Modelling and L1 Adaptive Control of pH inBioethanol Enzymatic Process

Remus Mihail Prunescu1, Mogens Blanke2 and Gürkan Sin3

Abstract— The enzymatic process is a key step in secondgeneration bioethanol production. Pretreated biomass fibers areliquefied with the help of enzymes to facilitate fermentation.Enzymes are very sensitive to pH and temperature and themain control challenge in the nonlinear process is to ensureminimum deviations from the optimal pH level.

This article develops a mathematical model for the pH, whichhas not been reported earlier for this particular process. Thenew model embeds flow dynamics and pH calculations andserves both for simulation and control design. Two controlstrategies are then formulated for pH level regulation: oneis a classical PI controller; the other an L1 adaptive outputfeedback controller. Model-based feed-forward terms are addedto the controllers to enhance their performances. A new tuningmethod of the L1 adaptive controller is also proposed. Further,a new performance function is formulated and tailored to thistype of processes and is used to monitor the performances ofthe process in closed loop. The L1 design is found to outperformthe PI controller in all tests.

I. INTRODUCTION

Bioethanol is thought to become the primary renewableliquid fuel [1], [2] and extensive endeavors have beenconducted to make the production process feasible on alarge scale [3]. In order to reduce operating costs, bio-refineries are integrated with power plants following the IBUSprinciple [4], [5]. The conversion of lignocellulosic biomass toethanol is performed only with steam and enzymes, thereforecategorizing the technology as a green process.

In a second generation bioethanol production process, theenzymatic liquefaction step prepares the pretreated biomassfor fermentation [4], [5]. In the pretreatment phase, thebiomass is soaked with acetic acid and then pretreated withsteam. Studies show that a steam/acetic acid combination im-proves the pretreatment process [6] and it will be consideredthat the stream of fibers is mildly acidic, thus lowering thepH level. Acetic acid is also produced in reduced quantitiesduring the pretreatment stage.

The enzyme activity is influenced both by pH and tempera-ture. Enzyme activity versus pH follows a certain bell-shapedcurve [7]. Optimal pH activity differs for each enzyme type.For example, in the case of Accellerase TRIO, a pH levelof 4.8 should be set 1. Another type of enzymes, i.e. Cellic

1R. M. Prunescu is with the Department of Electrical Engineering,Automation and Control Group, Technical University of Denmark, 2800Kgs. Lyngby, Denmark rmpr at elektro.dtu.dk

2M. Blanke is with the Department of Electrical Engineering, Automationand Control Group, Technical University of Denmark, 2800 Kgs. Lyngby,Denmark mb at elektro.dtu.dk

3G. Sin is with the Department of Chemical Engineering, CAPEC,Technical University of Denmark, 2800 Kgs. Lyngby, Denmark gs atkt.dtu.dk

1Accelerase R© TRIOTM

datasheet from Genencor.com

CTec3 produced by Novozymes, requires a pH of 5.0 2. Asmall deviation from the pH optimal value, e.g. 0.2, cancause a significant drop in the process efficiency, e.g. 20 %.Therefore, the main control challenge in such a process is tominimize deviations from the optimal pH level.

Controlling the pH has been the topic of many researchactivities and there are many generic solutions in the literature.A comprehensive review of the existing generic controlstrategies can be found in [8]. Control strategies vary frompure feed-forward control, where the inflow of hydroxideis manually adjusted by an operator, to more sophisticatedschemes like adaptive fuzzy control [9], nonlinear adaptivecontrol [10], [11] or model predictive control [12], [13]. Themost common application of pH control is the neutralizationprocess but, in an enzymatic liquefaction process, it is desiredto keep the pH level somewhere in the range 4-6 dependingon the enzyme type.

To our knowledge, pH modelling for an enzymatic lique-faction process has not been conducted earlier. Therefore,a process model is first formulated. Two control schemesare then designed, a PI controller and an L1 adaptiveoutput feedback controller. Classical PI control is widespread in industry and is used as a reference for controlperformance. The L1 adaptive controller represents a noveltyin control theory and has never been applied to pH control ofliquefaction processes. Major disturbances will be identifiedand model based feed-forward terms will be added to thecontrollers in order to improve their action. Also, a new tuningmethod of the L1 controller is proposed as an enhancementof the method developed in [14]. Finally, the controllersare tested on large scale benchmark scenarios that coverboth reference tracking and disturbance rejection cases. Aperformance function is formulated based on the enzymaticactivity curve and the controllers are compared using theenzymatic efficiency associated with their action.

