Active vibration control on a quarter-car for cancellation of road noise disturbance

Journal of Sound and Vibration 331 (2012) 3240–3254

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Active vibration control on a quarter-car for cancellation of road noise disturbance Walid Belgacem, Alain Berry, Patrice Masson n G.A.U.S., Mechanical Engineering Department, Universite´ de Sherbrooke, Sherbrooke, QC, Canada JIK 2R1

a r t i c l e in f o

abstract

Article history: Received 22 February 2011 Received in revised form 14 February 2012 Accepted 28 February 2012 Handling Editor: J. Lam Available online 17 March 2012

In this paper, a methodology is presented for the cancellation of road noise, from the analysis of vibration transmission paths for an automotive suspension to the design of an active control system using inertial actuators on a suspension to reduce the vibrations transmitted to the chassis. First, experiments were conducted on a Chevrolet Epica LS automobile on a concrete test track to measure accelerations induced on the suspension by the road. These measurements were combined with experimental Frequency Response Functions (FRFs) measured on a quarter-car test bench to reconstruct an equivalent three dimensional force applied on the wheel hub. Second, FRFs measured on the test bench between the three-dimensional driving force and forces at each suspension/chassis linkage were used to characterize the different transmission paths of vibration energy to the chassis. Third, an experimental model of the suspension was constructed to simulate the configuration of the active control system, using the primary (disturbance) FRFs and secondary (control) FRFs also measured on the test bench. This model was used to optimize the configuration of the control actuators and to evaluate the required forces. Finally, a prototype of an active suspension was implemented and measurements were performed in order to assess the performance of the control approach. A 4.6 dB attenuation on transmitted forces was obtained in the 50–250 Hz range. & 2012 Elsevier Ltd. All rights reserved.

1. Introduction Car manufacturers use lighter materials in the design of vehicles to reduce energy consumption. This loss in mass combined with the design of increasingly powerful vehicles lead to car frames more vulnerable to the propagation of vibration and the generation of noise. The acoustic environment of vehicles has become a key factor in sales and manufacturers are now considering acoustic quality in their design process. Many improvements have been achieved concerning acoustic comfort inside automobiles. However, two sources of noise still pose unresolved problems: road noise and wind noise. Below 50 km/h, in urban areas for example, road noise remains the dominating source of noise at low frequency (below 600 Hz) [1–4]. To reduce interior road noise in automobiles, passive techniques are used such as the application of sound absorbing materials and the use of passive suspensions. However it has been demonstrated that the requirement of a large static stiffness makes the passive suspensions ineffective at vibration isolation in the low frequency range [5]. As a solution to

n

Corresponding author. Tel.: þ 1 819 821 8000x62152; fax: þ1 819 821 7163. E-mail address: [email protected] (P. Masson).

