An active seat suspension design for vibration control of heavy-duty vehicles

Abstract

This paper presents the design, fabrication and testing of an innovative active seat suspension system for heavy-duty vehicles. Rather than using conventional linear actuators, such as hydraulic cylinders or linear motors, which need to be well maintained and are always expensive when high force outputs are required, the proposed seat suspension system directly applies a rotary motor in order to provide the required active actuation, without changing the basic structure of the existing off-the-shelf seat suspension. A gear reducer is also applied to amplify the output torque of the motor so that a high output torque can be achieved using a low rated power motor. A static output feedback $H \infty$ controller with friction compensation is designed to actively reduce seat vibration. Experiments are carried out to test the fabricated suspension prototype. The experimental results show that this type of seat suspension can achieve greater ride comfort in the frequency range of 2–6 Hz than a passive seat suspension. The newly designed active seat suspension is much more cost effective and can be suitable for heavy-duty vehicles.

Keywords

Active seat suspension rotary motor vibration control heavy-duty vehicles

Introduction

Drivers of heavy-duty vehicles are often exposed to severe vibration transferred from rough road and operation tools, and the vibration magnitude levels for heavy-duty vehicles are several times higher than those of passenger vehicles. Agricultural vehicles and industrial vehicles, in particular, need to work in harsh environments for a longer period of time. Thus, drivers of heavy-duty vehicles often suffer from the highest incident rates of injuries causing low back pain while working. This has resulted in an increasing demand for improvement of ride comfort of heavy-duty vehicles.¹ Tyres, seat suspension and chassis suspension are mostly considered for isolating vehicle vibration. Generally, it is impossible to modify the tyre parameters when the tyres are chosen. Even though many different approaches have been proposed to improve the chassis suspension performance, the chassis suspension movements of heavy-duty vehicles are always related to the operation tool performance, and driver comfort is often compromised. On the other hand, the seat suspension can be independent from the chassis suspension system and can isolate vibration transmitted directly to drivers. For this reason, a number of different types of seat suspension have been applied to heavy-duty vehicles in order to improve drivers’ working conditions^2,3 because they can be more easily modified and optimized. Now the seat suspension has become a simple and effective method to isolate the vehicle vibration transmitted to the driver’s body.

There are three main kinds of seat suspension reported in the literature. These are passive, active and semi-active suspension. Traditional passive seat suspension’s natural frequency is usually between 1.5 and 4 Hz. This may limit the seat performance in the low frequency range because heavy-duty vehicles normally suffer from high levels of vertical vibration in the frequency range of 1–20 Hz, especially from 3 to 5 Hz,^4,5 and hence, passive suspension could amplify vibration in the low frequency range so that ride comfort is affected. To overcome this problem, many different approaches have been proposed. For example, Le and Ahn⁶ proposed a negative stiffness structure for passive suspension in low frequency. Maciejewski et al.⁷ studied possibilities for improving the vibro-isolation properties of a seat suspension with an air-spring and shock absorber. Holtz and Van Niekerk⁸ designed a seat suspension with an air-spring and auxiliary volume for typical articulated or rigid frame dump trucks. Quasi-zero-stiffness devices and structures have also been studied for passive vibration isolation.^9,10 In recent years, much research has been conducted into seat suspensions with semi-active devices. Choi et al.^11,12 proposed semi-active seat suspensions using an electrorheological fluid damper and a magnetorheological (MR) fluid damper. Sun et al.¹³ proposed an MR elastomer-based isolator for horizontal vibration reduction of a driver seat. MR dampers used for helicopter crew seats to enhance occupant comfort have been studied in Hiemenz et al.¹⁴ On the other hand, active suspension has attracted more and more attention in recent years because it is widely accepted that an active suspension is the most effective way to improve suspension performance. Gan et al.¹⁵ presented an active seat suspension with two electromagnetic linear actuators. Maciejewski et al.¹⁶ proposed an active seat suspension system comprised of a hydraulic absorber and a controlled air-spring. Kawana and Shimogo¹⁷ used an electric servomotor with a ball screw mechanism as the active seat suspension actuator. Ahn¹⁸ proposed an active pneumatic vibration isolation system using negative stiffness structures. One of the main problems, however, is how to make use of active suspension without incurring high cost.