II. PROCESS DESCRIPTION

A generic enzymatic liquefaction process is illustrated inFigure 1.

The pretreated biomass was decomposed into fibers in thepretreatment stage and arrives in the liquefaction reactorhaving a high dry matter content TS typically between25−30 %. A high dry matter is required in order to make thetechnology cost-effective but it cannot increase indefinitelydue to mixing technical problems that may appear [4],[15]. A sample of fibers is extracted automatically and

2Cellic CTec3 datasheet from Novozymes.com

2013 American Control Conference (ACC)Washington, DC, USA, June 17-19, 2013

978-1-4799-0178-4/$31.00 ©2013 AACC 1888

Mixer

Fibers

Base

Water Enzymes

Enzymatic Hydrolysis Reactor

FFF

CA0

CB0

FB FW FE

FFM

pH

MFM

Fig. 1. Process diagram with instrumentation.

an NIR analysis is performed in order to determine itschemical composition, including the concentration of aceticacid denoted as [AcH]0 or CA0

, which is of interest in thiscase. The mass flow of fibers is also directly measured anddenoted as FFF .

pH control is achieved by pumping a strong base i.e. sodiumhydroxide, NaOH, into the fiber fraction before entering theliquefaction tank. The inflow of base is measured as FB andits concentration is 10 wt%.

Enzymes are pumped into the reactor proportional tocellulose quantity and the inflow of enzymes is measuredas FE . A quantity of water FW is also poured into thetank. The weight of the tank, the outflow and the pH valueare directly measured as MFM , FFM , and pH , respectively.Nominal values of the inflows, acetic acid concentration,tank load and total solids are presented in Table I. Thedata refer to a bioethanol plant that was designed to handle1000 kg h−1 of fibers. The enzymatic liquefaction tank hasa nominal load capacity of 5000 kg of fiber mash and theconcentration of acetic acid varies around 5 g kg−1 dependingon the pretreatment process parameters.

TABLE INOMINAL OPERATION OF A HYDROLYSIS PROCESS.

FFF 1000 kg h−1 [AcH]0 5 g kg−1

FE 20 kg h−1 MFM 5000 kgFW 80 kg h−1 TS 25 %

III. CONTROL CHALLENGE

Several theoretical enzymatic activity bell-shaped curvesare shown in Figure 2. The optimal pH level corresponds to anenzymatic activity of 100 %. In case of disturbances that occurin the pretreatment process, the acetic acid concentration inthe inflow changes and affects the pH level. A small deviationfrom the optimal pH level can cause a significant drop in theenzymatic activity. This means that the quality of the outflowdrops. An increase in enzyme quantity is necessary to meetthe same quality constraints on the outflow but enzymes are

3 3.5 4 4.5 5 5.5 6

0

50

100

pH [−]

Enz

ymat

icA

ctiv

ity[%

]

Enzymatic Activity as a Function of pH

E1

E2

E3

Fig. 2. Different enzymatic activity bell-shaped curves.

very expensive. It is a lot cheaper to properly control the pHlevel with a base.

Another control challenge arises from the large scale natureof the process. The pH sensor is positioned on the outflowof the tank because it is easier to measure the pH level ona liquefied substance. The flow dynamics of the reactor areslow and a large quantity of fibers can be compromised dueto a small deviation in the pH level. Therefore, a model andfeed-forward terms for the controllers are necessary to obtaina high performance control strategy.

IV. PROCESS MODEL

The pH calculation is derived using the classical physico-chemical approach, which considers a set of weak acid/baseequilibrium in liquid phase [16] and gas-liquid CO2 strippingprocess [17]. It is assumed that CO2 is not produced in theenzymatic liquefaction process but traces of bicarbonate canexist in the inflows due to upstream subprocesses or processwater utilization. The process model captures flow dynamicsand considers the mixture in chemical equilibrium at anygiven time.

A. pH Calculation

In total, the model has 6 weak acid/base equilibrium equa-tions and CO2 stripping. It is also assumed that production andconsumption of ions are negligible from enzymatic reactions.

Acetic acid is a weak acid and partially dissociates intoAc− and H+ with an equilibrium constant KA (1a). Sodiumhydroxide is a strong base and fully dissociates into Na+ andOH− (1b). Ac− and Na+ combine to form the salt sodiumacetate NaAc (1c). Water self-ionizes with an equilibriumconstant KW (1d). The liquid phase is not pure and isconsidered to contain CO2, which is the cause of a bufferformation that affects the pH level. Carbon dioxide formscarbonic acid H2CO3 in water, which dissociates with anequilibrium constant KC1 into bicarbonate HCO−3 and H+

as in (1e). The bicarbonate continues to decompose formingcarbonate CO2−

3 and H+ with an equilibrium constant KC2

like in (1f).

