Model Based Decoupling Control for Waste Incineration Plants

Transcription

1 Model Baed Decoupling Control for Wate Incineration Plant Martin Kozek and Andrea Voigt Intitute of Mechanic and Mechatronic, Vienna Univerity of Technology, Vienna, Autria VOIGTWIPP Engineer GmbH, Vienna, Autria Abtract A imple yet effective approach for a decoupling control of a wate incineration plant with fluidized bed i preented. The main problem for deigning a decoupling controller are the nonlinear inner dynamic of the proce, large timedelay, and unknown model parameter. The propoed control cheme utilize the inverion of imple balance equation with a minimum of parameter and compact nonlinear characteritic. The main advantage of thi concept i the imple incorporation of all relevant input and output of the plant into the decoupling equation. Thi enure robut performance even in the preence of nonmeaurable diturbance and imple retrofitting. The propoed control cheme ha been implemented in a 38 MW dometic wate incineration plant and the performance i demontrated by meaurement. Keyword decoupling control, wate incineration, model baed decoupling. I. INTRODUCTION Fluidized bed incinerator repreent tate of the art technology for wate combution and low grade fuel. Additionally, ewage ludge can be incinerated to form tabilized ah and to reduce the volume for depoiting. The main advantage of thi proce are high fuel flexibility in a large calorific value range, optimal combution can be adjuted through combution air and recirculation ga, high burnout typical reidue level in bed ah i 0.1%, low flue ga emiion, and limited mechanical proceing of both fuel and ahe. However, wate incineration plant are characterized by trong coupling between manipulated variable and control variable, nonlinearitie with repect to operating point, time delay, largely differing time contant, and uncertaintie in model parameter [1], [2], [3]. The control cheme of fluidized bed plant are currently mainly conventional, coniting of proportional-integral derivative PID-type controller in eparate control loop. In order to compenate effect of the nonlinear and trongly coupled proce, tatic decoupling together with gain cheduling ha been employed [4]. Neverthele, the proce performance how trong variation and intervention of the plant operator are frequent. In thi paper a model inverion baed approach i propoed, where the familiar problem of an imperfect model match i overcome by incorporating all relevant meaured input and output of the proce into the inverion. Thi multi-variable feedback concept for decoupling i hown to be robut in the preence of diturbance and with repect to model error. Moreover, the propoed control cheme require a minimum of analytical and experimental modeling. The computational effort i mall, and the propoed concept can be directly implemented in any modern ditributed control ytem DCS. Standard method for decoupling can be found in [5], [6], in modified form in [7]. Thee concept ue only the manipulated variable for decoupling while the propoed decoupling cheme ue all relevant input and output of the proce. Exact linearization [5], [8] require a complete nonlinear tatepace model of the ytem, and the reulting peudo-linear ytem i generally till coupled. More complex method are neceary to obtain decoupled peudo-linear ubytem a demontrated in [3]. A different approach i given by model reference adaptive control MRAC, which ha been propoed a an efficient and globally table control cheme [1], [2]. However, thi algorithm i mathematically complex, cannot be fitted into an exiting control cheme, and the treatment i limited to a 2-input 2-output ytem without power generation. Decoupling control cheme can alo be found for power plant application, where either adaptive algorithm uing fuzzy logic [9], a hybrid claical/fuzzy approach [10], or recurrent artificial neural net [11] have been propoed or implemented. All of thee method rely on either expert knowledge of plant operation or extenive training data. The remainder of thi paper i tructured a follow: In Section II the plant i decribed and the variable are defined. The control concept i outlined in Section III, and in Section IV the repective model equation and control law are developed. In Section V imulation reult are preented, and in Section VI the excellent performance of the propoed cheme i demontrated by an indutrial implementation. II. FLUIDIZED BED WASTE INCINERATION PLANT Fluidized bed furnace are ued for wate incineration due to their applicability for the combution of olid wate a well a ewage ludge. Many facilitie erve a threefold purpoe: 1 Environmentally correct and efficient dipoal of wate. 2 Steam generation for converion to electric energy. 3 Utilization of wate heat for ditrict-heating /08/$ IEEE