For both semi-active and active suspensions, there are also many reputable control strategies proposed, e.g. $H \infty$ control,^19,20 linear quadratic Gaussian control,^21,22 adaptive control²³ and intelligent control.²⁴ Du et al.²⁵ proposed an observer-based $H \infty$ controller with a Takagi–Sugeno fuzzy model to solve the non-linear problem of an MR damper. Choi et al.²⁶ presented an $H \infty$ control and sliding-mode control based on adaptive fuzzy sliding mode. Maciejewski²⁷ presented a control strategy which allows a desired dynamic behaviour of the seat for different requirements of the machine operator. Whether it is semi-active or active suspension control, the trade-off between driver comfort and vehicle handling needs to be considered in the controller design. When the seat suspension is installed in a vehicle, the measurable seat states are the relative displacement of suspension between its upper platform and base, and the accelerations. The relative velocity can also be determined according to the relative displacement. This means that a robust active controller that only uses measurable variables for feedback needs to be designed for practical applications.

In the above-mentioned literature, direct force output actuators, such as a single-controlled pneumatic spring¹⁶ and a linear motor,²³ have been chosen. These force output devices have the disadvantages of requiring big external power supplies and high cost when high force output is required. To overcome these drawbacks, in this study, an innovative active seat suspension is proposed. Due to the widespread application of rotary motors, their costs are cheaper than their linear counterparts. There are studies with rotary motors for active suspension using a screw mechanism¹⁷ and a rack/pinion device,²⁸ where these mechanisms have been utilized to transform torque into vertical force. In this paper, the torque of a rotary motor is amplified via a gear reducer and exerted directly on the scissor structure centre of the seat suspension. This means that a low rated power motor can be used and this will decrease the cost of an active seat suspension greatly. The proposed active seat suspension prototype is also easily fabricated through the use of a commercial passive seat suspension. Based on the identified model parameters, a friction force compensation-based $H \infty$ controller is developed using only relative displacement and relative velocity as feedbacks, and these can be measured directly from the seat suspension.

The remainder of the paper is organized as follows: the next section presents the innovative active seat suspension design and identifies its parameters. The static output feedback $H \infty$ controller with friction compensation is discussed in ‘ $H \infty$ controller design with friction compensation’ section. ‘Evaluation’ section presents the simulation and experimental results. Finally, the final section presents conclusions of this research.

Notation: I is used to denote the identity matrix of appropriate dimensions. * is used to represent a term that is induced by symmetry.

Innovative active seat suspension design

Seat suspension design

Electrical rotary motors are widely used in many areas. They have many advantages compared to linear actuators, such as lower price and ease of installation and control. In order to further reduce the actuator cost, a gear reducer can be applied to amplify the motor’s torque output. Thus, a low rated power motor can be used for active vibration control. Figure 1 shows a prototype of the proposed rotary motor-based active seat suspension. It is modified from a conventional commercial vehicle seat (GARPEN GSSC7) in which the original damper has been removed. The new torque output module consisting of one servo motor and one gear reducer is installed on the left side of the scissor structure of the seat suspension, and an additional gear reducer is assembled on the other side of the suspension in order to balance the friction force generated by the gear reducer. A further upgrade of this seat suspension to include an innovative rotary damper on this side is investigated but will not be discussed in this paper. The servo motor and gear reducer are connected in series. The gear reducer is installed on the rotation centre of the scissor structure. The gear reducer’s case is fixed on the outside of the scissor bar, and the shaft is fixed on another bar.

Figure 1.

A prototype of the proposed active seat suspension.

