A Multilevel Inverter Bridge Control Structure With Energy Storage Using Model Predictive Control for Flat Systems

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Hindawi Publishing Corporation Journal of Engineering Volume 2013, Article ID 750190, 15 pages http://dx.doi.org/10.1155/2013/750190 Research Article A Multilevel Inverter Bridge Control Structure with Energy Storage Using Model Predictive Control for Flat Systems Paolo Mercorelli Leuphana University of Lueneburg, Institute of Product and Process Innovation, Volgershall 1, 21339 Lueneburg, Germany Correspondence should be addressed to Paolo Mercorelli; mercorelli@uni.leuphana.de Received 5 Sept
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  Hindawi Publishing CorporationJournal o EngineeringVolume 󰀲󰀰󰀱󰀳, Article ID 󰀷󰀵󰀰󰀱󰀹󰀰, 󰀱󰀵 pageshttp://dx.doi.org/󰀱󰀰.󰀱󰀱󰀵󰀵/󰀲󰀰󰀱󰀳/󰀷󰀵󰀰󰀱󰀹󰀰 Research Article  A Multilevel Inverter Bridge Control Structure with Energy Storage Using Model Predictive Control for Flat Systems Paolo Mercorelli Leuphana University of Lueneburg, Institute of Product and Process Innovation, Volgershall 󰀱, 󰀲󰀱󰀳󰀳󰀹 Lueneburg, Germany  Correspondence should be addressed to Paolo Mercorelli; mercorelli@uni.leuphana.deReceived 󰀵 September 󰀲󰀰󰀱󰀲; Accepted 󰀳󰀰 December 󰀲󰀰󰀱󰀲Academic Editor: Claudio MazzottiCopyright © 󰀲󰀰󰀱󰀳 Paolo Mercorelli. Tis is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the srcinal work is properly cited.Te paper presents a novel technique to control the current o an electromagnetic linear actuator ed by a multilevel IGB voltageinverterwithdynamicenergystorage.Tetechniqueusesa“cascademodelpredictivecontrol(MPC),”whichconsistsotwoMPCs.A predictive control o the trajectory position predicts the optimal current, which is considered to be the desired current or thesecond MPC controller in which a hysteresis control technique is also integrated. Energy is stored in a capacitor using energy recovery. Te current MPC can handle a capacitor voltage higher than the source voltage to guarantee high dynamic current anddisturbance compensation. Te main contribution o this paper is the design o an optimal control structure that guarantees acapacitor recharge. In this context, the approach is quite new and can represent a general emerging approach allowing to reducethecomplexityothenewgenerationoinvertersand,inthemeantime,toguaranteeprecisionandacceptableswitchingrequency.Te proposed technique shows very promising results through simulations with real actuator data in an innovative transportationtechnology. 1. Introduction and Motivation Te perormance o a multilevel inverter is better than thato a classical inverter. Te total harmonic distortion o aclassical inverter is very high; that is, the total harmonicdistortion or a multilevel inverter is low. Tis topic hasbecome the ocus o a signi󿬁cant amount o research. Onestudy has simulated and implemented a multilevel inverter-ed induction motor drive [󰀱]. Te output harmonic contentis reduced by using a multilevel inverter. In a symmetricalcircuit,thevoltageandpowerincreaseasthenumberolevelsin the inverter increases. Te switching angle or the pulse isselectedtoreducetheharmonicdistortion.Tisdrivesystemhasseveraladvantages,includingreducedtotalharmonicdis-tortion and higher torque. A normal neutral point potentialstabilization technique using the output current polarity hasbeen proposed [󰀲]. Te neutral point potential balancingalgorithm or three-level neutral point clamped invertersusing an analytically injected zero-sequence voltage has beendeveloped [󰀳]. Modulation schemes to eliminate commonmode voltage in multilevel inverter topology have beensuggested[󰀴].Ageneralizedmultilevelinvertertopologywithsel-voltagebalancinghasalsobeensuggested[󰀵].Asurveyo topologies, control, and applications o multilevel invertershas been published [󰀶]. A