auto tuning of pid

8/2/2019 Auto tuning of PID

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1997 lEEE lnteriintioiinlConfcrcncc on ntelligent I'roccssing Systcills Octobcr 28 - 31. Ucijing. Cliin.1

Auto-Tuning of PID Parameters Based on S witch Step Response

Yang ZhiDept. of Electrical and Inform ation Engineering

GansuUniversity of TechnologyLanzhou, 730050

ChinaAbsfracr--A new switch step response method is proposed inthis paper to identify the character parameters of industryprocess , hen calciilated the parameters of PID controller bythe well-known Ziegler-Nichols fomulas. Therefore, self-tuning of the closed-loop control systems can be implemented.The effectiveness of this method is proved by theory analysisand simulation test.

I. INTRODUCTION

The conventional PID controllers are widely used fortheir simple structure , the effectiveness of the PID is veryobvious through theoretical research and long-term practicein process control [ I ] . Howev er, there are still someunsolved problems in practical applications.For example,the difficulty of debugging is focused on the tuning of thecontrollers parameters before the control system gets intooperation. The tuning of the PID controllers mainlydepends on the experience of expert operators and well-known regular iules,such as Ziegler-Nichols formulasetc.But these methods are usually based on trial, dependson ability and experience of the operator. There is alsosome difficulty of tuning PID due to the time delay,&nlinearity and time-variation in the practicalsystemsSince 1084, Swedish scholar K.J.Astrom ,etc.[2] presented a kind of intelligent relay oscillation self-tuning of PID parameters, which focused pelple's attentionagain to control $theory esearch and practical application.Later, a variety of commercialized intelligent PID self-tuners and adaptive PID controllers were presented torealized the auto-indentification of the math model inindusfrical process and auto-tuning of PID controllers [3].0-7503-4253-4/97/$10.00 0 997 1EEE

Wang JinglingDept. of Electrical and Inform ation Engineering Gansu

University of TechnologyLanzhou, 730050

ChinaThe intelligent relay oscillation self- tuning PIDcontroller proposed by Astrom [4] is a kind of simple andapplicable self-tuning controller, and is widely used inindustry process at present, especially in temperaturecontrol.But it needs to produce continuous oscillationduring the self-tuning process, which is not allowed inmany industry process control. To this end, a new closed-switch step response method is presented in this paper toidentify the character parameters of controlled processincluding equivalent delay time and m amu m-va rious slopeof the output step response, then use Z-N formulae tocalculated PID parameters, so the self-tuning parameters ofPID controller is completed.11 IDENTIFITION OF THE PROCESS CHARACTER

PARAMETERS

A . The Character Parameters of the Controlled ProcessIt is necessary to know the mathematical models of

controlled process when designing a controller, or characterparameters.The most popular plant models in industry canbe assumed to various forms,for instance:

The first-order model w ith time delayKe-"G(s)=-s+ 1

The second-orde r or nth-order model with time delayKe-"G(s) = ( T s + l)(T,s+l)

Ke-"(Ts+1)"G(s)=The high-order system can usually be described by a firstorder model with time delay. Fig.1 shows the equivalentrelation by a step response curve. Where K represents thestatic gain of the process, which isdirectly acquired through

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100

90

80

70

60

2s 5040

30

20

10

0

T ime (I )

2

Fig 1 u n i t step response of process

u t and output static value, The pcan be determined by a graphic methodthe follows:

Ma ent at the inflTime (5 )time axis at point A and the static asymptote at point Bnt time delay r and the inertia

d . R is the slope of the tatuning of the PI D parameters is mainly dependent on this t theorem can be achieved through these

6 Closed-Loop Switch Step Response

The graphic method is based on

PI D controllers.

begins working until the process variable

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function when r 5 t 5 t * +T and a monotone descreasefunction when f > f * +r that is

controllerPPI

PID

1- r- _y ( f )= K ( l - e ) ( T I f < t * + r )Kp TI TdIiR L

0.9R.L 3L1 2 R L 2L U2and

. y ' ( t ) = - ( e 7 - e * ) < OK -!z -5Tso y(t) reaches the maximu m value at t '= t * +zand the smooth moving time L achieved throughexperiment is:

(6 )= t'-t* =Equation (6) illustrates that smooth m oving time L canbe determined by simple closed-loop switch step response

test in first-order equivalent time delay system of industrialprocess, or process character parameters which isrepresented by 1- , the slope R can also be easily achievedthrouth the experiment.

111. SEL.F-TUNINGALGORITHM OF PI DPARAMETERS

A . Algorithm

The control effect is usually dependent on the structureand parameters of the controller after the math model ofcontrolled process is established, the algorithm isrepresented by the following non-interacting PIDcontroller:

e ( f ) S V - P V (7a)Tds P V ] (7b)M V = K,[(1 + - ) e ( t ) --;s 1+ aT,s

where SV is the setpoin t variable, PV is process variable e(t)is the error signal, MV is manipulation variable, Kp , Tiand Td are the proportional gain, reset time and derivativetime respectively. The parameter ci is the derivativecoefficeent (0.05SaSO.3). We adopted ~ 0 . 1 whensimulation.

Accor ding to the above closed-loop step response, thecharacter parameters of the controlled process,or equivalenttime delay L and the maximum slopk R of the responsecurve can be estimated conveniently. In view of the well-known Zieglar-Nichols tuning formula, we can derive thetuning param eters of the controller, see in table I.

In conclusion, the self-tuning algorithm of PID parameterscan be summ arized as follows:step I : under the auto-tuning pattern, measure the

process variable (Py)hrough the closed-loop switch stepresponse method and calculate the error e(t). When e(t)>O,manipulation variable M V becomes loo%, when e(t)


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auto tuning of pid

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