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DEGREE PROJECT IN MECHANICAL ENGINEERING,SECOND CYCLE, 30 CREDITSSTOCKHOLM, SWEDEN 2016Control Strategies forActive Suspension withPneumatic ActuatorsYUCHAO LIKTH ROYAL INSTITUTE OF TECHNOLOGYSCHOOL OF INDUSTRIAL ENGINEERING AND MANAGEMENT

Examensarbete MMK 2016:100 MDA 558Reglerstrategier för aktiv dämpning medpneumatiska aktuatorerYuchao LiGodkäntExaminatorHandledare2016-09-20Lei FengBjörn MöllerUppdragsgivareKontaktpersonSkogforskOlle GelinSammanfattningSkogsindustrin är en stor del av Sveriges ekonomi. Med hjälp av den såkallade kapa till längdmetoden, vilket betyder att träden först kapas till lämplig längd och sen forslas de till sidan av enväg med hjälp av "forwarders", går det det uppnåhög produktivitet och automatisering. Dock ärden ojämna terrängen ett problem för operatörernas hälsa vilket gör det viktigt att undersöka hurman kan förbättra arbetsförhålladena för dem genom att förbättra dämpningen i skogsmaskinerna.Detta examensarbete fokuserar påoperatörens säte och med hjälp av en prototyp av av stolen somär upphängd påpneumatiska aktuatorer, ett reglersystem har designats för att redusera devertikala och horizontella vibrationerna. Med hjälp av en PD kontroller som yttrelops positionskontrol strategier, tvåolika SMC kontroller och en MPC kontroller har jämnförts via simuleringsom innreloop strategi. Den bättre SMC strategin valdes, systemet implementerades via enmodellbaserad strategi och systemet testades utan last.När systemet utsattes för vertikal vibration med en amplitud på25 mm och en lateral amplitud på20 mm med varierad frekvens från 0.5 Hz till 1 Hz, kan ocilleringarna reduseras med över 75% ibåda riktningarna. Det nuvarande resultatet tros vara begränsat pågrund av asymetri i systemetsamt ostabilt luftflöde.Resultatet visar att föreslagen regler strategi är lovande för att redusera både laterala och vertikalavibrationer. Fördelen med modelbaserad utveckling är ocksåväluppskattad underframtagningsprocessen.

Master of Science Thesis 2016:100 MDA 558Control strategies for active suspensionwith pneumatic actuatorsYuchao LiApprovedExaminerSupervisor2016-09-20Lei FengBjörn MöllerCommissionerContact personSkogforskOlle GelinAbstractThe forest industry in Sweden plays an important role in its economy. Via the so-called cut-tolength approach, which means that trees are first cut to equal lengths by harvesters and then pickedup and transported to roadsides by forwarders, can high productivity and automation be achieved.Meanwhile, rough territory in forest has become a threat to operators’ health. Therefore, it is ofgreat interest to investigate possible improvement for suspensions of forest machineries.This work focuses on suspension of operator’s seat. Based on an undercarriage prototype withpneumatic actuators, a control system is designed to reduce both vertical and lateral vibration. WithPD controller as outer-loop position control approach, two different SMC controllers and one MPCunit have been compared via simulation as inner-loop approaches. Then the better SMC approachwas picked and the whole system was implemented via a model-based approach and the systemwas tested without load.When subjected to vertical vibration with an amplitude of 25 mm and lateral one with amplitudeof 20 mm with frequencies varying from 0.5 Hz to 1 Hz, reduction of oscillation can be more than75% in both directions. The current performance is believed to be limited because of asymmetryof the system and instability of air source.The results of tests indicate that proposed control approach is promising to reduce both vertical andlateral vibration. The advantages of model-based development approach is also highly appreciatedall along the development process.