A 400 W Panasonic servo motor (MSMJ042G1U) is used and is powered by a Panasonic servo driver (MBDKT2510CA1) which can control the torque output of the motor accurately. The rated torque output of the motor is 1.3 N m and the gear reducer ratio is 40:1, so the torque output can be amplified 40 times to a maximum of 52 N m.

Figure 2 shows a schematic diagram of the suspension design, where the follower and the cam compose a cam mechanism. The cam is fixed with the outside scissor bar and can push the follower to move along its guide. Then the follower can extrude the spring. The external load can be supported by the spring force.

Figure 2.

Schematic diagram of the active seat suspension design.

Friction model identification

The newly designed seat suspension’s dynamic performance was tested in the laboratory by MTS machine (Load Frame Model: 370.02, MST Systems Corporation) as shown in Figure 3. The MTS machine can hold the suspension with its upper and lower heads. The upper head, which is driven by a hydraulic cylinder, moves in sinusoidally with a 5 mm amplitude and at two excitation frequencies of 1 and 2 Hz. The force generated by the suspension was measured using a load cell mounted below the lower head, which was fixed to the machine bottom (see Figure 3). The force measured by the load cell is defined as

F load = F s + f r

(1)

where

F load

is the measured force by the load cell, f_r is the suspension friction force and F_s is the spring force; F_s was calculated when the MTS applied a 5 mm sinusoidal displacement on the suspension – the spring stiffness was already known, from previous measurements, to be

5600 N / m

. When F_s is eliminated from

F load

, the friction force f_r is obtained. Figures 4 and 5 show the relationships between the friction force and the corresponding displacement and velocity, respectively. For the experimental results shown in Figure 4, the friction forces with the excitation frequencies of 1 and 2 Hz overlap with each other. When the suspension deflection directions are inversed, there is an obvious hysteresis phenomenon in change of friction force.

Figure 3.

MTS machine testing. MTS:.

Figure 4.

Friction force–displacement relationship of the seat suspension.

Figure 5.

Friction force–velocity relationship of the seat suspension.

The friction force can be defined as a hysteresis model and is given by

f r = α z d

(2)

\overset{\cdot}{z d} = - γ d | v s | z d | z d | - β d v s | z d | 2 + A d v s

(3)

where v_s is the rate of suspension deflection; z_d is an intermediate variable and α,

γ d

β d

andA_d are model constants to be identified. With the genetic algorithms toolbox in Matlab,

α = 550

γ d = 734, 725

β d = - 650, 000

and

A d = 1000

were obtained by fitting the experimental data to the model in equations (2) and (3). Figure 6 shows comparison of simulated and measured friction forces at 1 and 2 Hz, respectively.

Figure 6.

Friction model simulation in (a) 1 Hz and (b) 2 Hz.

Torque to force transformation

As the rotatory motor can only output torque T to the seat scissor structure, the torque needs to be equivalent to a vertical force F exerted on the seat based on the geometry of the structure. Figure 7 shows the equivalent relationship between the torque applied on one suspension bar and the force to the seat. Due to the torque interaction between the two scissor bars, each bar exerts half of the force on the seat. The relationship of the torque output and the equivalent vertical force is given as

T = \frac{F}{2} W = \frac{F}{2} \sqrt{L 2 - H 2}

(4)

where L is the length of the scissor structure bar and H can be measured in real time.

Figure 7.

Force analysis of one suspension strut bar.

$H \infty$ controller design with friction compensation

Static output feedback controller

Figure 8 shows a simplified seat suspension model with suspension stiffnessk_f, suspension damping coefficientc_f, cushion stiffnessk_c, cushion damping coefficientc_c, friction forcef_r and active force $u$ . z_c, z_s and z₀ are the driver body, suspension upper and suspension base displacements, respectively. The dynamic model of the system can be described as

m s \overset{··}{z s} (t) = - k f (z s (t) - z 0 (t)) - c f (\overset{\cdot}{z s} (t) - \overset{\cdot}{z 0} (t)) + k c (z c (t) - z s (t)) + c c (\overset{\cdot}{z c} (t) - \overset{\cdot}{z s} (t)) - f r (t) + u (t)

(5)

m \overset{··}{z c} (t) = - k c (z c (t) - z s (t)) - c c (\overset{\cdot}{z c} (t) - \overset{\cdot}{z s} (t))

(6)

where m is the total mass of a driver’s body and seat cushion and m_s is suspension mass.