AcH ↽−−−⇀ Ac− + H+ (1a)

NaOH −−→ Na+ + OH− (1b)

Ac− + Na+ −−→ NaAc (1c)

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H+ + OH− ↽−−−⇀ H2O (1d)

CO2 + H2O −−→ H2CO3 ↽−−−⇀ HCO−3 + H+ (1e)

HCO−3 ↽−−−⇀ CO2−3 + H+ (1f)

Three variables are defined:

[AT] = [AcH] + [Ac−] (2a)

[BT] = [Na+] + [NaOH] (2b)

[CT] = [CO2] + [HCO−3 ] + [CO2−3 ] (2c)

The presence of other acids like lactic acid or succinic acidwas also recorded but in negligible amounts and there mightbe other buffers in the stream. Therefore, the concentrationof all unmodeled ions will be lumped into a single variable[Z−] and the charge balance is then formulated:

[H+]− [Z−] + [Na+]−−[OH−]− [Ac−]− [HCO−3 ]− 2[CO2−

3 ] = 0(3)

Each term from the charge balance can be found asa function of variables [AT], [BT], [CT] or [H+] andequilibrium constants KA, KW , KC1

and KC2. Therefore,

[H+] can be determined by finding the real positive zero of(3). Afterwards, the pH level is computed using its definition:

pHdef= − log10[H+] (4)

There might be an offset between the estimated and mea-sured pH level. The difference can be canceled by adjustingthe concentration of Z– i.e. CZ0

. An online estimation of[Z−] could be implemented in reality.

B. State Space Model

In this section, the flow dynamics and the pH calculationare embedded into a single model that has the structure fromFigure 3. It is important to conduct all pH calculations onlyon the liquid part of the mixture. All notations are gatheredin Table II with their measuring units.

Ideal Mixing EnzymaticReactor

FB

CB0

FFF CA0 FE CZ0

FW TS FFM

ui, uo

ua0 , ub0

uc0 , uz0

ypH

Fig. 3. Process flow scheme.

Perfect and instantaneous mixing of the tank is assumed andthis is represented as an Ideal Mixing block, which combinesall inflows into a single input ui without solids. The outflowwithout solids is denoted as uo. The inflow concentrationsua0

, ub0 and uc0 include a measuring unit transformationand are expressed in mol L−1.

The state variables of the dynamic model are defined as:

xz = [Z−] (5a)

xat = [AT] (5b)xbt = [BT] (5c)xct = [CT] (5d)

and xm, which is the mass of liquid inside the reactor.Two more algebraic variables are also defined:

xh = [H+] (6a)xco2 = [CO2] (6b)

The system dynamics read as:

dxmdt

= ui − uo (7a)

d(xmxz)

dt= uiuz0 − uoxz (7b)

d(xmxat)

dt= uiua0

− uoxat (7c)

d(xmxbt)

dt= uiub0 − uoxbt (7d)

d(xmxct)

dt= uiuc0 − uoxct + rctrxm (7e)

where rctr is the CO2 stripping rate [17]:

rctr = kctr(u∗co2 − xco2

)(8)

The dissolved concentration of CO2 is denoted as u∗co2 andis governed by the Henry law [17].

TABLE IIEXPLANATION OF SYMBOLS THAT WERE USED IN THE PROCESS MODEL.

ui Liquid part of fibre fraction inflow kg h−1

uo Liquid part of fibre mash outflow kg h−1

ua0 Inflow concentration of acetic acid mol L−1

ub0 Inflow concentration of sodium hydroxide mol L−1

uc0 Inflow concentration of carbon dioxide mol L−1

uz0 Inflow concentration of unmodelled ions mol L−1

xm Mass of liquid fibre mash kgxat Total molar concentration of acid species mol L−1

xbt Total molar concentration of base species mol L−1

xct Total molar concentration of carbonic species mol L−1

xz Molar concentration of unmodelled ions mol L−1

xh Total molar concentration of H+ mol L−1

xco2 Total molar concentration of CO2 mol L−1

uco∗2 Molar concentration of CO2 in the atmosphere mol L−1

kctr CO2 stripping process parameter h−1

KW H2O dissociation constant -KA AcH dissociation constant -KC1 CO2 dissociation constant -KC2

