Methane Number Control of Fuel Gas Supply System Using Combined Cascade/Feed-Forward Control

Journal of Marine Science and Engineering

Article Methane Number Control of Fuel Gas Supply System Using Combined Cascade/Feed-Forward Control

Soon-kyu Hwang 1 and Byung-gun Jung 2,*

1 Process Engineering Department, MODEC Oﬀshore Production System, 9 North Buona Vista Drive, Singapore 138588, Singapore; [email protected] 2 Department of Marine System Engineering, Korea Maritime & Ocean University, Busan 49112, Korea * Correspondence: [email protected]; Tel.: +82-51-410-4269

Received: 4 April 2020; Accepted: 25 April 2020; Published: 28 April 2020

Abstract: Liquefied natural gas began to attract attention as a ship fuel to reduce environmental pollution and increase energy efficiency. During this period, highly efficient internal combustion engines emerged as the new propulsion system instead of steam turbines. However, Otto-cycle engines must use fuel that meets the methane number that was given by the engine makers. The purpose of this study was to develop a system configuration and a control method of methane number adjustment using combined cascade/feed-forward controllers for marine Otto-cycle engines to improve reference tracking and the disturbance rejection. The main principle involves controlling the downstream gas temperature of the fuel gas supply system to meet the required methane number. Three controllers are used in the combined cascade/feed-forward control for adjusting the downstream of the gas temperature: the cascade loop has two controllers and the feed-forward has one controller. The two controllers in the cascade loop are designed with proportional–integral (PI) controllers. The remaining controller is based on feed-forward control theory. A simulation was conducted to verify the efficacy of the proposed method, focusing on the disturbance rejection and set-point tracking, in comparison with a single PI controller, a single PI controller with feed-forward, and cascade control.

Keywords: methane number; PI controller; cascade control; feed-forward control; natural gas; disturbance rejection

1. Introduction The International Maritime Organization (IMO) has adopted regulations to address the emission of air pollutants from ships and has implemented mandatory energy efficiency measures to reduce the emissions of greenhouse gases from shipping, under the International Convention for the Prevention of Pollution from Ships (MARPOL). First, sulphur oxides (SOx) and nitrogen oxides (NOx) were reduced as a solution to air pollution. Second, the energy efficiency design index (EEDI) was made mandatory for new ship’ construction as adopted by MARPOL [1–3]. In other words, it will increase energy efficiency to reduce environmental pollution. The final goal of these two items is to reduce pollutants and minimize fuel use. For that reason, liquefied natural gas (LNG) began to attract attention as a ship fuel [4,5]. During this period, various gas engines using natural gas (NG) for marine purpose emerged as new propulsion systems with high efficiency and low operational costs instead of steam turbines [6]. In other words, the Otto-cycle engine, which is one of the gas engine types, has begun to replace the existing ship propulsion system, the steam turbines. Figure1 shows the concept of the Otto-cycle engines. During compression stroke in the Otto-cycle engines, low-pressure fuel gas is injected from the middle of the cylinder liner to perform the compression stroke in the premixed state with the scavenging air.

J. Mar. Sci. Eng. 2020, 8, 307; doi:10.3390/jmse8050307 www.mdpi.com/journal/jmse J. Mar. Sci. Eng. 2020, 8, 307 2 of 16 J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 2 of 16 scavengingThen, at theair. endThen, of at the the compression end of the compression stroke, combustion stroke, proceedscombustion by injectingproceeds theby injecting fuel for the the ignition fuel forthrough the igniti fuelon through valves installed fuel valve ons theinstalled upper on part the of upper the cylinder part of head.the cylinder head.

FigureFigure 1. The 1. The concept concept of the of theOtto Otto-cycle-cycle engines engines [7]. [7].

However,However, the the Otto Otto-cycle-cycle engine engine has has the the disadvantage disadvantage of ofhaving having to tomeet meet the the proper proper methane methane numbernumber (MN) (MN) that that was was given given by by the the engine engine make makers.rs. On On average, values ofof 60–8060–80 are are provided. provided The. The MN MNdescribes describes the the ability ability of of NG NG to to withstand withstand compression compression before before ignition. ignition. Pure Pure methane methane has has a a MN MN of of 100, 100,and and pure pure hydrogen hydrogen has ahas MN a of MN 0. Fuels of 0. with Fuels lower with methane lower methane numbers numbers pose performance pose performance problems for problemsfuel gas for supply fuel gas systems supply (FGSSs) systems due (FGSS to combustions) due to combustion knocking knocking caused by caused higher by amounts higher amounts of ethane, of propane, ethane, propane, and heavier and hydrocarbons heavier hydrocarbons [8]. Major causes [8]. Major of low causes MN are of LNG low ageing, MN are temperature LNG ageing, rise of temperaturethe cargo tank rise inside,of the cargo and low tank MN inside LNG, and forced low vaporization MN LNG forced [9]. A vaporization list of the LNG [9] composition. A list of the andLNG MN compositionavailable fromand MN some available LNG terminals from some is provided LNG terminals in Table is1. provided With the lowin Table MN of1. With LNG the supplied low MN from of theLNG LNG supplied terminal, from it isthe highly LNG likelyterminal, that theit is MN highly will likely be lower that due the toMN the will increase be lower in the due temperature to the increaseof the in cargo the tanktemperature and LNG of ageing the cargo while tank sailing, and which LNG meansageingthat while a system sailing, capable which ofmeans controlling that athe systemMN iscapable needed. of controlling the MN is needed. Table 1. Liqueﬁed natural gas (LNG) compositions and methane number (MN) at some LNG terminals. Table 1. Liquefied natural gas (LNG) compositions and methane number (MN) at some LNG terminals. Description A B C

Description Methane (mol.%)A 89.60 86.26B 81.39 C Ethane (mol.%) 5.31 12.44 Methane (mol.%) 89.60 88.236.26 81.39 Propane (mol.%) 3.00 3.29 3.51 Ethane (mol.%) 5.31 8.23 12.44 Butane (mol.%) 1.47 0.96 0.64 Propane (mol.%) 3.00 3.29 3.51 Nitrogen (mol.%) 0.61 1.26 2.02 Butane (mol.%) MN1.47 71.10 069.30.96 67.40 0.64 Nitrogen (mol.%) 0.61 1.26 2.02 MN 71.10 69.30 67.40 The primary contribution of this study is the development of a system conﬁguration and a

methane number adjustment control method for marine Otto-cycle engines to improve reference The primary contribution of this study is the development of a system configuration and a tracking as well as the disturbance rejection with combined cascade/feed-forward controllers. First of methane number adjustment control method for marine Otto-cycle engines to improve reference all, we suggest how to adjust the MN using existing equipment in current LNG carriers (LNGCs) and tracking as well as the disturbance rejection with combined cascade/feed-forward controllers. First of LNG-fueled ships (LFSs). Some research has focused on calculation methods and test methods of the all, we suggest how to adjust the MN using existing equipment in current LNG carriers (LNGCs) and methane number. Partho et al. [8] developed a prediction model of the natural gas methane number. LNG-fueled ships (LFSs). Some research has focused on calculation methods and test methods of the Martin et al. [10] studied methane number test of the alternative gaseous fuels. However, a method for methane number. Partho et al. [8] developed a prediction model of the natural gas methane number. controlling the MN in ships’ Otto-cycle engines was needed. The method focusing on the fact that each Martin et al. [10] studied methane number test of the alternative gaseous fuels. However, a method gas has a diﬀerent boiling point was applied in this paper in order to control the MN of the natural gas. for controlling the MN in ships’ Otto-cycle engines was needed. The method focusing on the fact that each gas has a different boiling point was applied in this paper in order to control the MN of the natural gas.

