Berner, Josefin; Soltesz, Kristian; Hägglund, Tore; Åström, Karl Johan

Transcription

1 An experimental comparison of PID atotners Berner, Josefin; Soltesz, Kristian; Hägglnd, Tore; Åström, Karl Johan Pblished in: Control Engineering Practice DOI: 1.116/j.conengprac Docment Version: Peer reviewed version (aka post-print) Link to pblication Citation for pblished version (APA): Berner, J., Soltesz, K., Hägglnd, T., & Åström, K. J. (218). An experimental comparison of PID atotners. Control Engineering Practice, 73, DOI: 1.116/j.conengprac General rights Copright and moral rights for the pblications made accessible in the pblic portal are retained b the athors and/or other copright owners and it is a condition of accessing pblications that sers recognise and abide b the legal reqirements associated with these rights. Users ma download and print one cop of an pblication from the pblic portal for the prpose of private std or research. Yo ma not frther distribte the material or se it for an profit-making activit or commercial gain Yo ma freel distribte the URL identifing the pblication in the pblic portal Take down polic If o believe that this docment breaches copright please contact s providing details, and we will remove access to the work immediatel and investigate or claim. L UNDUNI VERS I TY PO Box L nd

2 An Experimental Comparison of PID Atotners Josefin Berner 1, Kristian Soltesz, Tore Hägglnd, Karl Johan Åström Abstract In this paper two novel atotners are compared with two indstriall available ones. The aim is to see if the research frontline can improve the indstr standard of toda. Experiments are made on three laborator processes with different characteristics. Two lag-dominated processes of which one is a level control problem with fast dnamics, and one a temperatre control problem with slow dnamics, as well as one dela-dominated level control process. Both the experiments and the obtained controller performances are evalated and discssed. The reslts show that the performance of the stateof-the-art indstrial atotners can be significantl improved. Index Terms PID control, Atomatic tning, Process indstr, Rela feedback, Comparative std. I. INTRODUCTION Atomatic tning of PID controllers is a sefl featre for an ser who does not have the time, knowledge or desire to manall tne his or her control loops. Especiall in the process indstr, where a factor ma have hndreds or thosands of different flows, levels, temperatres, concentrations etc. that need to be controlled, the benefit of a fast and reliable wa of finding appropriate controller parameters is large. One sch procedre that is common in indstr is the rela atotner. The principle of rela atotning is as follows. B closing the feedback loop with a rela fnction, that switches between two vales depending on the process otpt, the process is forced into oscillations. See Figre 1 for the setp and Figre 2 for a tpical experiment otpt. From the oscillations process data can be obtained and sed to tne a PID controller. The original rela atotner [1] ses the period time and amplitde of the indced oscillations in order to find the critical point where the process Nqist plot intersects the negative real axis. If a hsteresis band is added to redce shattering de to noise, a slightl different point is obtained. The controller parameters are then fond b moving this point to give the open-loop sstem specified amplitde and phase margins. The atotner from [1], that was developed in the 198 s, is probabl still the most common one in indstrial DCS sstems toda. Several of the major vendors se this procedre. It has been implemented in indstrial control sstems sch as the ABB ECA6, the ABB 8 XA and it is also the base of the atotner featre in e.g. Emerson Delta V. Even thogh the knowledge abot PID control has been improved and the available compting power of control sstems has increased dramaticall since the 198 s, it does not seem to have *The athors are members of the LCCC Linnaes Center and the ELLIIT Excellence Center at Lnd Universit 1 All athors are with the Department of Atomatic Control, Lnd Universit, Sweden. Contact josefin.berner@control.lth.se r e + Rela P 1 Fig. 1. Setp for the rela feedback experiment, where r is the constant reference vale, e is the control error, is the rela otpt and is the process otpt. Fig. 2. Otpts from a rela feedback experiment. The rela otpt (ble) switches between its two vales ever time the process otpt (red) leaves the hsteresis band (dashed black), casing the process to oscillate. If the amplitdes of the rela fnction are different, as in this figre, the rela is said to be asmmetric. affected available indstrial atotners mch. In academic literatre man modifications and improvements have been sggested to the rela atotner. For instance [2], [3], [4] have modified the atotner to find first- or second-order models with time dela of the process instead of a single freqenc point. The excitation of the process has also been improved b the sage of asmmetric rela fnctions in e.g. [5], [6]. A review of the crrent state of process modeling from rela experiments can be fond in [7]. However, these improvements do not seem to have made their wa ot to the indstrial prodcts. The qestion we aim to answer in this paper is whether this is since the old atotners are performing well-enogh, or if the cold actall be significantl improved b inclding recent scientific development. In order to do that, we compare two new atotners developed b the athors, to the ABB ECA6 [8] containing the traditional atotner [1] and the more recent atotning algorithm Acctne III TM provided in the Honewell UDC32 [9]. Since the atotners are mainl sed in indstrial settings, a simlation std wold not cover tpical problems. Conseqentl the comparisons will be performed on laborator processes that featre man of the isses encontered in practice like noise, non-linearities, distrbances, low converter resoltions etc. Even if the atotning possibilit has been available in most control sstems for some decades it is not alwas sed, reslting in nnecessaril poor control performances in man sstems [1], [11], [12]. Reasons for this ma be that the sers are either not aware of the featre or do not