HCO3 dissociation constant -ρFM Fiber mash density kg L−1

MA Molar mass of AcH g mol−1

MB Molar mass of NaOH g mol−1

CA0Inflow concentration of AcH g kg−1

CB0 Inflow concentration of NaOH g kg−1

CC0 Inflow concentration of CO2 g kg−1

CZ0 Inflow concentration of Z– mol L−1

TS Total solids in inflow stream %

The charge balance can be rewritten as a polynomial:

x5h + p1x

4h + p2x

3h + p3x

2h + p4xh + p5 = 0 (9)

where coefficients pi are found by identification after expand-ing equation (3). The nonlinearity of the process arises from

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the fact that coefficients pi are functions of model states andchange in time. xh is then determined as the positive realzero of polynomial (9) and the output of the model is definedas:

ypH = − log10 xh (10)

The numerical values of all model parameters are listed inTable III.

TABLE IIIMODEL PARAMETERS.

KW 1× 10−14 MA 60.052 21 g mol−1

KA 1.7378× 10−5 MB 39.997 15 g mol−1

KC1 4.3003× 10−7 MC 44.01 g mol−1

KC2 4.7995× 10−11 CA0 5 g kg−1

u∗co2 1.71× 10−5 mol L−1 CB0 100 g kg−1

ρFM 1.05 kg L−1 CC07.1673× 10−4 g kg−1

CZ00.08 mol L−1

C. Titration Simulation

The model is tested by performing a classical titrationsimulation, i.e. feeding into the process an inflow of hydroxideresembling a stairway shape with a stair amplitude of 1 kg h−1

starting at time 20 h. The concentration of Z− is disregarded.The results can be observed in Figure 4.

0

0.05

0.1

0.15

C[m

olL−1]

Concentration of Species and pH

CAT

CBT

CCT

0 200 400 600 800 1000

5

10

Time [h]

pH

[−]

Fig. 4. Titration simulation for verifying the implementation of the model.

The acetic acid and the carbonic acid keep a low pH butafter adding a substantial amount of base, approximately attime t = 500 h, the buffers are depleted and the pH increasesto a value greater than 7, which is an expected result.

V. CONTROL DESIGN

The enzymatic liquefaction tank is assumed to have a masscontroller, which can be easily constructed as a feed-forwardstrategy combined with feedback.

A bioethanol plant may switch between enzyme types butsuch an action does not happen often during production mode.Therefore, reference tracking is necessary but emphasis willbe placed on disturbance rejection. There are many sources

of disturbances that affect the pH level, e.g. pretreatmentconditions, which influence the concentration of acetic acid,the presence of other weak acids and negative ions or theimperfect mixing effects, which might be significant sincethe tank has a large volume and a homogenous environmentcannot be guaranteed.

A. Feed-forward Combined With PI Control

In this section, a classical PI controller combined with anonlinear feed-forward signal is derived following a traditionaldesign algorithm, i.e. linearization of the process modelaround the nominal operational point from Table I withpH = 5, and derivation of the controller using the Skogestadinternal model control (SIMC) approach. The pH level ismainly disturbed by the initial concentration of AcH, whichis measured through NIR analysis. A feed-forward term canbe created using the nonlinear model to compensate for thistype of disturbance. The block diagram of the closed loopsystem is shown in Figure 5.

Process ModelCB0

FFF CA0

FE CZ0

FW TS FFM

PI+

FF

+ypH

−rpH

+

Fig. 5. Closed loop system with a feed-forward and a PI controller.

The PI control law is defined as:

uPI(t) = KP e(t) +KI

t∫0

e(t) (11)

where uPI(t) is the feedback contribution to the flow ofhydroxide, e(t) is the pH error signal defined as e(t) =rpH(t)− ypH(t), rpH(t) is the pH reference signal, KP isthe proportional gain and KI is the integral gain. FollowingSIMC rules [18], KP and KI were set to:

KP = 22.8 kg/h/pH unit (12a)KI = 16.8 kg/h/pH unit (12b)

The feed-forward term is found from the charge balance(3) from where [Na+] or ub0 is isolated:

[Na+] = −[H+]+[OH−]+[Ac−]+[HCO−3 ]+2[CO2−3 ]+[Z−]

(13)The required concentration of [H+] is found from thereference level:

[H+] = 10−rpH (14)

and all the other concentrations are derived with the help of[H+] and using the steady-state values for [CT] and [AT].