0022-460X/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.jsv.2012.02.030

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the inefficiency of passive solutions at low frequency, active solutions such as Active Noise Control (ANC) and Active Structural Acoustic Control (ASAC) were developed. Dehandschutter [6], Bernhard [7] and Sano [8] demonstrated that the use of control loudspeakers and error microphones inside a car cabin (ANC system) can reduce the structure-borne road noise levels in the interior environment. Experiments showed that an ANC system can provide good road noise reduction: 10 dB in the 100–200 Hz frequency range, as obtained by Park [9], and 5.2 dB in the 60–300 Hz frequency range, as obtained by Dehandschutter [6]. However, the application of ANC to automotive road noise requires a large number of loudspeakers to control the sound pressure distribution throughout the air cavity. Consequently, this system can only create quiet zones around error microphone positions and can amplify noise in other areas of the cabin. In order to reduce the overall noise, active vibration actuators located on the car chassis can be used to reduce the interior noise level by modifying the vibration behavior of the radiating structure or by blocking some vibration transfer paths [10,11]. This solution is known as ASAC. A prototype of this ASAC technique was implemented by Dehandschutter and Sas [12,6] and their most successful configuration achieved a noise reduction of 6.1 dB at the passenger’s ear in the 75–105 Hz frequency range. Their active control system was composed of 4 acceleration reference signals measured at the centers of the wheels, 6 inertial control actuators mounted on the chassis and 4 error microphones inside the automobile cabin. Although significant reduction was obtained at error microphone positions, the use of error microphones in the cabin may result in local noise reduction and poor coherence with the reference accelerations measured on the wheel. As an alternative, this paper examines the use of vibration error sensors on the vehicle suspension itself. An experimental approach is conducted to optimize the configuration of an active vibration control system for cancellation of road noise disturbance on a quarter-car test bench. The active control approach is original as it reduces the forces transmitted to the chassis based on a comprehensive experimental characterization of a suspension on a test bench. The proposed method is an original approach consisting of: characterization of the road noise excitation; study and evaluation of the dominant transmission paths on the suspension; optimization of the control configuration (actuators and error sensors); implementation of active control on the test bench to evaluate its performance. Prior to the implementation of an active solution for road noise, the first step is to identify and characterize the noise source. A few authors have characterized road noise by Power Spectral Density (PSD) accelerations measured at the wheel hub [13] while others have characterized road profiles displacement PSD [14,15]. For the work reported in this paper, a quarter-car test bench was used and road noise was simulated by a force injected on the wheel hub. The test bench is further described in Section 2. A first step is thus to characterize, in Section 3, the road noise as an equivalent force applied on the wheel hub which reproduces the same accelerations as those measured on the road. Once the equivalent road noise has been characterized, a study of primary transfer paths follows in Section 4 to determine the dominant paths of vibration and noise propagation. Part of this was investigated previously for a vertical primary disturbance on the wheel hub [16,17]. In this paper, it is proposed to extend the approach by considering threedimensional primary excitation and transfer paths. To optimize the configuration of the control actuators (location and orientation), several authors have used an analytical model of the suspension [13]. Since accurate modeling of such a complex system is a challenging task, Section 5 presents an experimental model based on 585 primary and secondary Frequency Response Functions (FRFs). This experimental model was then used in conjunction with an evolutionary optimization algorithm to find the best configuration for the control actuators. Finally, Section 6 presents the prototype of the active control system that was implemented on the bench test. This prototype uses a feedforward Filtered-Reference-Least Mean Square (FX-LMS) controller. The active control is implemented for single-frequency disturbance in the 50–250 Hz frequency range and the performance of the approach is presented. 2. Laboratory test bench The laboratory test bench is presented in Fig. 1 and fully described in [17]. The test bench was designed with the goal to reproduce the vibro-acoustic characteristics of a typical suspension. This test bench includes a McPherson suspension from a Ford Contour 1999 mounted on a rigid frame. The system consists of the wheel lower A-arm, suspension spring and damper. The system is statically pre-loaded with a compression force corresponding approximately to 14 of the vehicle weight. Ideally, the vibro-acoustic behavior of the suspension/frame coupling should be representative of the behavior of the suspension/chassis coupling. However, it is very difficult to reproduce the suspension/chassis behavior on a frame. Therefore, the suspension is assembled on the test bench to achieve a clamped boundary condition at each suspension/ frame link. It was shown previously that the vibration behavior of the suspension connected to the chassis can be obtained from its behavior on the rigid test bench: force transmissibility in clamped condition can then be used to estimate force transmissibility in real suspension/chassis coupling condition provided that input mobilities of the suspension and chassis are known at each linkage [17]. The clamped boundary conditions are ensured by the very large mechanical impedance of the frame below its first natural frequency estimated at 255 Hz as compared to the impedance of the suspension at connecting points. This allows to estimate force transmissibilities for the suspension connected to the rigid frame in the 0–250 Hz frequency range. A static vertical pre-load of 3.3 kN, approximating the car’s mass distribution onto the strut tower, was applied onto the ¨ suspension. A Bruel and Kjaer 4809 dynamic shaker was attached to the spindle via a stringer to inject the primary

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Fig. 1. Quarter-car suspension test bench. (a) Shaker link with reference force sensor. Configuration for an injected primary force along the Y-axis. (b) Force transducers positions. B1, B2, B3, B4 and BH indicate force sensors locations on the suspension/frame linkages.

disturbance in the desired direction while minimizing moments injected on the spindle. The excitation at the wheel spindle was chosen because the previous literature showed that this properly simulates a real road excitation of the wheel [18,22]. To provide a reference for the measurement of force transmissibilities on the test bench, the stringer was connected to the spindle through a ICP PCB 208C04 single axis force sensor. Fig. 1(a) shows the configuration used to inject the primary disturbance along the Y-axis. The same process was repeated to inject the primary disturbance separately along the two other axes (X and Z). To measure the forces transmitted through suspension linkages (see Fig. 1(b)), the suspension was instrumented with several force sensors: ¨ and Kjaer 8200) to measure  The strut tower link (BH) was instrumented with three single-axis force sensors (Bruel forces transmitted in each direction by the top end of the damper to the vehicle chassis.

