Instituto Tecnol´ogico y de Estudios Superiores de Monterrey

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Monterrey Campus

School of Engineering and Sciences

Control of Semi-Active Suspensions For In-Wheel Electric Vehicles

A Thesis presented by

Mauricio Anaya Mart´ınez

Submitted to the

School of Engineering and Sciences

in partial fulfillment of the requirements for the degree of Master of Science

in

Manufacturing Systems

Monterrey, Nuevo Le´on, June, 2020

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Acknowledgments

I would like to thank my co-advisor, Dr. Jorge Lozoya, for sharing all his knowledge with me as well as for his invested time in mentoring and advising me.

His comments and advises were crucial for the development of this work.

I also would like to acknowledge my advisor, Dr. Ruben Morales-Menendez, who, since the beginning, trusted me in being part of the Automotive Consortium research group. He was always aware of my needs during my research, and his comments were always helpful for continuing in my pursuit of knowledge.

I would like to acknowledge the Automotive Consortium members for their comments and support when needed.

I would like to thank my friends and colleagues from the MSM program, for their support and for all the experiences we lived along this time together. I am sure that I have learned a lot from their comments and personal experiences.

And finally, I am thankful to the CONACyT program in Mexico for its finan- cial support as well as Tecnol´ogico de Monterrey for the institutional scholarship.

Without their support, I would have never been able to complete this academic degree.

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Dedication

To my mother Miriam,

who always encourages me to trust myself.

To my father Mauricio,

who always trusts and supports my dreams.

To my sister M´onica,

who always offers her unconditional support.

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Contents

1 Introduction 2

1.1 Motivation . . . 2

1.2 Problem description . . . 2

1.3 Aim and objectives . . . 2

1.3.1 Aim . . . 2

1.3.2 Objectives . . . 2

1.4 State-of-the-art . . . 3

1.5 Hypothesis . . . 5

2 Theoretical framework 6 2.1 Automotive Suspensions . . . 6

2.2 Quarter of Vehicle . . . 6

2.2.1 Normal . . . 6

2.2.2 In-Wheel . . . 7

2.3 Physical configuration . . . 7

2.3.1 Macpherson Strut Suspension . . . 7

2.3.2 Double Wishbone . . . 8

2.3.3 Trailing arm suspension . . . 8

2.4 Type of Suspension . . . 9

2.4.1 Passive Suspension . . . 9

2.4.2 Semi-active Suspension . . . 9

2.4.3 Active suspension . . . 9

2.5 Damping technology . . . 10

2.5.1 Passive damper . . . 10

2.5.2 Magneto-rheological (MR) Damper . . . 10

2.5.3 Electro-rheological (ER) Damper . . . 11

2.5.4 Electro-hydraulic (EH) Damper . . . 11

2.5.5 Electromagnetic damper . . . 11

2.5.6 Pneumatic (EH) Damper . . . 11

2.5.7 Actuator Curves . . . 11

2.6 Sensors . . . 12

2.6.1 Primary Sensors . . . 12

2.6.2 Secondary Sensors . . . 13

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2.7 Controllers . . . 13

2.7.1 Heuristic controllers. . . 13

2.7.2 Linear Controllers. . . 16

2.7.3 NonLinear Controllers. . . 17

2.7.4 Intelligent Controllers . . . 20

2.8 Controllers performance. . . 22

2.9 In-wheel electric motors . . . 27

2.9.1 Brushless DC motor . . . 27

2.9.2 Switched reluctance motor (SRM) . . . 27

2.10 Other applications . . . 28

3 Materials and Methods 30 3.1 Magnetorheological damper model . . . 30

3.2 F-class vehicle model . . . 30

3.3 QoV’s description . . . 34

3.4 Full vehicle model . . . 36

3.5 Controllers tuning for benchmark . . . 37

3.6 Tests definition . . . 39

3.6.1 QoV’s . . . 42

3.6.2 Full Vehicle . . . 44

3.7 Performance indexes for a full vehicle model . . . 44

3.7.1 QoV . . . 46

3.7.2 Full vehicle . . . 46

3.8 Performance improvement evaluation . . . 48

3.8.1 Time domain . . . 48

3.8.2 Frequency domain . . . 48

4 Results 53 5 Discussion 57 6 Conclusions 101 6.1 QoV’s . . . 101

6.2 Full Vehicles . . . 102

6.3 Contributions . . . 103

6.4 Further Work . . . 104

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A Figures and Tables From Experiments 117

A.1 QoV results . . . 117

A.1.1 ICE QoV . . . 117

A.1.2 Modified QoV . . . 126

A.1.3 EQoV . . . 126

A.2 Full vehicle results . . . 147

A.2.1 ICEV . . . 147

A.2.2 ModV . . . 147

A.2.3 EV . . . 193

A.2.4 EV with the new M1S and FEB controllers tuning . . . . 212

A.2.5 Full vehicle results in road type B-C tests. . . 212

A.3 QoV’s in full vehicles results . . . 212

A.3.1 Front corner of the ICE vehicle (FQoVICE) . . . 212

A.3.2 Front corner of the modified vehicle (FQoVMod) . . . 212 A.3.3 Front corner of the full in-wheel electric vehicle (FQoVEV) 213 B Lithium-ion Batteries And In-Wheel Electric Motors Parameters 257

C Vita 259

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List of Tables

1 SP asymmetric model parameters. . . 31

2 F-class vehicle parameters in CarSim. . . 32

3 Modified F-class vehicle parameters in CarSim. . . 33

4 QoV parameters . . . 35

6 EQoV parameters . . . 35

5 Modified QoV parameters . . . 35

7 Full vehicles parameters. . . 38

8 FEB bandwidths and current values for comfort. . . 39

9 FEB bandwidths and current values for road holding. . . 40

10 Values for damping coefficients computing. . . 40

11 FEB Frequency bandwidths for the QoV . . . 40

12 FEB Frequency bandwidths for the modified QoV. . . 41

13 FEB Frequency bandwidths for the EQoV. . . 41

14 Definition of the relative amplitude spectrum. . . 43

15 Performances to be evaluated in full vehicle model tests. . . 47

16 Experiments table. . . 50

17 Results for F-class baseline suspension . . . 53

18 Results for 1.25A baseline suspension . . . 54

19 Comfort enhancement from experiments 50, 66, 82, 58, 74, 90 with new tuning for M1S and FEB controllers. . . 54

20 Comfort enhancement from experiments 52, 68, 84, 60, 76, 92 with new tuning for M1S and FEB controllers. . . 55

21 Road holding enhancement from experiments 54, 70, 86, 62, 78 and 94 with new tuning for M1S and FEB controllers. . . 55