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Then, appropriate control methods could be applied in MN control systems. Feed-forward control and cascade control are considered two of the proper control methods. Feed-forward control is used to ensure constant control performance when a disturbance affects a process under feedback control. The weak point of feedback control is that a process variable (PV) is necessary before a manipulated variable (MV) change is taken when a disturbance affects a process. The application of feed-forward control is sufficient to compensate for this weakness. However, the performance of feed-forward control is limited by model uncertainty [11]. In practice, the disturbance rejection and accuracy of the system response are important. Cascade control was adapted to show how to use multiple process variables to improve the response to a disturbance and reference tracking. Several studies focused on control methods using cascade control and feed-forward control. Lee et al. [12] suggested the use of internal model controller (IMC) principles as a controller tuning method for both inner and outer loop controllers in cascade control. Kaya [13,14] proposed the application of the Smith predictor scheme in a long time delay system. Some researchers [15–18] studied feed-forward control with a feedback control system using advanced tuning methods such as robust control. Although many papers focused on controller tuning, others studied performance improvement by combining two types of controllers. Nguyen et al. [19] constructed a method combining an adaptively feed-forward neural controller and a proportional–integral–derivative (PID) controller to control the joint-angle position of robots. To be applied to a ship’s control system, stability must be ensured, and controllers should be easy to tune via modification by the crew of the ship. Considering these points, combined cascade/feed-forward control is suggested with a control strategy and configuration for a MN control system in this paper. Simple tuning methods using Ziegler–Nichols, Tyreus–Luyben, and rule of thumb were applied. Using MATLAB simulation results, the performances of a single PI control, PI control with feed-forward, cascade control, and combined cascade/feed-forward control were determined and compared.

2. System Configuration and Model The proposed MN control system shown in Figure2 consists of an orifice, an in-line mixer, a flow control valve, an LNG supply pump, and a separator. The main idea to remove C2+, such as ethane and butane, which lowers MN from NG, is to spray cold LNG to NG to lower the temperature of the fluid stream. If the cargo tank temperature is near 80 C, taking into account the boiling point of − ◦ each gas, an in-line mixer should be operated to remove C2+ from the NG. For use of the in-line mixer, valves 2 and 3 are opened and valve 1 is closed. When the temperature of NG is lowered to about 100 C, C2+ may condense. As opposed to the use of an in-line mixer, valve 1 is opened, and valves 2 − ◦ and 3 are closed. The condensed gas is divided inside of a separator and returned to the cargo tank, and only NG with a high MN value is sent to the fuel gas supply system. The high MN gas is supplied to Otto-cycle engines through the fuel gas supply system, which is effective in preventing phenomena such as knocking. It is advantageous from an OPEX perspective. In addition, this Otto-cycle engine has an inherent to reduce the formation of NOx by up to 90% compared to the diffusion combustion of the diesel [7]. J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 4 of 16

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Figure 2. Schematic diagram of the methane number (MN) control system. Figure 2. Schematic diagram of the methane number (MN) control system. 2.1. Block DiagramFigure of Combined 2. Schematic Cascade/Feed diagram- ofForward the methane Control number (MN) control system. 2.1.2.1. BlockIn Block the Diagram combinedDiagram of Combinedof cascade/feedCombined Cascade Cascade/Feed-forward/Feed-Forward - controlForward Control strategy Control shown in Figure 3, the temperature controlIn theisIn the the combined primary combined cascade control cascade/feed/ feed-forwardloop and- forwardthe controlflow control control strategy is strategy the shown secondary inshown Figure control in3 , Figure the temperatureloop. 3, Tablethe temperature 2 control shows theis thecontrol description primary is the control ofprimary the loopblock control and diagram. loop the flow and W hen controlthe flowa disturbance is control the secondary is the occur secondarys control in this loop.control system, Table loop. a feed2 Tableshows-forward 2 theshows controllerdescriptionthe description rapidly of the block act of s the to diagram. compensat block diagram. Whene for a disturbanceitW inhen the a system.disturbance occurs O inn- thisoff occur control system,s in thisfor a feed-forward motor system, and a feedhydraulic controller-forward valvesrapidlycontroller ( actsvalve to srapidly compensate1–3) was act excludeds forto compensat it in thein the system. esimulation for On-oit in ffthe incontrol thissystem. study for motorO. nThe-off and primary control hydraulic fordisturbance motor valves and (valves (NG hydraulic inlet 1–3) temperaturewasvalves excluded (valve change ins the 1–3) simulation fromwas excluded cargo in this tanks) in study. the directly simulation The primary affects in this disturbance the study primary. The (NG outputprimary inlet temperature( thedisturbance process change(NG outlet inlet temperaturefromtemperature cargo tanks) of the change directly NG controlled from aff ects cargo the by tanks) an primary in -directlyline output mixer) affects (thewithout process the aprimary direct outlet impact output temperature on(the the p of serocesscondary the NG outlet outputcontrolledtemperature (LNG by flowrate an ofin-line the from NG mixer) controlledthe pump). without byThe aan secondary direct in-line impact mixer) disturbance on without the secondary(LNG a direct fluctuation outputimpact from (LNG on the FG flowrate sepumpscondary offrom theoutput the cargo pump). (LNG tanks flowrate The in Figure secondary from 2) thecreates disturbance pump). the Theeffect (LNG secondary on fluctuationthe secondary disturbance from output FG (LNG pumps (f fluctuationlowrate of the is cargoadjusted from tanksFG bypumps ina controlFigureof the2 ) valve). createscargo tanksTherefore, the e ffinect Figure on we the adopted2 secondary) creates series the output effect cascade (flowrate on the control secondary is adjusted instead output by of a parallelcontrol (flowrate valve). cascade is adjusted Therefore, control by a bweecausecontrol adopted it is valve). seriesuseful Therefore, cascade when the control wesecondary adopted instead process ofseries parallel, such cascade cascade as the control LNG control instead flowrate because of, is parallel it naturally is useful cascade separated when control the fromsecondarybecause the primary process,it is useful process such when as [1 the3 ,the20 LNG]. secondary flowrate, process is naturally, such separated as the LNG from flowrate the primary, is naturally process separated [13,20]. from the primary process [13,20].