 Each lower A-arm link was instrumented with tri-axis force sensors (ICP PCB 260A01) to measure forces transmitted in each direction by the lower A-arm (B1, B2, B3 and B4) to the vehicle chassis. The measurements on the test bench were conducted in the 0–250 Hz frequency range. However, the active control configuration was optimized to cover 20–250 Hz frequency range and due to the force limitation of the control actuators at low frequency, the active control system was experimentally implemented in the 50–250 Hz frequency range. 3. Road noise characterization In the literature, road noise disturbance is usually characterized by acceleration Power Spectral Density (PSD) measured at the wheel hub or by road profile PSD. However, some previous work has been conducted to characterize road noise as spindle loads. An experimental methodology has been developed by Park [18] to quantify such spindle loads. This methodology uses an indirect measurement of the suspension Frequency Response Function (FRF) by replacing the wheel by a rigid mass with known weight and inertia properties. Our approach is more direct and consists to determine an equivalent force applied on the wheel hub of the test bench, which reproduces the same accelerations as those measured in drive conditions on the vehicle. 3.1. Acceleration measurements The road induced vibrations were measured on the front left suspension of a Cheverolet Epica LS that has many similarities with the suspension on the test bench (same McPherson suspension, similar geometric properties and mounting configuration). The measurements were conducted at 50 km/h to minimize wind noise in interior sound pressure data. The vehicle was towed to eliminate the engine contribution to vibration and acoustic measurements. The test track is made of 5 m long concrete blocks and is approximately 1 km long. To measure road excitation, two tri-axis accelerometers were placed on the left wheel close to the calliper and steering rod, with the help of small aluminium blocks. Fig. 2 shows the location of each accelerometer. The PSD of measured accelerations (Fig. 3) shows that most of the energy for all measured accelerations is limited to low frequencies, particularly below 50 Hz. The large vertical (Z-axis) accelerations around 12 Hz are due to the resonance

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Fig. 2. Location of the accelerometers on the Epica front left suspension to measure induced road vibrations. (a) Accelerometer (1) on calliper side. (b) Accelerometer (2) on steering rod side.

4

dB (re 1m2/s /Hz)

0

0

50

100

150

200

250

0

50

100 150 Frequency (Hz)

200

250

2

4

dB (re 1m /s /Hz)

0

Fig. 3. Epica wheel Accelerations PSD at 50 km/h (acceleration along the X-axis in dotted line; acceleration along the Y-axis in dashed line; acceleration along the Z-axis in bold solid line). (a) Calliper acceleration PSD. (b) Steering rod acceleration PSD.

of the wheel-suspension system (wheel hop mode). In the 50–250 Hz range, the acceleration levels in the X, Y, and Z directions are, on average, similar. 3.2. Reconstruction of the excitation force On the test bench, the road-induced vibration is reproduced with an electrodynamic shaker, and the reference for the various FRFs on the test bench is the injected force. It is therefore needed to reconstruct the force to be injected by the shaker that will reproduce, at best, the accelerations measured on the suspension for real road conditions. In the following, an inverse model is proposed to reproduce the 3D components of the force to be injected to the wheel hub for proper assessment of the proposed approach for active control of road noise on the test bench. First, the ¨ and Kjaer 4809 accelerometer configuration that was used for real road conditions is recreated on the test bench. The Bruel electrodynamic shaker was used to inject an arbitrary primary disturbance by successively exciting the wheel in the X, Y and Z directions to obtain 3D acceleration over injected force FRFs ðHÞ on the calliper and steering rod side. The relation between accelerations and injected forces is given by b 31 ðf Þ a61 ðf Þ ¼ H63 ðf ÞF where

0

1 0 a1X H1XX B C B B a1Y C B ^ C B a61 ¼ B B ^ CH63 ¼ B ^ @ A @ a2Z H2ZX

 ^ ^ 

H1XZ

1

C ^ C C ^ C A

H2ZZ

(1)

