Evaluation of Traction Control Systems for an Electric Forklift Truck

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Master of Science Thesis in Electrical Engineering

Department of Electrical Engineering, Linköping University, 2021

Evaluation of Traction

Control Systems for an

Electric Forklift Truck

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Master of Science Thesis in Electrical Engineering

Evaluation of Traction Control Systems for an Electric Forklift Truck Sebastian Johansson and Mattias Karlsson

LiTH-ISY-EX--21/5395--SE

Supervisor: Arvind Balachandran

isy, Linköping University

Johan Häggblom

Toyota Material Handling Manufacturing Sweden AB Examiner: Lars Eriksson

isy, Linköping University

Division of Vehicular Systems Department of Electrical Engineering

Linköping University SE-581 83 Linköping, Sweden

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Abstract

This thesis evaluates different controllers for traction control on an electric fork-lift truck and has been done in cooperation with Toyota Material Handling Man-ufacturing Sweden. The need for a traction control system has increased with the introduction of lithium-ion batteries replacing the older lead-acid batteries, re-ducing the battery weight and therefore the downward force on the driving wheel increasing the risk for slip. The forklift truck was modelled using Simulink and validated by experiment. Different possible control strategies were investigated and three were chosen for implementation in simulation. These were controllers based on Model Following Control, Maximum Transmissible Torque Estimation and Sliding Mode Control. Model Following Control makes use of a nominal model to compare actual wheel speed values with nominal wheel speed values to determine if slip is occurring, Maximum Transmissible Torque Estimation makes use of a closed-loop disturbance observer to compute the maximum transmissi-ble torque possitransmissi-ble without inducing slip and using it as a limitation on the input signal, and Sliding Mode Control uses different functions to “slide” along a slid-ing surface to stay around a specific slip value. All three controller types were developed both as speed controlled and torque controlled. All of the controllers could reduce slip heavily in simulation. The Maximum Transmissible Torque Es-timation controller reduced slip the most and kept oscillations at a minimum, but was not as responsive as the others to driver commands. The conclusion was that the controller of choice would depend on the working environment of the forklift truck. In a low friction environment where slip is expected to occur often, the Maximum Transmissible Torque Estimation controller is advisable, while the other two would be a better choice for environment with low slip occurrence. The use of torque control, while often better with regards to decreasing slip, could not be advised due to a perceived increase in implementation cost.

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Acknowledgments

We would like to thank our supervisor at Linköping University, Arvind Balachan-dran, who played a key role in helping us establish the foundations for this thesis as well as being a great help in its finalization. Further thanks goes to our exam-iner Professor Lars Eriksson. Professor Eriksson was not only our examexam-iner but provided invaluable help during the course of this project. We would also like to thank Doctor Johan Löfberg and Associate Professor Jan Åslund for lending us their expertise. Overall, we would like to express or gratitude to Linköping University as a whole, the Department of Automatic Control and the Division of Vehicular Systems.

This thesis was done in cooperation with Toyota Material Handling Manufactur-ing Sweden AB and would not have been possible without them. A great thanks goes out to the whole company and especially to Daniel Fahlén, Fredrik Larsson, Mats Karlsson, Jonas Flising, Emil Hall, Håkan Eklund, Magnus Carlson, and Kristian Olsson.

Lastly, we would like to give a special thanks to our supervisor at Toyota Material Handling Manufacturing Sweden AB, Johan Häggblom. His guidance, expertise and passion for the project was vital during the projects course.

Linköping, May 2021 Sebastian Johansson and Mattias Karlsson

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List of Figures

1.1 Picture of the LPE200. From [1], used with permission. . . 4 2.1 Truck schematic with velocity and force vectors. Adapted from [2],

used with permission. . . 5 2.2 Example of a slip-friction curve based on a static and kinematic

friction model where µ is the friction and λ is the longitudinal slip. 7 2.3 Example of slip-friction curves for pneumatic (pressurized) car

tires. . . 7 2.4 Control system for the MFC using a nominal model based on

equiv-alent mass. . . 8 2.5 Control system for the MTTE using an open-loop disturbance

ob-server. . . 10 2.6 Control system for the MTTE using a closed-loop disturbance

ob-server. . . 10 2.7 Basic figure of sliding mode theory. If σ(x) > 0, then f1(x) is used

to force the system to approach σ(x) = 0. If σ(x) < 0, then f2(x) is used to the same effect. . . 11 2.8 Figure showing the behaviour of the σ from different starting

con-ditions. The value of σ moves towards the zero value and then "zigzags" around it. . . 12 2.9 Control system for the sliding-mode. . . 13 4.1 The complete simulation model used to test different traction

con-trol systems. . . 18 4.2 The electrical subsystem. . . 19 4.3 The speed controller used to control the motor. . . 19 4.4 The mechanical subsystem containing the mechanical parts of the

model. . . 20 4.5 The models for the vehicle body and the five wheels of the forklift. 21 4.6 Filtered and unfiltered velocity measurements. . . 22 4.7 Comparison between simulated and measured data. Unloaded truck

at maximum acceleration with dry road conditions. . . 23 4.8 Comparison between simulated and measured data. Fully loaded

truck with maximum acceleration and dry road conditions. . . 24

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x LIST OF FIGURES

4.9 Comparison between simulated and measured data. Fully loaded truck with maximum acceleration and wet road conditions. . . 24 4.10 The Simulink model for the MFC using speed-based control. . . . 26 4.11 The Simulink model for the MFC using torque-based control. . . 27 4.12 The Simulink model for the MTTE using speed-based control. . . 28 4.13 The Simulink model for the MTTE using torque-based control. . . 28 4.14 The Simulink model for the sliding mode using speed-based

con-trol. . . 29 4.15 The Simulink model for the sliding mode using torque-based

con-trol. . . 30 5.1 The vehicle speed compared to the wheel speed of the unloaded

forklift truck when the speed-based MFC controller is activated/deactivated. 32 5.2 The motor torque and measured slip of the unloaded forklift truck

when the speed-based MFC controller is activated/deactivated. . . 33 5.3 The vehicle speed compared to the wheel speed of the unloaded

forklift truck when the torque-based MFC controller is activated/deactivated. 33 5.4 The motor torque and measured slip of the unloaded forklift truck

when the torque-based MFC controller is activated/deactivated. . 34 5.5 The vehicle speed compared to the wheel speed of the loaded

fork-lift truck when the speed-based MFC controller is activated/deactivated. 35 5.6 The motor torque and measured slip of the loaded forklift truck

when the speed-based MFC controller is activated/deactivated. . . 35 5.7 The vehicle speed compared to the wheel speed of the loaded

fork-lift truck when the torque-based MFC controller is activated/deactivated. 36 5.8 The motor torque and measured slip of the loaded forklift truck

when the torque-based MFC controller is activated/deactivated. . 36 5.9 The vehicle speed compared to the wheel speed of the unloaded

forklift truck when the speed-based MTTE controller is activated/deactivated. 37 5.10 The motor torque and measured slip of the unloaded forklift truck

when the speed-based MTTE controller is activated/deactivated. . 38 5.11 The vehicle speed compared to the wheel speed of the unloaded

forklift truck when the torque-based MTTE controller is activated/deactivated. 38 5.12 The motor torque and measured slip of the unloaded forklift truck

when the torque-based MTTE controller is activated/deactivated. . 39 5.13 The vehicle speed compared to the wheel speed of the loaded

fork-lift truck when the speed-based MTTE controller is activated/deactivated. 40 5.14 The motor torque and measured slip of the loaded forklift truck

when the speed-based MTTE controller is activated/deactivated. . 40 5.15 The vehicle speed compared to the wheel speed of the loaded

fork-lift truck when the torque-based MTTE controller is activated/deactivated. 41 5.16 The motor torque and measured slip of the loaded forklift truck

when the torque-based MTTE controller is activated/deactivated. . 41 5.17 The vehicle speed compared to the wheel speed of the unloaded

forklift truck when the speed-based sliding mode controller is ac-tivated/deactivated. . . 42