Figure 3 3.. BlockBlock diagram diagram of of the the MN MN control control system. Figure 3. Block diagram of the MN control system.

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Table 2. Description of block diagram abbreviations. Table 2. Description of block diagram abbreviations.

SymbolSymbol Description rr Process outlet temperature setpoint yy Process outlet temperature GC1GC1 Primary controller (NG temperature control) GC2GC2 Secondary controller (LNG flowflow control) GCFGCF FFeed-forwardeed-forward controller GP1GP1 Primary process (In-line(In-line mixer) GP2 Secondary process (Control valve) GP2 Secondary process (Control valve) GM1 Primary measurement (NG temperature) GM1 Primary measurement (NG temperature) GM2 Secondary measurement (LNG flowrate) GM2 GD1 Primary disturbanceSecondary (NGmeasurement temperature (LNG change flowrate) in cargo tanks) GD2GD1 SecondaryPrimary disturbance disturbance (NG (LNG temperature flow fluctuation change fromin cargo FG pump)tanks) GD2 Secondary disturbance (LNG flow fluctuation from FG pump)

2.2. System Modelling 2.2. System Modelling 2.2.1. Flowmeter and Temperature Sensor 2.2.1. Flowmeter and Temperature Sensor The flow control system consists of a flowmeter, a differential pressure cell, a P/I (pressure to The flow control system consists of a flowmeter, a differential pressure cell, a P/I (pressure to current) transducer, a flow controller, an I/P (current to pressure) transducer, and a control valve current) transducer, a flow controller, an I/P (current to pressure) transducer, and a control valve actuator, as shown in Figure4. actuator, as shown in Figure 4.

FigureFigure 4.4. InstrumentationInstrumentation diagramdiagram forfor ﬂowflow control.control.

TheThe inputinput to the the flowmeter flowmeter can can be be thought thought of ofas asthe the actual actual flowrate flowrate of the of theprocess process fluid. fluid. The Thevolumetric volumetric flowrate flowrate is related is related to tothe the pressure pressure drop drop across across the the orifice. orifice. Based Based on on the Bernoulli equationequation andand thethe continuitycontinuity equation,equation, thethe didifferentialfferential pressurepressure equationequation isis representedrepresented inin EquationEquation (1)(1) [[2121].]. ThisThisis ismodified modified as as Equation Equation (2) (2) using using information information on on the the process process data. data. r 2 2 πD휋2퐷2 2ρ2∆휌P∆푃 m =푚 C=d 퐶푑 √ (1)(1) 4 4 11 −B4퐵4 − m푚 2 ∆P∆푃== ( )2 (2)(2) 0.01054820.0105482 P C B wherewhereρ ρis is density; density;∆ ∆푃is is the the di ffdifferentialerential pressure; pressured; Cisd theis the discharge discharge coe coefficientfficient (0.995); (0.995);is B the is the ratio ratio of orifice to pipe diameter D /D (0.3895); D is the inner pipe diameter (0.0547878 mm); D is the orifice of orifice to pipe diameter1 D2 1/D2 (0.3895);1 D1 is the inner pipe diameter (0.0547878 mm)2 ; D2 is the innerorifice diameter inner diameter (0.0213425 (0.0213425 mm); and mmm);is and the m mass is the flowrate mass flowrate (kg/h). (kg/h). ThisThis equation for for the the differential differential pressure pressure across across the the orifice orifice is described is described in Figure in Figure 5. When5. Whencomparing comparing the pressure the pressure loss of lossa pipe of to a pipethe orifice to the pressure orifice pressureloss in this loss paper, in this the paper, two values the two are valuesalmost are the almost same, thewhich same, can which be considered can be considered a pipe. a pipe.

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Figure 5. Differential pressure across the orifice. FigureFigure 5. 5.Differential Differential pressure pressure across across the the orifice. orifice. Focusing on the temperature sensor of the separator downstream, this can also be considered a Focusing on the temperature sensor of the separator downstream, this can also be considered a pipingFocusing line for the on samethe temperature reason as the sensor orifice. of the Therefore, separator this downstream, cannot have this any can impacts also be on considered the system a piping line for the same reason as the orifice. Therefore, this cannot have any impacts on the system duringpiping the line performance for the same check reason in thisas the study. orifice. Therefore, this cannot have any impacts on the system duringduring the the performance performance check check in in this this study study. . 2.2.2. In-line Mixer 2.2.2.2.2.2. In In-line-line M Mixerixer An in-line mixer is used for lowering the NG temperature against the low MN. The temperature is loweredAnAn in in- byline-line the mixer mixer spray is is ofused used LNG for for using lowering lowering the nozzlethe the NG NG into temperature temperature the NG. An against against in-line the mixerthe low low consistsMN. MN. The The of temperature atemperature nozzle for isLNG islowered lowered spraying by by theand the spray aspray cylindrical of of LNG LNG mixingusing using the vessel,the nozzle nozzle as showninto into the the in NG. FigureNG. An An6 i.n i-nline-line mixer mixer consists consists of of a anozzle nozzle forfor LNG LNG spraying spraying and and a cylindricala cylindrical mixing mixing vessel vessel, as, as shown shown in in Figur Figure 6e .6 .

. .

FigureFigureFigure 6. 6. 6.ConConﬁguration Configurationfiguration of of of the the the in in-line in-line-line mixer mixer mixer [ [222 2[2].].2 ].

The in-line mixer property is indicated by the temperature curve for adjusting the LNG mass TheThe in in-line-line mixer mixer property property is isindicated indicated by by the the temperature temperature curve curve for for adjusting adjusting the the LNG LNG mass mass flowrate, which can ensure the downstream temperature of the in-line mixer for the NG is 100 C, flowrateflowrate, which, which can can ensure ensure the the downstream downstream temperature temperature of of the the in in-line-line mixer mixer for for the the NG NG is is− 100−100 °C◦ °C, , ensuring the MN is 80 or above. For simulating how much LNG is required for cooling the NG, ensuringensuring the the MN MN is is80 80 or or above. above. For For simulatin simulating ghow how much much LNG LNG is isrequired required for for cooling cooling the the NG, NG, HYSYS (Aspen Technology, Massachusetts, USA) dynamic simulation is used. The NG mass flowrate is HYSYSHYSYS (Aspen (Aspen Technology Technology, Massachusetts,, Massachusetts, USA) USA) dynamic dynamic simulation simulation is isused. used. The The NG NG mass mass flowrate flowrate calculated based on cargo tanks’ maximum boiled-off rate (BOR) in the stable tank condition, referring is is calculated calculated based based on on cargo cargo tanks’ tanks’ maximum maximum boiled boiled-off-off rate rate (BOR) (BOR) in in the the stable stable tank tank condition condition, , to Gaztransport & Technigaz (GTT) information [23]. When the flowrate of the NG generated from the referringreferring to to Gaztransport Gaztransport & & Technigaz Technigaz ( GTT (GTT) )information information [ 2 [32].3 ].When When the the flowrate flowrate of of the the NG NG cargo tanks flows to the in-line mixer, the LNG flowrate that must meet the MN is sprayed through the generatedgenerated from from the the cargo cargo tank tanks flowss flows to to the the in in-line-line mixer, mixer, the the LNG LNG flowrate flowrate that that must must meet meet the the MN MN is issprayed sprayed through through the the nozzle. nozzle. The The temperature temperature trend trend curve curve of of the the in in-line-line mixer mixer downstream downstream was was