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The contribution of the feed-forward term to the total inflowof hydroxide can then be computed. The total flow of basebecomes:

FOHi = uFF + uPI (15)

where uFF is the feed-forward contribution and uPI iscomputed by the controller using feedback action.

B. L1 Adaptive Control

The L1 adaptive controller is a modified version of themodel reference adaptive controller with a state predictor.In the MRAC architecture, the key to a high performancecontrol strategy is the adaptation gain, which is subject toa compromise and there are no systematic ways of findingan optimal value. A high adaptation gain introduces high-frequency noise in the control channel and the stabilitymargins are affected. In order to separate robustness fromadaptation performance, a filter C(s) is introduced in thecontrol channel [19]. The analysis of the new controller i.e.the computation of the uniform bounds on outputs and controlsignals, is performed using the L1 norm, hence the name ofL1 adaptive controller.

The process in open loop can be expressed as follows [19]:

y(s) = A(s){u(s) + d(s)} (16)

where y(s) is the pH level, A(s) is an unknown transferfunction, u(s) is the system input and d(s) lumps all theuncertainties and disturbances that affect A(s). Transferfunction A(s) can be approximated as the linearized modelaround the nominal point from Table I with a base flow setsuch that pH = 5.

The L1 adaptive output feedback controller consists of anoutput predictor, an adaptation law and a control law [20],[19]. The structure of the closed loop system with this typeof controller is presented in Figure 6.

Process ModelCB0

FFF CA0

FECZ0

FW TS FFM

C(s)+

FF

+rpH

+

Output Predictor

Adaptive Law

ypH

−+

y

y

+

σ

+

−

Fig. 6. Closed loop system with an L1 adaptive output feedback controller.

The output predictor is built with the help of a first ordermodel reference system:

˙y(t) = −my(t) +m {u(t) + σ(t)} (17)

where y(t) is the output estimation, 1/m is the desired timeconstant of the closed loop system, u(t) is the inflow ofhydroxide and σ(t) is the estimation of all uncertainties andunmodelled dynamics. The model reference system is alsodenoted as:

M(s) =m

s+m(18)

System (16) can be rewritten in terms of the modelreference system [19]:

y(s) = M(s){u(s) + σ(s)} (19)

where σ(s) is identified as [19]:

σ(s) ={A(s)−M(s)}u(s) +A(s)d(s)

M(s)(20)

The idea is to cancel all the uncertainties σ(s) with thehelp of the control signal u(s). Therefore, the control signalis defined as [19]:

u(s) = C(s){r(s)− σ(s)} (21)

where C(s) is a first order filter in this application:

C(s) =c

s+ c(22)

If Equation (21) is substituted in (19) then:

y(s) = M(s)C(s)r(s) +M(s){σ(s)− C(s)σ(s)} (23)

If σ(s) is perfectly estimated then σ(s) = σ(s) and thedisturbances will be rejected only in the bandwidth of C(s).

The adaptive estimate σ(t) is updated using a projectionalgorithm that ensures boundedness of the estimate within agiven ball [19]:

˙σ(t) = ΓProj (σ(t),−y(t)) (24)

where y(t) = y(t)−y(t) is the estimation error of the output.There are 3 parameters to set for the L1 adaptive output

feedback controller, i.e. the desired closed loop time constant1/m, the adaptation gain Γ and the eigenfrequency of thecontrol filter c.

The reference model and the control signal filter can bedesigned systematically [14]. Assuming perfect knowledgeof disturbances, an ideal system y(s) can be built and usedfor tuning [14]:

y(s) = H(s)C(s)r(s) +H(s){1− C(s)}d(s) (25)

where H(s)C(s) is the transfer function from r(s) to y(s)and H(s) is defined as:

H(s) =A(s)M(s)

C(s)A(s) + {1− C(s)}M(s)(26)

Parameters m and c must be chosen such that H(s) isstable and the following L1 norm holds [19]:

||G(s)||L1L < 1 (27)

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0.9

0.9

0.8

0.8

0.7

0.7

0.60.5

0.2 0.4 0.6 0.8

50

100

m [rad s−1]

c[r

ads−

1]

Choice of m and c

0.6

0.8

1.0

ζ

0 1000 2000 3000 4000 5000

0.4

0.6

0.8

1

Γ [−]

ζ Γ[−

]

Choice of Γ

Fig. 7. Tuning of the L1 adaptive controller.

where G(s) = H(s){1−C(s)} is the transfer function fromd(s) to y(s) and L is the Lipschitz constant required toguarantee BIBO stability (Lemma 4.1.1 in [19]).

