Decentralized SISO Active Disturbance Rejection Control Of .
Preprints of the9th International Symposium on Advanced Control of Chemical ProcessesThe International Federation of Automatic ControlJune 7-10, 2015, Whistler, British Columbia, CanadaMoPoster2.18Decentralized SISO Active Disturbance Rejection Controlof the Newell-Lee forced circulation evaporatorRainer Dittmar West Coast University of Applied Sciences, Heide, Germany(Tel: 49 481 8555-325; e-mail: dittmar@fh-westkueste.de)Abstract: Active Disturbance Rejection Control (ADRC) has received considerable attention in recentyears as an effective tool for advanced control practitioners to solve control problems for nonlinearuncertain systems. This paper presents results of a simulation study for the control of an evaporator systembenchmark, when a multiple linear ADRC control structure is used, and the controllers are designed basedon first and second order linear models approximating the process dynamics. In addition to the controlperformance under nominal conditions, the robustness with respect to plant-model mismatch is studied.The major advantage of ADRC compared to MPC and PI control approaches is the simple and transparenttuning, and that only a coarse process model is sufficient for the design. For a broader industrialapplication of ADRC in the process industries, user-friendly off-line design tools as well as real-timeADRC control software for PLCs and DCS still have to be developed.Keywords: Process control, Disturbance rejection, Decentralized control, PID control. 1. INTRODUCTIONIt is not a new statement that more than 95% of thecontrollers applied in the process industries are variants of thesingle-loop PID controller (Ogunnaike and Mukati, 2006). Inorder to overcome its limitations, several alternatives havebeen developed including SISO-constrained LQ control(Pannocchia, Laachi and Rawlings, 2005), RTD-A control(Ogunnaike and Mukati, 2006), Predictive Functional Control(Richalet and O’Donovan, 2009) and SISO Model PredictiveControl (Lu, 2004; Morrison, 2005). Only PFC and singleloop MPC have been implemented on DCS and PLCs yet,and the number of industrial applications is still small.Recently, a new control paradigm named “ActiveDisturbance Rejection Control” (ADRC) has been introducedwhich also claims to be a potential candidate for PIDreplacement (Han, 2009) and a promising addition to thetoolbox of control engineering practitioners (Rhinehart,Darby and Wade, 2011). ADRC is an unconventional designstrategy. The key difference to other controllers is that ADRCuses a so-called extended state observer (ESO) which jointlyestimates external disturbances and modelling uncertainties,and a control algorithm compensating the effect of this“generalized disturbance”. In contrast to MPC, only looseprocess information is required. On the other hand, the tuningof the ESO as well as the control algorithm itself is simplerand more transparent as PID controller tuning. For moredetailed information on the theoretical background and theproperties of ADRC, the reader is referred to (Gao, 2006;Huang and Xue, 2014; Zheng and Gao, 2014).An extensive list of industrial applications of ADRC isprovided on the Center for Advanced Control pyright 2015 IFAC(www.cact.csuohio.edu), some of them are briefly describedin (Chen, Zheng and Gao, 2007). They include drive andmotion control, robotics, power converters andsuperconducting RF cavities. To our knowledge, applicationsin the process industries are rare: they include web tensioncontrol and the control of a hose extrusion plant at ParkerHannifin Inc. Nevertheless, simulation studies have beenpublished which demonstrate the application of ADRC toprocess control problems. In (Chen, Zheng and Gao, 2007),ADRC is applied to (a) temperature and (b) outletconcentration control of nonlinear continuous stirred tankreactor (CSTR) models. In (Zheng, Chen and Gao, 2009), amultivariable CSTR model is used to demonstrate multi-looplinear ADRC control, where the process dynamics isapproximated with first order transfer functions. Huang andXue (2013) apply multi-loop ADRC control to the ALSTOMgasifier benchmark problem. Again, first order processdynamics is assumed to design the observer/controller systemfor three pairs of manipulated and controlled variables. In allcases, simulations are carried out using only