J. Mar. Sci. Eng. 2020, 8, 307 7 of 16 nozzle. The temperature trend curve of the in-line mixer downstream was implemented in an HYSYS dynamic simulation, as shown in Figure7. This curve was transformed into Equation (11) using system identiﬁcation in MATLAB Simulink (MathWorks, Massachusetts, USA). For creating a transfer function of the in-line mixer, time domain data were used with the same time interval. The measured input (LNG mass ﬂowrate) and the measured output (downstream temperature of the in-line mixer) were the independent variables, and the dependent variables were the predicted outputs. Equation (3) can be used to predict the parameters of the model [24–26]. J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 7 of 16 ( ) = ( ) 0 + ( ) 0 + + ( ) 0 y i ϕ1 i θ1 ϕ2 i θ2 ϕn i θn (3) implemented in an HYSYS dynamic simulation, as shown··· in Figure 7. This curve was transformed 0 whereinto Eyquationis the measured (11) using output system variable, identificationθn is the in parameters MATLAB of Simulink the model (MathWorks to be determined,, Massachusetts, and ϕn isUSA the known). For creat functioning a transfer called the function regressor. of the The in vectors-line mixer, are introducedtime domain in data Equations were used (4) and with (5). the same time interval. The measured input (LNG mass flowrate) and the measured output (downstream T ϕ = ϕ (i) ϕ (i) ϕn(i) (4) temperature of the in-line mixer) were the independent1 2 ··· variables, and the dependent variables were the predicted outputs. Equation (3) can be usedn to predicto the parameters of the model [24–26]. θ0 = θ0 θ0 θ0 (5) 1 2 ··· n

Figure 7. Temperature curve of the downstream of an in-line mixer. Figure 7. Temperature curve of the downstream of an in-line mixer. The model is indexed by the time interval. In this study, the time interval was 1 s. 0 0 0 푦(푖) = 휑1(푖)휃1 + 휑2(푖)휃2 + ⋯ + 휑푛(푖)휃푛 (3)     0  y(1) ϕ1(1) ϕ2(1) ϕn(1) θ    0  1  where y is the measured  output variable, 휃 is the··· parameters of the model 0 to be determined,  y(2)   ϕ (2) ϕ (2) 푛 ϕn(2)  θ     1 2 ···  2  and 휑푛 is the known. function =  called. the regressor. . The vectors. are. introduced .in Equations (4) (6)and  .   . . . .  .  (5).  .   . . . .  .      0  y(i) ϕ1(i) ϕ2(i) ϕn(i) θn 푇 ··· 휑 = {휑1(푖) 휑2(푖) ⋯ 휑푛(푖)} (4) During the calculation, θ should be chosen to minimize the least-square loss in Equation (7). 0 0 0 0 휃 = {휃1 휃2 ⋯ 휃푛 } (5) t X 2 The model is indexed by the timeV(θ, interval.t) = Iny( thisi) studyϕT(i)θ, the time interval was 1 s. (7) − 푦(1) 휑 (1)i=1 휑 (1) ⋯ 휑 (1) 휃0 1 2 푛 1 푦(2) 휑 (2) 휑 (2) ⋯ 휑 (2) 휃0 Equation (7) can be changed[ to Equation] = [ 1 (8) using2 the notation푛 ] of residuals;2 (6) ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ 푦(푖) 휑 (푖) 휑 (푖) ⋯ 휑 (푖) 0 1 X2t 푛 [휃푛 ] V(θ, t) = (ε(i))2 (8) During the calculation, 휃 should be chosen to minimize the least-square loss in Equation (7). i=1 푡 where residual ε(i) is deﬁned by 푉(휃, 푡) = ∑(푦(푖) − 휑푇(푖)휃)2 (7) 푖=1 ε(i) = y(i) yˆ(i) = y(i) ϕT(i)θ (9) Equation (7) can be changed to Equation− (8) using the− notation of residuals; and yˆ(i) is the predicted output of the system from Equation푡 (9). The solution to the least-squares 2 considering the matrix ϕTϕ is nonsingular, given푉(휃, 푡) by:= ∑(휀(푖)) (8) 푖=1 where residual 휀(푖) is defined by 휀(푖) = 푦(푖) − 푦̂(푖) = 푦(푖) − 휑푇(푖)휃 (9) and 푦̂(푖) is the predicted output of the system from Equation (9). The solution to the least-squares considering the matrix 휑푇휑 is nonsingular, given by: 휃 = (휑푇휑)−1휑푇푦. (10) This model, using Equations (3)–(10), is given by:

−0.2458푠−1.622푒−6 −0.2458푠−1.622푒−6 퐺푃1(푠) = = . 푠2+0.174푠+0.00247 (푠+0.1584)(+0.0156) (11)

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1 θ = ϕTϕ − ϕT y. (10)

This model, using Equations (3)–(10), is given by:

0.2458s 1.622e 6 0.2458s 1.622e 6 GP1(s) = − − − = − − − . (11) s2 + 0.174s + 0.00247 (s + 0.1584)(+0.0156)

2.2.3. Control Valve J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 8 of 16 The control valve is an important element in process industries. If the actual LNG flow is not properly2.2.3. Control controlled, Valve even if the measurement is good, problems will arise in temperature control. The flowThe coecontrolfficient valve (Cv) is isan the important key element element for controllingin process theindustries. valve with If the the actual proper LNG opening flow is ratio. not Ifproperly the flow controlled coefficient, even is higher if the measurement than the system is good, requirement, problems the will control arise in valve temperature cannot becontrol. operated The properly.flow coefficient This means (Cv) is that the the key temperature element for controlcontrolling fails the because valve awith large the control proper valve opening can allowratio. largeIf the amountsflow coefficient of LNG is tohigher cool than the boil-o the systemff gas (BOG)requirement, with small the control movements valve cannot of the actuators.be operated Therefore, properly. theThis characteristic means that the curve temperature of the control control valve fails is usedbecause for makinga large control a transfer valve function. can allow The large characteristic amounts curveof LNG of the to control cool the valve boil indicates-off gas ( theBOG relationship) with small between movement the flows of rate the through actuators. the Therefore, valve and the the positioncharacteristic of the curve stem thatof the changes control the valve valve is from used 0% for to making 100% [27 a]. transfer function. The characteristic curveFigure of the8 controlshows thevalve flow indicates characteristic the relationship curve of the between control the valve. flow Therate systemthrough identification the valve and and the HYSYSposition dynamic of the stem simulation that changes used the for thevalve in-line from mixer0% to modeling100% [27]. were applied to obtain the transfer functionFigure of the 8 shows control the valve. flow Equationcharacteristic (12) wascurve obtained of the control as a result valve. of thisThe simulation.system identification and HYSYS dynamic simulation used for the in-line mixer modeling were applied to obtain the transfer 9.6s + 0.7955 9.6s + 0.7955 function of the controlGP valve.2(s) = Equation (12) was obtained= as a result of this simulation. (12) s2 + 13.33s + 0.7542 (s + 13.2732)(s + 0.0568)