22 Road holding enhancement from experiments 56, 72, 88, 64, 80 and 96 with new tuning for M1S and FEB controllers. . . 56

23 Comfort enhancement from road type B-C tests. . . 56

24 Road holding enhancement from road type B-C tests. . . 56

25 Comfort enhancement from experiments 1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41 and 45. . . 214

26 Road holding enhancement from experiments 1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41 and 45. . . 214

27 Useful lifetime enhancement from experiments 1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41 and 45. . . 214

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28 Comfort enhancement from experiments 2, 6, 10, 14, 18, 22, 26,

30, 34, 38, 42 and 46. . . 214 30 Useful lifetime enhancement from experiments 2, 6, 10, 14, 18,

22, 26, 30, 34, 38, 42 and 46. . . 249 31 Comfort enhancement from experiments 3, 7, 11, 15, 19, 23, 27,

31, 35, 39, 43 and 47. . . 250 32 Road holding enhancement from experiments 3, 7, 11, 15, 19, 23,

27, 31, 35, 39, 43 and 47. . . 250 33 Useful lifetime enhancement from experiments 3, 7, 11, 15, 19,

23, 27, 31, 35, 39, 43 and 47. . . 250 34 Comfort enhancement from experiments 4, 8, 12, 16, 20, 24, 28,

32, 36, 40, 44 and 48. . . 250 35 Road holding enhancement from experiments 4, 8, 12, 16, 20, 24,

28, 32, 36, 40, 44 and 48. . . 251 36 Useful lifetime enhancement from experiments 4, 8, 12, 16, 20,

24, 28, 32, 36, 40, 44 and 48. . . 251 37 Comfort enhancement from experiments 49, 57, 65, 73, 81, 89. . . 251 38 Comfort enhancement from experiments 50, 58, 66, 74, 82, 90. . . 252 39 Comfort enhancement from experiments 51, 59, 67, 75, 83, 91. . . 252 40 Comfort enhancement from experiments 52, 60, 68, 76, 84, 92. . . 252 41 Road holding enhancement from experiments 53, 61, 69, 77, 85, 93. 253 42 Road holding enhancement from experiments 54, 62, 70, 78, 86, 94. 254 43 Road holding enhancement from experiments 55, 63, 71, 79, 87, 95. 254 44 Road holding enhancement from experiments 56, 64, 72, 80, 88, 96 254 45 Comfort enhancement from experiments 97, 105, 113, 121, 129, 137.255 46 Road holding enhancement from experiments 101, 109, 117, 125,

133, 141. . . 255 47 Useful lifetime enhancement from experiments 101, 109, 117,

125, 133, 141. . . 255 48 Comfort enhancement from experiments 98, 106, 114, 122, 130, 138.255 49 Road holding enhancement from experiments 102, 110, 118, 126,

126, 134, 142. . . 256 51 Comfort enhancement from experiments 99, 107, 115, 123, 131, 139.256

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52 Road holding enhancement from experiments 103, 111, 119, 127,

127, 135, 143. . . 256 54 Comfort enhancement from experiments 100, 108, 116, 124, 132,

140. . . 257 55 Road holding enhancement from experiments 104, 112, 120, 128,

128, 136, 144. . . 257 57 Technical performance by existing battery type. . . 258 58 In-wheel electric motors main characteristics. . . 258

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List of Figures

1 a) Normal Quarter of Vehicle (QoV), b) in-wheel QoV. . . 7

2 Macpherson strut suspension. . . 8

3 Double wishbone suspension system. . . 8

4 a)Semi-active suspension system normal QoV, (b) semi-active suspension system in-wheel QoV. . . 9

5 a)Active suspension system normal QoV, b) active suspension system in-wheel QoV. . . 10

6 Resulting curve continuous pressure. . . 12

7 Resulting curve continuous authority. . . 12

8 Heuristic controllers a) Skyhook b) Groundhook. . . 15

9 Janeway’s comfort criterion. . . 23

10 BLDC motor. . . 28

11 SRM diagram. . . 28

12 Regenerative suspension system with ball screw shaft. . . 29

13 F-class vehicle. . . 32

14 F-class vehicle physical dimensions. . . 33

15 Residual vertical force. . . 34

16 SRM residual vertical force diagram, adapted from [1]. . . 34

17 QoV’s for simulation. . . 36

18 Full vehicle model. . . 36

19 Force-electric current conversion with PI controller. . . 41

20 Nonlinear passive damping force F-V diagram of an F-class vehicle. 41 21 Time domain input signals . . . 42

22 Frequency domain input signal . . . 43

23 Time domain input signals for modified QoV . . . 43

24 Bump . . . 45

25 Sine Sweep Steering Signal. . . 45

26 Road Profile Type C-B. . . 46

27 Results from experiments 1,5 and 9. . . 118

31 PSD improvement from experiment 13. . . 122

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33 Pseudobode plots from experiment 13. . . 124

39 Results from experiments 17, 21 and 25. . . 131

63 Results from experiments 49 and 50 . . . 156

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83 Results from experiments 65 and 66. . . 174

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123 RMS improvement from experiments 50, 54, 66, 70, 82 and 86 with new FEB and M1S tuning. . . 215