3 feel confident in sing it. Therefore it is important to ensre that the atotners, apart from giving satisfactor reslts, are eas to nderstand and se also for non-experienced sers. In this std we will therefore do as few manal interactions as possible with the atotner settings, and will not assme an knowledge of neither the process nor control theor. II. THE STUDY This std compares and evalates for different atotners, described in Section III, on three processes that are described in Section IV. The atotners are evalated on their experiment drations, their ser-friendliness, and on the performance of the obtained controllers. Since the indstrial atotners do not provide the ser with an models that the base the controller designs on, no comparison can be made between estimated models. Three experiments are rn b each atotner, and a representative controller setting is chosen for comparison to the other atotners. The mltiple experiments are performed in order to redce the risk of distrbances affecting the reslt of one of the atotners casing an nfair comparison. All obtained controller parameters are presented in Section V, along with the performance experiments. The most important aim for a controller in process indstr is to be able to handle load distrbances, and the performance tests in this comparison are therefore focsed on load distrbance attenation. The distrbances were designed and controlled to ensre that identical distrbances affected each of the controllers on the specified process. III. THE AUTOTUNERS The for atotners sed in this std are presented in this section. As stated in the introdction the aim is to compare indstrial standard atotners to recent developments in academic literatre. The selection of indstrial atotners inclde the ABB ECA6 frther described in Section III- A and the Honewell UDC32 described in Section III-B. A motivation to this choice is that we wanted one atotner containing an implementation of the original procedre from [1], which is still the most common one, as well as one more recent version of a rela atotner available on the market toda. B this choice we want to find ot what improvements have been made in the indstrial controllers dring the last 3 ears. There are of corse other brands and procedres that cold have been chosen, as well as completel different atotning principles based on step responses or other openloop experiments. We did, however, restrict this std to onl contain rela atotners. The academic atotners we selected are implementations of two versions developed b the athors. The τ-tner, described frther in Section III-C, is procedre-wise ver similar to the original atotner, bt has some modifications to obtain better models. The NOMAD atotner, described in Section III-D, tilizes more data and reqires more comptational power, bt allows for shorter experiment times. We cold have chosen to inclde man other academic atotners in this std, e.g. the ones presented in [13], Fig. 3. The ABB ECA6 controller. [14], [15]. Since we did not have an implementations of these atotners, and since we wanted to find ot how or proposed atotners compared to the indstr standard, we decided to restrict orselves to this selection. A. ABB ECA6 The ABB ECA6 controller, in this paper referred to as ECA, is shown in Figre 3. The operator s manal [8] describes it as "... a dal loop controller with advanced control fnctions. In addition the ECA6 has comprehensive logical and arithmetical data processing facilities. Its five analog inpts, three analog otpts, for digital inpts and six digital otpts can be sed to solve almost an process control problem." The bilt-in atotner is based on [1] and provides PID parameters for a controller on serial form immediatel from the experiment. The atotner is accessible after enabling it in the configration men. Before starting the tning the ser has to make sre that the process vale is in stead state close to the setpoint, otherwise the tning ma fail. The atotner starts b measring the noise level for 5 s to set an appropriate hsteresis level. The rela amplitdes are restricted to 1 % of the control interval b defalt. If the atotner notices that the process variable deviations are too large (or too small) dring the experiment it will adjst the rela amplitdes if the restrictions allow it. The PID controller incldes a first-order filter for the derivative part of the controller with a filter time constant T f = T d /8. There is an option to tell the atotner whether the controller dnamics shold be Normal, DeadTime, PI or ppi. Since this std focses on how an nexperienced ser wold be able to se the atotners, we do not assme to have this kind of knowledge and hence alwas se the defalt Normal.

