Refinement of Cascade Tuning to Improve Control Performance

Article pubs.acs.org/IECR

Refinement of Cascade Tuning to Improve Control Performance without Requiring Any Additional Knowledge on the Process Elena Marchetti,†,§ Andrea Esposito,‡ and Claudio Scali*,† †

Chemical Process Control Laboratory (CPLab), Department of Chemical Engineering (DICCISM), University of Pisa, Via Diotisalvi n.2, 56126, Pisa (Italy) ‡ ENI, Refining & Marketing, Refinery of Livorno, Via Aurelia n.7, 57017, Livorno (Italy) ABSTRACT: A refinement of cascade control tuning to reduce oscillations in the inner loop without deteriorating performance of the controlled (outer) variable is proposed. It is illustrated that the problem can rise for very common process dynamics and tuning techniques. The basic idea is to perform a balanced retuning of master and slave controllers, by acting on proportional and integral components of the two (PI) controllers. A distinctive feature of the method is that, once the problem shows up, appropriate actions can be performed on the two controllers without any additional knowledge about process dynamics. The effectiveness of the technique is validated in simulation on a significant class of process dynamics and in application on industrial loops.

■

(1) INTRODUCTION Benefits of cascade control to obtain a more efficient neutralization of perturbations affecting an industrial process are known since the early era of process control. In the scheme reported in Figure 1, the outer controller (Ce, master) sets the

only for the controlled variable PVe. As known from textbooks,1,2 a two-step design procedure is usually employed: the internal controller is tuned first the on the basis of the internal process (external loop open); then, the external controller is tuned on the basis of the downstream process (P*, inner loop closed). P* reduces to Pe in the case of much faster inner dynamics (high value of the inner loop gain, KCi): C i = f (Pi);

P* =

PC i iPe 1 + PC i i

(1)

Cascade control is mainly devoted to improving the suppression of inner disturbance: in the design, attention has to be paid in order to not deteriorate performance in set point tracking and outer disturbance suppression. When the objective is to obtain acceptable performance, almost any tuning rule can be used for the two controllers, starting from classical Ziegler and Nichols,3 which is certainly the starting point for its applicability for general dynamics in P. As matter of principle, the presence of two controllers allows more ambitious objectives, for instance separation of tasks (set point tracking and disturbance suppression) for the two controllers. A simultaneous tuning procedure able to improve performance for both objectives, with respect to existing techniques, is proposed in the work of Lee et al.;4 enhanced tuning rules are also reported in Lee et al.5 and in Kaya et al.,6 where a modified cascade structure is presented. Optimization of the two tasks is further developed in Alfaro et al.,7 where both controllers have 2 degrees of freedom for improved robustness and performance in both responses. Related considerations regard process identification: automatic procedures are sought in order to reduce or eliminate operators efforts. The list of autotuning techniques proposed

Figure 1. Adopted scheme for series cascade loops.

set point (SPi) of the inner controller (Ci, slave), in order to maintain the controlled variable (PVe) on desired values (SPe); as a consequence, the internal variable (PVi) changes to compensate the effect of disturbances, which, according to different plant situations, disturbances can enter the inner (di) or outer (de) loop. The separation of the global process (P = PiPe) into the two components (Pi, Pe) is made possible by the availability of measurements of the internal variable (PVi), and this allows a faster action and then performance improvements with respect to a single feedback controller. Advantages increase with relative velocity of the internal with respect to external loop; therefore cascade control finds wide application in industrial plants: a large number of flow controls (FC) are slave loops in the cascade control scheme, being faster than outer loops (temperature, pressure, or level), which act as master controllers. Being composed by two controllers, a bit more complicated tuning/design is necessary, but the different loop speeds allow, in general, to obtain acceptable performance. Usually the two controllers have PI action and, in some cases, Ci is limited to proportional action, being an error free specification required © 2013 American Chemical Society

Ce = f (P*);

Received: Revised: Accepted: Published: 6193

October 9, 2012 March 29, 2013 April 1, 2013 April 1, 2013 dx.doi.org/10.1021/ie302750d | Ind. Eng. Chem. Res. 2013, 52, 6193−6200

