An industrial application of a performance assessment and retuning technique for PI controllers

ISA Transactions 49 (2010) 244–248

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An industrial application of a performance assessment and retuning technique for PI controllersI Massimiliano Veronesi, Antonio Visioli ∗ Dipartimento di Elettronica per l’Automazione, University of Brescia, Via Branze 38, I-25123 Brescia, Italy

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Article history: Received 13 May 2009 Received in revised form 7 October 2009 Accepted 26 November 2009 Available online 16 December 2009

abstract In this paper we show how a simple methodology for the set-point following performance assessment and automatic tuning of a PI controller can be employed effectively in a real industrial application. In particular, a flow control loop in a pharmaceutical plant is considered. Practical issues related to the implementation in a Distributed Control System are discussed. Results show that the technique is capable of significantly improving the performance of the controller. © 2009 ISA. Published by Elsevier Ltd. All rights reserved.

Keywords: PID control Performance assessment Tuning Set-point following

1. Introduction Proportional-Integral-Derivative (PID) controllers are undoubtedly the most widely adopted controllers in industry owing to their capability of providing a satisfactory performance for a wide variety of processes despite their relative simplicity. However, in spite of the available know-how related to their use, it is wellknown that in many practical cases PID controllers are poorly tuned, mainly because of the lack of time and of the lack of skill of the operator. This has motivated a significant research effort in devising tuning formulas [1] and automating tuning techniques [2,3] which are nowadays available in virtually all the commercial products. These tuning formulas are based on different concepts, for example Internal Model Control (IMC) [4] or pole placement [5,6]. Much research has also been devoted to performance assessment techniques [7] which should be capable, once the performance of the control system has been recognized as unsatisfactory, to suggest the way to solve the problem. In particular, if a bad controller tuning is detected, then new appropriate values of controller parameters should be determined. This is obviously of particular importance in large plants where it is almost impossible for operators to monitor manually hundreds of control loops. It has also to be taken into account that the derivative action is very often not

I This work has been supported partially by MUR scientific research funds.

∗

Corresponding author. Tel.: +39 030 3715460; fax: +39 030 380014. E-mail address: [email protected] (A. Visioli).

employed because of its sensitivity to measurement noise. In fact, a PI controller is sufficient to provide the required performance in many situations [3]. Typically, performance assessment techniques are related to stochastic and deterministic performance [8]. The stochastic performance is usually addressed by considering the minimum variance control [9,10]. On the other side, deterministic performance assessment techniques consider more traditional design specifications such as those related to the set-point following and load disturbance rejection tasks [11]. In this context, different methods have been proposed for PI(D) controllers [12–17]. See [18] for a comprehensive description of all these techniques. In particular, in [19] a methodology has been proposed which has the advantage of using the same data related to a set-point response both to assess the performance of the PID controller and, in case it is not satisfactory, to provide a new tuning of the parameters. Thus, a (possibly, time and energy consuming) special experiment devoted to the automatic tuning of the controller is no longer necessary. The technique aims at achieving the same performance of the SIMC tuning rules [20] for the set-point following task and is based on the determination of the sum of the time constants and of the dead time of the process. Its effectiveness has been shown by means of simulations and experiments with laboratory-scale equipment. In this paper we adapt this method to a PI controller and we discuss its use in a true industrial context, namely, for a flow control loop in a pharmaceutical plant. Issues related to the implementation with a Distributed Control System (DCS) are addressed and experimental results are given. We highlight that

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M. Veronesi, A. Visioli / ISA Transactions 49 (2010) 244–248

Remark 1. It is worth noting that, according to the so-called ‘‘half rule’’ proposed in [20], in case of a process with more than one pole, T0 represents in any case the sum of all the lags and of the time constant. Thus, it is a suitable parameter to handle the robustness issue.

Fig. 1. The control scheme considered.

the proposed methodology is capable of addressing linear singleinput single-output processes. However, these control loops are often the basis of more complex control systems and achieving a high performance in these control loops is often essential to obtain a high production rate and quality of the product, as in the industrial case presented in this paper. The paper is organized as follows. The performance assessment and retuning methodology is explained in Section 2. The implementation with an industrial control system is discussed in Section 3. The industrial application and the experimental results are presented in Section 4. Conclusions are drawn in Section 5. 2. Performance assessment and retuning of PI controllers We propose a method for the performance assessment and retuning of a PI controller. It has the same rationale as the method proposed in [19] for PID controllers, but it is greatly simplified because the derivative action is not employed.

