Robust Regulation of Heave-Induced Pressure Oscillations in Offshore...

Robust Regulation of Heave-InducedPressure Oscillations in Offshore MPD ?

Hessam Mahdianfar ∗ Naira Hovakimyan ∗∗ Alexey Pavlov ∗∗∗

Ole Morten Aamo ∗

∗ Department of Engineering Cybernetics, Faculty of InformationTechnology, Mathematics and Electrical Engineering, Norwegian

University Of Science and Technology (NTNU), Trondheim, Norway.(e-mails: [email protected], [email protected]).

∗∗ Department of Mechanical Science and Engineering, University ofIllinois at Urbana-Champaign (UIUC), 1206 West Green Street

Urbana, IL 61801, USA, [email protected].∗∗∗ Department of Advanced Wells and Enhanced Oil Recovery, Statoil

Research, N-3905 Porsgrunn, Norway, [email protected].

Abstract: This paper presents a modification to L1 adaptive control that allows for distur-bances entering at the output and application of this control strategy to Managed PressureDrilling with harmonic disturbances representing the heave motion of a floating drilling rig.By incorporating the disturbance at the output into the reference model, it is shown that theL1 adaptive control structure can be left unchanged while the original transient performancebounds are preserved. It is further shown that rejection of the output disturbance can betaken care of entirely in the filter design step of L1 adaptive control using the internal modelprinciple. A systematic filter design procedure based on LMIs is provided, that requires only onetuning parameter to be adjusted by the designer. The control design is applied to disturbanceattenuation and set-point tracking in the so-called heave problem in oil well drilling. We presentexperimental results of control system tests in a medium size test facility emulating a 900m longwell.

Keywords: Managed Pressure Drilling (MPD), Active Heave Compensation, Robust OutputRegulation, Drilling and Well Technology

1. INTRODUCTION

Deepwater offshore drilling operations are very complex.This is especially true in regions such as the Gulf ofMexico, where wells are drilled in water depths of upto 3 kilometers, drilling depths can exceed 6 kilometers,and geologic formation pressures can exceed 1400 bar Mac(2011).

In drilling operations, a fluid called mud is pumped intothe drill string, flows through the drill string and out ofnozzles in the bit. It then flows up the well in the annularvolume around the drill string carrying away cutting debris(see Figure 1). In addition to carrying cuttings, the drillingmud is used to control pressures inside the wellbore. Toavoid fracturing, collapse of the well, or influx of fluidsfrom the reservoir surrounding the well, it is crucial tocontrol the pressure in the open part of the well withina certain operating window. In conventional drilling, thisis done by mixing a mud of appropriate density and ad-justing mud pump flow rate. In Managed Pressure Drilling(MPD), the well is sealed and the mud exits through a con-trolled choke, allowing for faster and more precise controlof the pressure in the well. In automatic MPD systems, the

? This work was supported by Statoil ASA and the Research Councilof Norway.

choke is controlled by an automatic control system whichmanages the well pressure to be within specified upperand lower limits. Several disturbances and possible faultsaffect a drilling system. These include packoff, stuck pipe,washout, twist-off, delay in measurements and control, wellballooning (wellbore breathing), fluid loss, hole cleaningproblems because of gumbo shale, equipment failure, kick-loss scenarios, wellbore instability, tripping, and the heavemotion of the drilling rig while making connections Han-negan (2012); Skalle and Podio (1998); Mahdianfar et al.(2012a). Moreover, uncertainty in hydraulic parameters(such density, rheology of the drilling mud, temperaturedistribution in the well, frictional pressure loss for thepipe flow and the annular flow in the well, effective bulkmodulus, well geometry Lohne et al. (2008); Florence andIversen (2010); Mahdianfar et al. (2013)) makes drillingeven more challenging. Therefore, when designing MPDcontrol systems, one should take into account various op-erational procedures, uncertainties and disturbances thataffect the pressure inside the well.

The study presented in this paper is motivated by theheave disturbance challenge in offshore drilling. Whendrilling from a floating rig, the rig moves vertically with thewaves, referred to as heave motion. When drilling aheadwith weight on bit, a heave compensation system is ineffect that isolates the drill string from the heave motion

2nd IFAC Workshop on Automatic Control in Offshore Oil and Gas Production,May 27-29, 2015, Florianópolis, Brazil

Copyright © 2015, IFAC 112

Fig. 1. Schematic of an MPD system. Shown by courtesyof Statoil.