AcknowledgementFirst of all, I would like to express my special thanks to my examiner, Lei Fengand supervisor, Björn Möller for their support and inputs during the process. Theircreativity and professionalism has made me learn so much.Second, I am grateful to Skogforsk, Olle Gelin and Fredrik Henriksen for the preciouschance to get involved in such an interesting project. All the support from Skogforskhas been an important assure for the success of this project.Besides, I really appreciate all the efforts Einola Kalle and Leinonen Matti took tohelp me out. Their practical experience has been really beneficial.Last but not the least, I would also like to thank Anqing Duan, Zhen Li and QingxiaoAn for all the inputs and help. It has been a great journey for me all because ofthose nice people.

NomenclatureNotationsSymbol(xsd s , ysd s ch,dDescriptionDesired seat coordinates measured in the seat frameReference length of cylinder i, i 1, . . . , 4Nominal length of cylinder i, i 1, . . . , 4Reference piston displacement of cylinder i from Mid-position, i 1, . . . , 4Reference force on cylinder i, i 1, . . . , 4Desired static force component on cylinder i, i 1, . . . , 4Desired dynamic force component on cylinder i, i 1, . . . , 4Moment arm of Fi,st , i 1, . . . , 4Total mass load on the chairAcceleration of gravityEquivalent mass load of cylinder i, i 1, . . . , 4Volume of chamber ch of cylinder i, i 1, . . . , 4, ch a,bArea of chamber ch of cylinder i, i 1, . . . , 4, ch a,bRod area of cylinder i, i 1, . . . , 4Piston displacement of cylinder i from Mid-position, i 1, . . . , 4Actual force from cylinder i, i 1, . . . , 4Absolute pressure in chamber ch of cylinder i, i 1, . . . , 4, ch a,bLocal atmosphere pressureSupply pressureControl signal to the valve connected to chamber ch of cylinder i,i 1, . . . , 4, ch a,bIdeal gas constantAbsolute gas temperature in the cylindersMass of air inside the chamber ch of cylinder i, i 1, . . . , 4, ch a,bArea of valve opening connected to the chamber ch of the cylinderi, i 1, . . . , 4, ch a,bMass flow of air through unit areaUpstream pressure of the valve connected to the chamber ch ofcylinder i, i 1, . . . , 4, ch a,bDownstream pressure of the valve connected to the chamber ch ofcylinder i, i 1, . . . , 4, ch a,b

γCi,ch,fCcrvfloor evi,a evivi,p eKi,rxf eyf �i,fk,jSi,fkki,fkpi,ch,rfi,ch,pbi,ch,pSpecific heat ratio for airDischarge coefficient of the valve connected to the chamber ch ofcylinder i, i 1, . . . , 4, ch a,bCritical air pressure ratioVelocity of the cabin floor relative to earthVelocity component along the direction of cylinder i on the joint ofchamber a relative to earth, i 1, . . . , 4Velocity of piston movement along the cylinder i, i 1, . . . , 4Compound speed at the tip of the rod of cylinder i relative to earth,i 1, . . . , 4Reference stiffness of cylinder i, i 1, . . . , 4Filtered lateral vibration measured in the earth frameFiltered vertical vibration measured in the earth frameComplex variable for Laplace transformationTransfer function in continuous form from force to position of theequivalent mass load exposed to cylinder i, i 1, . . . , 4Stroke of cylinder i, i 1, . . . , 4Actual stiffness of cylinder i, i 1, . . . , 42 1 state vector for the second order force and stiffness model ofcylinder i whose element is Fi and Ki , where i 1, . . . , 42 1 control vector for the second order force and stiffness modelof cylinder i whose element is ṁi,a and ṁi,b , where i 1, . . . , 42 1 system vector for the second order force and stiffness modelof cylinder i whose element is denoted as fi,fk,1 and fi,fk,2 , wherei 1, . . . , 42 2 input matrix for the second order force and stiffness modelof cylinder i whose element is denoted as bi,fk,11 , bi,fk,12 , bi,fk,21 andbi,fk,22 where i 1, . . . , 42 1 sliding surface for the second order force and stiffness modelof cylinder i whose element is denoted as si,fk,1 and si,fk,2 , wherei 1, . . . , 4Sign for signum functionSign for saturation functionBoundary of saturation function for element of sliding surfacefor second order force and stiffness model of cylinder i, wherei 1, . . . , 4 and j 1, 22 2 saturation matrix for the second order force and stiffness modelof cylinder i where i 1, . . . , 42 1 slope vector for the control signal of second order force andstiffness model of cylinder i whose element is denoted as ki,fk,1 andki,fk,2 , where i 1, . . . , 4Reference pressure in chamber ch of cylinder i, i 1, . . . , 4, ch a,bSystem function for the first order pressure model of chamber ch ofcylinder i where i 1, . . . , 4 and ch a,bInput function for the first order pressure model of chamber ch ofcylinder i where i 1, . . . , 4 and ch a,b10