FigureFigure 8.8. CharacteristicCharacteristic curvecurve ofof thethe controlcontrol valve.valve. 2.2.4. Disturbance 9.6푠+0.7955 9.6푠+0.7955 퐺푃2(푠) = = (12) Disturbances can occur for both the푠2+13 primary.33푠+0.7542 control(푠+13. loop2732)(푠 and+0.0568 the) secondary control loop. A primary disturbance is caused from abrupt temperature changes in the NG of cargo tanks. The abrupt temperature2.2.4. Disturbance change can be ignored considering the size of the cargo tanks of LNG carriers. The cargo tank size of an LNGC currently varies from 140,000 to 260,000 m3. Figure9 shows the temperature Disturbances can occur for both the primary control loop and the secondary control loop. A changes in a cargo tank of an actual LNGC equipped with 140,000 m3 cargo tanks. The average primary disturbance is caused from abrupt temperature changes in the NG of cargo tanks. The abrupt temperature for six days changed from 158.88 to 158.56 ◦C. Considering this trend of temperature temperature change can be ignored considering− the− size of the cargo tanks of LNG carriers. The cargo change, we assumed that primary disturbance could be ignored. tank size of an LNGC currently varies from 140,000 to 260,000 m3. Figure 9 shows the temperature changes in a cargo tank of an actual LNGC equipped with 140,000 m3 cargo tanks. The average temperature for six days changed from −158.88 to −158.56 °C . Considering this trend of temperature change, we assumed that primary disturbance could be ignored.

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Figure 9. Temperature curve at a cargo tank for six days in an LNG carrier. FigureFigure 9. 9.Temperature Temperature curve curve at at a a cargo cargo tank tank for for six six days days in in an an LNG LNG carrier. carrier.

TheTheThe other other other disturbance disturbance disturbance typetype type is is is secondary secondary secondary disturbance. disturbance. disturbance. TheT Thehe LNGLNG LNG flowflow flow fromfrom from thethe the FGFG FG pump pump pump inin in the the the cargocargocargo tanks tanks tanks may may may fluctuate. fluctuate fluctuate. A .A A small small small amount amount amount of of of LNG LNG LNG is is is requiredrequired required in in in the the the in-linein in-line-line mixer, mixer, mixer, but but but a a a large large large amount amount amount ofofof flow flow flow may may may be be be sent sent sent to to to the the the in-line in in-line-line mixer mixer mixerwhen when when thethe the flowflow flowcontrol control controlof of ofthe the the dischargedischarge discharge ofof of thethe the FGFG FG pumppump pump fails.fails. fails. InInIn addition, addition, addition,if if if the the the constant constant constant flowflow flow control con controltrol fails fails fails downstream downstream downstream ofof of thethe the FGFG FG pump, pump, pump, thethe the LNGLNG LNG flowrateflowrate flowrate maymay may fluctuatefluctuatefluctuate significantly. significantly. significantly. This ThisThis phenomenon phenomenon phenomenon impacts impact impact the temperaturess thethe temperature temperature control of the control control separator of of the downstream.the separator separator Indownstream.downstream. other words, In In if other aother large words, words, amount if if a a oflarge large LNG amount amount is suddenly of of LNG LNG injected is is suddenly suddenly into the injected injected NG through into into the the the NG NG in-line through through mixer the the nozzle,inin-line-line controllingm mixerixer nozzle, nozzle, the temperaturecontrolcontrollingling the the becomes temperature temperature difficult. becomes becomes The LNG difficult difficult flowrate. .T The ishe relatedLNG LNG flowrate flowrate to the characteristic is is related related to to curvethethe characteristic characteristic of the FG pump, curve curve which of of the the is FG FG shown pump, pump, in which Figurewhich is 10is shown .shown in in Figure Figure 10 10. .

FigureFigureFigure 10. 10 10.Characteristic .Characteristic Characteristic curve curve curve of of of the the the FG FG FG pump. pump. pump.

MassMassMass flowrate flowrate flowrate over over over time time time was was was determined determin determineded using using using HYSYS HYSYS HYSYS dynamic dynamic dynamic simulation simulation simulation forfor for the the the initial initial initial start start start ofofof the thetheFG FGFG pump pumppump using usingusing the thethe characteristic characteristiccharacteristic curve curvecurve of ofof this thisthis pump. pump.pump. Figure FigureFigure 11 111 1shows showshowss how howhow much muchmuch LNG LNGLNG is isis sprayedsprayedsprayed at at at the the the in-line in in-line-line mixer mixer mixer for for for adjusting adjusting adjusting the the the NG NG NG temperature. temperature. temperature. The The The actual a actualctual mass mass mass flowrate flowrate flowrate requested requested requested for MNforfor MN controlMN control control ranges ranges ranges from from from 0 to 0 about0 to to about about 160 160 kg160/ h.kg/h. kg/h. During During During this this this cooling, cooling, cooling, the the samplingthe sampling sampling time time time applied applied applied is 0.2is is 0.2 s.0.2 Thes.s. The The transfer transfer transfer function function function of the of of secondary the the secondary secondary disturbance disturbance disturbance can be can can inferred be be inferred inferred from Equation fromfrom E Equationquation (13) using (13) (13) the using using system the the identificationsystemsystem identification identification in Figure in in11 Figure .Figure 1 111. . 2020.11.11푠푠−−00.002333.002333 2020.11.11푠푠−−00.002333.002333 퐺퐷퐺퐷22((푠푠))==20.11s 0.002333 ==20.11s 0.002333 (13) GD2(s) = 푠22 + 1−.698푠 + 0.1202= (푠 + 1−.624)(푠 + 0.074) (13)(13) s2푠++1.6981.698s +푠 0.1202+ 0.1202 (s (+푠 1.624+ 1.624)(s)+(푠0.074+ 0.074) )

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FigureFigure 11. 11LNG. LNG mass mass ﬂowrate flowrate injected injected at at an an in-line in-line mixer. mixer.

