EVALUATING PID TUNING RULES FOR FOLPD SYSTEMS

Transcription

1 EVALUATING PID TUNING RULES FOR FOLPD SYSTEMS P. Murphy*, T. O Mahony Cork Institute of Technology, Irelan, pmurphy@cit.ie*, tomahony@cit.ie, fax Keywors: PID tuning rules, pasteuriser unit, level control. Abstract This paper consiers the problem of tuning a PID controller for a first-orer lag plus ea-time (FOLPD) system. The authors examine over 2% of the reporte FOLPD tuning rules for performance an robustness. These rules are comprehensively evaluate in simulation, on a laboratory scale system an on a pilot-scale system. The results inicate that nine of the investigate rules perform well in general. It is the author s belief that these rules represent a useful an inustrially relevant subset of PID tuning rules, a potential replacement of the traitional Ziegler-Nichols technique. 1 Introuction Inustrial practice relies heavily on the use of tuning rules to ai the esign of PID controllers. Research in this area continues unabate [1], an an abunance of tuning rules have now been propose. There is some merit to this research in that the wie range of control problems necessitates a range of tuning techniques. Not withstaning this, in the authors opinion, much of this research is superfluous because the propose tuning rules are not stringently evaluate. In general, a new proposal is compare with the Ziegler-Nichols (ZN) technique an on that basis eeme a useful aition to the control engineer s toolbox. However, it is trivial to show that any reasonable tuning strategy, incluing trial-an-error, will outperform ZN, an hence the rational is seriously flawe an has resulte in a glut of controller tuning rules for the PID controller. The practical implication is that these contesting esigns present a bewilering array of choices to the control engineer, as there is little evience to inicate truly useful rules. This paper oes not propose any new tuning rule, but instea concentrates on thoroughly evaluating a selection of existing proposals. While this iea is not new, existing stuies have focuse on simulation comparisons, [2,3], an there is a earth of real time comparisons. Existing work is further limite in that a very small number (two or three) of tuning techniques are usually compare. Thus, the contribution of the research reporte here is that a large number (55) of tuning techniques are compare on a real-time application. The objective of the comparison is to etermine a truly useful subset of tuning techniques for inustrial practice, an ultimately a replacement of the ZN technique. 2 Methoology A significant ifficulty with the propose research programme is the large number of existing tuning rules (TR) some of which are exclusive to specific PID structures. For example, in the review conucte by [4] six PI controller structures an 28 PID variants were ientifie. The author collate 623 PID TR applicable to these 34 structures, an this number continues to expan. Given the scope of this work it is clear that some initial restrictions an assumptions must be mae to realise a tangible problem. The evaluation consiere in this paper is restricte to the stuy of PID TR for FOLPD moels. Since FOLPD moels account for 46% of the rules ocumente in [4], this still amounts to a consierable boy of work. Of these FOLPD TR, 95% of PI an 34% of PID are tune for the stanar textbook structure. However, this structure is rarely use in inustry. As the focus is on ientifying TR that pertain to inustrial practice, rules specific to the structure of Equation (1) 1 K 1 s T + + E( s) s T (1) i were neglecte in favour of rules, which were evise specifically for the commercial PID controllers of which there are two istinct alternatives [5]. The stanar form, or ISA form is given by Equation (2) 1 st K by ( ) ( ) + ( ) + ( ( ) ( )) sp s Y s E s cysp s Y s st st i 1 + N (2) an the series form is given by Equation (3) sct 1 1 ( ) + st ( ) 1 + (3) U s K b Y s Y ( s) st T sp T i st 1 + s i 1 + s N N where K, T i, an T are the proportional, integral an erivative gains, respectively. The signals U(s), Y(s), Y sp (s) an E(s) represent the Laplace transforms of the process input u(t), process output y(t), set point y sp (t) an control error e(t) y sp (t) - y(t). The parameters b an c are constants that can be tune to enhance the response to set-point changes while N selects the time constant of the erivative filter. The evaluate TR were selecte for controller structures base on their similarity to commercial structures shown in Equations (2)