124 RMS improvement from experiments 52, 56, 68, 72, 84 and 88 with new FEB and M1S tuning. . . 216

125 PSD improvement from experiments 58, 74 and 90 with new FEB and M1S tuning. . . 217

129 Pseudobode plots from experiments 58, 74 and 90 with new FEB and M1S tuning. . . 221

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130 Pseudobode plots from experiments 60, 76 and 92 with new FEB

and M1S tuning. . . 222

133 Comfort improvements in the road type B-C. . . 225

134 Road holding improvements in the road type B-C. . . 226

139 PSD improvement from experiments 105 and 106. . . 229

143 Pseudobode plots from experiments 105 and 106. . . 231

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Control of Semi-Active Suspensions For In-Wheel Electric Vehicles

By

Mauricio Anaya Mart´ınez

Abstract

With the electric vehicles highly adoption, there is a need for keeping improving automotive systems. This work is focused on exploring the use of semi-active suspension systems in in-wheel electric vehicles. For that, two different in-wheel concepts are considered. When a brush-less DC (BLDC) motor and when a switched reluctance motor (SRM) are employed. In the SRM, an unbalanced vertical force is taken into account for the vertical dynamics model. The vertical dynamics tests are performed making use of models from one-quarter of vehicle (QoV) and full vehicle. Four different semi-active controllers, as well as three current levels, are evaluated and compared in time and frequency domain when employed in the in-wheel and internal combustion engine (ICE) vehicles. The suspension objectives improvement is estimated by making use of some performance indexes. Where the obtained results are compared against the ones given by the 1.25A and F-class baseline suspensions. The results showed that when compared against the F-class baseline suspension, none of the controllers is giving human and ride comfort improvements for the in-wheel electric vehicles. While, in comparison with the 1.25A baseline, the FEB controller is providing the best increase (25% − 50%). By the side of the road holding and handling, the M1S guarantees the road holding and handling improvement (10%-25%) for the BLDC. While for the SRM, the FEB controller improves them when compared against the F-class baseline suspension. When taking as reference the 1.25A baseline suspension, the road holding and handling are enhanced by the 1.25A baseline and GH, respectively, for the BLDC.

While in the SRM, the FEB controller is giving the best improvement (10% − 55%). In most cases, high and low current values guarantee the comfort and road holding improvements, respectively.

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1 Introduction

1.1 Motivation

Today, automotive vehicles are considered the primary conveyance due to the high amount of people who perform their daily activities, making use of them. For that, continuous improvements focused on safety and travel experience may be reached. During the last years, these improvements have been devoted to enhanc- ing automotive suspension systems, where the road holding, as well as the comfort for vehicle passengers, have been improved. A balance between road holding and comfort has been the main goal in this area; however, most of the devoted work has been focused on internal combustion engine vehicles. For this reason, with the high and growing adoption of electric vehicles (EV’s), there is a need for solutions for guaranteeing the balance between comfort and road holding. Especially when working with an in-wheel powertrain configuration with semi-active suspension systems when a switched reluctance (SR) and brushless DC (BLDC) motors are employed. The use of SR instead of BLDC motors in in-wheel configurations has increased due to the low cost, efficient power transfer, high torque density, and direct drivetrain system features that the SR motors offer for this application, [2].

1.2 Problem description

There is no work which validates performance improvement in electric vehicles (EV) with an in-wheel powertrain configuration, when looking for vibrations mitigation making use of semi-active control strategies.

1.3 Aim and objectives 1.3.1 Aim

Explore the effect in in-wheel electric vehicles vertical dynamics when employing semi-active suspension systems as a way for improving suspension objectives.

1.3.2 Objectives

• Compare the vertical dynamics improvement in three different (ICE, ModV and EV) quarter of vehicles (QoV’s) performing open and closed loop simulations in the time and frequency domain when a magnetorheological damper is considered as the semi-active device.

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• Compare the vertical dynamics improvement in three different (ICE, ModV and EV) vehicles performing open and closed loop simulations in the time and frequency domain when a magnetorheological damper is considered as the semi-active device.

• Analyze the results employing time and frequency domain performance indexes.

1.4 State-of-the-art

Vehicles suspension systems aim to improve passenger’s comfort by reducing the vibration caused by the onboard engine and the road irregularities [3]. When trying to achieve the main objectives (comfort and road holding) of an automotive suspension using passive dampers, it is hard to get the desired results. As an alternative, passive suspensions have been replaced by semi-active suspensions, which consist of a passive spring with a controllable damper as an actuator. There are various ways for controlling the damping coefficient of semi-active suspension systems. But the use of magneto-rheological (MR) fluid dampers has received considerable interest due to its simplicity in mechanics, huge dynamics range, low power requirement, and robustness, [4]. They contain MR fluids that reversibly change their rheological properties in the presence of the varying magnetic field.

The fluid force can be acted on by charging the magnetic field amplitude. To use semi-active dampers for vibration isolation, they need to be appropriately controlled, [3]. To this end, several control approaches have been proposed.

According to a state of the art review, it can be said that Fuzzy [5], [6], [7], [8], [9], SkyHook [10], [11], [12] control strategies as well as their variations have been the most employed techniques for satisfying the main semi-active suspensions control objectives. The most common control output is the desired damping force that later is converted to current in order to manipulate the MR, but in some cases, as in [9], the control output is already current. The most employed control inputs are the accelerations of the sprung and unsprung mass, as well as their real-time displacements. For the validation of the controller by simulation, it is common to employ Matlab/Simulink [7], [13], [14], [9], Carsim [15], [16], [17], Bikesim [18], Trucksim [19] where parameters of the quarter of vehicle (QoV) are assumed, and some road disturbances are considered, to visualize the controller response the results are evaluated during the time(step and bump) and frequency (white noise) domain employing qualitative or quantitative principles, for quanti-

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tative evaluation root mean square (RMS, for evaluation in the time domain) [5], [20] and power spectral density (PSD, for evaluation in frequency domain) [21], [20]) are employed. For the experimental validation of the controller, it is possible to employ an experimental quarter of vehicle (Exp-QoV) [12], [22] Hardware in the Loop (HiL) [23], [24], [25] or a Vehicle (Exp-V) [21] where accelerometers and sensors are employed to obtain the information that will be processed by the controller in order achieve the main objectives of the control strategy.