of the rig. As drilling proceeds, the drill string needs to beextended with new sections. Thus, every couple of hoursor so, drilling is stopped to add a new segment of about27 meters to the drill string, referred to as a connection.During connections, the pump is stopped and the drill-string is disconnected from the heave compensation mech-anism and put into slips rigidly attached to the rig. Thedrill string then moves vertically with the heave motionof the floating rig, and acts like a piston on the mud inthe well. The heave motion can be as large as 3 meters inamplitude with a period of 10-20 seconds, Godhavn (2010),resulting in severe pressure fluctuations in the bottom ofthe well. Pressure fluctuations have been observed to bean order of magnitude higher than the standard limits forpressure regulation accuracy in MPD Pavlov et al. (2010).Downward movement of the drill string into the well givespressure increase (surging), and upward movement givespressure decrease (swabbing). Excessive surge and swabpressures can lead to mud loss resulting from high pressurefracturing the formation, or a kick-sequence (uncontrolledinflux from the reservoir) that can potentially grow intoa blowout, as a consequence of low pressure. The firstattempt at handling this problem by automatic control ofthe top-side choke was presented in Pavlov et al. (2010).Two nonlinear control algorithms based on a lumpedmodel were designed, and their performance were testedon a full-scale drilling rig. The controllers demonstratedgood performance for slowly varying vertical drillstringmovements, but failed in case of fast varying drillstringmovements. The identified cause of this was the distributednature of the flow, which was not taken into account inthose controllers, Landet et al. (2012a). A series of papersfollowed addressing the distributed nature of the systemby using a distributed parameters model of a hydraulicflow line. In Landet et al. (2012c,b) two controllers based

on a finite difference discretization of the flow line arepresented, and show in simulations to have significant at-tenuating effect on downhole pressure oscillations. In Mah-dianfar et al. (2012a) an infinite-dimensional observer thatestimates the heave disturbance is designed for a simplifieddistributed model that ignores friction. An observer-basedcontroller that rejects the effect of the disturbance on thedown-hole pressure is designed, and a model reductiontechnique based on the Laguerre series representation ofa transfer function is used to reduce the controller to asimple, rational transfer function. In Mahdianfar et al.(2012b) the results are extended by incorporating frictionpartially into the model, and in Aamo (2013) they areextended by rigorously incorporating friction. In Anfinsenand Aamo (2014) the results are further refined to allowfor attenuation of the effect of the disturbance at any pointin the well, for instance at the casing shoe. A constrainedmodel predictive controller is designed in Nikoofard et al.(2013, 2014) for handling heave disturbance and outputregulation constraints. MPC is also used in Albert et al.(2014), which was the first successful result from the so-called Heave Lab 1 .

Common for all previous works on the heave problem, isthat uncertainty in model parameters is not taken rigor-ously into account in the control design, although severalparameters in the well are uncertain during drilling oper-ations Lohne et al. (2008); Mahdianfar et al. (2013). Thisfact, along with the complexity of some of the proposedmethods such as MPC, motivate the present work in whichadaptive control theory is employed. Robust adaptive con-trol has been an active research topic for decades Ioannouand Sun (1996); Hovakimyan and Cao (2010); Lavretskyand Wise (2013). In this paper we employ L1 adaptive out-put control architecture from Cao and Hovakimyan (2008).A comprehensive overview of the L1 adaptive control the-ory can be found in Hovakimyan and Cao (2010). Severalsuccessful applications of L1 adaptive control, especiallyin aerospace and flight control systems, are reported inHovakimyan et al. (2011); Xargay et al. (2012). A keyfeature of the L1 adaptive control theory is that its ar-chitectures decouple the control loop from the estimationloop, which allows for employing fast estimation rateswithout sacrificing robustness. Furthermore, the versatilityof L1 adaptive control architecture allows for various mod-ifications to its basic blocks, as observed in Kharisov et al.(2011); Kharisov and Hovakimyan (2011). The filteringstructure of L1 adaptive controllers allows for developmentof systematic methods for robustness/performance tuning,and also for optimization of the positive invariant set in thepresence of saturation, Li et al. (2013). Similar to Kharisovet al. (2011); Kharisov and Hovakimyan (2011), but yet adifferent and novel modification of the main structure ofL1 adaptive output feedback controller is considered hereto accommodate the disturbance entering at the systemoutput.

In Section 2 of the paper it is shown that by incorporatingthe disturbance at the output into the reference model, theL1 adaptive control structure can be left unchanged whilepreserving the usual transient performance bounds. It is

1 The Heave Lab is a medium scale (900m well) experimental facilityat NTNU, tailor made for testing control strategies for the heaveproblem

IFAC Oilfield 2015May 27-29, 2015


further shown that rejection of the output disturbance canbe taken care of in the filter design step of L1 adaptivecontrol using the internal model principle. A systematicfilter design procedure based on LMIs is provided inSection 3, that requires only one tuning parameter to beadjusted by the designer. The control design is successfullyapplied to the heave problem described above and testedin the Heave Lab. Experimental results are reported inSection 4.