the nominalprocess model of the plant.In this paper, ADRC is applied to the evaporator systembenchmark originally developed by Newell and Lee (1989).The evaporator model is not too difficult but neverthelessconvenient to demonstrate the application of advancedcontrol technologies to a nonlinear multivariable system withstrong interactions. Recently, this example has been used todesign an offset-free 2x2 MPC controller based on ARXmodels identified from virtual plant tests (Huusom andJorgensen, 2014). In the present paper, a decentralized multiloop control structure with two linear ADRC controllers isdesigned. First and second order transfer function models areidentified from virtual plant tests. They establish the basis forthe design and tuning of the observers/control laws. In409
IFAC ADCHEM 2015June 7-10, 2015, Whistler, British Columbia, Canadaaddition to setpoint tracking and (external and internal)disturbance rejection performance, the robustness in case ofplant-model mismatch is studied.The remainder of this paper is organized as follows. Section 2gives an introduction into the design and tuning of linearSISO ADRC controllers. In Section 3, the evaporator systemmodel is briefly described. Section 4 presents results of asimulation study for the multi-loop ADRC controlledevaporator system focussed on control performance androbustness. Finally, Section 5 presents conclusions and openproblems.2. ADRC DESIGN AND TUNINGIn this section, following (Zheng and Gao, 2014) and (Herbst,2013), the linear ADRC design is described for a secondorder process with steady state gain K , natural period T anddamping factor D2T y (t ) 2 D T y (t ) y (t ) K u (t )abbreviating a K / T 2 leads togeneralized disturbance f ( t )(2)modelling error a , i.e. a a 0 a . The total disturbanceterm f ( t ) includes both internal uncertainties (unknowndynamics) and process parameter variations, and externaldisturbances including the effects of cross-couplings inmultivariable systems. By introducing f ( t ) , the processmodel has changed from second order low pass to a doubleintegrator. Defining an augmented state vectorTx 3 with the state variables x1 y , x 2 yand x 3 f , the process model can be represented as 0 0 0 1000 x1 1 x2 0 x 30cT 0 a 0 0 bAy ( t ) 1 x1 0 x2 x 300 0 a 0 0 l1 u (t ) l2 l 3 y (t ) (5)measured process inputs u ( t ) and outputs y ( t ) .In the case of a second order process, a linear (modified) PDcontroller is able to reject the disturbance f ( t ) . Thecontroller equation isu (t ) u 0 ( t ) fˆ ( t )a0with u 0 ( t ) K P r ( t ) yˆ ( t ) K D yˆ ( t ) (6)Assuming good estimates and inserting Eq. (6) into Eq. (2)gives f (t ) fˆ (t ) u0( t ) u 0 ( t ) K P ( r ( t ) y ( t )) K D y ( t )This finally leads (under ideal conditions) toKPy (t ) KDKP(8)y (t ) y (t ) r (t )which guarantees y ( t ) r ( t ) in steady state. The remainingtasks are to tune the controller parameters K P and K D , andto specify the observer dynamics by selecting appropriatevalues for the observer gains l l1l2Tl3 . A practicalapproach for controller tuning is to specify critically dampedclosed-loop setpoint tracking dynamics with a user-specified2% settling time T settle . Then, the controller parameters canbe chosen to get a negative real double pole s C L 6 / Tsettlefor equ. (8) which leads to2K P s C L 36 / T settle and K D 2 s C L 12 / T settle 0 u (t ) 0 f (t ) 1 (3) The basic idea of ADRC is to design an extended stateobserver (ESO) that provides an estimate of the generalizeddisturbance fˆ ( t ) - the third state variable in the extendedstate vector - and to design a control law that compensates itseffect on the process. The Luenberger observer equations canbe written asCopyright 2015 IFAC0 xˆ1 1 xˆ 2 0 xˆ 21The ESO then estimates yˆ xˆ1 , yˆ xˆ 2 and fˆ xˆ 3 from1Here, a is splitted into a known part a 0 and an unknown x1 x 2 x 3 l 1 l2 l3 (7) f (t ) a 0 u (t )x2 xˆ1 xˆ 2 xˆ 3y (t ) 11 2D y (t ) y (t ) y (t ) d (t ) a u (t ) a 0 u (t )22TT T (4)or(1)Adding an input disturbance d ( t ) , dividing by T 2 , andx x1xˆ ( t ) A xˆ ( t ) b u ( t ) l y ( t ) xˆ1 ( t ) 2(9)If one specifies the ESO dynamics using three poles with acommon pole location s E SO 3 s C L 10 s C L which is fastenough compared with the control loop dynamics, theobserver gains can be calculated:l1 3 s E SO2, l 2 3 s E SO and l3 s ESO 3(10)The resulting control structure is presented in Fig. 1.In a similar way, ADRC can be designed for a first orderprocess (model), see (Herbst, 2013). In this case, the observerequations are410