si,ch,pki,ch,pεi,ch,pui,ch,mpcvi,outvi,max , vi,minLi,rangeGf,hSliding manifold for the first order pressure model of chamber ch ofcylinder i where i 1, . . . , 4 and ch a,bSliding slope for the first order pressure model of chamber ch ofcylinder i where i 1, . . . , 4 and ch a,bSaturation boundary for the first order pressure model of chamberch of cylinder i where i 1, . . . , 4 and ch a,bMPC control signal for the first order pressure model of chamberch of cylinder i where i 1, . . . , 4 and ch a,bOutput voltage signal from position sensor mounted on cylinder iwhere i 1, . . . , 4Maximum and minimum output voltage signal from position sensormounted on cylinder i where i 1, . . . , 4Measuring range of position sensor mounted on cylinder i wherei 1, . . . , 4Transfer function in continuous form for high-pass PDRMSCANBODASDescriptionRoyal Institute of TechnologySeat effective amplitude nal–integral–derivativeSliding mode controlModel predictive controlInertia measurement unitElectronic control oller area networkA development enviroment for Bosch controllers

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Contents1 Introduction11.1Background and Problem Description . . . . . . . . . . . . . . . . . .11.2Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .21.3Delimitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .31.4Method Description . . . . . . . . . . . . . . . . . . . . . . . . . . . .31.5Expected Outcome . . . . . . . . . . . . . . . . . . . . . . . . . . . .41.6Research Ethics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .42 Reference Frame72.1Researches on Seat Suspension . . . . . . . . . . . . . . . . . . . . . .72.2Studies on Pneumatic Systems . . . . . . . . . . . . . . . . . . . . . .82.3Related Work in Skogforsk . . . . . . . . . . . . . . . . . . . . . . . . 102.4Previous Theses in KTH . . . . . . . . . . . . . . . . . . . . . . . . . 113 Modelling and Control3.13.23.33.413Suspension Structure Analysis . . . . . . . . . . . . . . . . . . . . . . 133.1.1Geometric Analysis . . . . . . . . . . . . . . . . . . . . . . . . 143.1.2Force Calculation . . . . . . . . . . . . . . . . . . . . . . . . . 15Seat Undercarriage Modelling . . . . . . . . . . . . . . . . . . . . . . 163.2.1Pneumatic System Model . . . . . . . . . . . . . . . . . . . . 173.2.2Structure Dynamics Model . . . . . . . . . . . . . . . . . . . . 19Controllers Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.3.1Piston Position Controller . . . . . . . . . . . . . . . . . . . . 213.3.2Force and Stiffness Controller . . . . . . . . . . . . . . . . . . 24Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.4.1Comparison of Force and Stiffness Controllers . . . . . . . . . 323.4.2Simulation of Both Directions . . . . . . . . . . . . . . . . . . 35