Notation. Throughout this paper subscripts n and ddenote the numerator and denominator of SISO trans-fer functions, respectively. For a signal ξ(t) ∈ R, t ≥0, its truncated L∞ and L∞ norms are ‖ξt‖L∞ =sup0≤τ≤t |ξ(τ)|, ‖ξ‖L∞ = supτ≥0 |ξ(τ)|. The L1 gain ofa bounded-input-bounded-output (BIBO) stable properSISO system is defined by ‖H(s)‖L1

=∫∞0

|h(t)|dt, whereh(t) is the impulse response of H(s). Denoting by u(t) andy(t) the input and output of system H, respectively, thebound ‖yt‖L∞ ≤ ‖H(s)‖L1

‖ut‖L∞ will be used frequently.

2. L1 ADAPTIVE CONTROL DESIGN

The main difference between derivations in this part andthe results in Cao and Hovakimyan (2008) is inclusion andtreatment of unmatched periodic disturbances at the plantoutput, hence the name L1 adaptive output regulator. Thisresults in new asymptotic output regulation constraints onthe underlying filter in L1 adaptive control. We considersystems in the form

y(s) = A(s)(u(s) + d(s)) +Do(s)do(s), (1)

where u(t) ∈ R and y(t) ∈ R are the input and outputof the system, A(s) is a strictly proper tranfer function,Do(s) is a strictly proper and stable transfer function, andd(s) and do(s) are disturbances at the input and output,respectively. The system is the same as the one in Caoand Hovakimyan (2008), with the exception of the outputdisturbance term Do(s)do(s), which satisfies the followingassumption.

Assumption 1. There exists a constant γd > 0 such that

|do(t)| ≤ γd, |do(t)| ≤ γd. (2)

Furthermore, do(s) has known structure defined by thedisturbance generating polynomial dn(s). That is,

dn(s)do(s) = d0(0, s), (3)

where d0(0, s) is a polynomial in s arising from initial

conditions of the disturbance do(t) (do(0), do(0), do(0),etc.).

In other words, dn(s) contains as zeros the poles of do(s).Please note that conditions (2) and (3) imply that thepolynomial dn(s) can only have zeros in the left-half planeor simple zeros on the imaginary axis. In particular, in theapplication to Managed Pressure Drilling we are interestedin the case when (3) describes a harmonic oscillator, heavedisturbance oscillations, with frequencies determined bydn(s) and initial conditions by d0(0, s).

d(s) is the Laplace transform of unknown disturbancesmatched with plant input, d(t) = f(t, y(t)), where f isan unknown map that satisfies the following assumptionsCao and Hovakimyan (2008).

Assumption 2. There exist constants L > 0 and L0 > 0such that for all y1, y2 ∈ R and t ∈ R+,

|f(t, y1)− f(t, y2)| ≤L|y1 − y2|, (4)

|f(t, y)| ≤L|y|+ L0. (5)

Assumption 3. There exist constants L1 > 0, L2 > 0 andL3 > 0 such that for all t ∈ R+,

|d(t)| ≤ L1|y(t)|+ L2|y(t)|+ L3. (6)

The control objective is the same as in Cao and Ho-vakimyan (2008), namely to design an adaptive outputfeedback controller that makes the output y(t) track theoutput of a reference model, that is

y(s) ≈ M(s)r(s), (7)

where r(t) ∈ R is a bounded and continuous referencesignal. As in Cao and Hovakimyan (2008), we considerM(s) = m/(s + m) with m > 0. Following Cao andHovakimyan (2008), we rewrite system (1) as

y(s) =M(s)(u(s) + σ(s)), (8)

σ(s) =(A(s)−M(s))u(s) +A(s)d(s) +Do(s)do(s)

M(s),(9)

and define the closed-loop reference model

yref (s) =M(s)(uref (s) + σref (s)), (10)

σref (s) =(A(s)−M(s))uref (s) +A(s)dref (s) +Do(s)do(s)

M(s),

uref (s) =C(s)(r(s)− σref (s)), (11)

where dref (t) = f(t, yref (t)) and

C(s) = Cn(s)/Cd(s) = (Cd(s)−C0(s)dn(s))/Cd(s). (12)

Remark 4. Notice that the reference system (10)-(11) isnot implementable, since it depends on the unknownsystem uncertainties and disturbances, and it is used onlyfor analysis purposes.