Figure 8.

Seat suspension model.

As relative displacement between the suspension base and the seat-top platform can be easily measured, and the relative velocity can also be calculated based on the measured relative displacement, in this paper, the seat variables are chosen as $x 1 = z s - z 0, x 2 = \overset{\cdot}{z s} - \overset{\cdot}{z 0}, x 3 = z c - z s, x 4 = \overset{\cdot}{z c} - \overset{\cdot}{z s}$ . $d = [\overset{··}{z 0} \overset{··}{z s}] T$ is defined as the disturbance. Thus, the system model can be rearranged in state–space representation as

\overset{\cdot}{x} (t) = Ax (t) + B 1 d (t) + B 2 (u (t) - f r (t))

(7)

y (t) = C 2 x (t)

(8)

where

A = [0100 - \frac{k f}{m s} - \frac{c f}{m s} \frac{k c}{m s} \frac{c c}{m s} 000100 - \frac{k c}{m} - \frac{c c}{m}], B 1 = [00 - 1 0000 - 1], B 2 = [0 \frac{1}{m s} 00], and C 2 = [10000100]

In order to satisfy the performance requirement, $z 1 = \overset{··}{z c}$ and $z 2 = x 1$ are defined as the controlled outputs, then

z (t) = C 1 x (t)

(9)

where

C 1 = ε [100000 - \frac{k c}{m} - \frac{c c}{m}], ε = [ε 1 00 ε 2]

is a weighting matrix for the controlled outputs. It is noted from equation (9) that both the acceleration

\overset{··}{z c}

and the relative displacement x₁ are defined as the control objectives. Hence, it is a multi-objective control problem. These two control objectives can be compromised by appropriately adjusting the weighting coefficients

ε 1

and

ε 2

. As the focus is mainly on the ride comfort performance in this study, the driver body acceleration is expected to be as small as possible but the relative displacement to be within an acceptable level to avoid the end-stop collision and to ensure controllability of vehicle by the driver. Thus, a bigger value for

ε 1

will be chosen compared to

ε 2

Because the friction force f_r can be approximately estimated as $\overset{\land}{f r}$ based on the measured state, which will be further discussed in ‘Friction estimation’ section, the static output feedback $H \infty$ controller with this friction compensation is designed as

u (t) = - KC 2 x (t) + \overset{\land}{f r} (t)

(10)

The friction estimation error is defined as

e fr (t) = f r (t) - \overset{\land}{f r} (t)

(11)

Substitute equation (10) into equation (7), to achieve

\overset{\cdot}{x} (t) = (A - B 2 KC 2) x (t) + \bar{B 1} ω (t)

(12)

where

\bar{B 1} = [000 - 1 0 - \frac{1}{m s} 0000 - 1 0], ω (t) = [d (t) T e fr (t) T] T

The L₂ gain of the system (12) and (9) is defined as

| | T z ω | | \infty = \sup \frac{| | z 2 | |}{| | ω 2 | |}

(13)

where $| | z 2 | | = \int_{0}^{\infty} z T (t) z (t) d t$ and $| | ω | | 2 = \int_{0}^{\infty} ω T (t) ω (t) d t \neq 0$ .