4 Fig. 4. B. Honewell UDC32 The Honewell UDC32 controller. To compare with a more recent controller we chose the Honewell UDC32 (referred to as Honewell) with the atotning featre Acctne III TM. According to its manal [9] it is "... an ideal controller for reglating temperatre and other process variables in nmeros heating and cooling applications, as well as in metal working, food, pharmaceticals, semicondctor, testing and environmental work". In spite of being mainl considered as a temperatre controller, the manal [9] also claims that "This standard featre [read: Acctne III TM ] provides a trl plg and pla tning algorithm, which will, at the toch of a btton or throgh a digital inpt, accratel identif and tne an process inclding those with deadtime and integrating processes". The tning can be started whenever TUNE has been enabled in the setp men, bt to start the atotner the controller mst be switched to atomatic mode. A choice between SLOW and FAST tning can be made. This does not affect the experiment, bt calclates the controller parameters differentl. Since we do not assme to know anthing abot the process we sed the SLOW option for all experiments. The atotner switches the rela otpt two fll ccles between the maximm and minimm control otpt levels, independent of the setpoint vale. PID parameters for a controller on serial form are obtained from the experiment and immediatel sed. As far as we know, this atotner does not design an filter for the controller, and the onl filter sed in or experiments is a noise filter with the defalt time constant vale 1 s. C. τ-tner The atotner described in [16], [17] is here denoted as the τ-tner. It ses an asmmetric rela fnction with adjstable amplitdes and rns ntil limit ccle convergence is reached. From the rela oscillations it ses the half-period times and the integral of the process otpt over one ccle, to calclate an integrating or first-order model with time dela of the process. It then ses the AMIGO [18] tning rles to obtain parameters for a PI or PID controller on parallel form. It ses the normalized time dela, τ, to select model and controller strctre. The normalized time dela is defined as τ = L L + T, (1) where L is the deadtime and T is the time constant of the process dnamics. More details abot how the atotner tilizes τ can be fond in [16]. The τ-tner is simple to implement and se, bt as was stated in [17] it can be qite sensitive to qantization, non-linearities and non-stationar starting conditions. The atotner setp in these experiments ses a restriction on the large rela amplitde to be maximm 1% of the available control range, it ses 1 s in the beginning of the experiment to measre noise and decide on a hsteresis level, bt also has a minimm hsteresis level of.5% of the process otpt range. In the papers [16], [17], no filter was designed for the controller. Since we need some roll-off for high freqencies to redce the impact of noise, we let the atotner design a second order filter on the form F(s) = The filter time constant T f is chosen as st f + (st f ) 2 /2. (2) T f = 1 5ω 18, (3) where ω 18 is the freqenc where the estimated process model has a phase lag of 18. The filter F(s) is sed on the entire controller, not onl the derivative part. The model, filter, controller parameters and some additional experiment data are available to the ser of this atotner. D. NOMAD-atotner The experiment and modeling part of the Noise-robst Optimization-based Modeling And Design Atotner (NO- MAD) is described in [19]. This atotner performs the same experiment as the τ-tner, with two exceptions. The first exception is that it does not have to be initiated in steadstate, since it estimates the initial conditions. The second exception is that it does not wait for convergence of the limit ccle oscillations bt instead stops the experiment after three rela switches. It then ses a gradient-descent algorithm to find first-order or second-order time-delaed models from the entire data set. It chooses which model to se b the Akaike Information Criteria [2]. The sage of the entire data set distingishes the NOMAD-atotner from the ECA and τ-tner, that onl se certain time intervals, amplitdes etc. to get their models. It can be arged that the need of less data is a benefit of these other methods, bt it is also what cases their need to wait for limit-ccle convergence as well as making them more sensitive to noise. No controller tning method was specified for the method in [19] so for this paper we added that to get a complete atotner. The filter design was chosen the same wa as for the τ-tner, hence described b (2) and (3). The controller