The polynomials C0(s) and Cd(s) must be designed suchthat C(s) is strictly proper,

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

C(s)A(s) + (1− C(s))M(s)(13)

is BIBO stable and

‖G(s)‖L1L ≤ 1, G(s) = H(s)(1− C(s)). (14)

The problem of designing C(s) is handled in Section 3.Enforcing the structure (12) on C(s), ensures that thedisturbance at the output is attenuated asymptoticallywith time.

Lemma 5. Consider the closed-loop reference model in(10)–(11), and suppose the filter C(s) has structure (12)and satisfies (13). Then the effect of do(s) on the closed-loop reference model output yref is rejected asymptoticallywith time.

Proof. is given in Mahdianfar et al. (2015).

Consider the L1 adaptive controller from Cao and Hov-akimyan (2008), given as

˙y =−my(t) +m(u(t) + σ(t)), y(0) = 0, (15)

˙σ =ΓcProj(σ(τ),−mP (y(t)− y(t))), σ(0) = 0, (16)

u(s) =C(s)(r(s)− σ(s)), (17)



wherem is the time constant of the desired reference model(7), P > 0, Γc > 0 and the projection operator confinesσ(t) to |σ(t)| ≤ ∆. While P is arbitrary, Γc and ∆ mustbe chosen sufficiently large. Block Diagram of the systemand controller is shown in Figure 2. The following resultholds under the stated conditions.

Theorem 6. Signals of the closed loop consisting of system(1) and controller (15)–(17) satisfy

‖y − y‖L∞ ≤ γ0, (18)

‖y − yref‖L∞ ≤ γ1, (19)

‖u− uref‖L∞ ≤ γ2, (20)

where γ0, γ1 and γ2 are constants inversely proportional to√Γc.

Proof. The proof follows the steps of the proof of Theorem1 in Cao and Hovakimyan (2008) and can be found inMahdianfar et al. (2015).

Remark 7. Precise conditions on Γc and ∆ are providedin Mahdianfar et al. (2015). They are different from theones provided in Cao and Hovakimyan (2008) due to thedisturbance entering at the output.

Remark 8. The bounds (18)–(20) are qualitatively thesame as in standard L1 adaptive control. Notice that (19)implies in addition that the controller attenuates the effectof the output disturbance in view of Lemma 4.

Control law with regulation constraints

Uncertain plant

projection adaptation law

Reference command measured output

Output Predictor

L1 Adaptive Output Regulator

u

-

dido

estimated output

y(t)

)(ˆ tσ

)(tr

)(ˆ ty

Fig. 2. L1 Adaptive Output Regulator.

3. SYSTEMATIC FILTER DESIGN

Linear matrix inequalities (LMIs) have been used fordesign and analysis of robust adaptive controllers in Liet al. (2008); Peaucellea and Fradkov (2008); Peaucelleet al. (2009). In the present work, the choice of C(s)is critical to stability and performance of the regulatorpresented in the previous section. Here, we present a designmethodology based on LMIs for selecting C(s) to meet thedesign objectives. To this end, insert

u(s) = KI(s)v(s) (21)

into (1), where KI(s) is an internal model compensatorthat will be specified shortly. Disregarding the disturbanceat the output, Do(s)do(s), which has no bearing on whatfollows, we get

y(s) = A(s)(KI(s)v(s) + d(s)). (22)

We now seek to find the compensator

v(s) = −K(s)y(s) (23)

that minimizes the peak-to-peak gain from d(s) to y(s).Inserting (23) into (22) we get

y(s) =A(s)

1 +A(s)KI(s)K(s)d(s). (24)

So, we want to find the K(s) that minimizes∥∥∥ A(s)

1 +A(s)KI(s)K(s)

∥∥∥L1

. (25)

The solution to this optimal control problem leads toirrational compensators Dahleh and Pearson (1987), butsub-optimal rational compensators can be found along thelines of Boyd et al. (1994); Abedor et al. (1998); Schereret al. (1997). We will use the procedure for computingK(s) and ζ, the upper bound on the norm in (25), providedin Scherer et al. (1997). Let

x=Ax+B1v +B2d, (26)

y =Cx, (27)

be a minimal realization of (22) and

xcl =Axcl + Bd, (28)

y = Cxcl, (29)

a minimal realization of the closed-loop (24). From Scherer

et al. (1997), we have that for fixed λ > 0, if X, Y , A, B,

C, D, µ, ζ satisfy the LMIsλX λI 0 ∗λI λY 0 ∗0 0 (ζ − µ)I ∗

CX C 0 ζI

> 0 (30)