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LIST OF FIGURES xi

5.18 The motor torque and measured slip of the unloaded forklift truck

when the speed-based sliding mode controller is activated/deactivated. 43 5.19 The vehicle speed compared to the wheel speed of the unloaded

forklift truck when the torque-based sliding mode controller is ac-tivated/deactivated. . . 43 5.20 The motor torque and measured slip of the unloaded forklift truck

when the torque-based sliding mode controller is activated/deactivated. 44 5.21 The vehicle speed compared to the wheel speed of the loaded

fork-lift truck when the speed-based sliding mode controller is acti-vated/deactivated. . . 45 5.22 The motor torque and measured slip of the loaded forklift truck

when the speed-based sliding mode controller is activated/deactivated. 45 5.23 The vehicle speed compared to the wheel speed of the loaded

fork-lift truck when the torque-based sliding mode controller is acti-vated/deactivated. . . 46 5.24 The motor torque and measured slip of the loaded forklift truck

when the torque-based sliding mode controller is activated/deactivated. 46 6.1 Slip comparison between different controllers, the truck being

ei-ther loaded or unloaded and using speed-based control or torque-based control. . . 51 6.2 Speed comparison between different controllers, the truck being

either loaded or unloaded and using speed-based control or torque-based control. . . 53 6.3 Torque comparison between different controllers, the truck being

either loaded or unloaded and using speed-based control or torque-based control. . . 53

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Notation

Latin symbols Notation Definition F Force f Function i Gear Ratio J Moment of Inertia

K Controller Gain Parameter

M Mass

r Drive Wheel Radius

s Laplace variable

T Torque

V Velocity

x Variable in equation, used to explain theory

Greek symbols

Notation Definition

α Relaxation factor in MTTE controller

γ Gain for sliding mode controller

∆ Difference λ Slip µ Friction Coefficient σ Sliding Surface τ Time Constant ω Rotational Velocity xiii

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xiv Notation Subscripts Notation Definition xd Drive xdr Driving Resistance xg Gear xm Motor xref Reference

xSMC Sliding Mode Controller

xw Wheel

Abbreviations

Notation Definition

ECU Electric Control Unit IMC Internal Model Control MFC Model Following Control MPC Model Predictive Control MTTE Maximum Transmissible Torque

PID Proportional, Integral and Derivative SMC Sliding Mode Controller

TCS Traction Control System

TMHMS Toyota Material Handling Manufacturing Sweden

Functions

Notation Definition Comments

˙x dx dt Time derivative sign(x) sign(x) =            1 if x > 0 0 if x = 0 −1 if x < 0 Signumfunction sat(x) sat(x) =            1 if x > 1 x if − 1 ≤ x ≤ 1 −1 if x < −1 Saturation function

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1

Introduction

With the ever increasing global trade the need for smart, efficient, safe and envi-ronmentally friendly supply chain solutions increases. A key part of the supply chain is the electric forklift truck. As of now, Toyota Material Handling Manufac-turing Sweden is in the midst of a transition from lead-acid batteries to lithium-ion batteries, which decreases the weight of the forklift. Making a forklift truck lighter while keeping the same battery power makes the truck more efficient and thus both increasing its drive time per charge cycle and making it more environ-mentally friendly. However, a decrease in mass is not without downsides. Due to the location of the batteries, a decrease in battery mass decreases the downward force on the driving wheel, increasing the risk for wheel slip.

Wheel slip is potentially dangerous as it can decrease the driver’s ability to con-trol the forklift truck [3]. In order to combat wheel slip cars tend to use traction control systems [4]. They usually work by comparing the speed of the driving wheels to that of the vehicle. The vehicle velocity is usually determined by mea-suring the speed of non-driving wheels. If the velocity of the vehicle is lower than what the driving wheels’ speed imply, a loss of traction can be inferred. Thus, the traction control system will lower the speed of the driving wheel to match that of the vehicle and hopefully regain traction [5].

As stated earlier, the vehicle velocity is usually estimated through the speed of non driving wheels, however, such sensors increase the cost of the vehicle. In order to keep the cost down alternative methods, not relying on wheel encoders, could be useful. Further, Toyota Material Handling forklifts use a speed reference input for driver speed control, while cars use torque-based control. Hence, trac-tion control systems tend to rely on direct torque control. Keeping a speed-based system could keep implementation costs to a minimum. Therefore, in

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2 1 Introduction

tion with Toyota Material Handling Manufacturing Sweden, this master thesis will aim to investigate different traction control system on a Toyota Material Han-dling forklift.

1.1 Purpose

The purpose of this thesis is to examine different methods for implementing trac-tion control on forklifts while keeping costs to a minimum and simplicity at a maximum.

1.2 Problem

There are multiple problems that must be considered when implementing trac-tion control on a forklift.

• How can slip be detected and controlled?

• How do non-wheel encoder methods compare to the conventional wheel encoder method in terms of speed, slip and oscillations?

• How do torque-based controllers compare to speed-based controllers in terms of speed, slip and oscillations?

1.3 Research questions

To judge the efficiency of the different traction control methods they will be com-pared against each other. This comparison will mainly examine differences in:

• Sensors needed for slip detection. • Maximum slip.

• Total slip value over time. • Acceleration ability. • Time for re-adhesion. • Driveline oscillations

Based on this comparison the advantages and disadvantages of each method will be obtained. Further, while no thorough investigation of differences in imple-mentation cost or driver experience will be conducted, it will still be a point of discussion.

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1.4 Scope 3

1.4 Scope

The scope of this thesis is limited to the hardware and software of a single forklift, the lowlifter BT Levio P-series LPE200, seen in Figure 1.1, from Toyota Material Handling, in order to limit the amount of modelling and testing needed. Further, the traction control will only be modelled for use in drive mode, i.e. when the forks are in a lowered position. This is when wheel-slip is most likely to occur due to the higher acceleration and maximum speed. The focus will be on reducing the longitudinal slip of the driving wheel, disregarding potential lateral slip as a result of turning. Further, the solutions will not be made to handle slopes. Each traction controller will also be split into two versions, a speed-based version and a torque-based version. The speed-based version uses a speed reference from the driver, while the torque-based version uses a torque reference from the driver.