3. Controller Design 3. ControllerCascade control Design is the most popular and commonly available method used for the rejection of disturbancesCascade arising control in is the the secondary most popular loop and commonly improving available the accuracy method of the used system for the response rejection [28 ].of Indisturbance this study, as cascadearising in control the secondary structure withloop PIand controllers improving was the used accuracy to adjust of the MNsystem to the response Otto-cycle [28]. engineIn this requirements. study, a cascade Feed-forward control structure control waswith then PI controllers applied considering was used theto adjust flowrate the fluctuation MN to the of Otto the - pump.cycle The engine advantage requirements of using. feed-forwardFeed-forward control control is its was quicker then compensation applied con ofsidering error compared the flowrate with feedbackfluctuation control. of the Based pump. on The these advantage advantages, of using we applied feed-forward combined control cascade is its/feed-forward quicker compensation controllers. of error compared with feedback control. Based on these advantages, we applied combined 3.1. Cascade Controller cascade/feed-forward controllers. Tuning the cascade controllers involves two steps. First, the secondary controller must be tuned with3.1. theCascade secondary Controller control loop. Once the secondary control loop is finished, the transfer function of the primary control loop can be used for tuning the primary loop controller. Following this procedure, these PITuning controllers the cascade were adjustedcontrollers using involves the Ziegler–Nichols two steps. First, method the secondary (ZN), Tyreus–Luyben controller must method be (TL),tuned and with rule the of secondary thumb (ROT) control used loop. in industry. Once the secondary control loop is finished, the transfer functionUsing of Equation the primary (14), control a secondary loop can controller be used in for PI formtuning is the applied. primary loop controller. Following this procedure, these PI controllers were adjusted using the Ziegler–Nichols method (ZN), Tyreus– Luyben method (TL), and rule of thumb (ROT) used in industry.1 1 GC2(s) = Kc(1 + ) (14) τi s Using Equation (14), a secondary controller in PI form is applied. where Kc is the proportional gain and τi is integral time. 1 1 퐺퐶2(푠) = 퐾푐(1 + ) (14) The ZN tuning method and the TL tuning method of closed휏푖 푠 loops in Table3 were used to obtain the controller parameters for critical gain kcu and critical period Pu. where 퐾푐 is the proportional gain and 휏푖 is integral time. The ZN tuning method and the TL tuning method of closed loops in Table 3 were used to obtain Table 3. Summary of controller tuning parameters. the controller parameters for critical gain kcu and critical period Pu.

Tuning Method Proportional Gain, Kc Integral Time, τi Table 3. Summary of controller tuning parameters. Ziegler–Nichols 0.45 kcu Pu/1.2

TuningTyreus–Luyben method Proportionalkcu/ 3.2gain, 푲풄 Integral2.2Pu time, 흉풊 Ziegler–Nichols 0.45 kcu Pu/1.2 The parameterTyreus values–Luyben for the PI controllerskcu/ in3.2 the secondary loop are2 summarized.2Pu in Table4.

The parameterTable values 4. Summary for the PI of controller parameters values in the for secondary secondary loop loop are controller. summarized in Table 4.

TableTuning 4. Summary Method of parameter Proportional values Gain, forK secondaryc Integral loop Time, controller.τi Ziegler–Nichols 8.1 0.067 Tuning method Proportional gain, 푲풄 Integral time, 흉풊 Tyreus–Luyben 5.625 0.176 Ziegler–Nichols 8.1 0.067 Rule of Thumb 0.65 0.25 Tyreus–Luyben 5.625 0.176 Rule of Thumb 0.65 0.25 Equation (14) applies equally to the main controller. The tuning method used in this paper was the sameEquation procedure (14) asapplies applied equally to the to secondary the main controller. controller. A The summary tuning ofmethod parameter used values in this of paper primary was controllersthe same procedure is provided as in applied Table5 .to the secondary controller. A summary of parameter values of primary controllers is provided in Table 5.

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J. Mar. Sci. Eng. 2020, 8, 307 11 of 16 Table 5. Summary of parameter values for primary loop controller.

Tuning method Proportional gain, 푲풄 Integral time, 흉풊 ZieglerTable–Nichols 5. Summary of parameter− values72 for primary loop controller.−0.267 Tyreus–Luyben −50 −0.704 Tuning Method Proportional Gain, Kc Integral Time, τ Rule of Thumb −10 −10i Ziegler–Nichols 72 0.267 − − Tyreus–Luyben 50 0.704 3.2. Feed-forward Controller − − Rule of Thumb 10 10 − − Equations (15) and (16) were derived using Figure 12 to design a feed-forward controller. 3.2. Feed-forward Controller 푦(푠) = 퐺퐷(푠)푙(푠) + 퐺푃(푠)푢(푠) = 퐺퐷(푠)푙(푠) + 퐺푃(푠)[푢 (푠) + 푢 (푠)] Equations (15) and (16) were derived using Figure 12 to design a feed-forward푓 푐 controller. (15) 퐺퐷(푠) + 퐺푃(푠)퐺퐶퐹(푠)퐺푀퐹(푠) 퐺푃h (푠)퐺퐶(푠) i y푦((s푠))==GD(s)l(s) + GP(s)u(s) = GD(s푙)(l푠()s)++ GP(s) u f (s) + uc(s) 푟(푠) (15)(16) 1 + 퐺푃(푠)퐺퐶(푠)퐺푀(푠) 1 + 퐺푃(푠)퐺퐶(푠)퐺푀(푠) GD(s) + GP(s)GCF(s)GMF(s) GP(s)GC(s) y(s) = l(s) + r(s) (16) Considering the process1 + GP variable(s)GC (doess)GM not(s) change, 푦(s)1 + isGP equivalent(s)GC(s) GMto 0.( sr(s)) can be consideredConsidering zero because the process there variable is no set does point not change. change, Basedy(s) is on equivalent r(s) and 푦 to(s) 0. beingr(s) can equivalent be considered to zerozero, because Equation theres (17 is) no and set (1 point8) can change. be derived Based from on r(s) Equationand y(s) (1being6). equivalent to zero, Equations (17) and (18) can be derived from Equation (16). 퐺퐷(푠) + 퐺푃(푠)퐺퐶퐹(푠)퐺푀퐹(푠) = 0 (17) GD(s) + GP(s)GCF(s)GMF(s) = 0 (17) 퐺퐷(푠) 퐺퐶퐹(푠) = − (18) 퐺푃GD(푠()s퐺푀퐹) (푠) GCF(s) = (18) If the disturbance measurement has no dynamics,−GP(s)GMF Equation(s) (17) can be obtained as: If the disturbance measurement has no dynamics, Equation (17) can be obtained as: 퐺퐷(푠) 퐺퐶퐹(푠) =GD− (s) (19) GCF(s) = 퐺푃(푠) (19) − GP(s)

Figure 12. Block diagram of feed-forward control. Figure 12. Block diagram of feed-forward control.

