNING PID CONTROLLER H. Takatsu, T. Kawano and K. Kitano Development & Engineering Dept., Process Automation Systems Div., Yokogawa Electric Corporation, Musashino-shi, Tokyo, Japan

ABSTRACT. A new self-tuning PlO controller has been developed for distributed process control syste.s. The self-tuning PlO controller is able to identify the process dyna.ics using a short period of process behaivior such as a setpoint change under the closed loop control condition. and to tunc PlO para.eters based on the identified .odel para.eters for both setpoint tracking and disturbance regulation characteristics. which .akes it easy to set up the inital PID para.eters and adapt the PlO values to the process dyna.ics changes. This paper describes the basic principles of the self-tuning controllers. and explains the functions to be i.ple.ented on. Finally. so.e application results illstrate the effectiveness of the self-tuning controllers. KEYWORDS.

Adaptive control: identification: intelligent control: PlO control: self-tuning control

INTRODUCTION (3) The esti.ated process .odel is displayed and utilized to detect if the process dyna.ics has changed and infor. operators of the necessity of retunig in case of the .on i tor i ng .ode. (4) The controller .ay be easily co.bined with conventional control functions to provide .ore sophisticated control.

Many different types of self-tunig PlO controllers have been introduced into the industrial .arket since 1980. However. so.e selftuning controllers need oscilation of process output: so.e need long duration of process output perturbations; so.e need long range observations of process output. These are disadvantages to be applied to the co••ercial practical plants regarded as the disturbances on plant operations. A new self-tunig control ler .ust satisfy the following users' needs: (1) It helps operators and engineers to tune PID para.eters without any special knowledge of the control theory and engineering. (2) It auto.atically updates PID para.eters in order to follow up changes in the plant dyna.ics quickly. (3) It is available online in the co•• ercial industrial plants without disturbing plant operations.

BASIC PRINCIPLES Process Identification Figure 1 shows the basic concept of the selftunig controllers. The self-tuning controller always observes and collects the process input and output data. Ihen the controller detects the process output .ove beco.es larger than a specified level after re.oving the noises. signal trend and sensor failure. it starts the identification co.putation using the collected process input and output data. The key technology is how to esti.ate the process .odel rapidly using a short duration of operating data in the closed loop control condition. because a self-tuning controller has to track the process dyna.ics change. Local identification such as a well known least square .ethod is inadequate to the identification using a short duration of experi.ent. le have adopted an orignal global identification .ethod. The difficult proble.s in on-line practical identification is the effects of unknown disturbances during the experi.ent. The proposed .ethod can deter.ine

Based on the analyses of these users' needs. a new self-tuning PID controller has been developed to be i.ple.ented into the industrial process control syste.s. The new selftuning controller .ainly consists of a process identification part and a PlO tuning part. and have realized the following features: (1) Only a single s.all step change in the setpoint or control output is applied under the closed loop control condition to esti.ate a process .odel and co.pute the opti.al PlO para.eters. (2) The co.puted PID para.eters are transfered to the control part when the certainty of the identified .odel is large enough.

11

i

---'i

L..-.

I

I PV I

PROCESS

VARIABLE Fig.

1

PROCC:SS VAR1.~BLE

Functional Block Diagra. of Self-tuning Controller

a reasonable .odel with .ore than a given level of ·.odel certainty·, taking into account .odelling errors. disturbances and so on. This .ethod has the following features: (1) The .odel is structured in the neighbourhood of the specified frequency do.ain to re.ove the effects of noises or disturbances. (2) One kind of nonlinear progra •• ing techniques is adopted to obtain the .odel using a short period input and output data iterativel

25.

Fig.

y. (3) PID para.eters of the controller is adapt

PID Tuning

ed to the identified .odel only if the certainty of the identified .odel is large enough. (4) Process behavior is observed every .onitoring period and the identification is triggered again when the process .ove beco.es large.

After the process identification, the opti.al PID values are calculated using the esti.ated process .odel and specified controller type, based on the equations described below: I-Ic = A(L/T)2 + B(L/T) + C Ti/T = D(L/T)2 + E(L/T) + F A, B, C, 0, E. F = funct ion( OS, CNT .... ) I: .odel gain, L: .odel delay, T: .odel ti.e lag, Kc: control gain, Ti: i n t e g r a I t i • e ,OS: tar get res po ns e type, CNT: PlO algorith. type

Figure 2 shows one of the .odel fitting trajectories of the adopted .ethod in the para.eter do.ain. The .odel is assu.ed to be a . first-order plus ti.e delay' .odel, which is a suitable .odel because our objective is PID tuning rather than .odel develop.enl. Contour lines in Fig. 2 indicate the sets of .odel para.eters ( gai n, lag, delay) which gi ve the sa.e .odel ing errors. More opti.al set of .odel para.eters is sequentially obtained in order to .ini.ize the .odeling errors, using a set of process inputs and outputs iterat i ve I y.