1.5 Platform overview

The forklift LPE200 has five wheels in total; one drive wheel, two castor wheels for balance, and two fork wheels. The drive wheel is the only driven wheel, mean-ing it is the only wheel for which longitudinal slip can occur. It is connected to a single-speed transmission which is directly connected to an electric motor. The motor has a speed encoder which effectively allows for the measurement of the drive wheel speed. Since the forklift uses an electric motor the torque can eas-ily be calculated from the motor current, allowing for the use of torque-based control algorithms [6].

1.6 Approach

The approach to answer the research questions was as follows.

• Develop a forklift truck simulation model to be used as a plant model. • Validate the truck model with real experiments.

• Perform a literature overview to find and choose suitable traction control systems.

• Implement the chosen traction control systems with the plant model in Simulink.

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4 1 Introduction

Figure 1.1:Picture of the LPE200. From [1], used with permission.

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2

Theory

This chapter covers the theoretical background of the thesis. It contains the theo-retical framework for the vehicle dynamics, slip and the different controllers.

2.1 Vehicle dynamics

The general dynamics of the vehicle are defined, allowing for the modelling of the forklift truck as well as the development of the traction control systems. Based on the definitions of the force and velocity vectors seen in Figure 2.1 the equations for the longitudinal dynamics of a vehicle are established [4].

Drive Wheel

Figure 2.1:Truck schematic with velocity and force vectors. Adapted from [2], used with permission.

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6 2 Theory Jw ˙ωw = Tw− rFd, (2.1) M ˙Vv= Fd− Fdr, (2.2) Vw = rωw, (2.3) Fd = µ(λ)FN, (2.4) ωw = ωm ig , (2.5) Tw = Tmig, (2.6) Tw = Fwr, (2.7)

where Jwis the wheel inertia, ˙ωwis the angular acceleration of the wheel, Twthe

motor torque acting on the wheel, r the radius of the wheel, and Fdis the driving

force caused by the friction of the road. M is the mass of the vehicle, ˙Vv the

longitudinal acceleration of the vehicle, and Fdrthe driving resistance. Vwis the

longitudinal velocity of the wheel, and ωw is the angular velocity of the wheel.

µ is the coefficient of friction between the road and wheel, and FN is the normal

force exerted by the vehicle. ωmis the angular velocity of the electric motor, ig is

the gear ratio, Tmis the motor torque, and Fw is the motor torque seen as a force

acting on the wheel.

2.2 Slip

Slip is the result of loss of traction during acceleration or deceleration [3], with the case of deceleration more commonly being referred to as skidding. There are two definitions commonly used for wheel slip in the literature. Depending on the paper one or the other is used, with (2.8) more often being used for braking and (2.9) more often being used for acceleration.

λb= ωw_|Vr− Vv

v| , (2.8)

λa= ωwr− Vv

ωwr , (2.9)

where λ denotes slip, and the subscripts a and b stands for acceleration and brak-ing. When there is no slip, i.e. when the wheel speed is equal to the vehicle speed,

λa= λb = 0, while at locked wheels the slip would be λb= −1 and λa−→ ∞. In

turn, λb −→ ∞ and λa = 1 during a “burnout”, i.e. when the wheel speed is

greater than 0 and the vehicle speed is 0. In this report the second definition is more often used, with the first definition only being used for comparison with the measurement data.

Generally, the friction force for a static object is larger than if the object is mov-ing. The former is referred to as static friction while the latter as kinematic or

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2.2 Slip 7

Coulomb friction. Given this, a simple slip model would have characteristics similar to Figure 2.2, with the friction suddenly decreasing as soon as slip occurs.

Rigid slip-friction curve

Figure 2.2:Example of a slip-friction curve based on a static and kinematic friction model whereµ is the friction and λ is the longitudinal slip.

Since neither wheels, tires, nor the ground are fully rigid objects this model is too simplified to be sufficient for modelling the wheel slip and a more advanced model is needed, namely the Magic Formula [3].

While the specific slip-friction curve described by the Magic Formula depends on the wheel/tire and ground/rail surface, the general characteristic of the slip-friction curve can be seen in Figure 2.3. As seen, according to the Magic Formula a small slip is always necessary for traction. Similar plots can be found in stan-dard textbooks on car/train modeling or dynamics, such as [4], [7] and [8]. Peak traction may vary in size and at which slip value the peak occurs between wheel-rail and tire-road interaction, but both share the characteristic seen in the figure. It will therefore be assumed that hard rubber wheels also follow this characteris-tic in its interaction with the floor.

Examples of typical slip friction curves

Example 1 Example 2 Example 3 Example 4

Figure 2.3: Example of slip-friction curves for pneumatic (pressurized) car tires.

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8 2 Theory

2.3 Traction Control Systems

Theory about the different traction control systems evaluated in this thesis is pre-sented in this section.

2.3.1 Model Following Control

Model Following Control (MFC) uses a nominal vehicle model to calculate the expected wheel speed when there is no slip occurring, and compares this with the measured actual wheel speed to compensate using the difference [9] [10] [11]. Using (2.3) and the following equation for equivalent mass:

J = Mr2, (2.10)

where J is the inertia, M is the mass, and r is the radius, (2.1) can be rewritten as:

MwV˙w = Fw− Fd. (2.11)

By inserting (2.2) into (2.11) and taking the Laplace transform with the assump-tion that there is no slip, meaning Vw= Vv, the following equation for the

nomi-nal wheel velocity is obtained

Vw= Fw− Fdr

Mw+ M ·

1

s, (2.12)

where s is the Laplace operator. The basic control system for the MFC can be seen in Figure 2.4, where the estimated nominal wheel speed is subtracted from the actual wheel speed to create an error signal. This error signal is fed back through a gain Kpto reduce the commanded wheel torque/force.

Plant model Fw 1 Mw+M 1 s Kp + Fw,ref + Vw − ˆ Vw + − Fdr − nominal model

Figure 2.4: Control system for the MFC using a nominal model based on equivalent mass.

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2.3 Traction Control Systems 9

2.3.2 Maximum Transmissible Torque Estimation

Maximum Transmissible Torque Estimation (MTTE) is used in the MTTE-controller as a way to estimate the maximum transmissible torque possible without slip oc-curring, and using this to limit the torque output from the motor. The maximum transmissible torque Tmaxis obtained using only the torque reference to the

mo-tor as well as the rotational velocity of the driving wheel [12].

Using (2.1) and (2.3) the driving force can be calculated as (2.13). During normal driving conditions, i.e. no slip, the driving force Fd is lower than the maximum

frictional force of the ground. When the wheel torque increases, so does the driving force. During slip Fdinstead equals the maximum frictional force of the

ground and does not increase with an increasing wheel torque [13].