2 8 9 c O2 T f econdary air 7 1 flue ga 10 team w 1 w 2 C 1 C 2 u 11 u 22 u 12 D 12 D 21 u 21 u 1 u 2 G 11 G 12 G 21 G 22 plant y 1 y 2 fuel 5 T b flue ga 6 3 flue ga 4 2 primary air Fig. 1. Plant cheme for a fluidized bed furnace Fig. 2. Conventional decoupling for a 2-input / 2-output ytem 3 y 3 : furnace temperature T f [ C] at the top 4 y 4 : bed temperature T b [ C] Manipulated variable u i of the furnace are: 1 u 1 : Volume flow of econdary air V [ 2 u 2 : Volume flow of recycled flue ga above bed V [ r 3 u 3 : Volume flow of primary air V [ p 4 u 4 : Volume flow of recycled flue ga below bed V r [ [ ] 5 u 5 : Fuel ma flow ṁ kg f Additionally meaured output variable are: 1 y 5 : temperature of recirculation ga T r [ C] 2 y 6 : O 2 -concentration in recirculation ga c O2,r [% vol ] A chematic drawing of a typical plant i depicted in Fig. 1. Primary air i fed through an air heater 2 into the fluidized bed 3 from the bottom of the furnace 1. A portion of the flue ga i recycled and alo fed into the fluidized bed 4 together with the primary air. Inide the fluidized bed the bed temperature T b i meaured. Fuel 5 i fed into the fluidized bed. Above the fluidized bed econdary air 7 a well a recycled flue ga 6 are blown into the furnace at different level. At the top part of the furnace 8 the furnace temperature T f and the concentration of oxygen c O2 are meaured. The hot flue ga i led into a heat recovery boiler HRB 9, where heat i tranferred to a heat exchanger 10. Finally, the flue ga i filtered, cleaned, and part of it i recycled. One of the main technological challenge of thi proce i the fluidization of the bed. The bed conit of inert media ilicate and, olid wate, poibly ludge and additional fuel. A decribed above, fluidization i achieved by blowing ga into the bed from below. Controlled variable y i of the fluidized bed furnace including HRB are: 1 y 1 : O 2 -concentration at the top c O2 [% vol ] and/or after the HRB 2 y 2 : total power [ of combution P Σ [kw] or live team produced ṁ t ] h III. CONTROL CONCEPT The baic concept i a decoupling network within a multivariable control cheme, and the reulting control cheme conit of peudo-linear, independent, and parallel control loop. In the following ection firt conventional decoupling i decribed and then the propoed model baed approach i outlined. A. Conventional decoupling In Fig. 2 a conventional decoupling cheme for a linear 2 2 proce i hown. Two input u 1 and u 2 and two output y 1 and y 2 with reference variable w 1 and w 2 are conidered. The output of the plant are defined by: Y 1 = G 11 U 1 G 12 U 2 Y 2 = G 21 U 1 G 22 U 2. 1 A decoupling tranfer function D 21 i deigned uch that the output U 21 atifie G 21 U 11 G 22 U 21 =0. 2 By ubtituting U 21 = D 21 U 11 into 2 G 21 G 22 D 21 U 11 =0 3

3 follow, and oberving that in general U 11 0the ideal decoupler tranfer function are given by D 21 = G 21 G 22 D 12 = G 12 G Ideal decoupler are not alway phyically realizable or enitive to modeling error; tandard procedure to avoid or minimize thee problem are ee [5], [6] Partial decoupling: only a ubet of decoupler i ued. Static decoupling: only the tatic gain of the decoupler tranfer function are implemented. Obviouly, thee method will reduce the control performance, and in the preence of trong nonlinearitie and nonmeaurable diturbance the performance of the conventional decoupling control will be poor. B. Model Baed Decoupling In general, every MIMO-plant with m calar control loop can be modeled by a tate-pace repreentation with m input u j, n tate variable x i, and a parameter vector θ. Inthe pecial cae where all tate can be directly meaured y i = x i aetofn firt-order tate equation dy i = f iy, u, θ, i =1,...,n 5 together with a et of n algebraic output equation y i = g i y, u, θ, 6 contitute the complete plant model, and u and y denote input and output vector, repectively. The nonlinear function f i and g i are typically derived from non-tationary and tationary balance of the plant variable. In both et of equation 5 and 6 the dependence of each plant output y i on all other plant output and input u j i explicitly tated. Now a ubet of m n output ỹ y i defined, where each ỹ j i the controlled variable of one of the m calar control loop ee Fig. 3. In the right hand ide of 5 and 6 the influence of all control input to a pecific controlled variable ỹ j i uniquely defined. Rearranging for the repective control variable u j of that pecific control loop yield an equation ỹ j = f j y, u, θ. j =1,...,m 7 Note that the nonlinear function f j may be compoed from a dynamic relation 5 or it may reult from a tatic relation 6. In any cae, a neceary condition for the contruction