In the last years, some solutions in automotive suspension systems in order to reduce vibration effects for in-wheel electric vehicles have been devoted. In [26], the in-wheel electric motor is employed as an ”Advanced-Dynamic-Damper- Motor” (ADM), where the electric motor is considered as a damper mass to de- crease tire contact force fluctuation in the vehicle. This by attaching the motor in the unsprung mass employing a spring and damper of exclusive use. As a result, the vibration of the sprung mass decreased. In [27], the ADM and an LQR active suspension system are considered for sprung mass vibration reduction, but also a vertical linear force (F_v) provided by the SR in-wheel electric motor is taken into account for the vertical dynamics analysis. In [1], an FxLMS (filtered-X-least mean square) is proposed for improving suspension performance with an active suspension system. In this case, the electric motor is considered as part of the unsprung mass, and the Fv is also considered as an extra force adding vibration to the unsprung mass. The FxLMS controller can generate a controllable force for suppressing the vibration generated by Fv. In [28], the ADM complemented by an active suspension system is employed, where the suspended motor and suspension parameters are optimized based on genetic algorithms (GA) and complemented by an LQR controller for the active suspension system. In [29], the stator (housing) of the in-wheel electric motor as the unsprung mass and the rotor are considered as an extra mass in the in-wheel vehicle dynamic model. A multi-objective optimization control method of active suspension for solving the negative vibration issues generated by Fv is presented. The Particle Swarm Optimization (PSO) method is employed for obtaining active suspension system optimal parameters. The results show that the optimized suspension system is able to reduce the effects of Fv. As can be seen, the current work in suspension systems for in-wheel electric vehicles is focused on active suspension systems. As it can be seen, there is no work which validates performance improvement in EV’s with an in-wheel powertrain configuration, when looking for vibrations mitigation making use of semi-active control

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strategies.

1.5 Hypothesis

• It is possible to improve the suspension objectives for in-wheel electric vehicles when a semi-active suspension system is employed for mitigating the vibrations given by the road profile and electric motor.

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2 Theoretical framework

In this section, some important concepts are explained to understand the main purposes of this work.

2.1 Automotive Suspensions

The suspension system of an automobile has the purpose of providing the oper- ator and users driving comfort and safety because it needs to be able to support the weight of the vehicle and distribute the incoming external forces through the structure. The components of this system are dampers, springs, and control arms [30]:

• The spring has the function to support the mass of the vehicle, and to isolate the body and its occupants from the disturbances that the road could introduce to the system. The spring has comfort related functionality.

• The damper, as its name suggests, it is used for damping the oscillations from the tyre to the body of the vehicle. It has both comfort and safety related functionality.

• The control arms are used to provide steering and manipulate the vehicle in general terms. Also, they have the purpose of joining the whole suspension system to the body or chassis of the vehicle.

2.2 Quarter of Vehicle

Two-quarter of vehicles are considered: normal and in-wheel, in the next para- graphs they will be described.

2.2.1 Normal

In this case, the powertrain comes from a motor that is not inside the wheel and is considered the most common configuration, for that, most of the researches [31], [5], [32], [33] have been focused on generating solutions for a normal QoV. The model of a normal QoV is presented in Figure 1 a). Using Newton’s second law, the differential equations of motion for the sprung mass ms and unsprung mass m_u for a normal QoV are respectively:

m_sz¨₁ + c_s( ˙z₁ − ˙z₂) + k_s(z₁ − z₂) = 0

m_uz¨₂ + c_s( ˙z₂ − ˙z₁) + k_s(z₂ − z₁) + k_tz₂ = k_tz₀ (1)

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ms

Ks cs

m_u

Kt

Z s

Zus

Rotor Stator housing

ms

Kt c t mur

Km F rZ

mus cs

Zg Zur Zus

K s Z s

b) a)

w

Zr

Figure 1: a) Normal Quarter of Vehicle (QoV), b) in-wheel QoV.

2.2.2 In-Wheel

For this configuration, an electric motor is located inside the wheel as it is shown in Figure 1 b), just few research have been devoted about the suspension systems when working with this configuration, and they have just been focused on imple- menting active suspensions systems ([34],[29], [35]). The model of an in-wheel QoV is presented in Figure 1b), where the actuator force is denoted by Fa [29].

Using Newton’s second law, the differential equations of motion for the sprung mass ms, total mass mu and unsprung mass mur are respectively:

m_sz¨_s + c_s( ˙z_s− ˙z_us) + k_s(z_s− z_us) − F_a = 0 m_urz¨_ur + c_t( ˙z_ur − ˙z_g) + k_t(z_ur − z_g) + k_m(z_ur − z_us) + F_rz = 0 musz¨us+ ct( ˙zus− ˙zs) + ks(zus− z_s) + km(zus− z_ur) − Frz + Fa = 0

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2.3 Physical configuration

Three physical configurations (Macpherson, double wishbone and trailing arm suspension) for the automotive suspension systems are described below.

2.3.1 Macpherson Strut Suspension

This kind of suspension is widely employed in many modern vehicles due to its lightweight, simple structure and compact size, as it can be seen in Figure 2, [36].

Macpherson strut is a further development of modification of the double wishbone type suspension. An upper transverse is replaced by a pivot point located on the end of the damper-spring assembly. This configuration can be employed for both

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Figure 2: Macpherson strut suspension, [37].

Figure 3: Double wishbone suspension system, [38].

front and rear suspensions, but it is highly typical to found it in the front of the vehicle.

The main advantage is that it takes up less space horizontally, and as a result, the passengers get more free areas in the car. Due to its simplicity (just one single assembly), it is accessible to manufacturing as well as a low-cost alternative.

2.3.2 Double Wishbone

In this type of suspension system, the wheel is guided by two control links, called upper and lower arms, which are connected to the chassis using revolute joints and to the steering knuckle. It is connected to the chassis employing the tie-rod using spherical joints, as it is shown in Figure 3.

The main advantage of a double wishbone suspension is the better stability that this configuration provides to the vehicle by maintaining the tires with better road holding.

2.3.3 Trailing arm suspension

Two or more links are connected between the axle and pivot point [37]. It is typically employed in the rear axle of a motorcycle.

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Figure 4: a)Semi-active suspension system normal QoV, (b) semi-active suspension system in-wheel QoV.