Fd= T_rw − Jw

˙

Vw

r2 , (2.13)

where ˙Vwis acceleration of the drive wheel, calculated as a longitudinal velocity,

Jwis the inertia of the drive wheel and r is the drive wheel radius. As mentioned

in Section 2.2 slip results in a difference in speed between the driving wheel and the vehicle chassis. If the acceleration of the driving wheel is greater than that of the vehicle chassis this slip will increase. In Section 2.2 it is also mentioned that a small slip is necessary to provide friction force. Based on this the approximation between the chassis acceleration and the wheel acceleration can be described by a relaxation factor α:

α = V_˙˙v∗

Vw∗, (2.14)

which can be expanded using (2.1), (2.2), and (2.3):

α = (Fd− Fdr)/M

(Tmax− rFd)r/Jw

. (2.15)

The relaxation factor α should be close to 1 for slip to not occur or become larger. If it is assumed that the driving resistance Fdr = 0 and a designed α is used, Tmax

must be reduced adaptively following the decrease of the friction force Fd when

the vehicle encounters a slippery surface. If it is possible to estimate the friction force, Tmaxcan be expressed as

Tmax= Jw

αMr2 + 1

r ˆFd. (2.16)

The control scheme of the MTTE can be seen in Figure 2.5. As shown, the esti-mated maximum torque is used in a limiter with a variable saturation value to limit the commanded torque Tref according to the dynamic situation. The

fric-tion force Fd which can be seen as a disturbance force [14] is estimated with an

open-loop disturbance observer [12] [15] which requires the commanded torque and a model inversion. Due to the model inversion, a differentiator is needed, creating a need for low-pass filters to smooth the noises of the digital signals and differentiator.

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10 2 Theory |Tmax| r F_d + T Vehicle model 1 τ2s+1 Vw 1 τ1s+1 1 r Jws r2 _J w αMr2 + 1 r T_ref −Td + − ˆFd Tmax

open-loop disturbance observer

Figure 2.5: Control system for the MTTE using an open-loop disturbance observer.

The control system seen in Figure 2.5 can be improved with the usage of a closed-loop disturbance observer instead of an open-closed-loop observer [13]. This change removes the need for a model inversion which might be difficult to obtain [14], and improves the robustness with the introduction of feedback, lessening the im-pact of modelling errors. The improved control system can be seen in Figure 2.6.

|Tmax| r Fd 1 Jws ω r ∆s(s) 1 Jws r Vw Kp+ Ki1_s 1 r _J w αMr2 + 1 r Tref T + e−Ls + − Td + + + ˆ ω − ˆ Vw ˆ Td + ˆF_d Tmax

closed-loop disturbance observer

Figure 2.6: Control system for the MTTE using a closed-loop disturbance observer.

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2.3 Traction Control Systems 11

The disturbance torque Tdcomes from the operation friction. This means Td will

become very small when the vehicle is operated on a slippery road due to the insufficient friction of the wheel. The nonlinear behavior of this slip is regarded as an uncertainty source that causes abnormal faults in the driving [12]. In this figure ∆s(s) denotes the slip perturbation of the wheeled motor [14], and the

dy-namics of ∆s(s) represents the role of different slippery driving conditions. This

means that the driving condition is fine when ∆s(s) ≈ 0, and when the road

sur-face is slippery ∆s(s) , 0.

2.3.3 Sliding Mode Control

There are several approaches to constructing a sliding mode controller for trac-tion control. The one used in this report can be found in [16] and in the com-parative study [17]. It should be noted that this controller requires a non-drive wheel speed sensor, which is used to calculate the slip value. Since the theory behind sliding mode controllers is outside the scope of this report, only minimal information on the theory will be provided. Interested readers can find both a theoretical background and more information regarding the use of sliding mode control in vehicle dynamics in [18].

A first order sliding mode controller defines a sliding surface. The sliding sur-face is defined as when a specific function is equal to zero. This is called the sliding surface or sliding manifold [18]. By rapidly changing the control func-tion the idea is to force the system to “slide” along the sliding surface.

If the sliding surface is

σs = 0, (2.17)

and there are two different control functions pointing towards σ = 0 from differ-ent sides of the function as seen in Figure 2.7,

f1(x)

σ (x) = 0 f2(x)

σ (x) > 0

σ (x) < 0

Figure 2.7:Basic figure of sliding mode theory. Ifσ (x) > 0, then f1(x) is used to force the system to approachσ (x) = 0. If σ (x) < 0, then f2(x) is used to the same effect.

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12 2 Theory

σ (x) will approach σ (x) = 0 even from different starting conditions and then

have it “zigzag” around the zero line by switching control functions as seen in Figure 2.8.

Figure 2.8: Figure showing the behaviour of theσ from different starting

conditions. The value ofσ moves towards the zero value and then "zigzags"

around it.

For the specific controller used in this report the sliding variable is chosen as

σs = λ − λref, (2.18)

ergo the difference between the slip of the tire and some wanted reference slip [17]. The control functions must allow for a change in speed due to driver de-mand, different slips and different reference slips.

Using (2.9) and taking the derivative, the result is

˙λ = −V˙vωwr + Vv ˙ωwr ω2wr2 = −V˙v ωwr + Vv ˙ωw ω2wr . (2.19) Inserting (2.1) results in ˙λ = −V˙v ωwr+ Vv ω2wr ·Tw− Fdr Jw = − ˙ Vv ωwr− VvFd Jwω2w + Vv Jwrω2w Tw. (2.20) (2.21)

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2.3 Traction Control Systems 13 Inserting (2.18) ˙σs = − ˙ Vv ωwr− VvFd Jwω2w + Vv Jwrω2w Tw− ˙λref, (2.22) ⇐⇒ Tw = Jwrω 2 w Vv ˙σs+ ˙λref + VvFd Jwω2w + V˙v ωwr . (2.23)

Using (2.23) a control law can be constructed. By switching the ˙σsto −γ · sign(σs)

and using it as control law, given a large enough γ the torque will move the slip to its reference value while still taking the dynamics and changes to the refer-ence slip into account. To clarify, if σs > 0 the control torque will be lowered,

while with σs< 0 it will be increased. However, the use of a sign()−function can

cause unwanted chattering in the driveline, due to the control signal becoming discontinuous and rapidly changing. Hence, a sat()−function is preferable. The resulting control law is then:

Tw= Jwrω 2 w Vv − γsat(σs)s+ ˙λref + VvFd Jwω2w + V˙v ωwr . (2.24)

Figure 2.9 shows the control system, where

b = Vv Jwrω2w , (2.25) f =−VvFd Jwω2w − ˙ Vv ωwr. (2.26) 1 −1 −γ f 1 b + λ − λ_ref σ + − − T_SMC + Tref _T

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3

Previous Research

The problem of traction loss has been known for a long time. For example, in the 19th century trains deployed sand over the railway during bad conditions in order to increase traction, a system which is still used today. Modern torque limit-ing computer aided traction control systems were first developed for combustion based cars within the automotive industry in the 70s.

According to [19] the commercial TCS in combustion cars generally utilized gain scheduling control with lookup tables. An IMC-PID solution for combustion ve-hicles was developed in [20]. A method using a PID controller and a Fuzzy con-troller can be seen in [21]. With the further development of electrical vehicles and electric motors the research into traction control increased during the 90s. As pointed out by Hori et al.[22] electrical vehicles offer some advantages with re-gards to advanced traction control over combustion vehicles, such as a fast torque response and an accurate estimation of output torque. The above mentioned Hori et al. [22] developed a traction control system based on an internal model. Hori was also involved in developing another controller that estimates the maximum transmissible torque [12]. Both of these methods had the advantage of not need-ing any extra speed sensors on non-driven wheels.