Industrial & Engineering Chemistry Research

Article

Figure 2. Examples of observed trends of SPi and PVe in industrial loops.

moves on the two controllers should be suggested, without any additional information. The paper has the following structure: section 2 presents the problem observed in industrial control and analyzes the effect of loops dynamics on its occurrence; section 3 illustrates the proposed retuning technique and its main features compared with a simple controller detuning; section 4 discusses results obtained in simulation and in industrial application; finally conclusions are given in section 5.

for cascade identification and design would be a heavy burden to complete; the standard relay feedback approach can be used in sequential (Hang et al.8) or simultaneous (Tan et al.9) applications, the second being less time-consuming. The simplicity of application and the reduced upset introduced in the process is presented as the main advantage of the procedure proposed by Leva and Donida;10 an interesting comparison of different approaches to the autotuning of cascade controllers is reported in Leva and Marinelli.11 Anyway, in the framework of industrial process control some peculiarities must be recalled: • Usually process knowledge is scarce and process parameters change with operating conditions; therefore, identification should be frequently repeated. • The introduction of perturbations in the plant is something to be possibly avoided or reduced to a minimum. • The aim is to obtain acceptable performance (rather than optimality), and simpler methods and control configurations are preferred. • The more common problem to face is the rejection of periodic (oscillating) perturbations (Skogestad12), and this is the major worry of process control people in routine activity. Therefore, too complicated control structures with modifications of the basic cascade scheme in Figure 1, multiobjective performance specifications, and the introduction of ad-hoc perturbations in the plant (step or relay tests) are not usually seen favorably. With this premise, the paper focuses on a very common problem encountered in industrial plants: often, the achievement of good performance on the external variable (that is acceptable attenuation on PVe amplitude) requires large oscillations in the inner loop (that is in SPi amplitude), with consequent large valve travel and wear. The objective of the paper is to analyze the main features of the problem, mainly for which cases (process dynamics and tuning techniques) it may show up and to indicate appropriate actions to be taken on the two controllers in order to reduce inner loop oscillations without deteriorate performance on PVe. Previous considerations about the lack of knowledge on the plant will be taken into consideration as a hard constraint; therefore, once the problem of large oscillations in SPi shows up, appropriate

■

(2) OBSERVED PROBLEM In Figure 2, examples of trends of PVe and SPi in industrial cascade loops are reported: it can be seen that periodic perturbations entering the loop may cause much larger oscillations in SPi than in PVe. Attenuation on PVe is considered quite acceptable by console operators, while amplitude and variability of SPi is absolutely not: in these cases, a trial and error retuning of both controllers is required to avoid excessive valve travel and consequent wear, maintaining good performance on the controlled variable. To avoid misunderstanding, all signals are properly scaled with respect to their ranges, and oscillations are not caused by noise as their frequency falls near the ultimate frequency of the system; these oscillations are the most difficult to suppress, as pointed out by many researchers (see for instance, the work of Hägglund13). This is one of many cases occurring in the application of a closed loop monitoring system (Scali and Farnesi14) featuring more than 1200 industrial loops, whose main objective is the diagnosis of valves affected by stiction and of controllers to be retuned. The problem has been already discussed in a previous activity by the same authors (Scali et al.15). There, the behavior was explained in terms of incorrect tuning of controllers and guidelines for retuning were given by assuming that a minimum of information about the process was known, in particular the frequency of the perturbation and the critical frequency of the process. Here the objective is more ambitious, that is to remove the need of information and to be able to give indication of general validity to eliminate the problem. As first, the possible occurrence of this behavior has been investigated in simulation. 6194

dx.doi.org/10.1021/ie302750d | Ind. Eng. Chem. Res. 2013, 52, 6193−6200


Article

tuning, has been elected as a reference case; parameters values are the following:

Some assumptions are necessary in order to reduce the number of possible combinations of process dynamics, disturbances, controller structure and tuning techniques. About process dynamics, rather general situations have been analyzed: the inner process (Pi) has been always assumed as FOPTD (first-order plus time delay), while the outer process (Pe) as FOPTD or IPTD (integrator plus time delay); this choice, allows to reproduce, respectively, the common situation of temperature (pressure) or level acting on a flow control loop. FOPTD: Pj(s) =

e−ϑjs ; τjs + 1

j = i, e;