FigureFigure 12 1 2can can be be brieﬂy briefly displayed displayed as as shown shown in in Figure Figure3. 3 From. From Equation Equation (19), (19), a feed-forwarda feed-forward controllercontroller is is derived derived as: as:

2 (20.11(20.11s 푠 0.00233− 0.00233) s )(+푠213.33+ 13s.33+ 0.7542푠 + 0.7542) GCF퐺퐶퐹(s()푠)== − − (20)(20) − (9.6(9s.6+푠 0.7955+ 0.7955)(s)2(+푠21.698+ 1.698s +푠0.1202+ 0.1202) )

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4. Simulation Results A total of four types of controllers, a single PI controller, a PI controller with feed-forward (FF), cascade controllers, and combined cascade/feed-forward controllers, were reviewed with a step response. We then checked the efficiency of disturbance rejection with these controllers. The performance measurement was based on the integral of the absolute value of the error (IAE), integral of the time weight absolute value of the error (ITAE), overshoot (OS), and settling time (ST). In this studyJ. Mar., Sci. simulation Eng. 2020, 8 time, 307 was 10 s for the case without disturbance and 100 s for the case with12 of a 16 disturbance. IAE and ITAE are defined in Equations (21) and (22), respectively. time was 10 s for the case without disturbance and∞ 100 s for the case with a disturbance. IAE and ITAE IAE = ∫ |푒(푡)| 푑푡 (21) are deﬁned in Equations (21) and (22), respectively.0

Z ∞ ∞ ITAEIAE == ∫ 푡 |e푒((t푡)) dt| 푑푡 (2(21)2) 00 Z = ∞ ( ) 4.1. Comparison between a Single PI ControllerITAE, a Single PIt eControllert dt with Feed-Forward, and Cascade (22) 0 Controllers 4.1. Comparison between a Single PI Controller, a Single PI Controller with Feed-Forward, and Cascade Controllers We first examined reference tracking using a step signal. The tracking results without the disturbanceWe first shou examinedld be almost reference same trackingbetween a using single a PI step controller signal. and The cascade tracking controller results withouts tuned by the ROTdisturbance. However, should to clearly be almost differentiate same between the a performance single PI controller of the and controller cascade against controllers disturbance, tuned by ROT. the performanceHowever, to of clearly the single differentiate controller the without performance disturbance of the controller should be against better disturbance, than cascade the controllers performance as shownof the in single Figure controller 13. We withoutdid not d disturbanceirectly compare should the besingle better PI than controller cascade with controllers feed-forward as shown and cascadein Figure controllers 13. We did, but not the directly findings compare show how the effective single PI the controllerse two controllers with feed-forward are in eliminat and cascadeing a disturbance.controllers, but the findings show how effective these two controllers are in eliminating a disturbance.

Figure 13.13. ReferenceReference trackingtracking results results without without a disturbancea disturbance for for a single a single controller controller and cascadeand cascade controllers. controllers. Figure 14 shows how the disturbance rejection was eliminated efficiently by a single controller, a single controller with feed-forward, and cascade controllers. The single PI controller showed good performanceFigure 14in shows the absence how the of disturbance a disturbance, rejection but the was settling eliminated time, overshoot, efficiently and by referencea single controller, tracking in athe single presence controller of a disturbancewith feed-forward, were poor. and cascade controllers. The single PI controller showed good performanceTable6 providesin the absence specific of a figures disturbance, on how but e fftheectively settling these time, controllers overshoot, respond and reference to disturbances. tracking inThe thecascade presence control of a disturbance system and were PI controlpoor. system with feed-forward perform better in rejecting a disturbance than the singe control system.

Table 6. Performance results of a single PI controller, a single PI controller with feed-forward, and cascade controllers.

Without Disturbance With Disturbance Classiﬁcation PI Feed-Forward Cascade PI Feed-Forward Cascade IAE 0.5703 0.5703 0.8157 10.08 1.02 2.31 ITAE 0.3668 0.3668 1.3570 137.80 27.32 55.60 OS 1.005 1.005 1.100 1.231 1.005 1.095 ST (sec) 1.9 1.9 6.0 45.0 1.9 8.6 J.J. Mar. Mar. Sci. Sci. Eng. Eng. 20202020, 8,,8 x, 307FOR PEER REVIEW 1313 of of 16 16

Figure 14. 14. ReferenceReference tracking tracking results results with with a disturbance a disturbance for a singlefor a controllersingle controller and cascade and controllers. cascade controllers. 4.2. Comparison between a Single PI Controller with Feed-Forward, Cascade Controllers, and Combined CascadeTable/Feed-Forward 6 provides Controllersspecific figures on how effectively these controllers respond to disturbances. The cascadeWe directly control compared system theand performance PI control system of a PI with controller feed-forward with feed-forward, perform better cascade in rejecting controllers, a disturbanceand combined than cascade the singe/feed control forward system. controllers. The PI controller with feed-forward performed the same as in Section 4.1. Cascade controllers and combined cascade/feed-forward controllers were tuned by ROT,Table ZN, 6. Performance and TL. A feed-forwardresults of a single controller PI controller, for combined a single PI cascade controller/feed-forward with feed-forward, controllers and was usedcascade with the controllers same controller. as a PI controller with feed-forward. In the case without a disturbance, cascade controllers and combinedWithout disturbance cascade/feed-forward controllersWith performed disturbance the same because Classification the feed-forward controllerPI doesFeed not-forward work without Cascade a disturbance PI in theFeed system.-forward Table 7 Cshowsascade the performanceIAE of each0 controller.5703 without0.5703 a disturbance.0.8157 10.08 1.02 2.31 ITAE 0.3668 0.3668 1.3570 137.80 27.32 55.60 TableOS 7. Performance1.005 results of1 a.005 single proportional–integral1.100 1.231 (PI) controller1.005 with feed-forward,1.095 ScascadeT (sec) controllers,1.9 and a combined1.9 cascade /feed forward6.0 controller45.0 without a disturbance.1.9 8.6

4.2. Comparison between a Single PI Controller with FeedWithout-Forward, Disturbance Cascade Controllers, and Combined Classification Cascade Cascade Cascade Cascade/Feed-Forward Controllers Feed-Forward (ROT) (ZN) (TL) We directly compared the performance of a PI controller with feed-forward, cascade controllers, IAE 0.5703 0.8157 0.0908 0.1448 and combined cascade/feedITAE forward controllers. 0.3668 The PI 1.3570 controller 0.0186 with feed 0.0623-forward performed the same as in section 4.1. CascadeOS controllers 1.005 and combined 1.100 cascade/feed 1.134-forward 1.100 controllers were tuned by ROT, ZN, and TLST. (sec) A feed-forward 1.90 controller for 6.00 combined 0.65 cascade/feed 1.19 -forward controllers was used with the same controller as a PI controller with feed-forward. In the case without a disturbance,Figure cascade15 depicts controllers the performance and combined when cascade a disturbance/feed-forward was input controller to eachs controller. performed Combined the same bcascadeecause /thefeed-forward feed-forward controllers controller showed does relatively not work better without performance a disturbance when incascade the system. controllers Table were 7 showsnot finely the performance tuned. In the of case each of thecontroller combined without cascade a disturbance./feed-forward controllers tuned by ROT, IAE and ITAE increased compared to the without disturbance case, but the settling time was faster than the case without a disturbance. Unlike the combined cascade/feed-forward controllers, the cascade controllers have a longer settling time. Well-tuned controllers, such as the ZN method and TL method, do not perform much differently between the cascade controller and the proposed method, but the combined cascade/FF controllers perform slightly better in IAE and ITAE with a rapid settling time when a disturbance was applied. A PI controller with feed-forward showed good overall performance but performed poorly compared with the combined cascade/feed-forward controllers in settling time. For the combined cascade/feed-forward controller, settling time decreased from 6 to 5.6 s with a disturbance, but a PI controller with feed-forward remained at 1.9 s regardless of the disturbance. Combined cascade/feed-forward