A Lyapunov function is defined for the system in equation (12) as

V (x) = x T Px

(14)

where P is a positive definite matrix. Differentiating equation (14) yields

\overset{\cdot}{V} (x) = \overset{\cdot}{x} T Px + x T P \overset{\cdot}{x} = [(A - B 2 KC 2) x + \bar{B 1} ω] T Px + x T P [(A - B 2 KC 2) x + \bar{B 1} ω]

(15)

Adding $z T z - γ 2 ω T ω$ to the two sides of equation (15) yields

\overset{\cdot}{V} (x) + z T z - γ 2 ω T ω = [x T ω T] [Ψ + C_{1}^{T} C 1 P \bar{B 1} * - γ 2 I] [x T ω T] T

(16)

where

Ψ = (A - B 2 KC 2) T P + P (A - B 2 KC 2)

If we consider that

\exists = [Ψ + C_{1}^{T} C 1 P \bar{B 1} * - γ 2 I] < 0

(17)

then

\overset{\cdot}{V} (x) + z T z - γ 2 ω T ω < 0

, and the L₂ gain defined in equation (13) is less than

γ > 0

with the initial condition

x (0) = 0

.²⁹

By Schur complement, $\exists < 0$ is equivalent to

Pre- and post-multiplying equation (18) by diag( $P - 1, I$ , I) and its transposition, respectively, and defining $Q = P - 1$ , $WC 2 = C 2 Q$ , $Y = KW$ , the $H \infty$ controller can then be obtained by solving the following linear matrix inequality (LMI)

[AQ - B 2 YC 2 + (AQ - B 2 YC 2) T \bar{B 1} (C 1 Q) T * - γ 2 I 0 * * - I] < 0

(19)

The definition $WC 2 = C 2 Q$ can equivalently be solved as³⁰

tr [(WC 2 - C 2 Q) T (WC 2 - C 2 Q)] = 0

(20)

To convert equation (20) into an LMI condition, the following inequality is introduced

(WC 2 - C 2 Q) T (WC 2 - C 2 Q) \leq μ I

(21)

where

μ > 0

is a very small positive number, e.g.

10 - 10,

to replace equation (20) for an approximate solution. By the Schur complement, equation (21) is equivalent to

[- μ I (WC 2 - C 2 Q) T * - I] \leq 0

(22)

A static output feedback controller can be obtained by solving a minimization problem

min γ 2 s . t . to LMIs (19) and (22)

(23)

Table 1 shows the parameters used for the suspension model. The controller is obtained as

K = [5498.8 70]

Table 1.

Parameters for the seat suspension model.

Parameter	m	m_s	k_f	c_f	k_c	c_c
Unit	kg	kg	N/m	N s/m	N/m	N s/m
Value	55	10	5600	10	80,000	2000

Friction estimation

In the practical experiment, when the friction force is estimated by Coulomb frication model as $f r (t) = F r sig n (x 2 (t))$ in equation (10), where F_r is a constant friction magnitude, additional disturbances will be introduced by active control in low relative velocity conditions because the displacement sensor noise will make the sign of the relative velocity change frequently in low velocity conditions, and this will lead to an unstable controller output. In order to solve these practical problems, the friction force is estimated as

\overset{\land}{f r} (t) = {F r sig n (x 2 (t)), | x 2 (t) | \geq β F r \frac{x 2 (t)}{β}, | x 2 (t) | < β

(24)

where

F r = 55

β > 0

is a relative velocity threshold. When a heavy-duty vehicle suffers from high level vibration from 3 to 5 Hz,

β = 0.05 m / s

is chosen in order to make the compensated friction as close as possible to the actual friction.

Evaluation

Numerical simulation evaluation

Numerical simulations were performed to show the effectiveness of the proposed control algorithm with friction compensation. Figure 9 shows the acceleration transmissibility of vibration from the seat bottom to the driver’s body. It is seen from Figure 9 that the vibration can be effectively controlled by this controller over a wide frequency range. Random vibration was also applied to test the seat suspension, in which the driver’s body vibration has been substantially reduced as shown in Figure 10. The analysis and comparison with practical experiments will be shown in the next subsection.

Figure 10.

Driver body acceleration under random vibration.

Figure 9.

Acceleration transmissibility from seat bottom to driver body.