IPTD: Pe =

θi = τi = 2; KC e = 3.87;

θe = 2; τIi = 2,

τe = 30; τIe = 31

KC i = 0.5; (4)

Results for the reference case, denoted by (°), are illustrated in Figure 3 in terms of Bode diagrams, that is: amplitude ratio

e−ϑes τes (2)

About disturbances, attention has been concentrated on disturbances entering the inner loop (di), being the main object of cascade control. About controllers, they have been assumed of PI (proportional and integral) type, therefore four parameters have been set: Cj(s) = KCj

τIjs + 1 τIjs

;

j = i, e (3)

Assuming the design procedure recalled in the introduction (eq 1), four different classical tuning techniquesZiegler and Nichols3 (ZN), Rivera et al.16 (IMC), Skogestad17 (SIMC), and Tyreus and Luyben18 (TL)have been explicitly tested in simulation. As general result, it has been found that in all cases, conditions for appropriate application of cascade control being respected (i.e.: Pi much faster than Pe), the key parameter appears to be the lag dominance of the outer process: in fact the problem shows up starting from τe > 5θe. Therefore it is possible to conclude that the observed problem can appear for rather general dynamics of internal and external processes, for the common case of inner disturbance suppression and for very popular tuning techniques for the two controllers. The possible occurrence in other different situations has also been studied and will be mentioned later on in the paper. Some remarks are appropriate: • Some model order reduction techniques were adopted, in order to use SIMC and IMC tuning for the outer controller (Ce); generally, P* (given by eq 1) has a very complex structure and higher-order dynamics with respect to FOPTD/IPTD transfer functions which have to be approximated. • For IPTD dynamics, only SIMC and TL were used, as ZN, which potentially can be used for general process dynamics, in this case gave unsatisfactory performance (too oscillatory a response). • Also the relative response time tuning,19 suggested as rule of thumb to achieve acceptable performance in cascade control, was investigated, and it was found to be affected by the same problem. • The observed inconvenience arises also in the case of inner controller (Ci) reduced to proportional action only (which is a commonly used simplification adopted in industrial practice). To illustrate the situation in full detail, the system constituted by two FOPTD processes and two PI controllers, with SIMC

Figure 3. Amplitude ratios of PVe and SPi vs frequency, for the reference case (°).

of the two variables PVe and SPi, in response to a sinusoidal signal, associated with the input to the inner process Pi. Referring to Figure 1: di = A sin(ωt ),

A = 1,

Pdi = Pi

(5)

Main comments to Figure 3: • The typical response of cascade control is shown, that is: at very low frequency (ω → 0), the integral action allows almost perfect disturbance suppression; the same happens at very high frequency (ω → ∞), as a consequence of the process capacity in attenuating disturbances. • SPi amplitude is larger than PVe in all the frequency range; in the intermediate frequency range, both PVe and SPi reach a maximum value, (0.26 for PVe and 1 for SPi): it is evident that the amplitude of SPi oscillation is much larger than PVe. For a quantitative illustration of effects, it has been assumed that an oscillation amplitude is acceptable if attenuated at least to 20% (AR* = 0.2). Let us denote with ωjL ° and ωjH ° low and high frequency for PVe or SPi to be off-specification (off-spec). Let also denote with δ°j , the off-spec range (j = i, e). Referring to Figure 3, the specification is not achieved on PVe, from ω°eL = 0.15 to ω°eH = 0.28 (then for a frequency range δe° = 0.13). The same happens on SPi, from ωiL ° = 0.05 to ωiH ° = 0.6 (then for a frequency range δ°i = 0.55, larger than δ°e ). The effect of the two different attenuations on PVe and SPi can be more directly illustrated in the time domain, in terms of responses to a sinusoidal periodic disturbance (amplitude A = 1), at frequency 0.2 rad/s (Figure 4). It is evident that the adopted tuning, able to make PVe oscillation almost acceptable (AR = 0.26), causes a much larger amplitude in SPi oscillation (AR has about the same value as di = 1). 6195