of a decoupling tructure i that: Neceary condition I for decoupling: The expreion f j for each controlled variable ỹ j ỹ j = f j y, u, θ, 8 mut explicitly contain the correponding manipulated variable u j uch, that the manipulated variable u j i either multiplied ỹ j = f j y, u, θ u j 9 w 1 w 2 Fig. 3. C 1 C 2 ũ 1 ũ 2 f 1 f 2 u 1 y 1,...,y n u 2 plant f i Nonlinear decoupling with model baed inverion. or Neceary and ufficient condition Ia for decoupling: The manipulated variable u j i additively coupled ỹ 1 ỹ 2 ỹ j = f j y, u, θαu j. 10 to the remaining nonlinear expreion f j α being a contant factor. In the cae of an additive manipulated variable 10 the control law can be formulated a u j = 1 [ỹj α f j y, u, θ ], 11 where no inverion of the nonlinear expreion f j i neceary. On the other hand, the tructure of 9 require another neceary condition to be met: Neceary condition II for decoupling: The expreion f j in 9 mut be invertible uch, that u j = f j y, u, θỹ j, 12 f j exit. The computation of require f j to be invertible with repect to u j. Thi i not a trong retriction, epecially for baic balance equation and toichiometric relation a often emerging while modeling incineration plant. In thi cae the neceary condition II i already the control law defining the manipulated variable u j. Both control law 11 and 12 can be directly implemented according to Fig. 3, if the ubtitution ỹ j =ũ j 13 i made. Then the governing relation for the control loop with index 1 in Fig. 3 are given by: ũ 1 = C 1 q w 1 ỹ 1 14 u 1 = f 1 y, u, θũ 1 15 u 1 = f 1, plant y, u, θỹ 1 16 The manipulated variable can therefore be expreed a u 1 = = f 1 y, u, θũ 1 f 1 y, u, θc 1q w 1 ỹ 1, 17

4 and 16 with 17 yield f 1, plant y, u, θỹ 1 = f 1 y, u, θc 1q w 1 ỹ Only if the model f 1 i identical to the plant inverted nonlinearity f 1, plant a complete cancelation of the nonlinearitie become poible ỹ 1 = C 1 q w 1 ỹ 1 C 1 q ỹ 1 = 1C 1 q w 1 = G w1 q w 1, 19 which i the tandard cloed-loop expreion where the open loop tranfer function i given by C 1 q. Note that 19 tate that the plant output ỹ 1 will follow the reference w 1 with arbitrary dynamic defined by G w1 q and zero poition error, if the tatic gain of G w1 q i equal to one. The expreion f j in 10 can be a differential or algebraic equation, repectively, depending on whether an equation of type 5 or 6 wa choen when defining f j in 7. In contrat to conventional decoupling, the decoupling expreion f 1 and f 2, repectively, are in general nonlinear, utilize a number of output variable of the plant, baed on very general model equation of the plant. Oberve that each decoupler f i in Fig. 3 already repreent a feedback loop, where all meaured output y i are ued to compute the actual feedback u j. If one or more inner variable of the plant change due to unmeaured diturbance a diturbance compenation i automatically performed by the decoupler according to 12. IV. PLANT MODEL AND CONTROLLER DESIGN A. Plant Model The combution and power generation proce i decribed by the controlled variable: 1 furnace temperature T f 2 O 2 - concentration at top of furnace c O2 3 bed temperature T b and 4 live team produced ṁ. In order to decouple the four main control loop the governing model equation for each loop are preented in the following. 1 Model for Oxygen Concentration: The main variable for oxygen control i the momentary rate of oxygen build-up V O2 of the combution. Thi variable can be computed from meaured output by a balance of oxygen in the furnace V O2 = V O2 V O2, 20 where 20 i given by V O2 = V V p c O2, air Vr V c O2,r V f c O2. 21 The variable V f denote the total flue ga at the top of the furnace. Note that the pecific oxygen demand of the fuel defined a ˆk f = V O2 22 ṁ f can be readily computed from meaured output uing 21. r 2 Model for Furnace Temperature: The furnace temperature T f can be decribed by an unteady balance of the enthalpy flow into or from the furnace. The baic equation i given by dt f C f = H i = H p H H r P c, 23 i where C f i the abolute heat capacity of the furnace and the net enthalpy contribution from the individual ga flow primary air, econdary air, and recirculated ga are H p = V p c p, air ρ air T p T f H = V c p, air ρ air T T f H r = V r c p, r ρ r T r T f P c = H n, j ṁ f, j 24 j and P c denote the um of power releaed by the combution of different fuel component of a net calorific value H n, j.the variable c p, i in 24 denote the pecific heat of the individual gae, and the ρ i denote their repective denitie. 