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Table 7. Performance results of a single proportional–integral (PI) controller with feed-forward, cascade controllers, and a combined cascade/feed forward controller without a disturbance.

Without disturbance Classification Cascade Cascade Cascade Feed-forward (ROT) (ZN) (TL) IAE 0.5703 0.8157 0.0908 0.1448 ITAE 0.3668 1.3570 0.0186 0.0623 OS 1.005 1.100 1.134 1.100 ST (sec) 1.90 6.00 0.65 1.19

Figure 15 depicts the performance when a disturbance was input to each controller. Combined cascade/feed-forward controllers showed relatively better performance when cascade controllers wereJ. Mar. not Sci. Eng.finely2020 tuned., 8, 307 In the case of the combined cascade/feed-forward controllers tuned by14 ROT of 16, IAE and ITAE increased compared to the without disturbance case, but the settling time was faster thancontrollers the case using without the TL a method disturbance. showed Unlike a fairly the fast combined settling time cascade/feed of 0.65 s- regardlessforward controllers, of disturbance. the cascadeTable8 shows controllers the performance have a longer of eachsettling controller time. with a disturbance.

Figure 15. Reference tracking results with a disturbance for a single controller with feed-forward (FF), Figure 15. Reference tracking results with a disturbance for a single controller with feed-forward (FF), cascade controllers, and combined cascade/FF controllers. cascade controllers, and combined cascade/FF controllers. Table 8. Performance results of a single PI controller with feed-forward, cascade controllers, and a Wellcombined-tuned cascade controllers/feed forward, such as controller the ZN inmethod case of and with T disturbance.L method, do not perform much differently between the cascade controller and the proposed method, but the combined cascade/FF controllers With Disturbance perform slightly better in IAE and ITAE with a rapid settling time when a disturbance was applied. Classification Cascade Cascade Cascade Combined Combined Combined A PI controllerFeed-Forward with feed-forward showed good overall performance but performed poorly (ROT) (ZN) (TL) (ROT) (ZN) (TL) compared with the combined cascade/feed-forward controllers in settling time. For the combined cascade/feedIAE-forward 1.019 controller, settling 2.31 time 0.0946 decreased 0.1604 from 6 to 5.6 1.789 s with a 0.0943disturbance, 0.1575 but a PI ITAE 27.32 55.60 0.2041 0.7775 52.16 0.2032 0.762 controllerOS with feed-forwa 1.005rd remained 1.095 at 1.9 s 1.133 regardless 1.092 of the disturbance. 1.100 Combined 1.134 cascade/feed 1.100 - forwardST (sec) controllers using 1.90 the TL method 8.60 show 0.66ed a fairly 1.27 fast settling 5.60 time of 0.650.65 s regardless 1.20 of disturbance. Table 8 shows the performance of each controller with a disturbance. 5. Discussion Table 8. Performance results of a single PI controller with feed-forward, cascade controllers, and a combinedAs the objective cascade/feed of this forward study, controller we proposed in case a methaneof with disturbance. number adjustment system and combined cascade/feed-forward controllers to meet the methane number required by engine manufacturers and With disturbance to ensure stable operation and robust performance of the methane number system. Regarding the Classification Cascade Cascade Cascade Combined Combined Combined Feed-forward control method of the methane number(ROT) system,(ZN) we obtained(TL) better(ROT) performance (ZN) than the(TL) existing methodsIAE by applying the1.019 tuning parameters2.31 used0.0946 in the0 industry.1604 by1 combining.789 two0.0943 di fferent0 controllers.1575 ratherI thanTAE focusing on27.32 tuning the5 controllers.5.60 0.2041 0.7775 52.16 0.2032 0.762 OS 1.005 1.095 1.133 1.092 1.100 1.134 1.100 (1) InST terms(sec) of performance,1.90 if the8.6 methane0 0 number.66 is1.27 lower than5.6 the0 engine0 requirements,.65 1.2 LNG0 is supplied to the in-line mixer to condense C2+ which lowers the MN. This is effective at eliminating hydrocarbon, which lowers the methane number of the NG. When applying the MN system, the Otto-cycle engine is advantageous from the OPEX of view as it prevents the part being damaged by the knocking phenomenon [29]. The necessary information about the amount of LNG required in the MN system is obtained from the HYSYS dynamic simulation. Approximately 160 kg/h of the LNG is required on a simulation basis at the speed of 19 knots if the boil-off rate is 0.15% for LNG carriers (174,000 m3); however, it is a small amount considering the FG pump capacity of actual LNGC. This issue could be solved by controlling an appropriate amount of LNG to be supplied through a MN control system. In the normal case, stable control is possible even with a general controller, but when a large amount of LNG is suddenly supplied to the MN system due to a failure to control the discharge amount of the FG pump, a robust control system is needed. J. Mar. Sci. Eng. 2020, 8, 307 15 of 16

(2) For ensuring an MN adjustment system’s stable operation and robust control, combined cascade/feed-forward controllers were applied considering a disturbance occurrence. This proposed method can ensure that the IAE and ITAE values are smaller than the values of the other controllers examined in this study when a disturbance occurs, so the error could reduce, and the settling time is faster or the same. This proposed method is more eﬀective for controller parameters used in industry in general than those tuned using the Ziegler–Nichols method and the Tyreus–Luyben method.

In future work, we will examine not only the contents in this study but also many ﬁelds of industry and compare performance through simulation and actual testing.

6. Patents The patent for the mechanism of MN adjustment was registered at the Korean Intellectual Property Oﬃce on 20 November, 2018. Patent applicant is Daewoo Shipbuilding and Marine Engineering and patent developer is SoonKyu Hwang. (Patent register number: 1019220300000, DOI: 10.8080/1020170144011)

Author Contributions: Conceptualization, S.H.; methodology, S.H.; software, S.K. Hwang; writing—original draft preparation, S.H.; writing—review and editing, S.H. and B.J.; supervision, S.H. and B.J. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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