4 Implementation374.1System Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374.2Hardware Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384.3Software Development and Data Analysis . . . . . . . . . . . . . . . . 414.3.1Model-based Development . . . . . . . . . . . . . . . . . . . . 414.3.2Digital Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . 434.3.3Data Logging and Analysis . . . . . . . . . . . . . . . . . . . . 445 Experiments5.15.25.3Force and Stiffness Traceability . . . . . . . . . . . . . . . . . . . . . 455.1.1Force Tracking under Vibration . . . . . . . . . . . . . . . . . 455.1.2Stiffness Tracking under Vibration6.2. . . . . . . . . . . . . . . 51Position Tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525.2.1Piston Position Tracking under Vertical Vibration . . . . . . . 525.2.2Piston Position Tracking under Lateral Vibration . . . . . . . 555.2.3Position Tracking under Vibrations in Both Directions . . . . 58Suspension Performance . . . . . . . . . . . . . . . . . . . . . . . . . 615.3.1Suspension Performance under Vertical Vibration . . . . . . . 615.3.2Suspension Performance under Lateral Vibration . . . . . . . 625.3.3Performance under Vibration in Both Directions . . . . . . . . 636 Conclusions and Recommendations6.14567Conclusions on Results . . . . . . . . . . . . . . . . . . . . . . . . . . 676.1.1Conclusion from Simulation . . . . . . . . . . . . . . . . . . . 676.1.2Conclusion from Methods . . . . . . . . . . . . . . . . . . . . 686.1.3Conclusion from Tests . . . . . . . . . . . . . . . . . . . . . . 68Obstacles and Future Work . . . . . . . . . . . . . . . . . . . . . . . 686.2.1Asymmetry of Seat Structure . . . . . . . . . . . . . . . . . . 686.2.2Instability of Air Source . . . . . . . . . . . . . . . . . . . . . 696.2.3Air Leakage in the Structure . . . . . . . . . . . . . . . . . . . 696.2.4On-line Tuning of Control Parameters . . . . . . . . . . . . . 706.2.5Suggestions on Future Work . . . . . . . . . . . . . . . . . . . 71Bibliography73

AppendicesA Connections of ECUs79A.1 Connections for vertical suspension system . . . . . . . . . . . . . . . 79A.2 Connections for lateral suspension system. . . . . . . . . . . . . . . 81

Chapter 1IntroductionThis chapter outlines the background and problem description of this thesis work,describes the purpose and the scope, and presents the method, the expected outcomes and the ethical concerns in this project.1.1Background and Problem DescriptionForest industry products play an important role in Sweden’s export business [1]. Areason for its leading performance is that felling operation here is conducted by cutto-length method, which means trees are first felled to proper lengths by a harvesterand then transported to roads by a forwarder, as shown in Fig. 1.1, for furthertransportation to sawmills [2, 3].Figure 1.1: ElephantKing Forwarder from PONSSE. The operator is seating in thecabine on the right. Image source: [4]Since forwarders must travel through uneven territory with heavy payloads rangingfrom 5 to 20 tons [5], operators are exposed to whole-body vibrations and work1