IFAC ADCHEM 2015June 7-10, 2015, Whistler, British Columbia, CanadaFig. 1: ADRC control structures for first and second orderprocesses (dashed: extension for second order plan) xˆ1 xˆ 2 l1 l 21 xˆ1 a 0 l1 u (t ) y (t )0 xˆ 2 0 l2 (11)Fig. 2: Evaporator system (Newell and Lee, 1989)and the control law is simplified to a P control lawu (t ) u 0 ( t ) fˆ ( t )a0Separator: The mass balance giveswith u 0 ( t ) K P r ( t ) yˆ ( t ) (12)with a K / T . The controller parameter and observer gainsare in this caseK P s C L 4 / T settle, l1 2 s E SO , l 2 s ESO 2(13)In the first order case, the ADRC control scheme in Fig. 1does not contain the signal path marked with dashed lines,and only two states ( xˆ1 yˆ and x̂ 2 fˆ ) are estimated andfed back to the controller. AdL 2dt F1 F 4 F 2(14)where is the liquid density, and A is the cross-sectionalarea of the separator.Evaporator: The mass balances for the liquid solute and thevapour areMCdX 2dtdP 2dtM F1 X 1 F 2 X 2 F4 F5(15)(16)In both cases, the only information required to design theADRC scheme is an estimate of a 0 K / T 2 (or a 0 K / T ,respectively), the desired settling time for the closed loop,and the distance between the observer and the control loopdynamics. For the selection of the observer pole locations, acompromise between estimation speed and noise sensitivitymust be found.wheredenotes the constant liquid holdup in theevaporator, and C is a constant that converts the mass ofvapour into an equivalent pressure. The liquid and vapourtemperatures are calculated from3. PROCESS DESCRIPTIONThese equations result from a linearization of the saturatedliquid line for water. The dynamics of the energy balance isassumed to be very fast, thereforeThe forced circulation evaporator model first presented byNewell and Lee (1989) has often been used as a benchmarkfor the application of advanced control technologies. Theevaporation process is shown in Fig. 2.The feed stream which contains at least one non-volatilecomponent is mixed with recirculating liquor and pumped toa vertical heat exchanger. Here, latent heat from condensingsteam is used to boil the mixture which is passed to aseparation vessel. The vapour is condensed by cooling withwater as a coolant. The liquid is recirculated while a part of itis drawn off as the product stream. The variables Fi , Xi andT i denote the flow rates, compositions and temperatures ofstream i , while Li , Pi and Q i are levels, pressures and heatduties in unit i . The model consists of the followingdifferential and algebraic equations:Copyright 2015 IFACT 2 0.5616 P 2 0.3126 X 2 48.43T 3 0.507 P 2 55F 4 ( Q 100 F 1 C P (T 2 T 1)) / (17)(18)(19)holds. Here, C P and denote the heat capacity and thelatent heat of vaporization of the liquor, respectively.Steam jacket: For the steam side of the evaporator, fastdynamics is assumed as well. Therefore, the steam jacket ismodelled by three algebraic equations:T 100 0.1538 P100 90Q 100 0.16 ( F 1 F 3) (T 100 T 2)(20)(21)F 100 Q 100 / S(22)with S as latent heat of saturated steam .411
IFAC ADCHEM 2015June 7-10, 2015, Whistler, British Columbia, CanadaCondenser: Again, fast dynamics is assumed leading to thealgebraic condenser equationsQ 200 U A 2 (T 3 T 200)1 U A 2 / (2 C P F 200)(24)F 5 Q 200 / (25)where U A 2 denotes the product of the overall heat transfercoefficient of the condenser and the heat transfer area. Moredetails about the modelling assumptions together with thenominal steady-state conditions and the values of the modelparameters can be found in (Newell and Lee, 1989).In the context of control design, the state (and also theoutput) vector isP2TX 2 (26)The manipulated variables areu F 2F 200TP100 T1X1F3RGA X 2 0.482 P 2 0.518TT 200 (28)F 2000.518 0.482 (29)This RGA matrix indicates strong interaction in themultivariable system. Fig. 3 presents the open-loop stepresponses ( F 200 10 kg / m in , P100 10 kP a ) of thenonlinear evaporator system model when the level controlleris in automatic mode.An attempt to tune PI controllers for the two loops independently using SIMC tuning rules lead to closed-loop instabilityof the controlled multivariable system. In (Newell and Lee,1989), the pressure controller