Yoshimura et al used Fuzzy control to reduce slip in an all wheel drive electric vehicle. V. Deli et al. developed both a sliding mode controller and a fuzzy controller that both showed similar results [23]. Sliding mode controllers are a common solution, and other examples of their implementation can be found in [23], [16], and [18].

In the comparative study [17] an H_∞-controller was developed for an electric

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16 3 Previous Research

vehicle, showing great results. Overall, the research is vast. A lot of controllers and different approaches have been developed and at least tested in simulation. A general problem is a lack of testing on actual physical systems. An extensive re-view of the current research is beyond the scope of this report. Interested readers can find a more extensive overview in [10].

3.1 Choice of controllers

Implementation of all controller types commonly found in the literature was not deemed possible due to time restraints. As such, three controllers were chosen. During the beginning of the project, the plan was to implement the controllers on a forklift truck. This turned out to not be possible during the given time frame, but it still impacted the choice of controllers. The short time frame for the project was not unknown, and as such a key factor in controller choice was per-ceived ease of implementation. Further, TMHMS stressed the limited calculation capabilities of the truck’s computer system as well as an interest in keeping the amount of sensor to a minimum. Due to the global Covid pandemic during the project the ability for on site work was limited and thus extensive experimenta-tion was deemed not possible. Hence, the key factors were:

• Perceived ease of physical implementation • Low computational cost

• Low amount of sensors • Low need of experiments

MPC based controllers are traditionally high in computational cost [24] and were therefore not seen as suitable for the project. Gain scheduling with a look up table requires extensive testing on different surfaces and different gains [17], and using a neural network instead of a look up table still requires large training sets for the training algorithm [25], thus both of these were also seen as unsuitable. Some work did go into a Fuzzy controller, since they are very common in the literature [26], but after consulting with the Control Engineering Department at Linköping University, this was abandoned. While, as stated earlier, an H_∞-based controller had shown great results in at least one study, it is a highly complicated controller and was therefore seen as nonviable. The MTTE controller and MFC were both deemed to be easy to implement, using no extra sensors while showing promising results. As a third and final controller a sliding mode controller was chosen due to its use of an additional wheel sensor, making it useful for comparison.

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4

Modelling

A major part of this thesis work was the creation of a simulation model of the forklift truck. This model was used for testing of the different traction control systems (TCS) described in Section 2.3, and it was created using normal Simulink operations and driveline components from Simscape. The resulting forklift truck model consists of two main subsystems; an electrical subsystem containing the internal speed controller of the electric motor as well as the electric motor itself, and a mechanical subsystem containing the transmission, wheel models, and ve-hicle body. Apart from these subsystems there is a third subsystem containing the TCS. An overview of the simulation model can be seen in Figure 4.1.

4.1 Electrical subsystem

The electrical subsystem seen in Figure 4.2 contains a torque following electric motor as well as the motor speed controller. The LPE200 forklift normally uses a 3-phase asynchronous electric AC motor, but in the simulation model this was simplified to a reference following electric motor containing a torque-speed-efficiency envelope obtained from motor experiments. The reference is a torque reference, which is proportional to the actual current reference used in the phys-ical system.

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18 4 Modelling wheel_speed torque acceleration slip vehicle_speed Mech Rot in Mechanical Vehicle rotational speed T* Reference speed wheel_speed Reference torque Mechanical rotation Electrical Signal 1 Group 1 Reference torque T* TCS slip wheel_speed acceleration Reference speed torque vehicle speed Controller off Controller on

Figure 4.1: The complete simulation model used to test different traction control systems.

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4.1 Electrical subsystem 19

Figure 4.2:The electrical subsystem.

The torque reference input to the motor is created by the speed controller seen in Figure 4.3. The speed controller uses wheel speed feedback to generate an er-ror signal used in the saturated PI-controller to create the reference torque. This PI-controller is also limited in the same way as the motor, using a speed-torque envelope to avoid too-large reference values. To avoid integrator windup in the PI-controller due to the saturation, clamping was used as an anti-windup method [24].

Even though both the wheel speed and the motor speed are shown to be part of a feedback loop, only one is necessary since there is a constant transmission between the motor and drive wheel.

Figure 4.3:The speed controller used to control the motor.

The output from the electrical subsystem is the reference torque, as well as the mechanical rotation created by the motor. Depending on whether a TCS is ac-tive or not, the reference torque is either output to the TCS or simply directly routed to the electric motor. The mechanical rotation is output to the mechanical subsystem.

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20 4 Modelling

4.2 Mechanical subsystem

The mechanical subsystem seen in Figure 4.4 contains the mechanical parts of the model. There is a fixed transmission as well as a rotational sensor for the motor speed which is converted to wheel speed with added measurement noise. The torque sensor is used instead of the torque calculation based on motor current as a simplification, and the moment of inertia of the rotating parts are added separately before and after the transmission.

Figure 4.4: The mechanical subsystem containing the mechanical parts of the model.

The models for the wheels and vehicle body can be seen in Figure 4.5. The forklift body has a multitude of ports of which the important ones are NF, NR, M, CG, and H.

• NF and NR ports are the normal forces applied to the front and rear wheels.

• M port is the mass of the load.

• CG port is the position of the load in relation to the center of gravity of the forklift.

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4.2 Mechanical subsystem 21

Figure 4.5:The models for the vehicle body and the five wheels of the fork-lift.

The wheels have 4 ports, N, A, S, and H. Of these the A and S ports are only used by the drive wheel.

• N port is used to apply the normal force from the vehicle body to the wheel.

• A port is used to apply mechanical rotation to a wheel.

• S port shows the current slip for the wheel and is used for controller testing. For the forklift, slip can only occur for the driving wheel.

• H port is used to apply the longitudinal force generated or required to the vehicle body. The drive wheel generates longitudinal force and the non-drive wheels require a longitudinal force to start moving.

The normal force is not evenly distributed between the drive wheel and the two castor wheels. The normal force acting on the drive wheel is around 50% of the total normal force acting on the front wheels together [27], which is modelled by splitting the normal force using gains.

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22 4 Modelling

4.3 Validation

In order to validate the created forklift truck model, a series of experiments were performed to create measurement data. A forklift truck was driven back and forth on a dry floor at maximum acceleration. The experiment was repeated with a load of two tons. Finally, the forklift truck was driven back and forth over wet floor in order to induce maximum slip. The forklift truck was equipped with a measuring wheel, which is a non-driven wheel meant to measure vehicle speed. A CAN-monitor was also used, which showed CAN traffic regarding measure-ment of motor speed, motor current, motor voltage and reference speed from the throttle.

Some of the gathered data contained a lot of noise. In these cases the data was fil-tered with a zero phase low pass filter. The most noisy measurement was the one of the non-driven velocity measuring wheel. The unfiltered and filtered results of that measurement, from the first experiment, can be seen in Figure 4.6.

0 10 20 30 40 50 60 70 Time t [s] -5 0 5 Vehicle Velocity V v [m/s]

Measured Vehicle Velocity from non-driven measurment wheel, unfiltered and filtered Unfiltered 0 10 20 30 40 50 60 70 Time t [s] -5 0 5 Vehicle Velocity V v [m/s] Filtered

Figure 4.6:Filtered and unfiltered velocity measurements.