digital modulation techniqueor dual three-phase alternating current (AC) machines hasbeen presented [󰀷]. A space vector pulse-width modulation(PWM)techniqueoradualthree-phaseACmachineanditsdigital signal processor (DSP) implementation has been pre-sented[󰀸].Practicalmediumvoltageconvertertopologiesorhigh power applications have been described previously [󰀹–󰀱󰀱]. Industrial topologies have been presented [󰀱󰀲]. Different pulse-width modulation techniques or symmetrical cascadeinverters with high and undamental switching requency havebeenshown,orinstance,in[󰀱󰀳,󰀱󰀴].Animprovementin terms o efficiency o the converter is presented in [󰀱󰀵] wherethe authors use different DC sources to reduce the switchinglosses. More recently in [󰀱󰀶], the authors proposed a novelH-bridge multilevel pulse modulation converter topology inwhich the structure is based on a series connection o high- voltagediode-clampedinverterandlow-voltageconventionalinverter.Tepresentworkimplementsacontrolledmultilevel  󰀲 Journal o Engineeringinverter eeding an electromagnetic actuator. In particular,two MPCs in cascade structure are presented to control 󿬁ve-level inverter electromagnetic actuators which are becom-ing increasingly important in many industrial applications.Tanks to recent progress in permanent-magnet technology, very compact and high-power electromagnetic actuators arenowavailable.Particularlyinautomotivesystems,theseactu-ators have ofen replaced conventional mechanical compo-nentsduetotheirhighefficiency,excellentdynamicbehavior,and control 󿬂exibility; thus, mechatronics is one o the mostnotableinnovative󿬁eldsintheautomobileindustry.Arecentdesign o such an actuator (e.g., [󰀱󰀷]) considers optimizingwithrespecttodimensionsandorces.Nevertheless,practicaltests show that this actuator structure is not always effectiveor a large variety o applications because a complex controlstructure is needed to control such a valve [󰀱󰀸]. Recently,or instance, a new type o electromagnetic valve drivesystem has been proposed and described [󰀱󰀹]. Tis paperpresents the control design or a novel permanent-magnetlinear valve actuator or use in a variable engine control toallow short-stroke and high-dynamic motions. In a linearactuator, the electromagnetic orce is totally independento the constrained motion. Speci󿬁cally, the electromagneticorceisparalleltothemagneticaxis,andthusitisorthogonalto the constrained motion. Tese perormance character-istics make this type o actuator an excellent candidate inapplications requiring both high precision and high-loadcapacity. In order to obtain an actuator structure that couldbe easily controlled, various linear designs with differentpermanentmagnetactuatortopologiesusingNdFeBmagnetswereconsidered.Inparticular,theobjectiveothispaperistodesign a controller structure consisting o (i) a 󿬂atness-based eedorward control,(ii) a multilevel inverter con󿬁guration,(iii) a cascade MPC structure based on optimized ener-getic unctions to control the proposed multilevelinverter with storage energy.An important aspect o this approach is the use o geometricsystem properties, such as the differential 󿬂atness neededto track the desired trajectories. In this context, recently published research results have been considered (e.g., [󰀲󰀰])in which the author proposed an interesting method tointegrateMPCandaeedorward󿬂atnesscontrol.Tesecondpart o the paper shows the structure o the cascade MPCde󿬁ned above. For trajectory-based motion cycles, there isusually a need to control the actuator current separately. Tereerencevalueortheactuatorcurrentisnormallygeneratedby the speed or position controller in an outer control loopbased on the desired speed or position pro󿬁les. Te currentcontrol is used to provide the orce or torque required or thedesired motion quickly and precisely. Generally, three maintechniques