Article

• On the contrary, for specified Pi, δ°i is about constant, as both ω°iL and ω°iH remain almost the same, for the same inner process dynamics (again, compare FF1 vs FF2, IF1 vs IF2, ...). • When the ratio θe/θi increases (see FF6−8 vs FF1−5), PVe specification is always satisfied while δi° is always larger than 0. For all cases reported in Table 1, the adopted tuning was SIMC. Results for the remaining tuning techniques mentioned in section 2 and for different dynamics (some additional related transfer functions for the two processes were also investigated in simulation) showed the same qualitative trends (not reported for the sake of brevity). It is worth noting that, for the cases analyzed in simulation, the problem appears starting from a correct tuning of the two controllers and then can be considered relevant in industrial applications: this means that it can occur, depending from process dynamics, without invoking errors in the controller design procedure. In the case of incorrect tuning (for whatever reason: inappropriate initial controller settings or changes in process dynamics), it cannot be excluded that the problem may not show up for the same dynamics or, on the contrary, also appear for different situations.

Figure 4. Time trends of PVe and SPi for the reference case (input disturbance di at f = 0.2 rad/s).

Table 1 reports a synthesis of results for different combinations of process parameters values, chosen in order to realize consequent changes in main features of the phenomenon (now (°) denotes the reference case with standard initial tuning). For each case, process parameters are reported together with controller parameters. Frequency ranges where the desired specification about attenuation (AR < AR*) is not obtained are also indicated. In Table 1, FF stands for both Pe and Pi as FOPTD processes, while IF stands for IPTD + FOPTD. Main remarks from Table 1: • Frequency ranges δ°i and δ°e , where specification (AR < AR* = 0.20) is not respected, change with process dynamics; to be noted that, for all the cases, δi° > δe°, (i.e., the range of off-spec on SPi oscillations is larger than on PVe oscillations). • For all dynamics, once Pi is specified, δ°e decreases, by increasing the ratio τe/θe; this is a consequence of the fact that ωeL ° increases, while ωeH ° decreases (compare FF1 vs FF2, IF1 vs IF2, ...).

■

(3) PROPOSED RETUNING METHOD As the inconvenience consists in a too oscillatory inner set point (SPi), while the controlled variable (PVe) is acceptable, the first suggestion is to detune the master controller Ce. It can be easily realized that this action may cause a deterioration in PVe. As a matter of principle, the global effect can be compensated by means of an increase of control action of the slave controller Ci. In practice, (as confirmed by industrial examples and specifically oriented simulations), a time-consuming trial and error procedure is necessary to achieve acceptable results, as unstable responses and unsatisfactory trends of closed loop variables may arise. For these reasons, a systematic approach to the problem is necessary, to find controller parameters able to improve the global loop performance (decreasing SPi oscillations, without worsening PVe) every time the perturbation appears, possibly without requiring any additional information about process

Table 1. Chosen Dynamics and Ranges of Missed Specifications inner process (Pi) FF1 FF2 FF3 FF4 FF5 FF6 FF7 FF8 IF1 IF2 IF3 IF4 IF5 IF6

slave (Ci)

outer process (Pe)

master (Ce)