• T~DJ'Ol 4..R."i='.=

;:> ~

:>-3::: ...

=

:'1-i

?H P...

~

0$=

?

?MlN=

! D

I,t.

ss cs

ex..

These equations are just like the ZieglerNichols .ethod. but each coefficients have been decided after large a.ount of si.ulation runs. Generally speaking, as the opti.al values for setpoint tracking and for disturbance regulation are of different form. The self -tunig controller has adopted two degrees of rreedo. structure in order to satisfy both control specif'cations .

SiC =

LCOP=':'. -

f+i

LL.

T;(

Although PlO para.eters are usually co.puted based on the identified .odel and the userspecified response type, special tunig .echaniz. is prepared for to stabilize the behavior rapidly. In the case of oscillating condition PlO control gain is decreased te.porarily; and vice versa in the case of overda.ping the gain is increased.

!MIN= [ffiX=

J.:'

r..s = T2CXXll

•

?t'fv' =

IT

I

I

!(~ ---

I I

1 C8:22

Fig.

;I~~ ~.O

I

600

j

i

I I

f7~

,

C8 :23

2 Exa.plc of Non-linear Progra •• ing Application

Auto Startup

... ,

Figure 3 shows the controller tuning panel on the display ter.inals. The self-tuning controller has .ore para.eters than conventional PlO controllers, .ost of which are prepared for safety and easiness of plant operation. Auto startup .ode sets up the initial values of these para.eters auto.atically. In this .ode step inputs are applied to the process under the .anual .ode and the subsequent ti.e response data are used to obtain the process .odel and co.pute the initial PlO values through the above described techniques.

C8:2~

3 Tuning Panel of Sclf-tunig Control

12

The estiaated aodel is displayed in the fora of an equivalent' first lag plus tiae delay' aodel with an error of aodel certainty 'Ci'. CR is noraalized to the input signal aaplitude and duration. If Ci is less than 51. the estimated model is adopted to be a reasonable aodel for PID coaputation.

Saapling perid and other paraaeters are also decided based on the response charactristics. LOOP SUPERVISOR Self-tuning control without loop supervising function is dangerous because it is difficult to distinguish process dynaaics changes froa the device failure such as sensors and actuators. In industrial applications aost of contol loops are set out of self-tuning .ode once the initial PID values have been set. In these situations. soae warning syste.s are indispensable to infora operators of the necessity of retuning. The self-tuning controller always coaputes the ratio of process output and aodel output variances. As the variance ratio becoaes large after the process dyna.cs changes. it occurs a warning for a request of retuning.

11 SAMPL I NG PER I 0D 11 STC MODE=AUTO

OPERAT I NG MODE 11

I DATA COL LE CT I NG I 11

AUTO ?

11

PV MOVED

I YES

1

I YES

I ~

MODE I S AUTO ? UUM-_N_O

I REFRESH 11

SI MBOL

1 ~

I YES PID VALUES

RETURN

I

11

Flow Chart of Self-tuning Control

Fig. TABLE 1

NO

PID COMPUTATION

Operation Mode AUTO STARTUP T

1!

IDENTIFICATION

11

Figure t is the flow chart of the self-tunig control. Four self-tunig aodes are available for use. (1) Auto Mode: The self-tunig controller always observes the process behavior. and tracks the process dynaaics changes by the above described identification and PID tuning functions. (2) Monitoring Mode: In this aode. the selftunig control only displays the coaputed process aodel and PID values; it does not set the coaputed PID values to the control part. This aode is effective for validating the self-tunig function or checking the dynaaics changes under practical operations. (3) Auto startup Mode: Auto startup aode is effective to coapute the initial PID paraaeters without any special pre-inforaation. In this aode. an open loop step response is utilized for the identification and PID coapu tation using the saae algorithas. (4) On-deaand Mode: On-deaand aode is available when setpoint changes are not preferable because of soae operating constraints. 'hen the on-deaand tuning is requested. the step signal is applied to the process input only once. The controller estiaates the process aodel using the subsequent closedloop tiae response data.

NO

MODEL CERTAINTY HIGH

I

SPECIFICATIONS

U

I YES

I 11

Self-tuning

STC MODE=OFF

I STC=O.1

Se I f - tun i ng Co n t r 0 I Par a_ e t er s

MANE

DESCR I PT ION

STC

STC MODE

To specify Self-tuning lode

TR

9SS RESPONSE

Approxilate value of rising tile. Used for sa I pi in g t i led ec i s ion.

TI ME NB

NOISE BAND

Noise a.plitude to be added on PV.

PM IN

MIN OF PROPO

Lower I i l i t

RTJONAL BAND

for self-tuning

MIN.

Lower l i l i t of integral tile for

I MIN

OF I NTE

0

f pro po rt i on a I band

GRAL TIME

self-tuning

DMAX

MIN.