(AX+XAT+B1C+(B1C)T+λX ∗ ∗

A+(A+B1DC)T+λI ATY+Y A+BC+(BC)T+λY ∗BT

2 Y B2 −µI

)(31)

then the closed-loop system is stable and∥∥∥ A(s)

1 +A(s)KI(s)K(s)

∥∥∥L1

≤ ζ(λ). (32)

To optimize the bound, a line search over λ > 0 can becarried out to obtain

ζ∗ = infλ>0

ζ(λ). (33)

After solving the LMIs, the controller construction pro-ceeds by finding nonsingular matrices M and N such that

MN T = I −XY. (34)

A state-space realization of K(s) is then given by

DK = D (35)

CK = (C −DKCX)M−T (36)

BK = N−1(B − Y B1DK) (37)

AK =N−1(A−NBKCX − Y B1CKMT (38)

−Y (A+B1DKC)X)M−T . (39)

The following result specifies the internal model com-pentsator KI(s) and provides the filter C(s) of the pre-vious section with the desired properties.



Theorem 9. Let KI(s) be a proper transfer function withpoles given by the polynomial dn(s) (i.e. KId(s) = dn(s)).If

A(s)

1 +A(s)KI(s)K(s)(40)

is BIBO stable with∥∥∥ A(s)

1 +A(s)KI(s)K(s)

∥∥∥L1

< ζ(λ), (41)

then the filter

C(s) =KI(s)K(s)M(s)

1 +KI(s)K(s)M(s)(42)

has the form (12), renders H(s) as defined in (13) BIBOstable, and ensures ‖G(s)‖L1L ≤ 1 for G(s) as defined in(14), with L = 1/ζ(λ).

Proof. is given in Mahdianfar et al. (2015).

Remark 10. The narrow margins between pore pressureand fracture gradient in offshore MPD operations leavelittle margin for safe drilling and completion. In MPDsystems, there are standard limits for pressure regulationaccuracy. These constraints are expressed in time-domainand therefore application of the proposed method fordesigning a controller to minimize error signal peak valuesubject to a peak value constraint on the control is verywell motivated.

4. APPLICATION TO THE HEAVE PROBLEM INMANAGED PRESSURE DRILLING

4.1 The Heave Lab

In this section, the theory from the previous sections isapplied to the heave problem described in the introduction.A medium scale lab has been built at NTNU, tailor-made for testing control strategies for the heave problem.Figure 3 shows the photograph of the lab. It consistsof a choke, a back-pressure pump, 900 meters copperpipe, a piston connected to an AC motor, 12 pressuretransmitters, 3 flow-meters, DAQ cards and a computer.This experimental setup represents a well with MPDequipment as shown in Figure 1. The copper pipe modelsthe annular volume of the well around the drill pipe. Sincethere is no flow through the drill pipe during connections,the drill pipe and mud pump are not represented inthe lab facility. The bottom-hole-assembly is representedby a piston, which is controlled by the AC motor togenerate heave-like disturbances. The piston moves insidea transparent plastic pipe connected to one end of thecopper pipe. The choke and the back-pressure pump areconnected at the other end of the copper pipe. Figure 4shows a schematic of the lab.

4.2 System Identification

A model for the heave lab in the form (1) is developedusing standard system identification techniques in MAT-LAB Ljung (2013). The inputs are choke opening, u(t),and piston velocity, v(t), while the output is down-holepressure, y(t) (pressure transmitter P2 in Figure 4). Thetransfer functions from choke and piston velocity to down-hole pressure are identified as

A(s) =0.15s− 0.29

0.67s2 + 0.8s+ 1(43)

3.3 components 15

Figure 2: Lab with central measurements and components marked

Figure 3: Locker with Control Buttons for the Backpressure PumpThe pump is currently turned on and is running at full capacity,100 %

Fig. 3. MPD Heave Lab Albert et al. (2014).

Fig. 4. MPD Heave Lab schematic Albert et al. (2014).

and

D(s) = −1.15s+ 3.39

1.31s+ 1, (44)

respectively. Two data sets were used for system identifi-cation and verification. Fit to estimation and verificationdata are 73.11% and 61.8% in terms of normalized rootmean square error (NRMSE) measure, respectively. Timedomain response and comparison with the identified modelis shown in Figure 5. Choke input and piston velocityspectrum of the identification data are computed usingFFT. They indicate the model is accurate for the frequencyinterval 0 − 0.5Hz, which is above our practical require-ments. Choke input frequency spectrum, used for systemidentification, is illustrated in Figure 6.