Experimental evaluation

Experimental set-up

A schematic diagram of the experimental set-up is shown in Figure 11. A dSPACE ds1104 board is used to run the control algorithm and send control signals to the motor driver for controlling the active seat suspension. A laser displacement sensor (MICRO-EPSILON optoNCDT) is applied to measure the relative displacement between the suspension top platform and base. The relative displacement is differentiated in order to obtain the relative velocity in ds1104. The friction compensation-based $H \infty$ controller calculates the output control signal based on the measured relative displacement and calculated velocity inputs and then sends a control signal to the motor driver. The motor will generate the designed torque based on the received control signal from the motor driver. A 6-degrees-of-freedom (DOF) vibration platform is used to generate the vertical vibration excitation to the seat base. This 6-DOF vibration platform has six electrical cylinders which are controlled by six motor drivers. One NI CompactRio 9076 is used to send movement signals to the motor drivers of the platform. Computer 1 is used for installing a ds1104 control card and sending vibration signals to CompactRio 9076. Two 6-DOF sensors (XSENS MTi) are fixed on the vibration platform and seat, respectively, for logging vibration signals. The vibration accelerations are stored using the software MT Manager installed in Computer 2. Figure 12 shows a photo of the experimental set-up.

Figure 11.

Schematic diagram of the experimental set-up.

Figure 12.

Photo of real experimental set-up.

Test results

Sinusoidal excitations were applied to test this seat suspension. Different sinusoidal vibrations with amplitudes of 7, 5, 3, 2.5, 2, 1 mm, and frequencies from 1 to 7 Hz were exerted on the seat suspension, respectively. The excitation vibrations for controlled and uncontrolled seat suspension experiments had the same magnitudes. Figure 13 shows the accelerations of the driver body in the time domain without control and with control when the frequencies of the excitation vibrations were given as 3 and 4 Hz, respectively. From Figure 13, it can be seen that the peak accelerations of the driver body can be obviously reduced, which means that much less high level acceleration is transmitted to the driver’s body.

Figure 13.

Accelerations of the seat suspension.

Figure 14 shows the motor torque outputs. The maximum torque was around 0.3 N/m which was amplified to 12 N/m by the gear reducer. The results show that a low power motor can be used as the suspension actuator.

Figure 14.

Motor torque outputs.

For further analysis of the suspension performance, the root mean square (RMS) is used to evaluate the measured accelerations. The RMS is defined as $RMS (a) = \sqrt{\frac{1}{N} \sum_{i = 1}^{N} a i}$ , and the results are listed in Table 2, where a_p is the RMS acceleration of the driver body in passive suspension experiments, a_a is the RMS acceleration of the driver body in active control suspension experiments and a_v is the RMS of the excitation vibration. The percentage reduction of the RMS acceleration of the driver body is defined as $\frac{a p - a a}{a p}$ . Table 2 indicates that the maximum reduction can reach 41.85% in 3 Hz for the proposed active suspension. Figure 15 shows the acceleration transmissibility, which is calculated as the ratio between the RMS acceleration of the excitation vibration and the RMS acceleration of the driver body. It can be seen that the controlled seat suspension performed better than the passive suspension from 2 to 6 Hz.

Figure 15.

Acceleration transmissibility from seat bottom to driver body.

Table 2.

RMS of accelerations under different frequencies.

Frequency (Hz)	Uncontrolled a_p( $m / s 2$ )	Controlled a_a( $m / s 2$ )	Percentage reduction of RMS acceleration of driver body (%)
1	0.2169	0.2048	5.5
2	0.8160	0.6264	23.2
3	0.8216	0.4777	41.85
4	0.8218	0.4937	39. 93
5	0.6694	0.4339	35.19
6	0.5821	0.4767	18.11
7	0.7012	0.6546	6.64

RMS: root mean square.

To further validate the effectiveness of the proposed suspension, a random road profile was applied to test the suspension’s performance. Figure 16 shows the accelerations of controlled and uncontrolled seat, from where similar conclusion can be drawn that the proposed active suspension and controller are effective in improving suspension performance.

Figure 16.

Random vibration test.