2.4 Type of Suspension

This classification refers to how does the suspension system works depending on the damping actuator that is being employed.

2.4.1 Passive Suspension

A passive suspension in normal and in-wheel setup is shown in Figure 1. This kind of suspensions is only able to dissipate the energy, and its damping characteristics are time-invariant [39], restricting its capabilities when trying to find a balance between comfort and road holding in certain road conditions employing a passive damper.

2.4.2 Semi-active Suspension

A semi-active suspension in normal and in-wheel setup is shown in Figure 4.

Semi-active suspensions provide real-time dissipation of energy to accomplish suspension systems objectives more efficiently, which are achieved employing an active damper instead of a passive damper [40]. To guarantee an adequate real- time response, some sensors, as well as a controller, need to be employed.

2.4.3 Active suspension

An active suspension in normal and in-wheel setup is shown in Figure 5. The active suspension employs pneumatic or hydraulic actuators in order to create the desired force when it is required to provide comfort and road holding, and it is known that the objectives of the system are reached efficiently [40], however, an

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Figure 5: a)Active suspension system normal QoV, b) active suspension system in-wheel QoV.

active suspension consumes large amounts of energy when providing the optimal control force.

2.5 Damping technology

In the following lines, the most common damping technologies implemented in automotive applications are described.

2.5.1 Passive damper

A passive damper is the one employed in passive suspension systems. The passive dampers are not able to modify their damping characteristics ([41], [42], [43], [44], [45], [46], [47], [48], [49]) in real-time and some researches have been focused on finding alternatives with better damping characteristics.

2.5.2 Magneto-rheological (MR) Damper

An MR damper contains MR fluids that reversibly change their rheological properties in the presence of the varying magnetic field, and the fluid force can be acted on by charging the magnetic field amplitude [39].

MR dampers are considered one of the best solutions to manage the balance between comfort and road holding, for that, several researches in suspension systems have been focused on working with MR dampers ([5], [13], [33],[23],[15],[50], [3], [51] ).

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2.5.3 Electro-rheological (ER) Damper

An ER damper has ER fluids to modify its rheological properties when varying in real-time the electric field to generate the required damping force [52]. The ER fluid behaves as a Bingham plastic material when an electric field is applied [53].

To model the behavior, an accurate mathematical model needs to be implemented.

2.5.4 Electro-hydraulic (EH) Damper

This technology is based on the valves with variable diameter between the cham- bers of the damper. The fluid level is regulated by employing an electrically controlled valve. The valve produces a continuous and controllable damping coefficient generating an infinite number of coefficients in a range [54],[55].

2.5.5 Electromagnetic damper

This kind of dampers is considered an alternative to be employed in lightweight electric vehicles [56], [57] for active suspensions, and its energy consumption is similar to MR dampers in semi-active suspensions providing better performance than when working with passive dampers.

2.5.6 Pneumatic (EH) Damper

This technology modifies the damping coefficient employing a pressure pump and the gas resistance. This technology is the most difficult to model due to its physical principle [54].

2.5.7 Actuator Curves

The way to identify the correct damper for an application is presented in [58]

where the main purpose is to analyze the relationship between the flow rate and the damper blades position. The characteristics curves from a damper are presented in a graph, where the stroke and the percent of the wide open are represented on the X-axis and y-axis, respectively. A function of two items (Figure 6) gives the resulting curve.

When the damper is not operating with constant differential pressure, the differential pressure across the damper will increase by the same amount as the differential pressure across the other components of the system decreased. This pressure shift from the system to the damper has a significant impact on the shape of the

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Figure 6: Resulting curve continuous pressure, [58].

Figure 7: Resulting curve continuous authority, [58].

curve. The amount of actual deviation from the shape of the inherent characteristic curve is related to the authority, which means the ratio of the wide open pressure drop though the damper to the total system pressure drop. In Figure 7 there is an example when working with different authority levels.

2.6 Sensors

In this section a brief description of the sensors that are employed in suspension systems which are monitored in real-time and how are they classified in [54].

2.6.1 Primary Sensors

Primary sensors are employed for the suspension control. The instrumentation required for the experimentation is:

• Chassis accelerometer. Its working range specified in ∓10g. Must be of MEMS type and of lateral montage.

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• Axis accelerometer. Its working range specified in ∓25g. Must be of MEMS type and of lateral montage.

• Suspension deflection sensor. Its working range specified in ∓15cm. Must be of MEMS type and of lateral montage. It could be a load-cell or a poten- tiometer.

• Damper body temperature. Its working range specified between −50 to 70.

It could be employed to obtain an analysis of the ratio of the damper performance due to the work environment.

2.6.2 Secondary Sensors

Secondary sensors are employed for the controllers’ evaluation. The secondary instrumentation required for the experimentation is:

• Dissipated force sensor. It measures the damping force applied to the chassis in order to compare it with a real time estimation to verify the quality of the damper model estimation.

• Relative speed sensor. It measures the deflection change speed to validate the estimation calculated employing the measured accelerations as well as to obtain in real-time the force vs speed.

The most employed sensors in research works ([5], [59], [32], [33], [60], [61], [62], [63]) are the accelerometers in order to visualize the behavior of the body accelerations when achieving suspension systems main objectives.

In most of the cases, at least a pair of accelerometers are considered for a correct suspension system performance. Still, some authors ([32], [11]) have proposed employing just one sensor, and the results have been trustworthy.

2.7 Controllers

In this section, the most common automotive suspensions controllers are classified and described. For classifying them, four categories are considered: heuristic, linear, nonlinear, and intelligent controllers.

2.7.1 Heuristic controllers.

The SkyHook(SH) (Figure 8a) strategy is the passenger’s comfort analysis reference point in suspensions control due to its performance, ease of implementation

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and design, [64]. This approach is not intended to improve road holding performance because the sprung mass vibration is not considered in its control law.