By considering A(s) as the linearized system around thenominal point, a (m, c) map can be built in order to facilitatethe choice of these two parameters. The closed loop systemhas several poles, which can cause oscillations if they arecomplex. As a criterion for (m, c) determination, the worstdamping ratio ζ should be higher than 0.7 in order to ensureacceptable oscillations. The damping ratio ζ is plotted as afunction of (m, c) in the top plot of Figure 7.

In order to accelerate the system, parameter m should beincreased. To reduce oscillations in the system response, thebandwidth of filter C(s) needs to be enlarged such that amore responsive control action would be allowed. The pair(0.6, 60) is chosen for this application, which corresponds toa ζ > 0.9:

m = 0.6 c = 60 (28)

The model reference has a time constant that corresponds to1.6 h. The Lipschitz constant, for the selected m and c, iscomputed to be:

L = 78.6851 (29)

which ensures a BIBO closed loop system according toLemma 4.1.1 [19].

In theorem 4.1.1 from [19] it is shown that the trackingerror between the real and the ideal system, which assumesperfect knowledge of the disturbance, is uniformly boundedwith respect to a constant proportional to 1/

√Γ. Therefore,

a high adaptation gain Γ is desired. At the same time, thestability and dynamics of σ are dependent on Γ. The transferfunction from r(s) and d(s) to σ(s) is [14]:

σ = F (s)[C(s){A(s)−M(s)}r(s) +A(s)d(s)] (30)

where F (s) is identified as:

F (s) =1

1Γs+ C(s)A(s) + {1− C(s)}M(s)

(31)

Γ should be chosen such that F (s) is stable. To reduce thehigh frequency noise due to adaptation, Γ can be set suchthat the worst damping ratio of F (s), denoted as ζΓ, wouldbe greater than 0.7. A plot of ζΓ as a function of Γ is shownin the bottom plot of Figure 7. A value Γ = 1000 would bea good choice for the current application ensuring a dampingratio of σ close to 1 and a relatively high adaptation gain.

Following the described procedure, the L1 controller canbe tuned in different pH operation points and parameters m,c and Γ could be adjusted in real time in order to maximizeperformances. Table IV contains the controller parameters in3 different operating points.

TABLE IVL1 CONTROLLER PARAMETERS IN MULTIPLE OPERATIONAL POINTS.

pH m c Γ

3 1 50 8005 0.6 60 10007 4 80 500

The feed-forward term developed in the classical controlsection is also added to the L1 controller to test its efficiency.

VI. BENCHMARK TESTS

Reference tracking is tested by performing a square waveof magnitude 2 as in Table V. The tests cover the entirepH interval 3− 7, which includes most of the nonlinearityfrom the titration curve. Even though enzymes normallyoperate around pH = 5, it is of theoretical interest to testthe controller for a wider range of operating points.

TABLE VREFERENCE TRACKING SQUARE WAVE SCENARIO.

# rpH Time interval

1. 5 0− 202. ↑ 7 20− 403. ↓ 5 40− 604. ↓ 3 60− 805. ↑ 5 80− 100

The disturbance rejection scenario is presented in TableVI and includes white noise perturbations with 0 mean andstandard deviation σ on the feed concentrations of acetic acid,base and unknown buffers.

TABLE VIWHITE NOISE DISTURBANCE REJECTION SCENARIOS.

# Scenario σ Time interval

1. Acid disturbances 1 g kg−1 0− 1332. Base disturbances 30 g kg−1 133− 2663. Unknown buffers 0.02 mol L−1 266− 400

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2

4

6

8pH

[−]

rpHypH

0 20 40 60 80 100

0

50

100

Time [h]

FB

[kg

h−1]

Fig. 8. Reference tracking with a PI controller. Top plot shows the pHmeasurement and the reference level while the bottom plot displays thecontrol effort or the addition of base.

4.8

5

5.2

5.4 AcidDisturbance

BaseDisturbance

ZDisturbance

pH

[−]

0 100 200 300 40020

40

60

Time [h]

FB

[kg

h−1] OL PI PI+FF

Fig. 9. Disturbance rejection with a PI controller. Top plot shows the reactorpH level in 3 cases: open loop (OL), PI controller (PI) and PI controller withfeed-forward action (PI+FF). The bottom plot displays the control effort.