Other than the directly measured values, the motor torque has to be calculated from the motor current. This was done by using a motor map and linearizing the relationship between the torque and the current for different working points. In order to make comparison with Simulink simulations easy, the slip was calcu-lated in the same way as in Simulink. Ergo, as the difference between the wheel velocity and the vehicle velocity, divided by the absolute value of the vehicle ve-locity. The same as (2.9).

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4.3 Validation 23

By using the measured speed demand from the experiments as speed demand in the simulated model, a comparison can be easily made. In Figure 4.7 - Figure 4.9 a comparison between measured and simulated values are shown for different scenarios. The ground conditions vary as do the load. The simulation uses differ-ent slip-friction curves for wet and dry ground conditions. Namely pneumatic tire standard values for dry and wet tarmac. Since the actual forklift truck uses a hard rubber wheels, driven on industrial floor concrete, the differences in to-tal slip is not surprising. Neither is the fact that some slip values become larger in the simulation and vice versa for the experimental case. The wheel-floor in-teraction is nonlinear and even during the same experiment they can vary a lot. However, as are seen in the figure, the slip peaks tend to coincide even though the values differs. As can also be seen in the figures, the model wheel speed and torque matches the experimental values well. In conclusion, the model is deemed “good enough” for traction control system evaluation.

0 10 20 30 40 50 60 70

-5 0 5

Wheel speed [km/h]

Simulated and measured vehicle data at maximum acceleration, no load and dry ground conditions Simulation Measurement 0 10 20 30 40 50 60 70 0 5 10 15 Torque [Nm] Simulation Measurement 0 10 20 30 40 50 60 70 Time [s] -0.1 -0.05 0 0.05 Slip [-] Simulation Measurement

Figure 4.7: Comparison between simulated and measured data. Unloaded truck at maximum acceleration with dry road conditions.

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24 4 Modelling 0 20 40 60 80 100 120 -5 0 5 Wheel speed [km/h]

Simulated and measured vehicle data at maximum acceleration, no load and dry ground conditions Simulation Measurement 0 20 40 60 80 100 120 0 10 20 30 Torque [Nm] Simulation Measurement 0 20 40 60 80 100 120 Time [s] 0 0.2 0.4 Slip [-] Simulation Measurement

Figure 4.8:Comparison between simulated and measured data. Fully loaded truck with maximum acceleration and dry road conditions.

0 20 40 60 80 100 120

-5 0 5

Wheel speed [km/h]

Simulated and measured vehicle data at maximum acceleration, no load and dry ground conditions Simulation Measurement 0 20 40 60 80 100 120 0 10 20 30 Torque [Nm] Simulation Measurement 0 20 40 60 80 100 120 Time [s] 0 0.5 1 Slip [-] Simulation Measurement

Figure 4.9:Comparison between simulated and measured data. Fully loaded truck with maximum acceleration and wet road conditions.

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4.4 Traction Control System 25

4.4 Traction Control System

Two main methods are used to model the traction control systems described in Section 2.3; speed-based control and torque-based control. With the speed-based control method, the TCS reduces or limits the commanded speed, allowing the existing PI speed controller to reduce the wheel speed when necessary. This al-lows the TCS to work together with the speed controller, resulting in a smooth response. The torque control method involves direct control of the torque, with-out using the existing PI speed controller. This results in a faster torque response, but involves major changes to the motor control.

4.4.1 Model Following Control

The main designs of the MFC models are similar to the control system shown in Figure 2.4 in Subsection 2.3.1, but there are a few important changes and addi-tions implemented which are needed to improve the reliability and performance of the controller. The two models can be seen in Figure 4.10 and Figure 4.11. The first addition is an anti-drift “filter” applied to the equivalent acceleration, which only allows accelerations greater than a set value to affect the equivalent speed. Without this “filter” the equivalent speed will start drifting during con-stant speeds due to measurement noise. Another change is the addition of a sign-switch for the driving resistance, necessary due to the ability of the forklift truck to drive both forwards and backwards. This sign-switch changes the direction of the applied driving resistance based on the direction of the equivalent speed. A similar switch is applied to the feedback signal, where a direction check is used to prevent the feedback from increasing the requested speed/torque. This means that if the forklift truck is moving in a positive direction, the feedback can only subtract, and if it is moving in a negative direction, it can only add.

The final major additions are a function determining when to activate the con-troller [17], and a change of input to the nominal model. The change of input to the nominal model is done to avoid needing to model the back-emf of the electric motor by using the measured torque instead of the requested torque, meaning the back-emf will already have been applied. The control activation function out-puts 0 when not active, and 1 when active. It activates when the slip estimated using the equivalent speed and the actual speed is greater than a fixed value. The deactivation is not at the same value, but at a lower one, reducing the oscillations of the system. Pseudo-code for this function can be seen in Algorithm 1. Here, λ denotes slip, λref the reference slip, while Kactivateis a constant used to achieve

an activation threshold for the controller linked to the reference slip.

Speed-based design

The Simulink model for the speed-based MFC can be seen in Figure 4.10. This model is slightly changed from the control system shown in Figure 2.4, in which

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26 4 Modelling

Algorithm 1:Activate deactivate controller persistent Activated; ifisempty(Activated) then Activated = 0; end ifλ > λ_ref then Activated = Activated + 0.5; Activated = min(Activated,1); end

ifλ < K_activate∗ λ_ref then Activated = Activated - 0.01; Activated = max(Activated,0); end

the feedback signal is shown to reduce the reference wheel force Fw,ref. In this

MFC model the feedback signal is instead the speed decrease, which decreases the requested speed going to the speed controller.

Figure 4.10:The Simulink model for the MFC using speed-based control.

Torque-based design

The Simulink model for the torque-based MFC can be seen in Figure 4.11, which is very similar to the speed-based MFC in Figure 4.10. The main difference be-tween the two, besides the torque-based MFC reducing the motor torque instead of the speed, is the lack of a speed controller for the torque-based MFC. If the speed controller was not removed it would compete with the MFC by trying to increase the torque when the MFC is trying to decrease it. Although this is still possible to use, it is not ideal and is therefore not used.

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Figure 4.11:The Simulink model for the MFC using torque-based control.

4.4.2 Maximum Transmissible Torque Estimation

As with the MFC models, the MTTE models seen in Figure 4.12 and Figure 4.13 are very similar to the control system seen in Figure 2.6. As with the MFC there are some changes and additions, though most are minor compared the MFC ad-ditions, and the largest change is not a change to the structure of the controller, but to how the speed-based MTTE is applied.

The only major addition to the structure of the MTTE controller is the addition of an acceleration compensation. This acceleration compensation is used to com-pensate for the low initial acceleration caused by system delay by increasing the torque limit during a commanded acceleration [12]. This compensation can be described by the following equation

Tmax0 = Tmax+ ˙TrefG, ˙Tref > 0, (4.1)

where G is the compensation gain, Tmaxis the estimated maximum transmissible

torque, ˙Tref is the change in reference torque, and Tmax0 is the compensated

maxi-mum transmissible torque.