CHAPTER 1. INTRODUCTIONunder rather discomfort conditions. Researches have shown that occupational neckand shoulder disorders during repetitive operations have been threatening the healthof machine operators for the past several decades [6]. Although the existing seatundercarriage can limit the vibrations to a bearable extent, increasing the efficiencyby speeding up fowarders would violate the regulation AFS 2005:15 Vibrationer[7] given by the Swedish Work Environment Authority (Arbetsmiljöoverket) basedon the test cases according to ISO 2631-1 Mechanical vibration and shock – Evaluation of human exposure to whole-body vibration – Part 1: General requirements[8]. Therefore, it is in the interests of logging industry to develop more advancedseat suspension of forwarders to provide better working environment and potentialsfor higher productivity. This has led the Swedish Forest Research Institute (Skogforsk), which seeks to provide practical knowledge for Swedish forest companies, toinvestigate possible improvements for seat undercarriages.Master theses related to this research topic haven been conducted in the Royal Institute of Technology (KTH) collaborating with Skogforsk in the past five years. In2012, the focus was put on the analysis of existing seat undercarriage [9]. From2013 to 2014, a new design for seat undercarriage with active damping was implemented [10, 11]. Last year, an active suspension system with vertical oscillationcompensation has been designed and implemented, and yet the performance is tobe enhanced [12]. Based on the current achievements, this thesis would focus onimproving the vertical control behaviors and achieving countability of both verticaland lateral movements.1.2PurposeThe overall purpose of the project is to develop a seat undercarriage with activedamping to provide good support for operators. Skogforsk states the thesis workwith the following motivation:The task, which is suitable for one student, is to further develop, implement, andverify an actively suspended operator seat. A seat under-carriage was designed andrealized 2014. A sub-solution for active suspension was developed and partially verified 2015. The present project is focused on further development of the integratedactuator and control system, and to verify the performance of the active system withphysical tests on a motion platform, and/or correlation studies between model-basedexperiments and available field test data.Given the time span and workload requirement, the purpose of this thesis work shallinclude the following items. Note that the order shows the priority of tasks. Identify the reasons for controller’s malfunction in some specific setups andfurther improve the performance of vertical cylinder controller. Investigate possible control strategies for lateral cylinders. Develop simulation2

CHAPTER 1. INTRODUCTIONmodels to test the potential candidates and implement the controller with bestoutcomes in the hardware. Integrate vertical controller with the lateral one to achieve sufficient controlperformance of vertical and horizontal movement.The ultimate purpose of all the tasks mentioned above is to ensure AFS 2005:15compliance. The regulation defines limit values of system vibration which shall notbe exceeded and are given based on test cases defined in ISO 2631-1. Therefore, theregulation AFS 2005:15 shall serve as a reference to evaluate all experiment resultsinvolved in this thesis work and the research question is formulated as below:What are optimal control strategies to decrease vibration for a suspended seat withactive pneumatic dampers in both vertical and lateral directions?1.3DelimitationThe delimitation of the thesis work is listed below. This thesis work only considers the hardware setup conducted in 2015. The focus is put on the controllability of vertical and lateral movement. Control of roll performance is considered with lowest priority. ISO 2631-1 is the reference for test case setup. Test signals are sinusoidalsignals.1.4Method DescriptionThe method used in this thesis project is an inductive reasoning approach. Morespecifically, case study will be performed on the specific setup of the seat carriage.All promising control strategies found during literature studies will be verified atfirst in simulation models and then in experiments.In order to answer the research question, literature study is carried out at first. Thisincludes the study of outcomes of previous theses work. The result of this study shallprovide a clear picture of the current situation of the project and potential strategiesready to use. It should lay the foundation for further development of existing modelfor vertical cylinders and improvement of the performance of existing controller.Then the focus shall be put on the development and the simulation of the behaviorsof lateral cylinders under the chosen control strategies to find out the best fit. Thefollowing steps shall be research on typical procedure and setup of tests regardingISO 2631-1. All the evaluation criteria will be developed according to AFS 2005:15.3

CHAPTER 1. INTRODUCTIONFinally, the developed controllers shall be implemented in the setup introduced in[12]. The case chosen here can be claimed as representative since it is one of themost common setups used in industry [13].The core activities of the thesis work include model and controller design, simulation and hardware verification. Due to the complexity of the system, these stepsare conducted by following an iterative approach. The process is illustrated inFig. egrationyesyes nnoControllerevaluationHardwarerealizationFigure 1.2: Iterative approach of model and controller design.1.5Expected OutcomeThe expected outcome of this thesis includes: Models of the pneumatic systems and seat undercarriage structure which areverified. Simulation and evaluation of different control approaches. Implementation of one controller approach in the seat undercarriage system. Physical testing and control parameters tuning. Documentation of testing results and analysis. Identification of existing obstacles and future work suggestions.1.6Research EthicsSince the project does not include any tests with passengers seating on the chairconnected to the undercarriage, there is no direct risk any human or animal are exposed to. However, there might be the possibility that the malfunction of controller4