was tuned using the ZieglerNichols (ZN) reaction curve method ( K C 176.5 ,Copyright 2015 IFACThese controller parameters were also used in this paper inorder to compare the PI controlled system with ADRCcontrol.4. IDENTIFICATION OF LOW ORDER MODELSThe separator level is an integrating process and must becontrolled. As in (Huusom and Jorgensen, 2014), a PIcontroller was used for level control with the product flowrate F 2 as manipulated variable, with a controller gain ofK C 1.33 and a reset time of Ti 20 m in (SIMC tuningrules). The remaining control variables are the evaporatorpressure P 2 and the product concentration X 2 . In (Newelland Lee, 1989), for single loop PI control the CV/MVpairings X2 - P100 and P2 - F200 were selected. Theresulting single loop control structure is shown in Fig. 1. Inpractice, P100 and F200 would be controlled by a slavecontroller, and X2 and P2 by a primary controller in acascade control structure. Since the dynamics of thesecondary control loops is much faster than the open loopdynamics of the primary control variables, subordinate PIcontrollers were omitted in this study.The static Relative Gain Array (RGA) can be calculated afterthe process model is linearized around the steady-statenominal operating point (Newell and Lee, 1989):P 100Fig. 3: Evaporator system step responses (first row: X2,second row: P2, left column: P100, right column: F200)(27)and the disturbance variablesd F1), and the purity controller using the ZN closed-(23)T 201 T 200 Q 200 / ( C P F 200)x L2Ti 9.77 m inloop tuning method ( K C 1, 64 , Ti 12.5 m in ).In practice, a rigorous nonlinear process model is usually notavailable. Linear ADRC controllers would have to bedesigned based on low order models identified from activeexperiments in the plant. To emulate this approach, PRBStest signals were applied to the cooling water flow rate F200( 10 kg / m in ) and the steam pressure P100 ( 10 kP a ), andopen-loop simulations of the nonlinear model were carriedout to generate “virtual” measurements of the productconcentration X2 and the evaporator pressure P2. During thesimulations, L2 level control was in automatic mode.The Matlab System Identification Toolbox was used toidentify low order transfer function models. For the MV/CVpair P2 - F200 , the best FOPDT model estimated wasG (s) 0.05133.03 s 1e 0.14 s(30)The estimated dead-time is very short compared to the timeconstant of the process and will later be neglected in ADRCdesign. Prediction (one step ahead and pure simulation) of theresponse based on validation data gives a fit of 95.83%.Fig. 4 presents the step responses for different linear modelapproximations of the X 2 P100 sub-model. The 4th orderstate space and ARX models are able to fit the step responseof the original nonlinear model, while the FOPDT andSOPDT models have significant errors in both the steadystate gain and the transient behaviour.The best second order process model estimated wasG (s) 0.161281.1 s 6.214 s 1(31)with a model fit of 79.8%. Although this model is certainlynot a good approximation of the original “hump” responsecharacteristic (see Fig. 3), it has been deliberately kept for412
IFAC ADCHEM 2015June 7-10, 2015, Whistler, British Columbia, CanadaADRC design in order to study the effect of un-modelleddynamics.Fig. 6: Closed-loop simulation with step changes inF1 and X1 (black: ADRC, dashed magenta: PI)Fig. 4: Step responses of different linear modelsidentified from virtual plant tests.5. SIMULATION RESULTSTwo SISO ADRC controllers (and related extended stateobservers) for P2 and X2 have been designed using theprocedure explained in section 2. The settling timespecifications were 50 minutes for both the pressure and theproduct purity controllers. This is approximately 50% of theopen-loop settling times of the processes. For the P2 ADRCcontroller, a delay-free model first order model was takenfrom Eq. (30), while for the X2 ADRC controller the secondorder process model Eq. (31) was used. The extended stateobserver dynamics was chosen using s E SO 5 s C L for bothcases which gave a reasonable compromise between observerdynamics and noise sensitivity. In the sequel, simulationresults are presented for the noise-free case only.Fig. 5 presents the setpoint tracking behaviour of the multiloop PI and ADRC control systems. For P2, ADRC and PIcontrol give similar