PVe off-spec range

SPi off-spec range

τi

θi

KCi

τIi

τe

θe

KCe

τIe

ω°eL

ω°eH

δ°e

ω°iL

ω°iH

δ°i

1 1 2 2 5 1 2 3 2 2 3 3 5 5

1 1 2 2 5 1 2 3 1 1 2 2 4 4

0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 1 1 0.75 0.75 0.62 0.62

1 1 2 2 5 1 2 3 2 2 3 3 5 5

7.5 15 15 30 60 24 84 120 10 15 15 22.5 35 52.5

1 1 2 2 10 4 14 24 2 2 3 3 7 7

2.5 4 2 3.87 2.33 2.8 3 2.667 1.25 1.87 1.5 2.25 1.6 2.38

10 16 16 31 70 28 98 144 32 32 40 40 88 88

0.25 0.3 0.1 0.15 0.04

0.85 0.52 0.4 0.28 0.12

0.1 0.18 0.08 0.08 0.03 0.04

0.45 0.25 0.35 0.27 0.17 0.13

0.6 0.22 0.3 0.13 0.11 0 0 0 0.3 0.085 0.27 0.19 0.14 0.09

0.1 0.1 0.05 0.05 0.019 0.1 0.045 0.03 0.08 0.08 0.04 0.04 0.02 0.02

1.32 1.2 0.6 0.6 0.19 0.5 0.12 0.06 0.5 0.5 0.4 0.4 0.2 0.2

1.22 1.1 0.55 0.55 0.171 0.4 0.075 0.03 0.41 0.41 0.36 0.36 0.18 0.18

6196



Article

dynamics and perturbation frequency. Our method aims to reach this objective. The effect of the two controllers on loop performance, that is on PVe and SPi in response to a disturbance di entering in the inner loop of the process (Figure 1) can be quantified by means of PVe PP i e = =ε di 1 + PC i i(1 + PeCe)

(6a)

−CePP SPi i e = = −Ceε di 1 + PC (1 + PeCe) i i

(6b)

KCe, by a factor F and, at low frequency (7b), by increasing KCi by the same factor F. • PVe attenuation, not affected by controller action at high frequency (7c), could get worse by a reduced action of the two controllers at low frequency (7a); this potential drawback can be mitigated by compensating the decreased control action in Ce with an appropriate increase of the control action in Ci. However, these considerations do not hold exactly in all the frequency range: an appropriate dosage of the proportional and integral components (UP = Kce(t); UI = (Kc/τI)∫ e(t) dt = KI∫ e(t) dt) of the two controllers can allow reaching a reasonable trade-off. Assuming as a starting point that decreasing the gain KCe of a factor F causes the same attenuation on SPi in all the frequency range (something that holds exactly only at high frequency), the remaining controller parameters (τIe, KCi, τIi,) were determined by intensive simulation for the analyzed dynamics reported in Table 1 (for both classes FF and IF). As result, the following tuning refinement is suggested for the two classes of processes FF and IF. New controller settings KCj, τIj, (j = i, e), are reported first, to be used as retuning values; the resulting (→) KIj expressions are also reported for an easier understanding of effects on the integral control action UI:

The effect of P and I components of the two PI controllers can be better understood by considering that loop functions change as function of the frequency ω, as reported in Figure 5.

For class FF KC e =

KC°e ; F

Kc i = Kc°i ;

τIe =

5τIe° ; 2F

→ KIe =

τIi =

10τIi° ; 3F

→ KIi =

2 KIe° 5

(8a)

3 FKIi° 10

(8b)

For class IF Figure 5. Amplitude ratios of different loop function vs frequency: (PI controllers) FOPTD (top) and IPTD (bottom).

KC e =

KC°e ; F

τIe =

25τIe° ; 6F

→ KIe =

6 KIe° 25 (8c)

12

Following the work of Skogestad (2006), loop function expressions can be simplified at low and high frequency, as PVe PP PP 1 i e i e ω → 0: ≈ ≈ = di 1 + PC P C PC P C C i i e e i i e e iCe

KC i = KC°i ;

SPi 1 = di Ci

PVe = PP i e di

(7c)

ω → ∞:

SPi = CePP i e di

(7d)

→ KIi =

3 FKIi° 10

In more detail, to illustrate relative changes in the proportional and integral action of the two controllers: • The proportional component (UP) undergoes the same variation for both classes; for the two master controllers, UP is decreased by a factor F (KCe = KCe ° /F); for the two slave controllers UP does not change (Kci = Kci°); therefore, a decrease of the global proportional action is performed. • The integral component (UI) undergoes different variations for the two classes of the process; for the master controller, UI decreases for both cases (class FF K°Ie = (2/5)K°Ie; class IF K°Ie = (6/25)K°Ie); for the slave controller, UI increases the same amount for the two classes (FF and IF KIi° = (3/10)FKIi°); globally, a decrease of the overall integral action is performed. • The decrease of the global control action (both UP and UI) is responsible for some “loss” of performance on PVe; the dosage of the two components allows minimization of this effect and will improve PVi attenuation (which was the initial problem, as felt by console operators).