2.2. Performance assessment In order to assess the performance of the PI controller in the set-point following task it is therefore necessary to verify, in principle, that Eqs. (5) and (7) are verified. The determination of the integrated absolute error IAE can be performed easily by evaluating the step response of the closed-loop system. Then, assuming null initial conditions without loss of generality, the apparent dead time θm of the system can be evaluated by considering the time interval from the application of the step signal to the set-point and the time instant when the process output attains 2% of the new set-point value A, namely, when the condition y > 0.02A occurs. Actually, from a practical point of view, in order to cope with the measurement noise, a simple sensible solution is to define a noise band NB [21] (whose amplitude should be equal to the amplitude of the measurement noise) and to rewrite the condition as y > NB. Then, expression (7) can be rewritten as ∞

Z

|e(t )|dt = 2Aθm .

IAE = 2.1. Generalities



Ti s + 1

(1)

Ti s

µ e−θ s . τs + 1

τ 2µθ

Kp

lim u(t ) =

Ti

t →+∞

(2)

With respect to the set-point following task, the PI controller parameters can be effectively selected by applying the IMC paradigm [4] where the desired closed-loop time constant is chosen to be equal to the process dead time [20], namely by selecting Kp =

As shown in [19], the process gain µ can be determined by considering the following trivial relations which involve the final steady-state value of the control variable u:



and the process P is assumed to be self-regulating with a firstorder-plus-dead-time (FOPDT) transfer function P ( s) =

(8)

0

We consider the unity-feedback control system of Fig. 1 where C is a PI controller whose transfer function is: C (s) = Kp

245

,

(3)

Ti = τ . By defining as T0 the sum of the time constant and of the dead time of the process, namely, T0 := τ + θ ,

(4)

∞

Z

e(t )dt = 0

A

(9)

µ

and therefore we have

µ=A

Ti Kp

R∞ 0

e(t )dt

.

(10)

The determination of the value of T0 can be performed by considering the following variable: eu (t ) = µu(t ) − y(t ).

(11)

By applying the Laplace transform to (11) and by expressing u and y in terms of r we have C (s)(µ − P (s))

Eu (s) = µU (s) − Y (s) =

1 + C (s)P (s)

R(s).

(12)

By considering (1) and (2), expression (12) can be rewritten as E u ( s) =

µKp (Ti s + 1) ((τ s + 1) − e−θ s )R(s). Ti s(τ s + 1) + µKp (Ti s + 1)e−θ s

it is trivial to verify that T0 = τ + θ = Ti +

Ti 2µKp

(13)

.

(5)

Note that the SIMC tuning rule aims at achieving a closedloop transfer function (this can be easily ascertained by again approximating the delay term as e−θ s = 1 − θ s) F (s) :=

C (s)P (s) 1 + C (s)P (s)

∼ =

1

θs + 1

e−θ s

|e(t )|dt = 2Aθ

t →+∞

eu (v)dv = lim s 0

µKp (Ti s + 1)

A

s→0

s Ti s(τ s + 1) + µKp (Ti s + 1)e−θ s

(τ s + 1) − e−θ s

(6)

 = A lim

s 1 − e−θ s

s→0

∞

IAE =

t

Z lim

×

for which the step response integrated absolute error is

Z

By applying the final value theorem to the integral of eu when a step is applied to the set-point signal we finally obtain

(7)

0

where e(t ) = r (t ) − y(t ) and A is the amplitude of the set-point step.

= A (θ + τ ) = AT0 .

s

+

(τ s + 1) − 1



s (14)

Thus, the sum of the lag and of the dead time of the process can be obtained by evaluating the integral of eu (t ) at the steady-state

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the step. It is worth noting that both the value of the gain and of sum of the lags and of the dead time of the process are determined by considering the integral of signals and therefore the method is inherently robust to the measurement noise. For the purpose of assessing the controller performance based on (5) and (7) it is worth considering the following performance indexes, named respectively Sigma Index SI and Close-loop Index CI: T

SI =

Fig. 2. Example of the implementation of the on-line parameter estimation technique by means of a DCS (courtesy of Yokogawa Italia srl).

(which does not depend on the PID parameters) when a step signal is applied to the set-point and by dividing it by the amplitude A of

Ti + 2µiK p T0

2Aθm CI = R ∞ . |e(t )|dt 0

(15) (16)

In principle, the performance obtained by the control system is considered to be satisfactory if CI = 1. However, it has been found from a large number of simulations that, from a practical point of view, the controller can be considered to be well-tuned if

Fig. 3. Process and Instrumentation diagram of the plant.

M. Veronesi, A. Visioli / ISA Transactions 49 (2010) 244–248

247

Note that with this tuning rule, the value of the Sigma Index (15) is equal to one.

FCV638

3. Practical implementation

I/P

FY 638B

FIC 638

FY 638A

P/I

FT 638

FE 638

Fig. 4. Detail of the considered flow control loop in the Process and Instrumentation diagram of the plant.