3 Model for Bed Temperature: The bed temperature i decribed by two relation: The dependence of the bed temperature on the air ratio and the repective oxygen balance. The oxygen balance equation for the fluidized bed i given by V b dc O2 = i ṁ O2,i = ṁ O2,p ṁ O2,r ṁ O2,c, 25 where V b i the volume of the fluidized bed and the individual right-hand expreion oxygen ma flow are ṁ O2,p = V p c O2,p ρ air ṁ O2,r = V r c O2,r ρ r ṁ O2,c = λ k f, j ṁ f, j. 26 j A nonlinear tatic model of the bed temperature T b = fλ, V fluid, 27 wa identified from meaured data. The dependence from the air ratio become one-dimenional if the total ga flow for fluidization V fluid i kept contant: V p V r = V fluid = cont Model for Live Steam Production: Under the aumption of a toichiometric combution the amount of live team produced i coupled to the fuel conumption of the combution. The influence of other manipulated variable like T b, T k,or Vr will be comparably inignificant. Since the HRB and therefore the ma flow of live team i ituated at the very end of the conidered plant an analytical model will be complex and contain many unknown parameter. A linear tranfer function model G f ṁ = G f q ṁ f 29

5 therefore ha a coniderable time-delay. However, during toichiometric combution the fuel ma flow ṁ f require an appropriate total oxygen flow V Σ,O2 : V Σ,O2 = k f ṁ f 30 PΣ[W ] Tk[ C] Here, k f i the mean oxygen demand of the fuel which i known from continual laboratory meaurement. The variable V Σ,O2 i given by V Σ,O2 = c O2, air c O2 Vp V c O2,r c O2 V dc O2 r V f. 31 V f i the total volume of the furnace, and the expreion dc V O2 f contitute an oxygen drain due to chemical conumption in the combution. B. Controller Deign 1 Control Law for Oxygen Control: The econdary air flow for perfect combution can be calculated from the model 21 together with 22. The econdary air flow i defined a ṁ f ˆk f V f c O2 V p c O2, air Vr V r c O2,r V = c O2, air 32 2 Control Law for Furnace Temperature Control: The furnace temperature T k i controlled by the flow of the recirculated flue ga above the bed. Rearranging 23 give dt k H r = C k H p H P c, 33 and inerting the relation 24 and olving for V r yield V r = C k dt k H p H P c. 34 c p, r ρ r T r T f 3 Control Law for Bed Temperature Control: Uing 28 the recirculation ga flow into the bed i given by V r = V fluid V p. 35 Inerting 35 in 25 and rearranging for V p yield the control law V p = V dc O2 b V fluid c O2,r ρ r λ j k f, j ṁ f, j. 36 c O2,p ρ air c O2,r ρ r In 36 the air ratio λ can be computed from the deired bed temperature T b uing the invere of 27 for a given V fluid : λ = f T b 37 4 Control Law for Live Steam Control: The fuel feeding rate can be computed from the inverion of the model 29 a ṁ f = G f q ṁ only if G f q i realizable. Since thi i not the cae, the neceary fuel rate i computed from 30 and 31 a ṁ f = [c 1 kf O2, air c O2 Vp V c O2,r c O2 V r V f dc O2 ]. 38 Tb[ C] co2 [%] time [] time [] Fig. 4. Simulation reult. Top left: thermal power, top right: furnace temperature, bottom left: bed temperature, bottom right: oxygen concentration at top of furnace. Solid line - new control, dah-dotted line - original control, dahed line - et-point. V. SIMULATION STUDY A numeric imulation tudy wa performed in order to ae the poible improvement of the propoed control cheme. The imulation conit of detailed non-tationary ub-model of all plant ection. All actuating element are modeled with aturation and limitation in actuation rate. Stochatic model have been ued for the calorific value H f average 9.5 MJ/kg fuel, tandard deviation 0.63 MJ/kg fuel and the mean oxygen demand of the fuel k f average 14.8 kg air /kg fuel, tandard deviation 1 kg air /kg fuel. The imulation model wa validated uing meaured data from the plant. Due to enor noie the non tationary expreion dyi in the control law 34, 36, and 38 were omitted. A. Simulation Reult The imulation demontrate the effect of a udden increae in fuel feed of 50% at t=500 for a duration of 20. Original control and the propoed decoupling cheme are compared. The parameter of the linear controller tranfer function C i the are identical in both cae. In Fig. 4 top left plot the deviation of the thermal power of the HRB i hown. A reduction of approximately 50% i viible. In the top right plot the furnace temperature i hown. The reduction in amplitude i around 70% with a much reduced error effect. The bottom left plot demontrate an almot perfect decoupling for the bed temperature. Any remaining coupling effect are maked by the tochatic fluctuation. In the bottom right plot the variation in oxygen concentration i hown. Strong reduction and a much earlier compenation can be een. Although mot output till how coupling effect due to imperfect implementation of the model, all amplitude and diturbance duration are trongly reduced. Moreover, the performance of the propoed decoupling i equally good over the whole operating region.