CHAPTER 1. INTRODUCTIONmay cause uncontrollable oscillation which may be dangerous for testing people.Therefore, people involved in the testing shall be informed of the potential risk inadvance and they shall wear proper protection while conducting the test.5

CHAPTER 1. INTRODUCTION6

Chapter 2Reference FrameThis chapter presents the theoretical framework for the thesis work, including previous researches on seat suspension, control strategies for pneumatic systems andrelevant regulations and standards.2.1Researches on Seat SuspensionSeat suspensions on vehicles are designed to provide good supports for drivers andpassengers. In general, they can be categorized as three different types, whichare passive, semi-active and active suspensions [13]. Consisting of only passivecomponents, such as springs and dampers, passive suspensions have been widelyused because they are simple, cheap and relatively effective in vibration isolating.However, off-road vehicles like forwarders face rather harsh road conditions andtherefore call for more advanced seat undercarriages, namely semi-active or activesuspensions. As illustrated in Fig. 2.1, semi-active suspensions have time-varyingspring stiffness or controllable damping coefficient but no actuator while active onesall can add energy to the system due to the existence of external power source [14].mkd(a)kmmmkd(b)d(c)(d)Figure 2.1: Semi-active and active suspensions. (a) Semi-active suspension withchangable stiffness. (b) Semi-active suspension with changable damper. (c) Activesuspension with actuator and passive components. (d) Active suspension only withforce actuators.Since previous advance in the project has shown that pneumatic suspension ispromising in vibration isolation in this context, the literature study has narrowed7

CHAPTER 2. REFERENCE FRAMEdown to the ones with pneumatic actuators. Due to the complexity of suspensionsystem, detailed and precise models can be hard to obtain. Therefore, model-freecontrol approaches for seat suspensions have been explored by some researchers.Sathishkumar et al. [15] propose a control scheme for force control of semi-activesuspension containing air spring actuators and verify its effectiveness via simulation.Huseinbegovic and Tanovic [16] present a zero order Sugeno-type fuzzy controller forstiffness control and evaluate the performance by seat effective amplitude transmissibility (SEAT) value according to ISO 2631-1 [8]. The simulation results indicatethat this approach can isolate up to 62% vibration. The controller is further developed and tested via physical experiments by Salihbegovic et al. [17]. Based onthe similar hardware setup, Tanovic and Huseinbegovic [18] also explore a hybridapproach by combining fuzzy controllers with neural network while Avdagic et al.[19] compare the abilities of fuzzy logic based and artificial neural network basedapproaches with elaboration of benifits and drawbacks of them.While there have been some achievements via non-modeled approaches, many groupshave also tried to attack this problem through model-based methods. Votrubec[20] proposes a pneumatic seat suspension with feedback controllers for valves yetthe system-level control scheme is to be designed. Kupka [21] implements a statefeedback controller where the control signal contains either integral or proportionalregulation of observed states designed according to a linearized model. Pan and Hao[22, 23] develop a linear-quadratic-Gaussian (LQG) controller with some parameters assumed stochastic to improve the robustness which makes the active suspensionoutperform its passive counterpart. Lee et al. [24] investigate the capability of negative stiffness device for vibration reduction. Likewise, Danh and Ahn [25] introducea pneumatic isolation composed of negative stiffness structure which is controlled bya so-called adaptive intelligent backstepping controller. Maciejewski and his grouphave worked on either semi-active or active suspensions for a long time with fruitful results [26, 27, 28, 29] and their recent publication [29] summarizes a controlsynthesis applicable for both semi-active and active cases with verification of physical tests where the excitation signals are EM3, EM5 and EM6 from ISO 7096:2000Earth-moving machinery – Laboratory evaluation of operator seat vibration [30].2.2Studies on Pneumatic SystemsAs introduced in [12], the external actuators in this project are pneumatic cylinderscontrolled by flow valves. Therefore, it is beneficial to learn some new advances onpneumatic systems design. Many positive outcomes [31, 32, 33, 34] were achieved viaconventional proportional–integral–derivative (PID) regulation or PID-based methods in late 20th and early 21st century, among which the approach proposed byWang et al. [33] is well received and characterised by high stability and small timedelay. However, with the development of hardware, nonlinear control approachesare increasingly applied to handle the inherent nonlinearaties of pneumatic systems,such as gain scheduling [35], backstepping control [36], sliding mode control (SMC)8