(7b)

ω → ∞:

10τIi° ; 3F

(8d)

(7a)

ω → 0:

τIi =

The objective is to attenuate SPi oscillations without worsening PVe; the two degrees of freedom structure allows us to pursue this goal, reducing possible conflicts. A closer look at the behavior at limit frequencies (eq 7a−7d) indicates that • SPi attenuation can be improved at high frequency, by a smoother tuning of Ce, and at low frequency by a tighter tuning of Ci. In particular, a decrease of a factor F on SPi, could be obtained, at high frequency (7d), by decreasing 6197



Article

Figure 6. Effect of retuning on PVe (left) and SPi (right) for the reference case.

Table 2. Off-Spec Frequency Ranges before and after Retuninga PVe° off-spec range FF1 FF2 FF3 FF4 FF5 FF6 FF7 FF8 IF1 IF2 IF3 IF4 IF5 IF6 a

SPi° off-spec range

PVe off-spec range

ωeL °

ωeH °

δe°

ωeL

0.25 0.3 0.1 0.15 0.04

0.85 0.52 0.4 0.28 0.12

0.25

1

0.1

0.5

0.1 0.18 0.08 0.08 0.03 0.04

0.45 0.25 0.35 0.27 0.17 0.13

0.6 0.22 0.3 0.13 0.11 0 0 0 0.3 0.085 0.27 0.19 0.14 0.09

0.035 0.028 0.028 0.012

0.045 0.03 0.03 0.025

ωeH

SPi off-spec range

δe

ωiL °

ωiH °

δi°

0.75 0 0.4 0 0 0 0 0 0.01 0 0.003 0.003 0.013 0

0.1 0.1 0.05 0.05 0.019 0.1 0.045 0.03 0.08 0.08 0.04 0.04 0.02 0.02

1.32 1.2 0.6 0.6 0.19 0.5 0.12 0.06 0.5 0.5 0.4 0.4 0.2 0.2

1.22 1.1 0.55 0.55 0.171 0.4 0.075 0.03 0.41 0.41 0.36 0.36 0.18 0.18

ωiL

ωiH

δi

ρe = δe/ δe°

ρi = δi/ δi°

0 0 0 0 0 0 0 0 0 0 0 0 0 0

1.25 0 1.33 0 0 0 0 0 0.033 0 0.011 0 0.0928 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0

(°) denotes before detuning.

■

(4) RESULTS IN SIMULATION AND INDUSTRIAL APPLICATION

In addition, the suggested retuning (eq 8) maintains its validity for all the studied dynamics (Table 1) and always allows SPi amplitudes to decrease in the middle-high frequency range by a factor larger than the desired attenuation. Results applying the proposed new settings for controller parameters to all process dynamics in Table 1 are synthesized in Table 2. New ranges of missed attenuation of oscillations on PVe and SPi are reported together with the ratios (ρj = δj/δj°), that is before and after retuning. Ratios ρj represent improvement in the case ρj < 1 and worsening in the case ρj > 1; a value ρj = 0 indicates that the specification (AR < AR*) is respected by adopting the new tuning in the whole frequency range (as δj = 0). From Table 2, the following can be observed: • The ratio between ranges of missed specification for SPi attenuation (ρi = δi/δi°) is always equal to 0: this means that with new settings, the desired spec is respected in all the frequency range. • The ratio between ranges of missed specification for PVe attenuation (ρe = δe/δe°) before and after retuning is slightly larger than 1 in the worst case (FF1, FF3): the amplitude never become large, anyway. It is always much less than 1 for process dynamics IF1, IF3, IF4, IF5, and,

(4.1) Simulation Results. At first, results obtained by applying the technique proposed in simulation for the reference case are illustrated in Figure 6. Some remarks to highlight most important features: • In this case, after retuning, the attenuation specification (AR < AR* = 0.2) is fulfilled in all frequency ranges, both on SPi and PVe (δi = δe = 0). • Attenuation of SPi amplitude is achieved for all frequencies; in particular, the desired value of attenuation is achieved at high frequency, attenuation is much larger in the middle frequency range (where the problem showed up), and it is slightly smaller at low frequency • PVe attenuation is not affected by retuning at high frequencies, improves at middle frequencies, and gets worse at low frequency (where the attenuation is very large, anyway). • Both PVe and SPi become flat in the middle frequency range, close to the ultimate frequency; the attenuation of oscillations in this critical frequency range (Hägglund13) can be seen as a positive feature of the technique. 6198