The control system uses 2 accelerometers, and the speed and relative speed of the sprung are usually estimated. The control law is:

c =

c_SH if ˙z_s( ˙z_s − ˙z_us) ≥ 0

c_min_SH if ˙z_s( ˙z_s − ˙z_us) < 0 (3) and the damping force (F_SH) is given by:

F_SH =

c_SH ˙z_s if ˙z_s( ˙z_s− ˙z_us) ≥ 0

c_min_SH( ˙z_s − ˙z_us) if ˙z_s( ˙z_s − ˙z_us) < 0 (4) where c_SH y c_min_SH represent the damping coefficient limits (maximum and minimum, respectively), ˙z_s and ˙z_us are the sprung and unsprung mass speeds, respectively. The SH performance is limited to low frequencies, and new improvement proposals have been proposed, [64]. One improvement was presented by Savaresi et al. [65], named Mix-SH-ADD (Mixed SkyHook Acceleration Driven Damper), which includes the damping derivative from the acceleration measurement in the control law to improve comfort performance to high frequencies. This proposal works in two damping states; however, 3 input variables are needed: velocity and acceleration of the sprung mass as well as the relative velocity. The control law Mix-SH-ADD is:

c_{M R} =











c_max if (¨z_s² − α ˙z²_s ≤ 0

∧ ˙z_s( ˙z_s− ˙z_us) ≥ 0)∨

(¨z_s² − α ˙z_s² > 0 ∧ ¨z_s( ˙z_s− ˙z_us) ≥ 0) c_min if (¨z_s² − α ˙z_s² ≤ 0

∧ ˙z_s( ˙z_s− ˙z_us) < 0)∨

(¨z_s² − α ˙z_s² > 0 ∧ ¨zs( ˙zs − ˙z_us) < 0

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where ¨z_s is the sprung mass acceleration and α represents the SH-ADD break frequency, that is to say, is the intersection frequency of the SH and ADD (Accel- eration Driven Damper).

A strategy known as GroungHook(GH) (Figure 8b) focuses on improving the road holding, and it is presented in [66], where a fictitious element (damper) between the ground and the wheel (parallel to the tire) is considered. This controller follows a similar principle to the SH, but it is oriented to the dynamic tire-forces

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ms

c (t) Ks

m_u

Kt

Z s

Zus

c_SH

Zr

ms

c (t) Ks

m_u

Kt

Z s

Zus

c_GH

Zr

a) b)

Figure 8: Heuristic controllers a) Skyhook b) Groundhook, [58].

reduction to guarantee the desired level of road holding. The control law is given by:

c =

c_GH# if − ˙z_us( ˙z_s− ˙z_us) ≥ 0

c_min_GH if − ˙z_us( ˙z_s− ˙z_us) < 0 (6) and the generated damping force (FGH) is given by:

F_GH =

c_GH ˙z_us if − ˙z_us( ˙z_s − ˙z_us) ≥ 0

c_min_GH( ˙z_s − ˙z_us) if − ˙z_us( ˙z_s − ˙z_us) < 0 (7) To reduce instrumentation costs, Savaresi et al.[32], developed an experiment to validate the Mix-1 Sensor(M1S) controller performance following the SH- ADD principle employing just one sensor (suspended mass acceleration), obtaining good comfort performance. This algorithm chooses the maximum or minimum damping coefficient at the end of each sample according to the vertical movement of the sprung mass. The control law is:

c_{M 1S} =

c_{M 1S} if (¨z_s² − α²˙z_s²) ≤ 0

c_{minM 1S} if (¨z_s² − α²˙z_s²) > 0 (8) where α is given by the masses resonance frequencies. The damping force (F_{M 1S}) is given by:

F_{M 1S} =

c_{M 1S}˙z_s if (¨z_s² − α²˙z_s²) ≤ 0

c_{minM 1S}˙z_s if (¨z_s² − α²˙z_s²) > 0 (9)

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on the other way, Sohn et al.[67] and Hong et al.[11], propose a modified (Sky Hook) employing 2 damping coefficients (sky and variable), which is an online adjustable controller for an EH suspension. The main idea is to consider the vibrations generated by the unsprung mass in the control law as a way to guarantee a road holding performance despite the excessive vibrations. The control law is:

u = c_sky˙z_s− c_v( ˙z_s− ˙z_us) (10) .

in Hong et al.[11], a damping coefficients csky y cv optimization function is proposed depending on road type. Five road types are considered to simulate employing HiL, where the dynamic wheel and sprung mass acceleration are considered to minimize a pondered RMS (Root Mean Square) criterion. The HiL validation showed that the computing algorithm time is so high. Therefore the sampling frequency was limited to 100Hz.

Liu et al. [12], propose a control law which mixes the SH and PDD as a way for guaranteeing the performance improvement. For applying the strategy, the sprung and sprung mass displacements are required. The control law is:

c_{SH−P DD}(t) =











c_max if ( ˙z_s² − ˙z_us² ) ≥ 0

or (k_sz_su˙z_su+ c_max˙z²_su) < 0 c_min if (¨z_s² − α²˙z_s²) > 0

and (k_sz_su˙z_su+ c_max˙z_su² ) ≥ 0

−k_sZ_su

˙zsu

, otherwhise

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by employing numerical analysis, it was demonstrated that the SH-PDD re- duces the sprung mass vibration in a better way than the SH-ADD, SH, PDD and ADD strategies. That is why the SH-PDD controller can be considered as almost the optimal semi-active algorithm for guaranteeing the ride comfort.

2.7.2 Linear Controllers.

The linear controllers base their control structures in linearized dampers models.