5 tning chosen is the convex-concave optimization method described in [21]. Here the integrated error IE = e(t)dt (4) from a step load distrbance on the process inpt, is minimized with constraints on the maximm vales of the sensitivit fnction S(s) = and complementar sensitivit fnction T (s) = P(s)C(s), (5) P(s)C(s) 1 + P(s)C(s). (6) The process P(s) that is entered to the optimization program is the filtered process, since the controller design and the filter design are connected. The PID parameters obtained are for a controller on parallel form. Since both the modeling and controller design are optimization-based, this atotner reqires a lot more comptations than the original atotner. However, the calclations performed are rather cheap, and with an efficient implementation and the compting power available toda the can be made in the order of seconds. IV. PROCESSES To evalate the atotners on different tpes of dnamics we chose three processes with different characteristics. Two lag-dominated processes, where one has fast dnamics and one is slow, as well as one process that is dela-dominated. This information abot the process dnamics was onl sed to choose sitable processes and was assmed to be nknown throghot the tning experiments. The process hardware consisted of a qadrple tank and a batch tank available at the control laborator at Lnd Universit. Even thogh the chosen processes are simple, the have significant nonlinearities and noise, making them representative for the processes o enconter in indstr. The inpt and otpt signals of the processes were normalized to [,1] and [,1]. The processes will be described frther in their respective sbsections. A. The qadrple tank The qadrple tank shown in Figre 5 is a version of the one described in [22]. The tank can be sed as both a singleinpt single-otpt sstem and as a mltivariable sstem. For the experiments in this paper onl one side of the qadrple tank was sed, in order to get the single-inpt single-otpt configration. This sstem consists of a pmp that pmps water into the pper tank, which then flows throgh down to the lower tank. For the first experiment, called Level control, the measred process variable is the water level of the lower tank. The dnamics can be described b a second-order lagdominant sstem with time constants T 1 and T 2, and an average residence time T ar = T 1 + T 2 2 s. Fig. 5. The qadrple tank sed for level control experiments on the lower tank and the delaed pper tank. The qadrple tank was also sed for the dela-dominant process. For the Delaed tank experiment, the measred variable was the water level of the pper tank. The dnamics of this process can be described b a first-order sstem with a time constant T 1 s. To get it dela-dominated a time dela of 2 s was added to the control signal. B. The batch tank The batch tank is shown in Figre 6. It consists of one inflow pmp, one otflow pmp, a heater, a cooler, and an agitator. Measrements of the water level and temperatre are available. For the experiment on this process, referred to as Temperatre control, we sed a fix water level, with both pmps trned off. The agitator was on all the time and a split-range controller was sed to control the heater and cooler. The control range of -1 was split p so that = 5 corresponded to Cooler = 1% % and = 5 1 corresponded to Heater = % 3%. The restriction on the heater was made to balance the heating and cooling capacities of the process. V. EXPERIMENTS AND RESULTS The reslts from the three processes are illstrated b plots of the rela experiments as well as the obtained controller performance for load distrbances acting on the process inpts. The choice of performance evalation was made since decreasing the inflence of load distrbances is the main focs in process control [23]. Before the experiments were started the processes were broght to stead-state at the desired setpoint levels. This startp phase has been discarded in order to onl show the actal experiments. For each process three experiments were made with each atotner to see how consistent the were. Obtained PID controller parameters for the different experiments are listed