are employed or current control o a voltage-source inverter (VSI):(i) closed loop control (e.g., PID control) using pulse-width modulated terminal voltages [󰀲󰀱],(ii) hysteresis control techniques [󰀲󰀲, 󰀲󰀳], (iii) predictive current control [󰀲󰀴–󰀲󰀶]. Te PWM technique is currently the most popular methodor an inverter current control. Te main advantage o PWM techniques is that the inverter switches operate at a󿬁xed requency, and hardware- or sofware-based standardmodulators are available as industrial products (e.g., on-board microcontrollers). A staggered space vector modula-tion technique applicable to three-phase cascaded voltage-source inverter topologies has also been demonstrated witha single-phase cascaded voltage-source inverter that uses aseries connection o insulated gate bipolar transistor (IGB)H-bridge modules with isolated DC buses [󰀲󰀷]. Among various modulation techniques or a multilevel inverter, thespace vector pulse width modulation (SVPWM) is widely used. However, implementing the SVPWM or a multilevelinverter is complicated because it is difficult to determinethe location o the reerence vector, calculate on times, anddetermine and select switching states. A previous paperhas proposed a general SVPWM algorithm or multilevelinvertersbasedonstandardtwo-levelSVPWM.However,thesystem response is affected by the stability requirements o the eedback loop, which also depend on load parameters;moreover, appreciable phase lag may arise even in the steady state. Recently, many studies have ocused on solving theseproblems (e.g., [󰀲󰀸, 󰀲󰀹]) o multilevel inverter modules with independent controlo the phase angle and magnitudeo theoutputvoltage[󰀲󰀹].Controlandnewpowerbridgestructureshave been studied. Very recent works have presented a novelbridge structure [󰀳󰀰, 󰀳󰀱]. In both structures, capacitors are used but not recharged. In particular, an MPC strategy isproposed or a three-phase power bridge [󰀳󰀰]. Hysteresiscurrent control has a ast response and a good accuracy.It can be implemented with a simple hardware structure,and, in many cases, it does not require any knowledgeo load parameters. However, it can sometimes cause very high switching requencies or, i the maximum switchingrequency is limited, the current waveorm may vary widely and the current peaks may appreciably exceed the hystere-sis band depending on the operation conditions and loadparameters. Conventional predictive current control uses asimplegradientmodeltopredictloadcurrentinvectorspaceand determine the proper switching voltage vector basedon the one-step prediction [󰀲󰀴–󰀲󰀶]. However, no eedback  loop is applied to compensate or model uncertainties. oovercome the disadvantages o the mentioned methods, thisstudy develops a novel approach that combines hysteresiscontrol with a model predictive control (MPC) strategy. Teproposed control system integrates 󿬂atness and two cascadeMPCs. Te 󿬁rst MPC generates an optimal desired currentby minimizing position error. Te second MPC considersthis optimal desired current to be the reerence signal to󿬁nd an optimal switching law in combination with thehysteresis control. A special energy storage and chargingcircuit was designed to provide multilevel voltages or aneffective current control. By applying the proper voltagelevel, which was determined by the MPC strategy, to theactuator, dynamic current changes and small current ripples  Journal o Engineering 󰀳 CoilValveLower springIron polePermanent magnetUpper spring F󰁩󰁧󰁵󰁲󰁥 󰀱: Cross-section o the perpendicular linear actuator. are possible in spite o relatively low switching requencies.A recent work [󰀳󰀲] proposes “ast” algorithms based oncomputing the ormulated problems in parallel. In act, theoptimization technique uses subsets o the state subspaceoffline and then optimizes them in parallel. In this paper, acascade