Several theoretical bell shaped enzymatic activity curveswere shown in Figure 2. The maximum efficiency of theenzymatic process is considered to be 1 and is reached whenthe pH level equals the optimal value. A small deviation fromthe optimal level can cause a significant drop in the enzymaticactivity. The monitoring cost function is constructed byintegrating the deviations from maximum enzymatic activitywithin a time window:

J =

t1∫t0

{1− E(ypH)}dτ (32)

where t0 is the initial time, t1 is the final time and E(ypH)is the enzymatic activity associated with pH level ypH andcan be approximated with a Gaussian bell-shaped curve:

E(ypH) =1

σ√

2π· exp

−0.5(ypH−µ

σ

)2

(33)

2

4

6

8

pH

[−]

rpHypH

0 20 40 60 80 100

0

50

100

Time [h]

FB

[kg

h−1]

Fig. 10. Reference tracking with an L1 controller. Top plot shows thepH measurement and the reference level while the bottom plot displays thecontrol effort or the addition of base.

4.8

5

5.2

5.4 AcidDisturbance

BaseDisturbance

ZDisturbance

pH

[−]

0 100 200 300 40020

40

60

Time [h]

FB

[kg

h−1] PI+FF L1+FF

Fig. 11. Disturbance rejection with an L1 adaptive controller. Top plot showsthe reactor pH level in 2 cases: PI+FF and L1 controller with feed-forward(L1+FF). The bottom plot displays the control effort.

where σ = 0.2 and µ = 5 for this application. These valuescorrespond to E2 from Figure 2. The enzymatic activity isusually experimentally determined and can be represented asa table based map in reality.

Both control strategies are tested in the scenarios describedabove and the results are commented in the next section.

VII. RESULTS

The results for the reference tracking scenario can beviewed in Figures 8 and 10.

The classical control strategy has overshoots that increase asthe system moves further from the design point. On the otherhand, the L1 controller has a significant overshoot only in theneutral area of pH = 7. Otherwise, the L1 controller respondsbetter than the PI controller following the model reference.The overshoots could be accommodated by a reference filterin both cases. The control signal is within acceptable limits.

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The disturbance rejection scenario is shown in Figures 9and 11 and the evaluation of the cost function is performed inTable VII. In the case of measured disturbances, i.e. acetic aciddisturbances, the L1 controller with feed-forward performsbetter than the PI controller leading to a full rejection of thesedisturbances. The nonlinear feed-forward term significantlyhelps both controllers.

In the second scenario, i.e. base disturbances, the L1

controller has better results leading to smaller variations ofthe pH level, thus to a much lower J value. The feed-forwardterm does not help in this case.

In the last scenario, i.e. unknown buffers, the L1 controlleroutperforms the classical PI. Overall, regarding variations inthe pH level, the L1 controller has better performances.

TABLE VIIPERFORMANCE COST FUNCTION.

Scenario PI PI+FF L1+FF

1. 62.87 18.67 6.932. 188.19 187.16 24.423. 237.39 184.95 21.44

VIII. CONCLUSIONS

In this article, for the first time to our knowledge, apH model of the enzymatic liquefaction process has beendeveloped. Reference tracking and disturbance rejectionscenarios were formulated resembling the production modeof a large scale bioethanol plant and both measured andunmeasured disturbances were considered.

As classical control is wide spread within industry, a PIcontroller with feed-forward action was first designed. A novelL1 adaptive output feedback controller was then built andtuned in a systematic way in order to ensure high performance.The feed-forward term was also added to the L1 controller. Inthe case of reference tracking, the PI controller performed wellwith small overshoots that increased as the process movedfurther from the design point. Re-tuning of the controller isnecessary when switching to a different pH level in order topreserve performances. The L1 controller proved to behavesimilarly regardless of the nominal pH level except in theneutral highly nonlinear area of pH = 7. However, the closedloop system remained stable.

In the case of measured disturbances, both control strategieswere effective and it was shown that the feed-forward termconsiderably improves the system response. In the case ofunmeasured disturbances, the L1 adaptive controller had betterperformances.

A new cost function was derived from the enzymatic bell-shaped activity curve to assess closed loop performances.This cost function was further used to monitor the efficiencyof the enzymatic process.

Finally, a tuning method was proposed for the L1 controllerthat proved to be very effective for this application. Thistuning procedure is an enhancement of the method presentedin [14].

ACKNOWLEDGEMENTS

The close collaboration and very helpful suggestions anddetailed comments received from Dr. Jakob M. Jensen onthis research are gratefully acknowledged.