6 TABLE I PID PARAMETERS AND IAE VALUES FROM THE LEVEL CONTROL EXPERIMENTS. FOR EACH AUTOTUNER THREE EXPERIMENTS WERE PERFORMED, THE CHOSEN PARAMETERS FOR EACH AUTOTUNER ARE MARKED WITH BOLD TEXT. NOTE THAT ECA AND HONEYWELL ARE ON SERIAL FORM, WHILE τ-tuner AND NOMAD ARE ON PARALLEL FORM. Atotner K [-] T i [s] T d [s] IAE ECA Honewell τ-tner NOMAD Fig. 6. The batch tank sed for temperatre experiments. in Table I-III. Since both the parametrization and the filter design differ between the controllers, a comparison of the Bode plots of the reslting (filtered) controllers are shown for each process. From these reslts a representative set of parameters was chosen and sed for the controller performance experiments. The performance experiments are shown, and the integrated absolte error IAE = t end (t) r(t) dt, (7) for each performance experiment, where t end is the experiment dration, is listed along with the controller parameters in the respective table. A. Level control of the lower tank A representative rela experiment for each of the atotners is shown in Figre 8. Note the differences in experiment dration and signal deviations. This is a rather fast process, hence the short experiment drations. The reslting controller parameters are listed in Table I and Bode plots of the (filtered) controllers are shown in Figre 7. It can be seen that ECA, Honewell and the τ-tner are ver consistent, while NOMAD is varing a bit more de to differences in the estimated models. However, the performance was still similar between the obtained NOMAD controllers. To evalate the controller performance two step load distrbances, of eqal magnitde bt opposite sign, were added to the inpt of the process. This was done b opening a valve at t = 1 s, decreasing the inflow to the pper tank with 5 %, and then closing that valve again at t = 3 s so that all the pmped water once again entered the tank. The performance of the obtained controllers are shown in Figre 9. Mag. [abs] Phase [deg] Fig. 7. Bode plot of the obtained controllers for the level control of the lower tank. The different atotners are ECA (green), Honewell (black), τ-tner (red) and NOMAD (ble). Two versions of the τ-tner are shown in this plot. As was described in [16] this atotner makes some decisions based on the estimated vale of the normalized time dela τ. In this case the estimated vale was low, τ =.7, and the process was wrongl classified as an integrating model with time dela. The dashed crve shows what the controller performance wold have been if the process wold instead have been classified as a first-order model with time dela, and the controller tning wold have been based on that. The reslts indicate that the threshold vale for this classification shold be reconsidered. The reslts show that the NOMAD responds mch faster and otperforms the others. The ECA controller comes in second place while the Honewell controller has too little integral action and recovers ver slowl. The τ-tner is abot as bad as Honewell for the solid crve, bt improves a bit for the dashed crve. B. Temperatre control of the batch tank An illstrative rela experiment for each of the atotners is shown in Figre 11. Note that the time scale for this

7 ECA τ-tner Time [s] Honewell NOMAD Time [s] Fig. 8. Rela experiments on the level control of the lower tank for the for atotners. Note the short experiment time of the NOMAD atotner and the large control and process deviations of the Honewell atotner ECA Honewell τ-tner NOMAD Time [s] Time [s] Fig. 9. Controller performance for level control of the lower tank. At t = 1 s a step load distrbance was added to the process inpt and at t = 3 s that distrbance was removed. The τ-tner has two versions in this plot, one controller based on an integrating model with time dela (solid), and one version tned from a first-order model with time dela (dashed).