structure o MPCs is utilized to control a multilevelinverter.wodifferentoptimizationtechniquesarepresentedas well. Te main contribution o the paper is the optimalcontrol structure, which also guarantees that the capacitorrecharges. In this context, the approach is quite new. Tepaper is organized in the ollowing way.Section 󰀲 describes the model. In Section 󰀳, the 󿬂atness property o the system is shown. In Section 󰀴, the generalMPC goal is de󿬁ned and the main idea o using a cascadepositional MPC ollowed by a current MPC is explained. InSection 󰀵, a positional MPC  around   the desired trajectory isproposed. Section 󰀶 is devoted to analyzing and optimizingthe current MPC. Te simulation results and some conclud-ing remarks end the paper. 2. Description of the Physical Systems Te electromagnetic actuator is depicted in Figure 󰀱. Testructure o this actuator is a moving coil; thus, the coilsare mounted on the upper part o the stem o the valve.Te moving valve was connected to the power system toeed the coil with two normal cables with 󿬁x contacts. Tisarrangement is possible because o the short stroke to becovered (󰀸mm). Te valve can be modeled mathematically in the ollowing way: 󽠵 coil  (􍠵)􍠵 = −󝠵 coil  coil 󽠵 coil  (􍠵) +  in  (􍠵) −   󽠵 coil  (􍠵),(􍠵) coil ,  (󰀱) (􍠵)􍠵 = (􍠵),  (󰀲) (􍠵)􍠵 =  󽠵 󽠵 coil  (􍠵),(􍠵) 󽠵 coil  (􍠵)+ − 􍠵 (􍠵) −  󝠵 (􍠵) +  0 (􍠵) , (󰀳)where  󽠵 󽠵 coil  (􍠵),(􍠵) = Φ ℎ 󽠵 coil  (􍠵),(􍠵) coil  coil ,  󽠵 coil  (􍠵),(􍠵) =  󽠵 󽠵 coil  (􍠵),(􍠵)(􍠵).  (󰀴)It is important to note that   󽠵 (󽠵 coil (􍠵),(􍠵)) > 0  or all  󽠵 coil (􍠵) and or all  (􍠵) .  󝠵 coil  and   coil  are the resistance and theinductance o the coil windings;   in (􍠵)  is the input voltage;   (􍠵)  is the induced back voltage;  Φ ℎ  is the magnetic 󿬂uxpenetrating the coil;  󽠵 coil (􍠵)  is the coil current;   coil  is the coillength.  (􍠵) ,  (􍠵) , and    are the position, velocity, and masso the actuator, respectively, while   􍠵 (􍠵) ,   󝠵 (􍠵) , and   0 (􍠵) represent the viscose riction, the total spring orce, and thedisturbing orce acting on the valve. Equation (󰀱) representstheelectricalsystemotheactuator.Both(󰀲)and(󰀳)describe the mechanical behavior o the actuator, and (󰀲) and (󰀴) also represent the magnetic system. In particular, the ollowingexpression   (􍠵) =  󽠵 󽠵 coil  (􍠵),(􍠵)󽠵 coil  (􍠵)  (󰀵)describes the Lorentz orce generated by the actuator. Essen-tially, the magnetic 󿬂ux, generated by the permanent mag-nets, has two components in the air gap: (󰀱) the main 󿬂ux Φ ℎ (󽠵 coil (􍠵)) , which does not depend on the displacemento the mover and is responsible or the Lorentz orceand the induced back voltage, and (󰀲) the leakage 󿬂ux Φ  (󽠵 coil (􍠵),(􍠵)) , which disperses around the coil and doesnotcontributetotheelectromagneticorceandinducedback  voltage: Φ ℎ 󽠵 coil  (􍠵) + Φ  󽠵 coil  (􍠵),(􍠵) = Φ PM  󽠵 coil  (􍠵).  (󰀶)However, due to the special actuator design, the leakage 󿬂uxis almost equal to zero. Tus, it is possible to conclude  󽠵 󽠵 coil  (􍠵),(􍠵) ≈  󽠵 󽠵 coil  (􍠵) = Φ PM  󽠵 coil  (􍠵) coil  coil .  (󰀷) 3. Differential Flatness of the System Roughlyspeaking,asystemisdifferentially󿬂atiitispossibleto 󿬁nd a set o outputs equal in number to the number o inputssuchthatallstatesandinputsareexpressedintermso those outputs and their derivatives. o be more precise, i thesystem has state variables  x   ∈  R  and inputs  u  ∈  R  , thenthe system is 󿬂at i the outputs  y   ∈  R  have the ollowingorm:  y   =  y  󰀨 x  , u , ̇ u ,..., u () 󰀩,  (󰀸) x   =  x  󰀨  y  , ̇  y  ,...,  y  () 󰀩;  u  =  u 󰀨  y  , ̇  y  ,...,  y  (+1) 󰀩.  (󰀹)Differentially 󿬂at systems are especially interesting insituations in which explicit trajectory tracking is required.Because the behavior o the 󿬂at system is given by the 󿬂atoutput, it is possible to plan trajectories in output space andthen map them to the appropriate inputs. Concerning the  󰀴 Journal o Engineering  − 󽠵 󽠵Δ PM 􍠵 󝠵 􍠵􍠵 PM F󰁩󰁧󰁵󰁲󰁥 󰀲: Permanent-magnet demagnetization curve. 