CHAPTER 2. REFERENCE FRAME[37, 38, 39, 40, 41, 42, 43].SMC uses control signal to turn system’s initial phase portrait to one where systemstates are convergent to desired equilibrium points. A typical phase portrait underSMC is illustrated in Fig. 2.2 where f denotes the differential equations of the statespace model of the system and s(x) 0 stands for the sliding manifold. SMC ispreferred by many researchers due to its capability to handle the large extent ofparametric uncertainty of plants to achieve robust control performance. AlthoughSMC is applied in all those solutions, the emphasis is certainly different. Someresearchers analyzed the impact of models on the control performance. For example,Bone and Ning [41] challenged the necessity of using nonlinear model for this contextsince, according to their research, the degradation of linear based controller is verylimited compared to the nonlinear one. Richer and Hurmuzlu first developed adetailed model for pneumatic system [44] and then applied it in the following research[37] to find out the impact of model complexity on the performance where SMCis used for force control. Other groups have mainly focused on the effectivenessor limitation of SMC based control and tried to improve the behavior where thesystem model is developed mainly based on ideal gas equation and therefore losessome details. Pandian et al. [38] presented an approach to achieve controllabilityof pneumatic system with partial observability of chamber pressure by introducinga pressure observer. Zhu and Barth [39] achieved force control by manipulatingthe chamber pressure and the tracking has shown good outcome up to 10 Hz. Shenand Goldfarb [42] achieved simultaneous force and stiffness control of the system viaSMC. This achievement is especially of interests for this project since it’s necessary toprovide a comfortable chair and meanwhile a good support for the drivers. Therefore,their principle idea was applied in previous thesis work and it fitted well into thecontext.f (x,t,u )f (x,t,u-)s(x) 0Figure 2.2: A typical phase portrait under sliding mode control. Image source: [45]Based on these researches, there have also been some proposals for comprehensivecontrol strategies by combining SMC with other approaches to get better performance in some aspects [46, 47]. For example, Taheri et al. [47] took one stepfurther, compared with Shen and Goldfarb [42], by combining SMC with backstep9

CHAPTER 2. REFERENCE FRAMEping control to include the dynamics of valves. The test results established that theproposed approach outperformed the stand-alone SMC method but called for moredetails of valves.Moreover, on-line control approaches, especially model predictive control (MPC),have became popular since they are widely believed to cope better with constraintsand disturbances [48]. Fig. 2.3 presents the performance of a second order systemunder noise along with its signal with MPC controller. It’s clear that the plant isable to follow the reference despite disturbance. Although MPC demands intensivecomputational resources, with continuous advances in hardware in recent years, it’snot a problem anymore. Moreover, many researches achieve solid performance withonly on/off solenoid valves, instead of servo ones, in their setups [49, 50, 51], whichmeans a lower cost could be expected. As for the ones with servo valves [52, 53],their results confirmed the reputation of r

Resultatet visar att föreslagen regler strategi är lovande för att redusera både laterala och vertikala . unit have been compared via simulation as inner -loop approach es . Then the better SMC approach . PID Proportional–integral–derivative SMC Slidingmodecontrol