8 TABLE II PID PARAMETERS AND IAE VALUES FOR THE TEMPERATURE CONTROL EXPERIMENTS. FOR EACH AUTOTUNER THREE EXPERIMENTS WERE PERFORMED, THE CHOSEN PARAMETERS FOR EACH AUTOTUNER ARE MARKED WITH BOLD TEXT. NOTE THAT ECA AND HONEYWELL ARE ON SERIAL FORM, WHILE τ-tuner AND NOMAD ARE ON PARALLEL FORM. Atotner K [-] T i [s] T d [s] IAE ECA Honewell τ-tner NOMAD process is in mintes since it is a mch slower process than the level control. From the experiment plots it is clear that the Honewell controller is fastest for this process de to its larger rela amplitdes. The ECA controller is also fast, while the other two are slower. In this case it is not the nmber of rela switches that inflences the experiment dration the most, bt rather the time period of the oscillations. Wh the different experiments get different time periods is discssed frther in Section VI. It is also ver clear from the experiment plots that the resoltion of the AD-converters is low for this process, the qantization levels are clearl visible. The controller parameters obtained from the experiments are listed in Table II, and Bode plots of the controllers are shown in Figre 1. As can be seen the indstrial controllers are both ver consistent while the τ-tner and NOMAD are varing more. It can also be noted that the ECA controller chose to se a PI controller for this process, this selection is a bilt-in featre of the ECA controller and nothing that we have inflenced. The controller performances for the respective atotners are shown in Figre 12. The Honewell controller performs well on this process, while the ECA is slow and almost not reaching stead-state within the 7 s shown in the plots. The NOMAD and τ-tner performance are qite similar, bt the high gain of the NOMAD controller makes it satrate the control signal for a short while in the beginning of the distrbance. The both ield a small overshoot, bt recover from it mch faster than the ECA does. It can also be noted that even if the Honewell controller does not have as high gain as the NOMAD and hence rises slightl slower and withot an overshoot, the control signal is at least as varing as for the NOMAD controller, de to its large high-freqenc gain (seen in Figre 1) that is amplifing the qantization noise. Mag. [abs] Phase [deg] Fig. 1. Bode plot of the obtained controllers for the temperatre control of the batch tank. The different atotners are ECA (green), Honewell (black), τ-tner (red) and NOMAD (ble). C. Level control of the delaed pper tank The rela experiments for the delaed tank are shown in Figre 14. Worth noting in the figre is that both the ECA controller and the τ-tner are adjsting their rela amplitdes dring the experiment to decrease the process deviation. This increases the experiment time for them b a few half-periods. It is also clear from the figre that the Honewell controller does not perform a good experiment on this process. Its large rela amplitdes make the tank overflow and then become empt at ever second rela switch. This makes the reslt from the Honewell controller ver nreliable for this process, and onl one experiment was performed, bt the reslting controller parameters will still be sed and evalated for comparison. The obtained controller parameters are listed in Table III and Bode plots of the controllers are shown in Figre 13. From the parameters it is seen that the τ-tner chooses a PI controller since it classifies the process as dela-dominated, see [16] for details on this choice. The controller performances are shown in Figre 15. A step load distrbance was introdced at t = 1 s b adding an additional constant flow of water to the tank. The additional flow was removed again at t = 8 s. The NOMAD and τ-tner are showing ver good control reslts for this process, while the ECA is reall slow and Honewell is both oscillating and slow. Comparing the IAE vales gives a different message, since the IAE for the Honewell controller is slightl smaller than for the τ-tner. This implies that IAE shold be combined with restrictions on robstness. VI. DISCUSSION The reslts show that ECA is performing well for the level control of the lower tank, bt is slow for the other two processes. The atotner is eas to se, bt the ser has to ensre that the process is in stead-state before starting the experiment in order to get good reslts. If the process vale is far from the setpoint when starting the experiment, the sstem will isse a warning, bt apart from that it is the ser s responsibilit to ensre stationarit. The Acctne III TM in the Honewell controller works ver well for the temperatre control process, bt ields ver slow controllers for the other processes. Its large experiment

9 ECA Honewell τ-tner Time [min] NOMAD Time [min] Fig. 11. Rela experiments for the temperatre control of the batch process. Note that the time scale is in mintes for this process. Also note the different experiment drations that is a conseqence of the different oscillation periods, this will be discssed frther in Section VI ECA Honewell τ-tner NOMAD Time [min] Time [min] Fig. 12. Controller performance for the temperatre control of the batch tank. At time 5 s a load distrbance was introdced b changing 2 ml of the heated water to ambient tempered water in the tank.