0 10 20 30 40 50 60−6

−4

−2

0

2

4

6

Time (seconds)

bar

P2

PredictedReal

Fig. 5. Predicted and real measurements.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.70

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1Single−Sided Amplitude Spectrum of choke position

Frequency (Hz)

|Y(f)

|

Fig. 6. Choke input frequency spectrum.

4.3 Control Design

Wave elevation of regular waves in deep water can bemodeled by a single sinusoid Perez (2005). Therefore, thespeed of the drill string v(t) can be considered to be theoutput of a harmonic oscillator with frequency ω. A morethorough analysis of the effect of sea waves on floatingdrilling rigs is done in Nikoofard et al. (2013, 2014).Please note that during connection operations drillingis stopped and therefore the angular velocity of drill-string is zero. Robust adaptive regulators are designedand tested successfully for the scenarios of pure harmonicheave disturbance with periods t = 3, 5, 10s and a constantoffset, that is

v(t) = c1 + c2 sin(ωt+ φ) (45)

for some constants c1, c2 and φ. For these cases, the outputdisturbance in (1) takes the form

Do(s) =− 1

1.31s+ 1, (46)

do(s) =1.15s+ 3.39

s(s2 + ω2)(47)

for ω ∈ {2π/3, 2π/5, 2π/10}. One of the constraints im-posed on Do(s) is strict properness, which is the reasonwhy the zero of D(s) in (44) is placed in do(s) ratherthan Do(s) in the definitions (46)–(47). This is possiblesince the resulting do(s) has a well defined Laplace inversewhich is bounded. The denominator of do(s), which comesfrom the form of v(t) in (45), defines the disturbancegenerating polynomial to be included in the filter designas dn(s) = s(s2 + ω2). The reference model is selected asM(s) = m

s+m , m = 0.2, so that it gives the desired settlingtime of about 20 seconds. The desired adaptation rate, pro-jection bound, and projection tolerance bound are set atΓc = 1200 and ∆ = 50, ε = 0.1 respectively. Based on thechosen reference model M(s), and the identified transferfunction A(s) from (43), using the filter design procedurein Section 3 the filters are derived. LMIs (30)-(31) aresolved using YALMIP Lofberg (2004) as the interface andSeDuMi 1.3 Sturm (1999) as the solver. To optimize thebound in (32), a line search over λ is performed between[0.03, 1.5], 50 steps, LMIs (30)-(31) are solved and thecorresponding ζ values are computed. The Bode plots offilters are shown in Figure 7.

−150

−100

−50

0

50

Mag

nitu

de (d

B)

10−1 100 101 102−720

−540

−360

−180

0

180

Phas

e (d

eg)

Bode Diagram

Frequency (rad/s)

10s5s3s

Fig. 7. Bode plots of designed filters.

4.4 Experimental Results

The set-point for the desired bottom-hole pressure isr = 5 bar. For the scenarios of heave disturbance with5, and 10 seconds period, the bottom-hole pressure, andthe choke control signals are illustrated in Figures 8, and9 respectively. In these experiments at about t = 75s andt = 120s the closed-loop control is switched to constantchoke opening, and as a result surge and swab pressuresare not compensated afterwards. Experimental results forthe case of heave disturbance with period of 3 seconds, themost challenging scenario, are shown in Figure 10. Clearlythe proposed regulator has been successful in regulatingthe output to the desired set-point and attenuating theeffect of heave disturbance.



10 20 30 40 50 60 70 80 90 1000

2

4

6

8

10

Pres

sure

[bar

]

Bottom−hole pressure

10 20 30 40 50 60 70 80 90 10035

40

45

50

55

60

Time [s]

Deg

rees

[deg

]

Choke opening

Fig. 8. Bottom-hole pressure and choke opening, heavedisturbance with 5 seconds period.

20 40 60 80 100 120 140 1600

2

4

6

8

10

Pres

sure

[bar

]


20 40 60 80 100 120 140 16040

45

50

55

Time [s]

Deg

rees

[deg

]

Choke opening


5. CONCLUSIONS

In this paper, a control system design approach is proposedand applied for disturbance attenuation and set-point reg-ulation in the so-called heave problem in oil well drilling.Furthermore it is tested in a medium size experimentaltest facility. The results demonstrate that the proposedregulator efficiently regulates the down-hole pressure tothe desired set-point, with significant attenuation of pe-riodic disturbances. The control system methodology is amodification to L1 adaptive control that allows for dis-turbances entering at the plant output. By incorporatingthe disturbance at the output into the reference model,it is shown that the L1 adaptive control structure can beleft unchanged while the original transient performancebounds are preserved. It is further shown that rejection ofthe output disturbance can be taken care of entirely in thefilter design step of L1 adaptive control using the inter-nal model principle. A systematic filter design procedure

10 20 30 40 50 60 70 80 90 100 110 1200

2

4

6

8

Pres

sure

[bar

]


10 20 30 40 50 60 70 80 90 100 110 12035

40

45

50

55

60

Time [s]

Deg

rees

[deg

]

Choke opening


based on LMIs is provided, that requires only one tuningparameter to be adjusted by the designer.