settling times, PI control has 10%overshoot but a smaller rise time. The cross-coupling effecton X2 is much smaller for ADRC as for PI control. For X2,the settling time for PI control is twice as much as for ADRC.Regarding the effect on X2, the maximum deviation of X2 issmaller for PI control, while the settling times are similar.ADRC leads to little more aggressive P100 and F200movements (not shown here). Much shorter settling times areachievable with ADRC without increasing the overshoot, butthat would lead to extensive MV movements.Fig. 6 shows the response to a step change in the feed flowrate and feed composition (external disturbances F 1 0.5 kg / m in , X 1 1% ).Fig. 5: Closed-loop simulation with setpoint step changes inP2 and X2 (black: ADRC, dashed magenta: PI)Copyright 2015 IFACADRC control provides a much better disturbance rejectionfor the product concentration X2. For P2, ADRC givesshorter settling times (in particular for the feed flow ratedisturbance), but a bigger maximum deviation from setpoint.Again, manipulated variable movements are a little moreaggressive in case of ADRC control.Fig. 7 presents the response to a step change in the heattransfer coefficient of the condenser (internal disturbance).Fig. 7: Closed-loop simulation with step change in UA2(black: ADRC, dashed magenta: PI)Again, ADRC provides a much better disturbance rejectionfor X2. The settling time is halved, and the maximumdeviation from setpoint is less than one third compared withPI control. On the other hand, PI gives a better performancefor pressure control.Next, the robustness of the control structures with respect tochanges in the process gains has been studied. To do that, theprocess gains were varied in the range of(32)0, 5 K P , nom K P , nom 1, 5 K P , nomand the setpoint step and disturbance responses have beensimulated again. Figs. 8 and 9 show the results for thenominal gains and for the lower and higher limits
ADRC control software for PLCs and DCS still have to be developed. Keywords : Process control, Disturbance rejection, Decentralized control, PID control. 1. INTRODUCTION It is not a new statement that more than 95% of the controllers applied in the process industries are variant s of the
4. Active Disturbance Rejection Control . The active disturbance rejection control was proposed by Han [9][10][11][12]. It is designed to deal with systems having a large amount of uncertainty in both the internal dynamics and external disturbances. The particularity of the ADRC design is that the total disturbance is defined as
ON ACTIVE DISTURBANCE REJECTION CONTROL: STABILITY ANALYSIS AND APPLICATIONS IN DISTURBANCE DECOUPLING CONTROL QING ZHENG ABSTRACT One main contribution of this dissertation is to analyze the stability char-acteristics of extended state observer (ESO) and active disturbance rejection control (ADRC).
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ing control technology, known as active disturbance rejection con-trol to this day. Three cornerstones toward building the founda-tion of active disturbance rejection control, namely, the track-ing di erentiator, the extended state observer, and the extended state observer based feedback are expounded separately. The paper
practical control strategy that is Active Disturbance Rejection Control (ADRC) [10-14] to the EPAS system. The controller treats the discrepancy between the real EPAS system and its mathematical model as the generalized disturbance and actively estimates and rejects in real time, the disturbance
shift. The active disturbance rejection concept, introduced in section III, could very well serve as the basis of the new paradigm, which is characterized in section IV. Also included in section III is the demonstration of the broad range applications of the active disturbance concept. Finally, the paper is concluded with a few remarks in .
The Active Disturbance Rejection Controller (ADRC), invented by Han Jing-Qing who serves in Chinese Academy of Science, is a new type of nonlinear controller which is based on active disturbance rejection control technology. It does not depend on system model andcan estimate and compensate the influences of all the
1 Archaeological Laboratory Techniques [8/2015]. Suggested Reading. Adkins, Lesley, and Roy Adkins . 2009 . Archaeological Illustration. Paperback ed. Cambridge Manuals in