REFERENCES

[1] R. Datta, M. A. Maher, C. Jones, and R. W. Binker, “Ethanol - theprimary renewable liquid fuel,” Journal of Chemical Technology &Biotechnology, vol. 86, pp. 473–480, 2011.

[2] A. Limayem and S. C. Ricke, “Lignocellulosic biomass for bioethanolproduction: Current perspectives, potential issues and future prospects,”Progress in Energy and Combustion Science, vol. 38, pp. 449–467,2012.

[3] J. Larsen, M. Ø. Petersen, and L. Thirup, “Inbicon makes lignocellulosicethanol a commercial reality,” Biomass and Bioenergy, 2012.

[4] H. J. rgensen, J. Vibe-Pedersen, J. Larsen, and C. Felby, “Liquefactionof lignocellulose at high-solids concentrations,” Biotechnology andBioengineering, vol. 96, pp. 862–870, 2007.

[5] J. Larsen, M. Ø. Petersen, L. Thirup, H. W. Li, and F. K. Iversen, “Theibus process - lignocellulosic bioethanol close to a commercial reality,”Chemical Engineering & Technology, vol. 5, pp. 765–772, 2008.

[6] S. Zabihi, R. Alinia, F. Esmaeilzadeh, and J. F. Kalajahi, “Pretreatmentof wheat straw using steam, steam/acetic acid and steam/ethanol and itsenzymatic hydrolysis for sugar production,” Biosystems Engineering,vol. 105, pp. 288–297, 2010.

[7] P. D. Fullbrook, “Practical limits and prospects (kinetics),” IndustrialEnzymology 2nd Edition, pp. 505–540, 1996.

[8] J.-P. Ylén, “Measuring, modelling and controlling the ph value andthe dynamic chemical state,” Ph.D. dissertation, Helsinki University ofTechnology, 2001.

[9] F. Wan, H. Shang, and L.-X. Wang, “Adaptive fuzzy control of aph process,” IEEE International Conference on Fuzzy Systems, pp.2377–2384, 2006.

[10] T. K. Gustafsson and K. V. Waller, “Nonlinear and adaptive controlof ph,” Industrial & Engineering Chemistry Research, vol. 31, pp.2681–2693, 1992.

[11] S. S. Yoon, T. W. Yoon, D. R. Yang, and T. S. Kang, “Indirectadaptive nonlinear control of a ph process,” Computers and ChemicalEngineering, vol. 26, pp. 1223–1230, 2002.

[12] J. C. Gómez, A. Jutan, and E. Baeyens, “Wiener model identificationand predictive control of a ph neutralisation process,” IEEE ProceedingsControl Theory Applications, vol. 151, pp. 329–338, 2004.

[13] A. Altınten, “Generalized predictive control applied to a ph neutral-ization process,” Computers and Chemical Engineering, vol. 31, pp.1199–1204, 2007.

[14] R. Hindman, C. Cao, and N. Hovakimyan, “Designing a highperformance, stable L1 adaptive output feedback controller,” AIAAGuidance, Navigation and Control Conference and Exhibit, vol. 1, p.6644, 2007.

[15] Z. Fan, C. South, K. Lyford, J. Munsie, P. van Walsum, and L. R.Lynd, “Conversion of paper sludge to ethanol in a semicontinuoussolids-fed reactor,” Bioprocess Biosystems Engineering, vol. 26, pp.93–101, 2003.

[16] T. J. McAvoy, E. Hsu, and S. Lowenthal, “Dynamics of ph in controlledstirred tank reactor,” Industrial & Engineering Chemistry ProcessDesign and Development, vol. 1, pp. 71–78, 1972.

[17] G. Sin and P. A. Vanrolleghem, “Extensions to modeling aerobic carbondegradation using combined respirometric-titrimetric measurements inview of activated sludge model calibration,” Water Research, vol. 41,pp. 3345–3358, 2007.

[18] S. Skogestad, “Simple analytic rules for model reduction and pidcontroller tuning,” Journal of Process Control, vol. 13, pp. 291–309,2003.

[19] N. Hovakimyan and C. Cao, L1 Adaptive Control Theory - GuaranteedRobustness with Fast Adaptation. SIAM, 2010.

[20] C. Cao and N. Hovakimyan, “L1 adaptive output feedback controllerfor systems of unknown dimensions,” IEEE Transactions on AutomaticControl, vol. 53, pp. 815–821, 2008.

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