REFERENCES

(2011). Macondo well-deepwater horizon blowout: Lessonsfor offshore drilling safety. Technical report, Committeefor Analysis of Causes of the Deepwater Horizon Explo-sion, Fire, and Oil Spill to Identify Measures to PreventSimilar Accidents to the Future; National Academy ofEngineering and National Research Council.

Aamo, O.M. (2013). Disturbance rejection in 2 x 2 linearhyperbolic systems. IEEE Transactions on AutomaticControl, 58(5), 1095–1106.

Abedor, J., Nagpal, K., and Poolla, K. (1998). A linearmatrix inequality approach to peak-to-peak gain mini-mization. International Journal of Robust and Nonlin-ear Control, 6(9-10), 899–927.

Albert, A., Aamo, O.M., Godhavn, J.M., and Pavlov,A. (2014). Disturbance rejection by feedback controlin offshore drilling: Experimental results. In IFACconference. IFAC, Cape Town, South Africa.

Anfinsen, H. and Aamo, O.M. (2014). Rejection of heave-induced pressure fluctuations at the casing shoe inmanaged pressure drilling. In IFAC World Congress.IFAC, Cape Town, South Africa.

Boyd, S., Ghaoui, L.E., Feron, E., and Balakrishnan, V.(1994). Linear Matrix Inequalities in System and Con-trol Theory, volume 15 of Studies in Applied Mathemat-ics. Society for Industrial and Applied Mathematics(SIAM).

Cao, C. and Hovakimyan, N. (2008). L1 adaptive outputfeedback controller for systems of unknown dimension.IEEE Transactions on Automatic Control, 53(3), 815–821.

Dahleh, M. and Pearson, J., J. (1987). L1 optimal compen-sators for continuous-time systems. IEEE Transactionson Automatic Control, 32(10), 889–895.

Florence, F. and Iversen, F. (2010). Real-time modelsfor drilling process automation: Equations and applica-tions. In IADC/SPE Drillng Conference and Exhibition,



128958-MS. Society of Petroleum Engineers, Louisiana,USA.

Godhavn, J.M. (2010). Control requirements for auto-matic managed pressure drilling system. SPE DrillingCompletion, 25(3), 336–345.

Hannegan, D. (2012). Health, safety and environmentalbenefits of managed pressure drilling on offshore highpressure-high temperature wells. Exploration Produc-tion - Oil Gas Review, 10(1), 74–82.

Hovakimyan, N. and Cao, C. (2010). L1 Adaptive ControlTheory: Guaranteed Robustness with Fast Adaptation.Advances in Design and Control. Society for IndustrialApplied Mathematics.

Hovakimyan, N., Cao, C., Kharisov, E., Xargay, E., andGregory, I.M. (2011). L1 adaptive control for safety-critical systems. IEEE Control Systems Magazine,31(5), 54–104.

Ioannou, P. and Sun, J. (1996). Robust Adaptive Control.Prentice-Hall.

Kharisov, E. and Hovakimyan, N. (2011). L1 adaptiveoutput feedback controller for minimum phase systems.In American Control Conference (ACC), 1182–1187.IEEE, San Francisco.

Kharisov, E., Kim, K.K.K., Wang, X., and Hovakimyan, N.(2011). Limiting behavior of l1 adaptive controllers. InAIAA Guidance, Navigation, and Control Conference.American Institute of Aeronautics and Astronautics(AIAA), Portland, Oregon.

Landet, I.S., Mahdianfar, H., Aarsnes, U.J.F., Pavlov,A., and Aamo, O.M. (2012a). Modeling for mpd op-erations with experimental validation. In IADC/SPEDrilling Conference and Exhibition, SPE-150461. Soci-ety of Petroleum Engineers, San Diego, California.

Landet, I.S., Pavlov, A., and Aamo, O.M. (2012b). Mod-eling and control of heave-induced pressure fluctuationsin managed pressure drilling. IEEE Transactions onControl Systems Technology.

Landet, I.S., Pavlov, A., Aamo, O.M., and Mahdianfar, H.(2012c). Control of heave-induced pressure fluctuationsin managed pressure drilling. In American Control Con-ference (ACC), 2270–2275. IEEE, Montreal, Canada.