Upper I i l i t of derivative tile for

VAT I VE T I ME

self-tuning

MI

TEST SIGNAL

Test signa I allplitude applied to

AMPL I TU DE

MV on aut 0

PA

NE' PROPORT I

Newl y computed proport iona I band

OF DER I

S

tar tan don de mand

I

od e

ONAL TIME IA

NE' INTEGRAL

Newl y computed integral time

TIME DA

NE' DERIVATI

Newl y cOlputed derivative tile

VE T I ME CR LM

MODELLING

Error of the identified lodel

ERROR

certainty

MODEL DEAD

Dead ti le ( delay) of the iden t i-

TIME

fied lodel Tile constant ( I ag )of the

Paraaeters for Self-tunig Control

TM

MODEL TIME CONSTANT

identified lodel

Table 1 shows the paraaeters of self-tunig control and Fig. 3 is the tuning panel of the controllers. 'TR' is specified to be an approliaately 951 response tiae of the process. which is used to decide the saapling period and data collecting duration. 'OS' is the control target. which corresponds to the overshoot or rising tiae of the responses or control criterions shown in Table 2.

GM

MODEL GAIN

Ga in of the identified model

TABLE 2 OS

TARGET RESPONSE

CRITRION

0

NO OVERSHOOT

1

OVERSHOOT SMALL ( SS )

ITAE MINIMUM:

SETTL I NG TIME LARGE

Min. Lie It· d t

2 3

13

Control Target

NO OVERSHOOT

OVERSHOOT MIDIUM ( 10 S )

IAE MINIMUM:

SETTLING TIME MEDIUM

Min. LIe

OVERSHOOT LARGE ( 15 S )

ISE MINIMUM:

SETTL I NG TIME SMALL

Min.Le 2 ·dt

I .dt

IMPLEMENTATION The self-tuning control function has been e.bedded into our single loop controllers and distributed process control syste.s. It is possible for all the control loops to have the self-tuning function. Ihich helps the operators to tune each loops at the plant startup phase. Co.bination of the self-tuning function lith other control functions and sequence logics are effective for practical applications. For exa.ple. it is possible to be adapted to particular process control just like PH process for instance. by co.bining lith nonlinear co.pensation. deadti.e co.pensation and so on . Start and stop operations of self-tunig control according to the plant operating conditions is also available fro. other cont ro I fun c t ion s.

Si.ulation Result for a first-lag lith delay process

Fig. 5

SIMULATIONS Figure 5 indicates a si.ulation result of self-tunig control. The si.ulation process is assu.ed to be as follols: Gp(S)

=

exp( -lOS ) /

Fig. 6

( 1 + lOS )

In si.ulation. step changes arc applied to setpoint iteratively. At pointCD. process output rises slolly because the initial values of proportional band and integral ti.c are large. At point®. the nCI PID para.eters are set up and the process output rises again after the identification using the process be ha v i 0 r bet lee n po i n t CD and ~. The 0 pt i • a I values are allays obtained after point~ to produce exellent responses as a result. Figure 6 is another exa.ple of si.ulation. The si.ulated process is an integral process descrived bclol: Gp(S)

=

Si.ulation Result for an integral process

,

I

I

I

'

Li~W~J~~, tL ~

;.HnN

-: _.~--r-:~!--1-H'-H-:Fig. 7 a)

Step Response of Presure Control Loop

exp( -lOS ) / 20S( 1 + S ) FIC-PV

After setpoint changes lith large initial PID para.cters. the satisfactory PID settings can be obtained.

,

PIC-MV

FIELD TESTS PlC - I' V

So.e field tests lere done in the pilot plant to evaluate the effectiveness of the selftuning controller. The control target is the flol control and pressure control in a pipe line. each of the. interacts each other. Figure 7a) is the step response of the pressure control loop in the setpoint change after auto startup. Figure 7b) shols the effects to the pressure control loop against the sctpoint change of the flol control loop. Even though the process has noises and the interactions betleen control loops. the opti.al PID para.eters lere co.puted online using the short period of operating data.

Fig. 7b)

14

Effects of Setpoint Change of Flow Control Loop

CONCLUSIONS A lot of control techniques have been e.bedded to the PID controller as -intelligence- in developing the new self-tuning control. One is a process .odel which is used to co.pute the PID para.eters and detect the process dyna.ics changes. Another is the identification technique which enables the controller to identify the process dyna.ics fro. a short duration of operating data. The other is the PID co.putation rules to co.pute the opti.al PID values according to the identified process .odel and the current process behavior. Prediction of future behaivior is also possible using the e.bedded process .odel.

REFERENCES Hi •• elblau.D.M. (1972). Applied nonlinear proga•• ing. McGraw-Hill. lita.ori. T. and S.Sin(1990). Special Issue of Adaptive Control. Co.putrol. 32. Corona. Japan y uwan a. M.. and Se bo r g. D. E. (1 982) . A New Method for On-line Controller Tuning. AlchE Journal. 28. 434-440. Ziegler. 1. G. and N. B. Nichols (1942). Opti.u. Settings for Auto.atic Controllers. Trans. ASME. 64. 759.

15