10 TABLE III PID PARAMETERS AND IAE VALUES FROM THE EXPERIMENTS ON THE UPPER TANK WITH DELAY. FOR MOST AUTOTUNERS THREE EXPERIMENTS WERE PERFORMED, THE CHOSEN PARAMETERS FOR EACH AUTOTUNER ARE MARKED WITH BOLD TEXT. NOTE THAT ECA AND HONEYWELL ARE ON SERIAL FORM, WHILE τ-tuner AND NOMAD ARE ON PARALLEL FORM. SINCE THE HONEYWELL CONTROLLER WAS NOT ABLE TO DO THE EXPERIMENT WITHOUT OVERFLOWING THE TANK AND EMPTYING IT, ONLY ONE EXPERIMENT WAS PERFORMED ON IT. Mag. [abs] Phase [deg] Atotner K [-] T i [s] T d [s] IAE ECA Honewell τ-tner NOMAD Fig. 13. Bode plot of the obtained controllers for the level control of the delaed pper tank. The different atotners are ECA (green), Honewell (black), τ-tner (red) and NOMAD (ble). amplitdes are a problem, especiall for the time-delaed process, where the case the process vale to satrate at ever switch, reslting in nreliable reslts and casing operational problems. The Honewell controller is branded as a temperatre controller so it is not srprising that it gives the best reslts for the temperatre control process. However, since it claims to give good reslts for an process inclding those with deadtimes the performance for that process is rather nsatisfactor. The atotner featre is qite eas to se, and it is not as sensitive to starting in stead-state as the ECA since the experiment is the same no matter if the process vale is at the setpoint or not. Since the rela alwas ses the maximm amplitdes the experiment becomes more or less asmmetric depending on the chosen setpoint. The need to pt it in atomatic before starting the experiment seems a bit strange since it does not have an appropriate controller parameters for the process et. However, since the ser is spposed to start the tning procedre right after and it does not have to be stead it does not matter that mch. The τ-tner has an experiment ver similar to ECA, except for the asmmetr in the rela. The sometimes differ a few rela switches before convergence is reached, bt both the process deviations, amplitde restrictions, and amplitde adjstments are similar. The wa of finding models and controller parameters are different thogh. The reslts from the τ-tner are slightl worse than ECA for the level control of the lower tank, (especiall for the version where the process is classified as integrating), bt better than Honewell. For the temperatre control the τ-tner is worse than Honewell bt better than ECA, and for the time-delaed sstem the τ- tner is mch better than both ECA and Honewell. Overall it can be arged that the τ-tner gives a rather consistent performance. It ma not be the best, bt it gives acceptable controllers for all the tried processes. The τ-tner, however, sffers the same problem as ECA b reqiring the sstem to be in stead-state before the experiment starts. This is even more crcial for the τ-tner since the asmmetr level of the rela will not be correct if the otpt is drifting, casing erroneos model estimations. This ma be the reason wh the controller parameters sometimes differ between consective experiments for the τ-tner. The NOMAD atotner gives best controller performance for all tested processes. The increase in compting to get more accrate models allows for more aggressive controller designs, which is clearl seen for instance in Figre 9. Even thogh the response is mch faster, the control signals are not mch larger than for the other controller designs. Since the NOMAD is sing a second-order filter, the noise is not affecting the reslt mch even if the derivative parts of the controller design are large. In fact, looking at the Bode plots it can be seen that both the τ-tner and the NOMAD are less sensitive to high freqenc noise than the indstrial controllers. Apart from the good performance, the short drations and low process deviations of the experiment are also great benefits of the method. The experiment can also be started with non-stationar initial conditions, so the problem encontered in ECA and the τ-tner to ensre stead state before starting the atotner is removed. The benefit of short experiment dration is especiall sefl since it redces the risk of distrbances entering dring the experiment, which is one of the largest risks of failre for the rela atotners. The experiment is similar to those of both ECA and the τ-tner, bt with approximatel half the nmber of rela switches. As can be seen in Figre 11, the nmber of rela switches are not alwas what is most significant for the experiment dration. If there wold have been no hsteresis in the relas, the wold all oscillate with the same freqenc. With hsteresis the rela amplitdes and hsteresis amplitde will have a large impact on the oscillation period for certain processes. This cold be nderstood b looking at the Nqist crve in Figre 16. The approximative describing fnction method tells that a sstem nder smmetric rela feedback will oscillate with a freqenc decided b the intersection of the process Nqist crve with the horizontal line with imaginar part Im = πh 4d, (8)

11 ECA τ-tner Time [s] Honewell NOMAD Time [s] Fig. 14. Rela experiments for the level control of the delaed tank. The Honewell controller is overflowing and empting the tank at ever switch, which make its experiment reslts nreliable. ECA Honewell τ-tner Time [min] NOMAD Time [min] Fig. 15. Controller performance for the delaed tank process. A step load distrbance is added to the inpt at time 1 s and then removed at time 8 s.