In this work, the parameters defined in ISO 2631-1 were used to evaluate the human body exposure to vibration on the basis of time history of the frequency-weighted acceleration (a_w) and the fourth power vibration dose value (VDV). The seat effective amplitude transmissibility (SEAT) and VDV ratio are obtained as follows

a w = [\frac{1}{T} \int_{0}^{T} {a w (t) 2 d t}] 1 / 2, VDV = [\int_{0}^{T} {a w (t) 4 d t}] 1 / 4, SEAT = \frac{a w, driver}{a w, vibration}, VDV ratio = \frac{VDV driver}{VDV vibration}

(25)

Table 3 shows that the SEAT and VDV ratio can both be effectively reduced by 43.41 and 42.68%, respectively, which means that the proposed seat suspension and control method are very effective for practical applications.

Table 3.

Random vibration control performance.

	Uncontrolled	Controlled	Percentage reduction
	( $m / s 2$ )	( $m / s 2$ )	(%)
RMS a	0.6636	0.4515	31.96
Weighted RMS a_w	0.6606	0.3738	43.42
VDV	1.216	0.6936	42.96
SEAT	0.8735	0.4943	43.41
VDV ratio	0.6569	0.3765	42.68

RMS: root mean square; SEAT: seat effective amplitude transmissibility; VDV: vibration dose value.

The energy consumption is an important issue for practical applications of an active seat suspension. The theoretical power of this active seat suspension in a random vibration test can be defined as $P (t) = u (t) x 2 (t)$ , which is shown in Figure 17. The maximum power is 12.1 W, which means a low rated power actuator can be used for the active seat suspension and the cost can be substantially reduced. The RMS power used is 3.711 W, which indicates low energy consumption.

Figure 17.

The power of active seat suspension in random vibration test.

Comparison between simulation results and experimental results

Both simulation results and experimental results indicate the effectiveness of the designed active seat suspension and the proposed control algorithm. The differences between simulation and experimental results mainly come from the inaccuracy of the friction model. A hysteresis viscous friction model has been applied in the simulation which can accurately describe the kinetic friction. However, the stick–slip phenomena caused by the static friction cannot be described by the adopted friction model. In the real experiments, the stick–slip phenomenon occurs when the seat suspension works in low frequency excitation.

Conclusions

In order to improve the ride comfort for drivers of heavy-duty vehicles, an innovative active suspension system has been proposed. A rotary motor is applied as the actuator and its torque output is amplified by a gear reducer. A low rated power motor can be used for this active suspension and this can reduce the cost of the suspension set-up. This rotary motor is installed in the scissor structure centre of a passive suspension. Unlike most designs proposed in the existing literature, this active suspension uses torque output directly rather than force output. The suspension parameters are identified by force–displacement response tests, where the friction force is found to be a main part of the disturbance. A static output feedback $H \infty$ controller with friction compensation has been developed and tested. The experimental results show that this active seat suspension can suppress the vibration acceleration in the low frequency range, especially around 4 Hz. In the case that the heavy-duty vehicle suffers from high level vibration from 3 to 5 Hz, this active seat suspension can significantly improve driver comfort.

Footnotes

Acknowledgement

The authors wish to gratefully acknowledge the help of Dr Madeleine Strong Cincotta in the final language editing of this paper.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research was supported under University of Wollongong Global Challenge Project and the Open Research Fund Program of the State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University (31515001) and China Scholarship Council joint scholarships.

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An active seat suspension design for vibration control of heavy-duty vehicles

Abstract

Keywords

Introduction

Innovative active seat suspension design

Seat suspension design

Friction model identification

Torque to force transformation

H ∞ controller design with friction compensation

Static output feedback controller

Friction estimation

Evaluation

Numerical simulation evaluation

Experimental evaluation

Experimental set-up

Test results

Comparison between simulation results and experimental results

Conclusions

Footnotes

Acknowledgement

Declaration of conflicting interests

Funding

References

$H \infty$ controller design with friction compensation