Unlike the MFC, the MTTE controller does not make use of an activation func-tion. This means it does not have to estimate the slip, but it also means the performance of the vehicle is always limited. This leads to lower accelerations when the vehicle is operated in good driving conditions.

The Simulink model for the speed-based MTTE can be seen in Figure 4.12. The only real change in the model is a change of output to the compensated maximum torque instead of the actual torque. The more major change is that this output is converted to a maximum acceleration by dividing with the wheel moment of inertia and using it to limit the change of the commanded speed to the speed controller, effectively limiting the maximum requested torque.

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28 4 Modelling

Figure 4.12:The Simulink model for the MTTE using speed-based control.

The Simulink model for the torque-based MTTE can be seen in Figure 4.13, and as with the MFC the main difference between it and the speed-based version of the controller is the lack of a speed controller. Instead it directly limits a requested torque to reduce the slip of the vehicle.

Figure 4.13:The Simulink model for the MTTE using torque-based control.

4.4.3 Sliding Mode Control

The models for the sliding mode controllers can be seen in Figure 4.14 and Fig-ure 4.15. These models are the most similar to each other of the three controllers, only having different output gains resulting in a speed decrease or a torque de-crease. The models are also very similar to the model in Figure 2.7, only contain-ing a few additions.

As with the MFC there is a “direction switch” implemented to make sure the con-troller will not increase the commanded speed or torque above the commanded value but only reduce it, meaning a positive speed/torque command can only be reduced, and a negative speed/torque command can only be increased. The control activation function from the MFC described in Algorithm 1 is also im-plemented for the sliding mode, and since the vehicle speed is measured for the sliding mode controller the slip can be obtained directly instead of having to be estimated. This gives a more accurate activation of the controller compared to

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the MFC which is more affected by modelling errors.

Another addition is a saturation of the resulting control signal. This saturation is used to limit the maximum speed/torque decrease to avoid chattering.

The Simulink model for the speed-based sliding mode controller can be seen in Figure 4.14. As with the MFC this controller applies a speed decrease to the com-manded speed which the existing speed controller then tries to follow, resulting in reduced slip depending on the speed reduction. Since the theory about the slid-ing mode is based on results in a torque decrease, see Section 2.3.3, this torque is converted to a speed decrease using the gain KSMC. This gain is also used as a

tuning parameter together with γ.

Figure 4.14: The Simulink model for the sliding mode using speed-based control.

The Simulink model for the torque-based sliding mode controller can be seen in Figure 4.15. In the same was as for the other torque-based controllers the speed controller is removed and a torque reference is used instead which is reduced us-ing the output of the controller. Although this controller does control the torque it still utilizes an output gain as a tuning parameter together with γ in the same way the speed-based version does.

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30 4 Modelling

Figure 4.15: The Simulink model for the sliding mode using torque-based control.

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5

Results

In this chapter the results of the simulations using the traction control systems described in Section 4.4 are presented. The simulations were performed with different reference values depending on the version of the controller. The speed-based versions of the controllers used a step as reference signal to simulate a com-manded speed. Due to the existing rate limiter in the speed controller this step is converted to a ramp which the traction controllers affect. The torque-based versions of the controllers used a ramp as reference signal to simulate an acceler-ation command.

Each controller was simulated four times with different settings; speed-based unloaded, torque-based unloaded, speed-based loaded, and torque-based loaded. For the unloaded cases there is no load on the forks of the forklift, and for the loaded cases there is a load of 2000 kg applied to the forks of the forklift. All simulations were done with an assumed ground-tire friction of µ ≈ 0.3 to allow wheel slip to occur.

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32 5 Results

5.1 Model Following Control

The results of the simulations performed with the different variants of the MFC controller using different load cases are presented in the following subsections.

5.1.1 Unloaded speed-based case

The simulation results for the unloaded forklift truck using the speed-based MFC controller can be seen in Figure 5.1 and Figure 5.2. In Figure 5.1 a comparison between the wheel speed and the vehicle speed is shown when the controller is on and when it is off. Both vehicle speeds reach the reference speed, with the controlled vehicle reaching it faster. The controlled vehicle has a faster initial ac-celeration and manages to greatly reduce the speed difference between the wheel speed and vehicle speed, but it is slowed down slightly later around 4.5 s.

0 2 4 6 8 10 12 14 16 18 20 Time [s] 0 5 10 Speed [km/h]

Speed comparison (MFC-Speed-Unloaded)

Wheel speed, ctrl off Vehicle speed, ctrl off Wheel speed, ctrl on Vehicle speed, ctrl on

Figure 5.1: The vehicle speed compared to the wheel speed of the unloaded forklift truck when the speed-based MFC controller is activated/deactivated. The motor torque as well as the measured slip for the forklift truck with the con-troller activated and deactivated is shown in Figure 5.2. The motor torque is initially similar, causing a similar initial slip. Following this the motor torque of the controlled vehicle is reduced more than that of the non-controlled vehi-cle, causing re-adhesion. This increased traction allows a greater torque to be transferred to the ground, resulting in a greater motor torque for the controlled vehicle. The drop in acceleration seen in Figure 5.1 can also be seen as a reduc-tion in the motor torque, while the non-controlled vehicles torque remains large. Besides the initial slip, it can be seen that the controller manages to reduce the slip compared to the non-controlled vehicle.

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5.1 Model Following Control 33 0 2 4 6 8 10 12 14 16 18 20 0 2 4 6 Torque [Nm]

Motor Torque (MFC-Speed-Unloaded)

Controller off Controller on 0 2 4 6 8 10 12 14 16 18 20 Time [s] 0 0.2 0.4 Slip [-]

Measured slip (MFC-Speed-Unloaded)

Controller off Controller on

Figure 5.2: The motor torque and measured slip of the unloaded forklift truck when the speed-based MFC controller is activated/deactivated.

5.1.2 Unloaded torque-based case

The simulation results for the unloaded forklift truck using the torque-based MFC controller can be seen in Figure 5.3 and Figure 5.4. As with the speed-based version of the controller both vehicles reach the maximum speed determined by the torque-speed envelope mentioned in Section 4.1, but in this case it is due to the increasing torque reference and not a speed reference set to the maximum speed. Unlike with the speed-based controller the non-controlled vehicle reaches the maximum speed first, since in this case the controlled vehicle does not have a higher acceleration initially. It still greatly reduces the wheel slip compared to the non-controlled vehicle.

0 2 4 6 8 10 12 14 16 18 20 Time [s] 0 5 10 Speed [km/h]

Speed comparison (MFC-Torque-Unloaded)

Figure 5.3: The vehicle speed compared to the wheel speed of the unloaded forklift truck when the torque-based MFC controller is acti-vated/deactivated.

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34 5 Results

As seen in the motor torque and slip results in Figure 5.4 the motor torque is very oscillatory for the controlled vehicle with rapid and large changes in magnitude. This can result in increased driveline wear [28]. As with the speed-based version in Figure 5.2 the initial part of the motor torques is similar, but the torque is quickly reduced resulting in a low slip.