6 ṁ[t/h] Tb[ C] Tf [ C] co2 [%] time [] time [] Fig. 5. Application reult. Top left: live team, top right: furnace temperature, bottom left: bed temperature, bottom right: oxygen concentration at top of furnace. The decoupling control i activated at t=6000. TABLE I INCREASE IN ABSOLUTE PLANT CAPACITY variable conventional decoupling wate capacity max. 15 t/h max. 17 t/h team production 45.6t/h 54.0 t/h VI. INDUSTRIAL APPLICATION The control cheme wa implemented in a municipal wate incineration plant. Preproceed dometic wate and ometime additionally ewage ludge i incinerated. The plant ha a maximum wate capacity of 12.5 t/h, a maximum wet ewage ludge capacity of 15.3 t/h 36% dry ubtance, a furnace capacity of 38.2 MW, and a maximum team production of 45.6 t/h at 54 bar and 354 C. The decoupling control cheme wa implemented on the exiting DCS without the neceity for hardware or oftware extenion. For each individual control loop a fall-back poibility to the original control tructure and parameter wa programmed. Some important data for the wate incineration plant are lited in table I. The abolute value of wate capacity and team production have been ignificantly increaed while the furnace temperature ha been reduced imultaneouly. The furnace temperature i a key variable for the ervice life expectancy of both furnace and HRB. In Fig. 5 reult for the controlled variable are hown. At t=6000 the new control i activated and after a hort tranient all variable how a ignificantly reduced variance. In table II the tandard deviation of the controlled variable before and after implementation under tationary operation full capacity are hown. The reduction in variation i mot important ince it enable a plant operation cloer to technological and legal limit. The reduction in variance of the controlled variable ha different effect on the manipulated variable: Some of them alo exhibit maller activity e.g. Vr while other how TABLE II STANDARD DEVIATIONS OF CONTROLLED VARIABLES variable σ σ new unit ṁ t/h c O %vol T B C T f C a ignificant increae both in amplitude and bandwih e.g. ṁ f and V p. Although not hown here, the control cheme i alo performing excellent in part-load operating condition. VII. CONCLUSION A model baed decoupling control for a fluidized bed wate incineration plant ha been preented. The decoupling control of the MIMO-plant i baed on explicit phyical model, a well a black-box model from ytem identification. If the model are invertible, a perfect decoupling between the individual control loop become poible. The main advantage of the propoed control cheme i the incorporation of all available plant output for a perfect decoupling; even if a thi i not realizable a robut and efficient decoupling can be achieved. Furthermore, due to the explicit incorporation of all relevant plant output each decoupler alo act a a diturbance compenator for external diturbance. The performance of the propoed control cheme i demontrated by a numeric imulation and in a full cale implementation. The comparion between the original and the decoupling cheme how a ubtantial increae in efficiency and a minimization of crocoupling and diturbance. Due to the compact formulation of the overall control cheme the implementation in a DCS i traightforward, and retrofitting of exiting plant become eaily poible. A drawback of the propoed concept i the partly heuritic choice of the balance equation, where expert knowledge i definitely of advantage. Global tability of the propoed concept i till not analytically proven, which will be a tak for future reearch. REFERENCES [1] Y. Jia, H. Kokame, and J. 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