2 an (3). In total 55 ifferent TR were evaluate, which represents 42% of the non-textbook FOLPD TR collecte in [4]. Details of these rules are summarise in Appenix A. 3 Controller Design The controller esign was implemente using MATLAB an Simulink. An expert-base graphical user interface (GUI) tool was esigne to ai this process. The tool consists of the list of TR presente in Appenix A. The user specifies a FOLPD moel an these TR realise 55 ifferent PID controller esigns. Each of these esigns are then evaluate in simulation to etermine stanar performance an robustness criteria e.g. IAE, settling time, percent overshoot, gain margin (Gm) an phase margin (Pm), etc. The user may then specify bouns on any of the performance an/or robustness criteria. Designs, which o not ahere to these bouns, are iscare while the remainer are sorte in terms of the IAE criterion an then presente to the esigner. The objective of the controller esign was to achieve a fast close-loop response, goo isturbance rejection properties an goo robustness. These general requirements were translate into the following specific bouns on robustness 6B Gm 3B, 45º Pm 2º, 1 elay margin, 1 maximum sensitivity 2.2. Performance was evaluate by examining the IAE (servo + regulator), settling time (servo + regulator) an the control signal variance. 4 Simulation analysis An initial evaluation of the tuning rules was performe in simulation where 21 ifferent FOLPD moels were investigate using the expert base tuning tool escribe in the previous section. The steay state gain of the moel was varie accoring to K m {1, 5, 1} while the ratio of timeelay to time constant was varie as τ m / T m {.1 1 5}. It is well appreciate that the ifficulty of the control problem increases as this ratio increases an hence these moels represent a goo test of the TR. The various moels were applie to the expert base tuning package an the resulting close-loop performances were evaluate. Figure 1 summarises the results where the horizontal axis represents the tuning rule number an the vertical axis the frequency with which the tuning rule was successful. For example, TR number 4 [Chien (1988)] yiele in a goo PID controller in 2 out of the 21 moels investigate while the TR numbere 7, 2 an 44 yiele a goo PID controller for only one of the moels. In general, it was foun that the majority of the tuning rules performe well for systems where the ratio τ m / T m 1. However as the ratio ecrease fewer rules were applicable, while for large ratios only TR 4 realise an aequate esign. Also the TR equippe with an extra tuning parameter (1, 3, 4, 6, 1, 41, 43, 52), outperforme the other TR as the aitional parameter enable robust performance for a wie range of process moels. Clearly the TR numbere 1, 3, 4, 5, 6, 1, 31, Frequency of occurrence Tuning Rules Figure 1: Frequency of TR that performe well on range of moels in simulation. 41 & 43 performe well an therefore represent a subset of useful generic PID controller TR for FOLPD systems. This hypothesis will be further teste in the next two sections where trials will be performe on two real-time systems. 5 Laboratory system To assess the performance of the PI(D) TR a level/flow process control system, esigne by Feeback Instruments Lt., was use. Water is fe from a slump tank to a ual compartment process tank via a circulating pump controlle by a motorise flow gate valve. A potentiometer float level sensor observes the level of the compartment tank. Both use a current range of 4 2mA. The MATLAB System Ientification Toolbox, [6] was use to facilitate the moelling process. Base on a-priori open an close-loop tests a suitable sampling time of one secon was chosen. Close loop irect system ientification, [7], was performe using a PI controller in series with the process while the set point sequence was a step of magnitue.5 units. The close-loop experiments were replicate three times an the average control signal an process output were use in the ientification. The estimate FOLPD moel is e 5s G LAB ( s) (4) s + 1 This moel was applie to the expert-base tuning package an, as before, the TR were evaluate base on the closeloop criteria specifie in section 3. Of the 55 TR, eleven satisfie all of these metrics. These eleven PID esigns were then evaluate in real-time. The real-time performance was assesse using IAE (servo an regulator) an settling time (servo an regulator). The IAE metric was relatively consistent for each of the TR teste while the settling time varie consierably, Figure 2. If the tuning rules are compare on this basis, four of the rules (TR 1, 5, 6 an 41) perform very well. All of these rules are containe in the subset ientifie in the previous section.