In linear controllers, the most applied semi active control technique corresponds to the H_∞. The main idea of this control technique is to design a robust controller to

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minimize the stochastic perturbations during the road in terms of stability of system performance during the close loop. In Du et al.[33], an H∞ of static feedback controller is proposed. The controller designed is multi-objective (deflection, road holding, and comfort) with an MR damper. Therefore, weight functions between the controlled output (¨z_s, z_s−z_usand z_us−z_r), and measurement outputs to achieve the objectives are specified. In this work, two sensors are required (deflection and sprung mass acceleration) to be implemented. The main objective of H_∞ control is to find a K to guarantee that the close loop is limited by a constant γ > 0, that is to say, an optimization problem is stated. To obtain a controller solution that accomplishes with stability and performance requirements, some optimization algorithms are followed, such as: genetic algorithms, inequality of linear matrix or Riccati equations. In Du et al. [33] genetic algorithms are employed. Simulation results show that the semi-active suspension contains betters results in the control objectives than a passive suspension, showing similar results as in active suspensions. In F´elix-Herr´an et al. [9], an H_∞ based on Takagi-Sugeno (T-S) fuzzy model for a two-degrees-of-freedom (2-DOF) QoV with an MR damper is proposed. The advantage of having T-S system as a reference is that each piece wise linear system can be exposed to the well-known control theory. The control law is:

u(t) =

N

X

i=1

h_i(x(t))K_ix(t). (12)

the solution proposed herein, considerably enhances the reported work in three out of four indexes. The control output is a current value to the damper instead of a theoretical ideal force generated in an instant time.

2.7.3 NonLinear Controllers.

There are different nonlinear control techniques that have been tested for the semi active suspensions regulation. The most commons are Sliding Mode Control (SMC), Linear Parameter Varying (LPV) and Linear Quadratic Regulator (LQR).

One of the advantages of these controllers is that the road holding and comfort are considered during their design.

The SMC is a nonlinear strategy that allows to design an insensitive control system to parametrical variations or external disturbances. In Dong et al.[5], an SMC is designed for an MR semi-active suspension and is compared against other heuristic control techniques. The control inputs are: the displacements and accelerations

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of the masses. An error vector and a surface are considered, the error vector is employed to adjust the error between the QoV dynamic and the reference model, the surface is employed to describe the error dynamics in an asymptotic way. The control law is:

F_{SM C} =

(f_deq + m_s e sign(s) if [f_deq + m_s e sign(s)]( ˙z_s− ˙z_us) < 0 0 if [f_deq + m_s e sign(s)]( ˙z_s− ˙z_us) ≥ 0

(13) where f_deq = f_sky−r + m_sc1 e₁ + (m_sc2 − k_s) e₂ + k_s(z_us − z_us−r) represents the required damping force depending on the displacement and on the velocity of the sprung mass as well as on deflection velocity. The experimental results show a better performance in comfort when using SMC instead of the rest of the controllers. The sprung mass acceleration is reduced by 15% and the road holding increases by 2% compared with a passive suspension.

The LPV controllers are based on linear controls and, at the same time, are adaptive to the control system variations. This can be achieved by employing online measurements that modify the controller. Their advantages are: consider multiple objectives, simpler online calculus, they are capable of working with nonlinear systems which employ intelligent control strategies. Poussot-Vassal [21]

proposes a control strategy which satisfies the suspension actuator main limita- tions, including an static plane: force vs speed. The control law is:

u = −c_p( ˙z) + u^H^∞ (14)

where c_p˙z is the linearized endogenous force generated by the mechanical part of the semi-active damper, and u^H^∞ is the output of LPV control. The ponderable functions (W_z_r, W_n, W_z_s, W_z_us, y W_u(ρ)) are added to a linear system of the QoV, where each one regulates the performance during the frequency domain to the state variables zs, zus, as well as the inputs zr and u. It emphasizes that u depends on ρ, which is the online measured parameter. The online measurement is at the time a differential function between the calculated force by the control and the reachable one. The main purpose is to apply the control strategy when the desired force is located in the semi-active zones (quadrants) instead of when it is outside of the semi-active zone. When this occurs, the suspension is dominated by the passive law designed by the suspension manufacturer. The controller is found following the procedures to solve Linear Matrix Inequalities (LMI) [68], [69].

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In Lozoya et al.[20], LPV and Frequency Estimated Based (FEB) semi-active control strategies are defined. Where a balance between comfort and road holding is desired. Both strategies are evaluated in the time and frequency domain. For the LPV approach, an accurate model is required. The LPV output vector is:

z = (¨z_s, z_us)^T. (15)

For the FEB controller, a harmonic motion of the damper piston is assumed, piston deflection and piston deflection velocity are approximated employing RMS and then, the frequency ( ˆf ) is estimated with the next equation:

f =ˆ s

˙z₁² + ˙z₁² + ... + ˙z_n²

(z₁² + z₂² + ... + z_n²)4π² (16) the FEB control law is given by the following criteria:

I =











I₁, if 0 < ˆf < f₁ I₂, if f₁ < ˆf < f₂ I₃, if f₂ < ˆf < f₃ I₄, if f₃ < ˆf < f₄

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where I is the current which will be applied to the semi active damper and the frequencies f1, f₂, f₃ and f4 are the bandwidths limits given by:

f1 = fms + f_ms

2 f2 = fmus− f_mus

4 (18)

f₃ = f_mus+ f_mus

4 (19)

the first step is to estimate the masses resonance frequencies (fms and fms) of the QoV employing:

f_ms = 1 2π

r k_r

m_s f_mus = 1 2π

r k_r+ k_t

m_us (20)

where k_r = (k_w × k_t)/(k_w + k_t) is the ride rate, kw = k_s × µ² is the wheel rate and, µ is the motion ratio of the damper.

One of the main characteristics of both controllers is that the control output is a current value, which means that a conversion from force to current is not needed.

On the other side, it is possible to modify controllers’ performance by modifying

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the LPV matrices as well as the current look-up table values for the FEB controller.

2.7.4 Intelligent Controllers

The control techniques that are based on learning systems have been employed in semi-active suspensions. The most commons are the fuzzy control algorithm or the controllers based on neuronal networks; however, there are other not conven- tional techniques such as HSIC (Human Simulated Intelligent Control) proposed by Yu et al.[70]. In Dong et al.[5], a two levels diffusive control is proposed and analyzed (action and coordination) to the control of an MR semi-active suspension. In the action level, a fuzzy controller with the sprung and unsprung mass velocities as well as the relative velocity as inputs, is employed. The damping force is employed as the output of the controller. For each input, five functions of membership are selected, including positive and negative values. Twenty-five fuzzy rules are built based on SH’s control experience to relate the sprung mass velocity with the relative one, looking for the good safety performance of the vehicle. The 50 fuzzy rules give as a result five possible output membership functions.