0

1 Fb X C b 31 ¼ B F @ Fb Y A Fb Z

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dB (re 1N)

dB (re 1N)

dB (re 1N)

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20 0

0

50

100

150

200

250

0

50

100

150

200

250

0

50

100 150 Frequency (Hz)

200

250

20 0

20 0

Fig. 4. Forces injected to the center of the wheel spindle on the test bench to reproduce wheel accelerations measured in real road conditions. (a) FX. (b) FY. (c) FZ.

f, frequency; i, measurement accelerometer (1: calliper side; 2: steering rod side); aij, acceleration measured by accelerometer i along direction j, j ¼ ðX,Y,ZÞ; Fb k , road equivalent force along direction k, k ¼ ðX,Y,ZÞ; Hijk ¼ aij /Fk, FRF measured on the test bench, with the primary disturbance along direction k. Thus, by using the accelerations a measured in real road conditions and the test bench FRF matrix H, a reconstructed excitation force can be obtained from b ¼ ðHH HÞ1 HH a F

(2)

H

where the exponent is the Hermitian transpose. As the problem is over-determined, the least square method is used in Eq. (2) to solve Eq. (1) and find the unknown b Þ. The relative error on the reconstruction of the 6 measured accelerations can be obtained equivalent road force vector Fðf from eðf Þ ¼

b JaHFJ JaJ

(3)

The frequency spectrum of the reconstructed excitation forces using Eq. (2) is presented in Fig. 4. The relative error defined by Eq. (3) is 19.6 percent on average in the 0–250 Hz frequency range. This error can be explained by the used model which does not include the effect of moments on the accelerations measurements. The results of Fig. 4 reveal that the force injected along the Z axis is larger than along the X and Y axes: the force amplitudes, averaged over the 0–250 Hz range are Fb X ¼ 9:4 N, Fb Y ¼ 2:7 N, Fb Z ¼ 18:1 N. The amplitude of the various force components is larger at low frequency, particularly for the vertical component. By considering only the frequency band 20–250 Hz (thus removing the wheel-hop mode), the averaged force amplitudes become Fb X ¼ 2:25 N, Fb Y ¼ 1:83 N, Fb Z ¼ 1:3 N. This last result is in accordance with previous results [13] which revealed that a 1.4 N level was required to be injected along Z-axis on the wheel axis to reconstruct the vertical ISO ‘‘good road’’ profile PSD of the displacement [14]. Assuming a single excitation force along the vertical axis, it was envisioned that rather small actuators could be used in the active control approach [13]. However, the current results, which consider 3D excitation force, tend to indicate that the control forces will be more important, and thus more powerful control actuators will be required to minimize the force transmission through the suspension along all three axes. 4. Energy transmission In the previous section, a 3D excitation force applied at the wheel hub was obtained to reproduce, on the test bench, the accelerations measured on the suspension for real road conditions. The objective of this section is to study the force transmission paths through suspension/frame linkages that will be actively controlled in the following sections. For this purpose, a force transmissibility factor tmkl is used which is defined as the frequency averaged ratio of the vibration energy transmitted to each linkage m along each axis k for a primary disturbance along axis l. Therefore, the force transmissibility factor tmkl takes the form: R f1 JF tmk J2 df (4) tmkl ¼ 100  Rf 0f 2 1 f JF el J df 0

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where m, index for linkages B1, B2, B3, B4 and BH, respectively (1, 2, 3, 4, 5); k, transmitted force direction (X, Y, Z); l, input force direction (X, Y, Z); Fel, input force on wheel hub along direction l; Ftmk, transmitted force at suspension/frame linkage m along k direction. The lower and upper frequency bounds in Eq. (4) have been chosen as f 0 ¼ 20 Hz and f 1 ¼ 250 Hz in the following since most of the audible road noise is contained in this frequency range. One can also define a force transmissibility factor tkl as the ratio of vibration energy transmitted to all suspension/ frame linkages along k axis for a primary disturbance along l axis

tkl ¼

5 X

tmkl

(5)