3 Settling time (secons) Tuning rules Servo Regulator Combine Figure 2: Comparison of real time experiments settling time for laboratory system. where the process output is taken as the milk temperature exiting the heating section (the start of the holing tube). The manipulate variable is the percentage opening of the steam valve as illustrate in Figure 3. The system was ientifie by applying a set-point step change from Close loop irect ientification was performe using a PI controller an two FOLPD moels were ientifie. The first of the moels (G S ) was ientifie using the existing manipulate an controlle variables, while for the secon moel (G E ) the controlle variable was efine as the milk temperature at the en of the holing tube. Both moels are represente by Equations (6) an (7) where the principle ifference is the length of the elay e 2s G S ( s) (6) 18.83s e 28s G E ( s) (7) s Chille Milk Out 3 Chille Water In Cooling Section Section 3 Chille Water Out 13 Tetra Plex C3 Plate Heat Exchanger 18 6 o C RAW MILK IN Flow Divert F T Regenerato r Section Holing Tube Heating Section Section 1 77 Setpoint Figure 3: Diagram of Pasteurisation Unit 6 Pilot-scale inustrial system HOT WATER OUT HOT WATER IN 75 PID Controller Braze Heat Ex. ABB - Sattline STEAM STEAM FLOW VALVE The pilot-scale system use in this work is a pasteurisation plant locate at Moorepark Technology Lt., Dairy Proucts Research Centre, Fermoy, Co. Cork, Irelan. The milk is pasteurise using the High Temperature Short Time (HTST) process [8]. This process is escribe as follows; with reference to Figure 3, the raw unpasteurise milk is pumpe at 5l/h from the balance tank into the regeneration section of the PHE. This milk is preheate to about 63 by the returning pasteurise milk. The preheate milk then passes to the heating section where it is heate to the pasteurisation temperature, say 74, using hot water as the meium. The milk is hel at the pasteurisation temperature for 15 to 2 secons in the holing tube. The pasteurise milk is coole via the regeneration an cooling sections. The hot water use in the heating section is heate in a braze heat exchanger (BHE) by regulating the flow of steam through the BHE. The plant is monitore an controlle by ABB s Sattline istribute inustrial control system. Control is performe using a PID controller efine as 1 T s K ( ) E ( s) + E ( s) + Y ( s) (5) Ti s T Filter s Moel G S (s) Equation 6 was use with the expert-base PID tuning package an nine TR resulte in aequate performance. These tuning rules were 1, 3, 4, 6, 1, 2, 22, 41 an 43. To minimise experimental time at Moorepark, these results were refine using an accurate non-linear first principles moel that ha previously been evelope, [9]. TR 3, 2, 22 an 41 were subsequently eliminate as the close-loop responses were not sufficiently ampe. The other controller esigns were evaluate using the IAE an the settling time criteria. Tuning rules 1, 4, 6 an 43 yiele practically ientical results, while both the settling time an IAE was significantly reuce via tuning rule 1. These five tuning rules were selecte for real-time evaluation. However, these five rules yiel four ifferent controller structures, cf. Appenix A. The controller resulting from TR 1 can be implemente exactly, while those resulting from rules 4 an 6 are closely approximate by Equation 5. However Equation 5 is not representative of the other two structures, hence these were not evaluate on the pilot-scale system. Attempts are ongoing to aress this problem by implementing a library of PID controllers on the Sattline system. In Table 1 the settling time (t s ), overshoot (Os), steay state peak to peak (SSPP) an IAE were calculate for the remaining three rules using a step set-point change from 6 7. The process output was allowe to settle at 6 C to avoi bias ue to variable start-up conitions. All three of the controller esigns worke well in practice, though it is arguable that TR number 1 outperforme the other two. TR t s (secons) Os (%) SSPP ( C) IAE Table 1: Real time evaluation of TR for G S (s).