As a defuzzification method, a ponderable summary is employed for obtaining the damping force Ff uzzy. Finally, at the coordination level, an adaptive adjuster to correct the real output force in the time. The control law is:

F (nT ) = F_{f uzzy}(nT ) + M_m Y (nT ) (21) where n is the number of samples, T is the period of sampling, Y is the correction matrix, and M_m is a proportional factor between 0 and 1.

In Yildiz et al.[13], a nonlinear multi-objective (comfort and road-holding) adaptive controller is proposed for mitigating vibration in a QoV when an MR damper is employed. The unsprung and sprung mass displacements are employed as inputs. A formal stability analysis is developed employing Lyapunov function. For validating performance improvement, some simulations in MATLAB-SIMULINK were done, making a focus on the acceleration and displacement of the sprung mass performance. According to the results, the designed controller gives an improvement in road-holding and comfort.

In Zhang et al.[14], genetic algorithm (GA) is employed to construct an optimal decision scheme making use of Fuzzy Logic Control (FLC) for semi-active suspensions as well as a new control structure for multi-body systems is presented.Velocity error is required. The control rule for ride comfort is optimized

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employing GA. AA GA, which considers a population size of 10, is proposed.

The simulation shows satisfactory results when employing this approach.

In Song et al.[7], a fuzzy control algorithm approach is proposed. Which is ex- pected to be implemented in a multi-degree-of-freedom vibration system. In this case, the output forces are considered for the fuzzy control design. And as defuzzier, the center-of-gravity method is considered. The results from simulation show that the proposed fuzzy control improves the performance in comparison with a PID control. The same occurs in the experimental tests.

In Qin et al.[6], an hybrid control based on SH and GH controllers which is able to perform road estimation, is presented. The main objective is to adaptively adjust the gains for optimizing the ride comfort as well as the road handling considering the constraint of rattle space. The problem is faced as a MOOP (Multiobjective Optimization Problem) making use of analytical expressions for the suspension objectives. Additionally, a new road estimation method based on ANFIS (Adap- tive Neurofuzzy Inference System) is also described. The control law is:

F_d = ηF_sky − (1 − η)F_grd. (22) in accordance with the simulation results, the proposed road estimation method identifies the road level in a good way, and the control gains switch is able to adapt the hybrid control to different roads. However, the suspension objectives (comfort and road-holding) cannot be improved at the same time.

In Fu et al. [71], the isolation structure and base are taken as inputs of a proposed control law while the control output is the current I. The proposed FLC not model dependent and robust. The inputs of the FLC are directly from the integral results of the acceleration sensors, which are converted into linguistic variables through the process referred to as fuzzifier and then are processed by fuzzy control law (rules) after that, the results of the fuzzy interference are transformed into numerical output values employing a defuzzier (center-of-gravity), which can be implemented for practical control. Both the results of the numerical simulations and experiments show that the micro-vibration could be significantly suppressed with FLC for single-frequency and multi-frequency excitation.

In Gu et al. [72], an MR base isolation system is controlled by a LQR controller and GRNN (General Regression Neural Network) inverse model. The performance is evaluated, employing numerical and experimental validations. For the GRNN, fewer input variables (displacements, speeds, and forces at the moment

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and one moment before) are required, and the training process is faster. In the LQR controller, the control output is the desired force. While in the GRNN, a current value is directly obtained.

2.8 Controllers performance.

To analyze the controller performance in the QoV, different proves based on time and frequency domain are specified. The transit response during the time allows to analyze the dynamic behavior of the QoV when facing disturbances in the road in terms of recovery and/or maximum deviation in the process variable (displacement, speed and/or acceleration), step proves, bump proves mainly employed which can be expressed as half sinusoidal cycle functions and low frequency or road standardized profiles. On the other way, the frequency response analysis is mainly employed to determine the bandwidth of the system for comfort and road holding when facing frequency inputs. The main frequency proves are the random road signals (white noise) and the sinusoidal excitation signals, this could be of constant amplitude and frequency, of incremental frequency and constant amplitude or incremental frequency and decreasing frequency, known as sweep frequency prove.

For the simulation tests in the time, the step and bump are usually between 3 and 15 cm of magnitude. For example, Savaresi and Spelta [32] simulated a 5cm step of 1.5 seconds length. In Dong et al.[5], a transit response was analyzed facing a sustained step of 10cm and a 15cm bump. In Zhang et al.[73], the system is proved under a harmonic excitation with an amplitude of 2.5cm at a frequency of 1.5Hz. By the other way, different road standards, according to its rugosity coefficient from grade A to H, been A the road with more quality , while grade H refers to a road of very low quality. In Qin et al. [6], the controller is proved in five different road levels: B,D,E,F and C in successive order as in changed ev- ery 20 seconds, the velocity remains unchanged during the prove. In Yildiz et al.

[13], the control is tested by using reached parameters under three different cases, including bump, sine-shaped and C-grade road surface inputs. In Liu et al [12], a speed bump test is employed; the bump is 0.05m high and 0.2m wide at 7.2km/hr as well as random road unevenness tests in which road displacements where generated according to International Standard Organization (ISO). In Lozoya et al.

[20], time domain tests are employed, the amplitudes of the sinusoidal tests were

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+- 10nm and +- 1mm. The improved percentage of RMS validates the benefit of using a controlled suspension.

One performance valuation criterion known as Janeway’s comfort criterion was presented in [74]. In which the vertical vibration amplitude of the chassis is related to comfort and establishes the largest chassis displacement allowance for each frequency. This proposal is shown in Figure 9, where the zone under the line indicates the presence of comfort.

Figure 9: Janeway comfort criterion, [74].

There are 2 different evaluation criteria for temporal tests as well as frequency domain tests, known as qualitative and quantitative. The qualitative evaluation criteria in the time domain more employed in literature are variable temporal tests graphics in the variables of:

• Sprung mass vertical acceleration. It is employed to the comfort analysis.

• Relative displacement and/or between the 2 masses. It is employed for the suspension deflection analysis.

• Contact force between road profile and the wheel. It is employed for the road