Article

finally, it is equal to 0 in many cases (FF2, FF4−8; IF2, IF4, IF6). • About class FF dynamics: in the worst cases ωeL is equal to ωeL ° and ωeH is a little larger than ωeH ° . Therefore, the deterioration of performance shifts toward higher frequency. • About class IF dynamics: in the worst cases both ωeL and ωeH are much smaller than ωeL ° and ωeH °. It is confirmed that the new retuning method is valid for all the studied dynamics: it allows SPi oscillation to be attenuated at least of a reasonable factor (F ≈ 5) in all frequency ranges without significant worsening of PVe. No additional information about process dynamics and disturbance frequency is required: once the problem of excessive amplitude in SPi oscillations shows up, the operator can act successfully in suppressing them. Information about process type (i.e., integrator or not), in order to choose the right detuning (eq 8) has not to be considered an additional information, because is something well-known to the operator, does not require any tests, and is not subject to change with time. For a full verification of the suggested retuning, a check of control system performance in the presence of step inputs (in Figure 1: di = 1/s; Pdi = Pi) has been performed, even though, in complete agreement with Skogestad,12 most common disturbances in industrial control are of periodic type. In Figure 7, results are reported for the reference process

proposed retuning continues to be effective: SPi oscillations are more attenuated in the middle-high frequency range, at the expense of a smaller attenuation of PVe in the low-medium frequency range (small values, anyway). Analogously, in the case of a load disturbance (de = 1), slightly slower responses are obtained. As conclusion from the investigation of the effect of disturbances entering in the outer loop, the slight loss of performance seems to be an acceptable price to pay to the detuning of the outer controller and the drawback is compensated by improved performance in the case of disturbances entering the inner loop, which remains the main scope of the cascade control. As a general conclusion, the improvement in attenuating periodic disturbances remains a major advantage of the proposed retuning technique. 4.2. Industrial Application(s). Two examples of application results are reported in Figure 8; in both cases they represent retuning of level control loops acting on flow control loops of refinery units. The reported cases have been chosen as they represent a really common control configuration of bottom column levels acting on the exit flow, but the situation can arise for different control loop type (PC, LC, TC, acting in cascade on FC or PC). As discussed in section 2, oscillations of the controlled variables were considered quite acceptable (PVebottom), while oscillations in the inner loop were not (SPi and PVi top). After application of the proposed retuning rules, at time t ≈ 2000 s for the first loop (also reported in Figure 2, to introduce the general problem) and at time time t ≈ 6000 s for the second loop, amplitude of PVe oscillations remains almost constant, while significant attenuation in SPi is achieved. Quite a significant number of cascade loops were improved adopting the proposed retuning technique that was successfully accepted by plants operators.

■

(5) CONCLUSIONS The occurrence of large oscillation in the variables of the inner loop (with consequent valve travel and wear), while the controlled variable (PVe) presents acceptable oscillations, is a frequent and important problem in industrial control. It can show up for very common process dynamics, as it appears when the outer process becomes lag dominant, whatever the adopted tuning rule: therefore it is likely to appear for the very common cases of temperature, pressure, or level control acting on a faster flow control loop. The objective of reducing inner loop oscillations without worsening attenuation of PVe can be achieved by the proposed refinement of the existing controller parameters setting, in all the frequency range of interest. Technically, the basic idea consists in a balanced action on the proportional and integral component of the two (PI) controllers: the decrease of the global control action after retuning causes a limited loss of performance on PVe, while main effect results in the desired attenuation of the inner loop set-point (SPi). A significant contribution of the study is that no knowledge on process dynamics or frequency of oscillation is required: once the problem shows up, the application of the proposed tuning allows to get rid of it and to obtain a reasonable attenuation in the amplitude of inner loop variables.

Figure 7. Response for step SP tracking followed by step disturbance rejection (di), reference case.