󿬂at output, or dating neither the necessary and sufficientcondition nor a general method or the determination o the 󿬂at output has been provided. ypically, a 󿬂at output is  guessed,  and De󿬁nitions (󰀸) and (󰀹) are used to veriy that the chosen output is 󿬂at. Once the system is proven to bedifferentially 󿬂at, the basic approach o two degrees o ree-dom controller design consists o two steps: 󿬁rst, separatingthe nonlinear controller synthesis problem into designing aeasible eedorward controlled trajectory or the nominalmodel o the system and second regulating that trajectory using controllers, that guarantee robust perormance in thepresence o uncertainties and disturbances. o explain themeaning o 󿬂atness intuitively, it is adequate to consider asystem to be 󿬂at when the dynamic o at least one output is“visible”romthestateandtheinputothesystem;thus,thereisatleastoneoutputthatcanbeunctionallycontrolledbytheinputs as well by the states.Now the 󿬁rst step is to show that our model representedin (󰀱), (󰀲), and (󰀳) is 󿬂at. I the position    o the moving parto the actuator is chosen as “guessed output,” then (􍠵) = (􍠵) ⇒ (􍠵) = (􍠵) ̇(􍠵) = ̇(􍠵) ⇒ (􍠵) = ̇(􍠵),  (󰀱󰀰) 󽠵 coil  (􍠵) 󽠵 󽠵 coil  (􍠵) = 􀀨 􍠵 (􍠵) +  󝠵  (􍠵) + (􍠵)􍠵 􀀩, (󰀱󰀱)  in  (􍠵) =  coil 󽠵 coil  (􍠵)􍠵 + 󝠵 coil 󽠵 coil  (􍠵) +  󽠵 󽠵 coil  (􍠵)(􍠵). (󰀱󰀲)o veriy the 󿬂atness property it is necessary to look at(󰀱󰀳). As evident rom (󰀷),   󽠵 (󽠵 coil (􍠵))  is proportional to the󿬂ux coupled with the permanent magnets which is againproportional to the 󿬂ux density    PM . Te operating point ( PM , PM )  o the permanent magnets is mainly determinedby the magnet geometry and the demagnetization curve(Figure 󰀲). Te coil current only changes the 󿬁eld strengtharound the operating point  (Δ)  algebraically. An exactanalytical expression between  Δ  and  󽠵 coil (􍠵)  is very difficulttobederivedbecauseitalsodependsonthesaturationlevelo the iron parts. However, a numerical solution exists. In other Linear motorInverter bridgeEnergy storePower source U  s U  c D 1 C Z  1 V  2 V  3 V  1 V  5 V  4 RLu q + F󰁩󰁧󰁵󰁲󰁥 󰀳: Multilevel inverter bridge structure. words, there is always a (locally) unique solution or  󽠵 coil (􍠵) that depends on   󽠵 󽠵 coil (􍠵) . Tus, using (󰀱󰀳), the coil currentcan always be determined uniquely by the actuator positionand its derivatives. Considering additional system equations,it can be easily seen that the 󿬂atness conditions de󿬁ned in(󰀹) are satis󿬁ed. Relationships(󰀱󰀳) and(󰀱󰀲) de󿬁ne the inverse system. Based on the 󿬂atness o the system, the linearizingtrajectory o the model (󰀳) and (󰀲) is as ollows: 󽠵 􍠵 (􍠵) =  󽠵 󽠵 􍠵 (􍠵) 􀀨 􍠵  􍠵 (􍠵) +  󝠵   􍠵 (􍠵) +  􍠵 (􍠵)􍠵 􀀩,  (󰀱󰀳)where   􍠵 (􍠵)  is the desired trajectory and  󽠵 􍠵 (􍠵)  is the corre-sponding eed orward control current. As it was explainedbeore, the 󿬂ux does not depend on the position o thearmature because the leakage 󿬂ux is almost equal to zero.Tismeansthatthe󿬂uxisaunctionothecurrent.Function  󽠵 (󽠵 coil (􍠵))  is never equal to zero, at least or our conceivedstructure,becauseocontrollability.Teactuatorisconceivedanddesignedinawayinordertoguaranteethecontrollability at any point o its movement. For (󰀱), the inverse systemthat determines the desired eedorward control input   􍠵 (􍠵) is de󿬁ned as ollows:  􍠵 (􍠵) =  coil 󽠵 􍠵 (􍠵)􍠵 + 󝠵 coil 󽠵 􍠵 (􍠵)+  󽠵 󽠵 􍠵 (􍠵),(􍠵)  􍠵 (􍠵)(􍠵) .  (󰀱󰀴)Based on the eed orward control presented previously, thenext step is to build a eedback control law that, in thepresence o external disturbances and uncertainties in theparameters, takes the system around the desired trajectory. 4. General MPC Problem Formulation Figure 󰀳 shows the power electronic circuit eeding thepermanent magnet linear actuator. Te power supply is a
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