Although the presented algorithm can be applied to off-line data recorded, for example, on the hard-disk of one of the operator workstations in the control room, the nature of the performance monitoring methods is to be applied to on-line data, so that the operators can have a real-time feedback about the control loops behavior. Indeed, the proposed algorithm is simple enough to be implemented in a function block of a DCS currently available in the market, as is shown in Fig. 2. The relatively high sampling interval available for PID control in the DCS (usually 50 or 100 ms) is not a problem because, in fact, the algorithm, which consists of a few simple computations, is performed in a one-shot execution after the end of the transient set-point step response. Note also that there is no need to store a large amount of data in the memory (the integrals can be computed by incrementing a value each sampling time). In any case, especially when the DCS has to perform hundreds of control loops, it is not wise to increase the CPU load by giving to the controller tasks that are not strictly related to the process control. Thus, it is better to implement performance monitoring techniques by external routines, running on-line in the operator workstations or in some dedicated PC-server, allowed to import automatically the process data from the DCS network through a standard protocol (such as OPC, which is nowadays very popular). These routines have to compute the performance index and send back to the DCS some kind of messages which help the operators to identify the loop performing poorly, together with the new values of the PID parameters suggested to improve the performance. It is worth stressing that the algorithm does not increase the system network load because it exploits routine operating data that are in any case sent through the network to be viewed by the operators by means of the human/machine interface. 4. Industrial application

Fig. 5. Set-point step response with initial tuning.

CI > CI d with CI d = 0.6. Note that this last value has been selected by considering the SIMC tuning rule applied to many different processes [20] but, in any case, another value of CI d can be selected by the user depending on how tight are its control specifications. 2.3. Retuning If the performance provided by the controller turns out to be unsatisfactory, the PI controller has to be retuned. This can be done easily by considering the tuning rule (3) and the parameters that have been estimated, namely, by setting Kp =

T0 − θm 2µθm

Ti = T0 − θm .

,

(17)

The proposed method has been applied in a pharmaceutical plant, in particular to the flow controller named FIC638 in the Process and Instrumentation diagram shown in Fig. 3 (see Fig. 4 for the detail of the flow control loop, which is in the top right part of the P&I diagram). The PI controller controls the flow of hydrochloric acid (HCL) that comes from the tank D-19500 and is sent to a neutralization column, where it reacts with anhydride-trimethylamine to generate trimethylamine hydrochloride (TMAHCL 56). The latter is used in the production of a salt, i.e. choline chloride, which is further used to synthesize a vitamin endowed with liver-protective properties. The FIC638’s performance affects significantly the quality of TMAHCL. Indeed, by providing a fast, but accurate, set-point following it is possible to avoid the pH correction of the raw product that exits the reactor C19111, because the hydrochloride would already be within the design range. Therefore, the IAE is a good measure of the controller’s performance. During the commissioning phase the FIC638 was manually tuned with Kp = 0.2 and Ti = 60, and the resulting response to a set-point step change from 1500 kg/h to 1750 kg/h was the one shown in Fig. 5; the set-point and the process variable are in the upper part of the figure while the controller output is shown in the lower part. The corresponding value of the IAE was 7.585 kg (the flow is measured in kg/h but the values are stored at each second). When the system attained its steady-state value, the following values of the process parameters were estimated: θm = 19 s, µ = 3.125, and T0 = 58 s. The value of the Sigma Index SI resulted to be 1.86, while the value of the closed-loop index CI resulted

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The technique uses closed-loop data available by a routine operation such as a set-point step response. Further, it is based on the determination of the sum of dead time and of the lags of the process by integrating appropriate signals, therefore it is robust to measurement noise and suitable to implement in a practical context, as it has been shown. References

Fig. 6. Setpoint step response after having retuned the PID controller.

equal to 0.35, which means that both indexes indicate that the controller had to be retuned. By applying the retuning algorithm, the following values of the PID parameters were determined: Kp = 0.33 and Ti = 39 s. These values were applied to the PID controller before changing the set-point from 1750 kg/h back to the value it had previously (1500 kg/h). The step response obtained is shown in Fig. 6. It can be seen that, although a small overshoot appeared, the settling time was shorter. Indeed, the value of the integrated absolute error IAE decreased to 4.01 kg and the Closed-loop Index increased to 0.66. Finally the new value of the Sigma Index was obviously SI = 1. Thus, the set-point following performance was improved significantly. 5. Conclusions A methodology for the set-point following performance assessment of a PI controller and for the retuning of the parameters has been successfully employed in a real industrial application. The method is capable to assess the controller performance and to tune effectively the parameters (independently on the initial settings). Thus, it can be employed to tune effectively a possibly large number of single-input single-output control loops in a plant without applying time-consuming strategies and independently of the skill of the operators.

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