(represented by eq 4) in the case of SP tracking followed by suppression of a load disturbance acting in the inner loop. It can be seen that the response becomes only a bit slower, with smaller peaks; therefore, it can be considered completely acceptable. It can be of interest also to analyze responses to disturbance entering in the outer loop (in Figure 1, de ≠ 0), possibly with various dynamics (Pde ≠ Pe); only the more usual situation Pde = Pe has been studied in simulation; details of results and figures not reported for brevity sake (a synthesis of results follows). In the case of a sinusoidal disturbance (de = A sin(ωt), A = 1), the observed problem (i.e., acceptable attenuation in PVe and large SPi variations required) can also appear and the 6199



Article

Figure 8. Two examples of application of the proposed technique: before and after retuning. (top) SPi and PVi. (bottom) SPe and PVe. (13) Hägglund, T. A Control Loop Performance Monitor. Control Eng. Pract. 1995, 3, 1543, 125, 252. (14) Scali, C.; Farnesi, M. Implementation, Parameters Calibration and Field Validation of a Closed Loop Performance Monitoring System. IFAC Ann. Rev. Control 2010, 34, 263. (15) Scali, C.; Marchetti, E.; Esposito, A. Effect of Cascade Tuning on Control Loop Performance Assessment. IFAC−PID’12: International Conference on Advances in PID Control, Brescia, March 28−30, 2012, paper no. FrB1.1 (16) Rivera, D. E.; Morari, M.; Skogestad, S. Internal Model Control. 4. PID Controller Design. Ind. Eng. Chem. Res. 1986, 25, 457. (17) Skogestad, S. Simple Analytic Rules for Model Reduction and PID Tuning. J. Proc. Control. 2003, 13, 291. (18) Tyreus, B. D.; Luyben, W. L.; Tuning, P. I. controllers for integrator/dead time processes. Ind. Eng. Chem. Res. 1992, 31, 2625. (19) RRT: Relative Response Time. http://www.expertune.com/ articles/UG2007 /CascadeTuning.pdf.

This is certainly an interesting feature in the perspective of industrial applications, where process information is scarce: only the knowledge of loop type (level or not) is required.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Present Address §

E.M.: AspenTech Srl, Lungarno Pacinotti 6, 56100, Pisa (Italy) Notes

The authors declare no competing financial interest.

■

REFERENCES

(1) Stephanopoulos, G. Chemical Process Control: An Introduction to Theory and Practice; Prentice Hall Int: Englewood Cliffs (USA), 1984; p 399. (2) Visioli, A. Practical PID Control; Springer-Verlag: London, 2006; p 251. (3) Ziegler, J. G.; Nichols, N. B. Optimum Settings for Automatic Controllers. Trans. ASME 1942, 64, 759. (4) Lee, Y.; Oh, S.; Park, S. PID Controller Tuning to Obtain Desired Closed Loop Responses for Cascade Control Systems. Ind. Eng. Chem. Res. 1998, 37, 1859. (5) Lee, Y.; Oh, S.; Park, S. Enhanced Control with a General Cascade Control Structure. Ind. Eng. Chem. Res. 2002, 41, 2679. (6) Kaya, I.; Tan, N.; Atherton, D. P. Improved Cascade Control Structure for Enhanced Performance. J. Proc. Control 2007, 17, 3. (7) Alfaro, V. M.; Vilanova, R.; Arrieta, O. Robust Tuning of TwoDegree-of-Freedom (2-DoF) PI/PID Based Cascade Control Systems. J. Proc. Control. 2009, 19, 1658. (8) Hang, C. C.; Loh, P. A.; Vasnani, V. U. Relay Feedback AutoTuning of Cascade Controllers. IEEE Trans. Control Syst. Technol. 1994, 2, 42. (9) Tan, K. H.; Lee, T. H.; Ferdous, R. Simultaneous On Line Automatic Tuning of Cascade Control for Open Loop Stable Processes. ISA Trans. 2000, 39, 233. (10) Leva, A.; Donida, F. Autotuning in Cascaded Systems Based on a Single Relay Experiment. J. Proc. Control. 2009, 19, 896. (11) Leva, A.; Marinelli, A. Comparative Analysis of Some Approaches to the Autotuning of Cascade Controls. Ind. Eng. Chem. Res. 2009, 48, 5708. (12) Skogestad, S. Tuning for Smooth PID Control with Acceptable Disturbance Rejection. Ind. Eng. Chem. Res. 2006, 45, 7817. 6200


Refinement of Cascade Tuning to Improve Control Performance

Recommend Documents