12 Im(P) T p 2 T p 3 T p Re(P) Fig. 16. Nqist plot of the model obtained from the NOMAD atotner for the temperatre control process. Depending on the ratio between rela amplitde and hsteresis, different points on the crve will be intersected b the rela describing fnction, casing different oscillation periods. Freqencies corresponding to oscillation periods T p ={1 s, 2 s, 3 s} are marked in the figre. where h is the hsteresis of the rela and d is the rela amplitde. The hsteresis levels seem to be qite similar between the different atotners, bt since the rela amplitde is abot five times larger for the Honewell controller than the others it will oscillate with a mch higher freqenc and shorter period time. The ECA controller has a slightl higher amplitde than the τ-tner and the NOMAD since it allows 1 % both p and down, while the have 1 % as their large amplitde. Hence ECA gets a faster oscillation than the do. To exemplif, consider the τ-tner. The average rela amplitde is 7.5 % and the hsteresis.5 %. This wold give an intersection with imaginar part Im =.5π/(4 7.5).5. Looking in Figre 16 this implies an oscillation period a bit larger than 3 s, which seem to be a reasonable approximation. For processes that do not change so drasticall in freqence in this area the difference between oscillation periods are barel noticeable and for the other experiments in this paper the oscillation periods are therefore more or less the same. A fndamental benefit of the τ-tner and NOMAD compared to the others is the provision of explicit process models. That makes it possible to change tning method and filter design withot having to perform a new experiment. However, that is mainl a benefit for experienced sers or developers. Prodctified atotners need to be ser-friendl in order to be sed. Decisions shold be made atomaticall, mabe allowing, bt not reqiring, ser inpts. Ideall, good reslts shold be provided ever time withot an manal interaction. The τ-tner and NOMAD-tner aim for this b making both model and controller selections atomaticall. Another featre we propose for the atotners is that the provide a sitable filter in addition to the controller parameters, since the are strongl connected. ECA does that, and filter designs were inclded in the implementations of the τ-tner and NOMAD. The atotner cold also propose set-point weighting constants, anti-windp tracking constants and other parameters connected to the PID controller. VII. CONCLUSIONS AND FUTURE WORK It is time to pdate the indstrial standard atotners from the 198 s technolog to the 21st centr. The enormos increase in compting power and data storage provides the possibilit to se mch more data than jst a handfl of vales from an experiment. B sing optimization methods on the entire data set, the experiments can be made shorter and still provide more accrate models, reslting in controllers with better performance. Even thogh the ECA gives fnctioning controllers for all processes evalated in this std, the reslts show that the NOMAD improves the performance significantl. The NOMAD atotner also decreases the two main risks of failre for the ECA controller. The first risk is that the process is not in steadstate when the experiment is started. This is handled b the optimization method in NOMAD, that allows non-stationar initial conditions in its estimations. The second main risk is that some distrbance enters the sstem while the experiment is ongoing, deteriorating the obtained controller. This risk is redced significantl b the mch shorter experiments sed in the NOMAD. The short experiments are also ver beneficial for the availabilit of the control loop. 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