4 IAE & Settling time (secons) Tuning Rules IAE Settling Time Figure 4: Non-linear verification of TR for G E (s). 6.2 Moel G E (s) As mentione in section 6 this transfer function is base on the milk temperature at the en of the holing tube. Applicable TR were initially etermine using the expertbase PID esign tool an 18 TR resulte in aequate performance. The increase number of aequate tuning rules is ue to the increase in the ratio τ m / Tm associate with this moel. These rules were evaluate using the non-linear firstprinciples moel, the results of which are summarise in Figure 4. All 18 of these tuning rules performe aequately on the non-linear moel. Since most of these structures iffer significantly from the PID controller that exists in Moorepark, it was only possible to verify the performance of tuning rules 1, 3, 6. Table 2 summaries the real-time results. All three of the esigns yiel aequate performance, but relative to Table 1, the performance is very poor. In both of these tables the settling time, overshoot, steay state peak to peak an IAE were calculate using process output i.e. the milk temperature at the en of the holing tube. TR t s (secons) Os (%) SSPP ( C) IAE Table 2: Real time evaluation of TR for G E (s). TR Simulation Laboratory G S G E Robustness Table 3: Summary of Results 7 Conclusions This paper has attempte to istil a useful subset of PID controller TR for practitioners from the plethora that exist via a simulation analysis an two real-time applications. A summary of the results is presente in Table 3 where the tuning rules that performe well in simulation are tabulate. Of those nine PID esigns only one performe consistently on the laboratory scale system an on both moels of the pilotscale plant. Hence, the obvious conclusion is that tuning rule 6 [Leva & Colombo (2)] may represent a viable alternative to the traitional ZN tuning technique. However, a significant isavantage with this rule is that it incorporates an aitional robustness parameter but there are no guielines to ai this choice. Consiering that inustrial practice tens to avoi the complexity of erivative action, it is unlikely perhaps that such a tuning rule will be wiely aopte. However, Table 3 oes suggest that this woul appear to be the real trae-off. The tuning techniques that appear frequently (rules 1, 4, 6, 1 an 41) all incorporate a similar robustness parameter. Hence, a general conclusion woul appear to be that enhance performance can only come at the cost of aitional complexity. It was also foun that, in general, rules base on the FOLPD parameters { τ m, Tm, K m} outperforme those base on the ultimate gain an ultimate frequency criterion. Thus, while simple tuning rules e.g. ZN may yiel a PID controller, highperformance ictates more accurate moels an aitional tuning effort. As with any evaluation the results are biase by the choice of performance criteria. In this evaluation the controllers were require to satisfy a certain minimum robustness criteria. An subsequently evaluate base on multiple performance criteria e.g. servo IAE, regulator IAE, servo settling time an regulator settling time. Incorporating robustness criteria ensures that the esigns are inustrially viable while the use of multiple performance criteria minimises the bias. This is reflecte in the results where only one of the nine rules of table 3 is biase on minimising IAE an the most consistent rule Leva an Colombo is base on internal moel control. The analysis performe in this paper is obviously limite by the application