Lavretsky, E. and Wise, K.A. (2013). Robust and Adap-tive Control; With Aerospace Applications. AdvancedTextbooks in Control and Signal Processing. Springer-Verlag, London.

Li, D., Hovakimyan, N., and Cao, C. (2013). Positiveinvariant set estimation of l1 adaptive controller in thepresence of input saturation. International Journal ofAdaptive Control and Signal Processing, 27(11), 1012–1030.

Li, D., Hovakimyan, N., Cao, C., and Wise, K. (2008).Filter design for feedback-loop trade-off of l1 adaptivecontroller: A linear matrix inequality approach. InAIAA Guidance, Navigation and Control Conferenceand Exhibit. AIAA, Honolulu, Hawaii.

Ljung, L. (2013). System Identification Toolbox. TheMathWorks, Inc., r2013a edition.

Lofberg, J. (2004). Yalmip : a toolbox for modeling andoptimization in matlab. In IEEE International Sympo-sium on Computer Aided Control Systems Design, 284–289. IEEE, Taipei.

Lohne, H.P., Gravdal, J.E., Dvergsnes, E.W., Nygaard,G., and Vefring, E.H. (2008). Automatic calibration of

real-time computer models in intelligent drilling controlsystems - results from a north sea field trial. InInternational Petroleum Technology Conference, 12707-MS. International Petroleum Technology Conference,Kuala Lumpur, Malaysia.

Mahdianfar, H., Aamo, O.M., and Pavlov, A. (2012a).Attenuation of heave-induced pressure oscillations in off-shore drilling systems. In American Control Conference(ACC), 4915–4920. IEEE, Montreal, Canada.

Mahdianfar, H., Aamo, O.M., and Pavlov, A. (2012b).Suppression of heave-induced pressure fluctuations inmpd. In Proceedings of the 2012 IFAC Workshop onAutomatic Control in Offshore Oil and Gas Production,volume 1, 239–244. IFAC, Trondheim, Norway.

Mahdianfar, H., Hovakimyan, N., Pavlov, A., and Aamo,O.M. (2015). L1 adaptive output regulator design withapplication to managed pressure drilling. to be publishedin Journal of Process Control.

Mahdianfar, H., Pavlov, A., and Aamo, O.M. (2013).Joint unscented kalman filter for state and parameterestimation in managed pressure drilling. In EuropeanControl Conference. IEEE, Zurich, Switzerland.

Nikoofard, A., Johansen, T.A., Mahdianfar, H., andPavlov, A. (2013). Constrained mpc design for heavedisturbance attenuation in offshore drilling systems. InIEEE/MTS OCEANS. IEEE, Bergen, Norway.

Nikoofard, A., Johansen, T.A., Mahdianfar, H., andPavlov, A. (2014). Design and comparison of con-strained mpc with pid controller for heave disturbanceattenuation in offshore managed pressure drilling sys-tems. Marine Technology Society (MTS), 48(2), 90–103.

Pavlov, A., Kaasa, G.O., and Imsland, L. (2010). Experi-mental disturbance rejection on a full-scale drilling rig.In 8th IFAC Symposium on Nonlinear Control Systems,1338–1343. IFAC, University of Bologna, Italy.

Peaucelle, D., Khan, H.M., and Pakshin, P.V. (2009).Lmi-based analysis of robust adaptive control for linearsystems with time-varying uncertainty. Automation andRemote Control, 70(9), 1540–1552.

Peaucellea, D. and Fradkov, A. (2008). Robust adaptive l2-gain control of polytopic mimo lti systems — lmi results.Systems Control Letters, 57(11), 881–887.

Perez, T. (2005). Ship Motion Control: Course Keepingand Roll Stabilisation Using Rudder and Fins. Springer.

Scherer, C., Gahinet, P., and Chilali, M. (1997). Multi-objective output-feedback control via lmi optimization.IEEE Transactions on Automatic Control, 42(7), 896–911.

Skalle, P. and Podio, A.L. (1998). Trends extractedfrom 800 gulf coast blowouts during 1960-1996. InIADC/SPE Drilling Conference, 39354-MS. Society ofPetroleum Engineers, Dallas, Texas.

Sturm, J.F. (1999). Using sedumi 1.02, a matlab toolboxfor optimization over symmetric cones. OptimizationMethods and Software, 11(1-4), 625–653.

Xargay, E., Dobrokhodov, V., Kaminer, I., Pascoal, A.,Hovakimyan, N., and Cao, C. (2012). Time-criticalcooperative control of multiple autonomous vehicles:Robust distributed strategies for path-following controland time-coordination over dynamic communicationsnetworks. IEEE Control Systems Magazine, 32(5), 49–73.



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