0 2 4 6 8 10 12 14 16 18 20 0

5 10

Torque [Nm]

Motor Torque (MFC-Torque-Unloaded)

Controller off Controller on 0 2 4 6 8 10 12 14 16 18 20 Time [s] 0 0.2 0.4 0.6 Slip [-]

Measured slip (MFC-Torque-Unloaded)

Figure 5.4: The motor torque and measured slip of the unloaded forklift truck when the torque-based MFC controller is activated/deactivated.

5.1.3 Loaded speed-based case

The simulation results for the forklift truck loaded with 2000 kg using the speed-based MFC controller can be seen in Figure 5.5 and Figure 5.6. In the results of the speed comparison seen in Figure 5.5 it can be seen that increased load greatly affects the performance of both the vehicle and the controller. Compared to the unloaded case seen in Figure 5.1 the maximum speed of around 10 km/h is not achieved during the 20 s simulation time, and both the non-controlled and controlled vehicle slip initially. The controlled vehicle does manage to reduce the slip considerably after a time, resulting in a greater acceleration than the non-controlled vehicle. In Figure 5.6 the large initial slip is clearly visible, and it is reflected in the motor torque which oscillates initially creating the slip. It can also be seen that the torque of the controlled vehicle is greater due to the increased traction as a result of the lower slip.

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5.1 Model Following Control 35 0 2 4 6 8 10 12 14 16 18 20 Time [s] 0 5 10 Speed [km/h]

Speed comparison (MFC-Speed-Loaded)

Figure 5.5: The vehicle speed compared to the wheel speed of the loaded forklift truck when the speed-based MFC controller is activated/deactivated.

0 2 4 6 8 10 12 14 16 18 20 0

5 10

Torque [Nm]

Motor Torque (MFC-Speed-Loaded)

Controller off Controller on 0 2 4 6 8 10 12 14 16 18 20 Time [s] 0 0.5 1 Slip [-]

Measured slip (MFC-Speed-Loaded)

Figure 5.6:The motor torque and measured slip of the loaded forklift truck when the speed-based MFC controller is activated/deactivated.

5.1.4 Loaded torque-based case

The simulation results for the forklift truck loaded with 2000 kg using the torque-based MFC controller can be seen in Figure 5.7 and Figure 5.8. In Figure 5.7 it can be seen that the wheel speed of the controlled vehicle is kept from slipping compared to the large slip of the non-controlled vehicle. As with the previous result for the speed-based version this reduced slip increases the traction and therefore the acceleration of the vehicle.

In Figure 5.8 it can be seen that the torque-based MFC results in a very oscillatory behavior of the motor torque. As with the speed-based controller the torque is larger than the non-controlled torque due to the increased traction, and it can be

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36 5 Results 0 2 4 6 8 10 12 14 16 18 20 Time [s] 0 5 10 Speed [km/h]

Speed comparison (MFC-Torque-Loaded)

Figure 5.7: The vehicle speed compared to the wheel speed of the loaded forklift truck when the torque-based MFC controller is acti-vated/deactivated.

seen that the slip is quickly reduced with the fast torque response when it occurs initially. 0 2 4 6 8 10 12 14 16 18 20 0 5 10 Torque [Nm]

Motor Torque (MFC-Torque-Loaded)

Controller off Controller on 0 2 4 6 8 10 12 14 16 18 20 Time [s] 0 0.5 1 Slip [-]

Measured slip (MFC-Torque-Loaded)

Figure 5.8: The motor torque and measured slip of the loaded forklift truck when the torque-based MFC controller is activated/deactivated.

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5.2 Maximum Transmissible Torque Estimation 37

5.2 Maximum Transmissible Torque Estimation

The results of the simulations performed with the different variants of the MTTE controller using different load cases are presented in the following subsections.

5.2.1 Unloaded speed-based case

The simulation results for the unloaded forklift truck using the speed-based MTTE controller can be seen in Figure 5.9 and Figure 5.10. In the speed comparison seen in Figure 5.9 it can be seen that the controlled vehicle manages to effectively reduce the slip that occurs for the non-controlled vehicle. Both vehicles reach the maximum speed around a similar time due to the larger acceleration of the controlled vehicle being countered by its initial delay in acceleration.

0 2 4 6 8 10 12 14 16 18 20 Time [s] 0 5 10 Speed [km/h]

Speed comparison (MTTE-Speed-Unloaded)

Figure 5.9: The vehicle speed compared to the wheel speed of the unloaded forklift truck when the speed-based MTTE controller is acti-vated/deactivated.

The delayed torque response caused by the MTTE controller is clearly visible in Figure 5.10. As can be seen the torque increases as the “maximum transmissible acceleration” increases, eventually resulting in a minor slip occurring. This slip is quickly reduced by the controller.

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38 5 Results 0 2 4 6 8 10 12 14 16 18 20 0 2 4 6 Torque [Nm]

Motor Torque (MTTE-Speed-Unloaded)

Measured slip (MTTE-Speed-Unloaded)

Figure 5.10: The motor torque and measured slip of the unloaded forklift truck when the speed-based MTTE controller is activated/deactivated.

5.2.2 Unloaded torque-based case

The results for the unloaded forklift truck using the torque-based MTTE con-troller can be seen in Figure 5.11 and Figure 5.12. The speed comparison in Figure 5.11 is very similar to the speed comparison for the speed-based MTTE in Figure 5.9, with a similar delay of the controlled vehicle and a slightly higher acceleration. 0 2 4 6 8 10 12 14 16 18 20 Time [s] 0 5 10 Speed [km/h]

Speed comparison (MTTE-Torque-Unloaded)

Figure 5.11: The vehicle speed compared to the wheel speed of the unloaded forklift truck when the torque-based MTTE controller is acti-vated/deactivated.

In Figure 5.12 it is clearly seen that the motor torque of the controlled vehicle has a slower torque increase than the non-controlled vehicle. This is a result of the

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5.2 Maximum Transmissible Torque Estimation 39

maximum torque initially limiting the motor torque, greatly reducing the slip. As with most previous controllers, this allows the torque of the controlled vehicle to exceed the torque of the non-controlled vehicle due to the increased traction.

0 2 4 6 8 10 12 14 16 18 20 0

5 10

Torque [Nm]

Motor Torque (MTTE-Torque-Unloaded)

Measured slip (MTTE-Torque-Unloaded)

Figure 5.12: The motor torque and measured slip of the unloaded forklift truck when the torque-based MTTE controller is activated/deactivated.

5.2.3 Loaded speed-based case

The simulation results for the forklift truck loaded with 2000 kg using the speed-based MTTE controller can be seen in Figure 5.13 and Figure 5.14. In Figure 5.13 it can be seen that the non-controlled vehicle is greatly affected by the increased load, resulting in a much larger slip than the no-load case and a much slower acceleration of the vehicle. The controlled vehicle manages to effectively reduce the slip and increase the acceleration of the vehicle, but it still has a delay in acceleration caused by the MTTE controller.

The more gradual increase in torque is seen in Figure 5.14, and it is clearly seen that the increased acceleration is a result of the large motor torque during the middle of the simulation, this motor torque being around 60% greater than that of the non-controlled vehicle. As seen the slip is kept low throughout the entire acceleration phase.

Evaluation of Traction Control Systems for an Electric Forklift Truck

Master of Science Thesis in Electrical Engineering

Department of Electrical Engineering, Linköping University, 2021