examples use to test the tuning rules in realtime. It is the authors opinion that in general the ratio τ m / T m was smaller than typically foun in the process inustry an this will obviously bias the results. To reress this a secon inustrial valiation is commencing on a commercial evaporator/spray-ryer. Acknowlegements This work was sponsore by the Irish Government uner the National Development Plan 2-26 through the HEAPRTLI. Funing was also receive from the CIT Scholarship Scheme. The authors wish to acknowlege this support an that receive from staff at Teagasc Moorepark. References [1] Z. Gajić, an M. Lelić, A reference guie to PID controllers in the nineties, IFAC workshop on igital

5 control Past, present an future of PID Control, Terrassa, Spain,pp , (2). [2] M. Chong Ping, K. Ezra Kwok an P. Li, A moel base augmente PID algorithm, Journal of Process Control, vol. 1, pp. 9-18, (2). [3] Y. Lee, J. Lee an S. Park, PID controller tuning for integrating an unstable processes with time elay, Chemical Engineering Science 55, pp , (2). [4] O Dwyer, A., Hanbook of PI an PID controller tuning rules, Imperial College Press, Lonon, UK, (23). [5] K.J. Åström, an T. Hägglun, PID Controllers: Theory, Design, an Tuning, Instrument Society of America, Research Triangle Park, North Carolina, (1995). [6] L. Ljung, System ientification toolbox for use with MATLAB, The MathWorks, Inc. (22). [7] T. Söerström an P. Stoica, System Ientification, Prentice-Hall, UK, (1989). [8] Alfa-Laval, Dairy Hanbook, Alfa-Laval, Lun, Sween, (1986). [9] B. Griffin an T. O Mahony, Moelling an Simulation of a pilot scale milk pasteurisation unit, Proceeings of Inustrial Simulation Conference 23, Valencia, Spain, pp , (23). Appenix A PI PID -(TR similar to ISA structure) PID - (TR similar to series structure) Structure TR # Ieal controller with a 1 st orer filter Riveria & Jun (2) 1 Controller with set-point weighting Taguchi & Araki (2) 2 Ieal controller with a 2 n orer filter Tsang et al. (1993) 3 Chien (1988) 4 Controller with filtere erivative Two Degree of freeom controller Non-Interacting controller 3 with set-point weighting Non-Interacting controller 2 Non-Interacting controller 4 Classical controller 1 Gong et al. (1996) 5 Leva & Colombo (2) 6 Davyov et al. (1995) 7 Kasahara et al. (1999) 8 Taguchi & Araki (2) 9 Huang et al. (2) 1 Hang & Astrom (1988) 11 Hang et al. (1991) 12 Hang & Cao (1996) 13 Min. ISE Zhuang & Atherton (1993) 14 Min. ISTSE Zhuang & Atherton (1993) 15 Min. ISTES Zhuang & Atherton (1993) 16 Servo Min. ISTES Zhuang & Atherton (1993) 17 Regulator & Servo Regulator & Servo Regulator Min. IAE Shinskey (1988) 18 Min. IAE Kaya & Schieb (1988) 19-2 Min. ISE Kaya & Schieb (1988) Min. ITAE Kaya & Schieb (1988) Hang et al. (1993b) 25 Witt an Waggoner. (199) 26 Witt an Waggoner. (199) 27 St Clair. (1997) (Conservative) 28 Shinskey (2) 29 Min. IAE Kaya & Schieb (1988) 3-31 Min. ISE Kaya & Schieb (1988) Min. ITAE Kaya & Schieb (1988) Min. IAE Witt & Waggoner (199) Min. ITAE Witt & Waggoner (199) Tsang an Ra. (1995) 4 Tsang et al. (1993) 41 O Dwyer (21a) 42 Chien (1988) 43 Min. IAE regulator Shinskey (1994) 44 Min. IAE regulator Shinskey (1988) 45 Inustrial controller Min. IAE Kaya & Schieb (1988) Regulator Min. ISE Kaya & Schieb (1988) & Servo Min. ITAE Kaya & Schieb (1988) 5-51 Classical controller 5 Chien (1988) 52 Regulator - Min. IAE Huang et al. (1996) 53 Non-Interacting controller 1 These tuning rules may be reference via [4]. Servo - Min. IAE Huang et al. (1996) 54 Huang et al. (2) 55