m¼1

Fig. 5(a)–(c) presents the force transmissibility factors tmkl and tkl for an injected force at the center of wheel spindle along the X, Y and Z axis, respectively. It can be observed that for any direction of the injected force on the wheel hub, the dynamics of the suspension are such that vibrations are transmitted, mainly, through suspension/frame linkages along the Z-axis. However, the transmission along the X-axis is far from being negligible. Considering now only one primary excitation along the Z-axis and normalizing the force transmissibility factor with respect to the total energy transmitted to the chassis for an excitation along the Z-axis, the force transmissibility factor (t0mkZ ) can be written R f1 JF tmk J2 df t 0 ¼ P mkZ tmkZ ¼ 100  R f Pf 0 (6) 2 0 1 0 0 m0 ,k0 tm0 k Z m0 ,k JF tm0 k J df f

20 15 10 5 0 Total

X k,

Transmissibility factor (%)

Transmissibility factor (%)

0

Y

ec

tio

Z

B1

10 5 0 Total

B3 e B2 kag n i l m,

B4 re

Y

ct

io

n

B1

Z

BH

Transmissibility factor (%)

n

15

X k, di

B4

dir

20

B3 e B2 kag n i l m,

BH

20 15 10 5 0 Total

X k,

B4 di

B3

Y

re

ct

io

n

B2 Z

B1

in m, l

kag

e

BH

Fig. 5. Force transmissibility factors tmkl and tkl ; X, Y, Z indicate the direction of the transmitted force; B1, B2, B3, B4 and BH indicate the linkage. The row ‘‘Total’’ indicates the transmissibility factor of all the suspension/chassis linkages along each direction ðtkl Þ. (a) Force transmissibility factor for an excitation along X-axis ðl  XÞ. (b) Force transmissibility factor for an excitation along Y-axis ðl  YÞ. (c) Force transmissibility factor for an excitation along Z-axis ðl  ZÞ.

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×103 N2

10

5

0 X k,

Total B4 dir

Y

ec

tio

n

B1

Z

B3 B2 ge n i ka m, l

BH

Fig. 6. The squared force transmitted by each linkage along each direction for a realistic road disturbance Fb .

One can also define t0kZ as the force transmissibility factor of all suspension/chassis linkages along k axis for a primary disturbance along Z axis

t0kZ ¼

5 X

t0mkZ

(7)

m¼1

The measured values of t0kZ are 35.2 percent, 12 percent and 52.8 percent along the X, Y and Z-axis respectively, which is in accordance with previous results on a similar test bench [17] where it was shown that 56.5 percent of the vibratory energy transmitted to the chassis is along the Z-axis, while 34.3 percent and 9.2 percent of the vibratory energy was transmitted along the X-axis and Y-axis respectively. Finally, using the results of Section 3, it is possible to determine the forces transmitted through each linkage and along each direction for a realistic road disturbance. Fig. 6 shows that for a realistic road excitation injected on the test bench, most of the force transmitted to the chassis between 20 and 250 Hz is in the X and Z directions. Therefore, an active vibration control system of road noise transmission should predominantly target forces transmitted in the X and Z directions. The distribution of transmitted forces to the chassis also shows that the vibration energy is mainly transmitted through linkages B3, B4 and B1.

5. Optimization of the active control configuration Section 3 presented the characterization of the road noise and a 3D primary excitation force was obtained to simulate real road conditions on the test bench. In Section 4, a study of the vibrations transmitted though the suspension was conducted to evaluate the dominant transmission paths to the suspension/frame linkages. The next step is to exploit this information to optimize the active control configuration. The active control strategy implemented on the test bench is to minimize the force transmitted to the test bench frame using a feedforward FX-LMS controller which is composed of:

 One reference signal obtained from a force transducer (ICP PCB 208C04) that measures the primary disturbance ¨ and Kjaer 4809 shaker on the wheel spindle. injected by the Bruel ¨ and Kjaer 8200) located at the top end of the  Nine error signals obtained from three uniaxial force transducers (Bruel



damper and two three-axis force transducers (ICP PCB 260A01) located between two of the four suspension lower Aarm linkages and the rigid frame. Two control signals feeding two inertial control actuators ADD from Micromega Dynamics mounted on the suspension.

The proposed control system thus involves 10 sensors and two control actuators per wheel. In the literature, many works propose control systems which use a large number of transducers. The originality of this work is to propose an active control system to reduce the vibrations transmitted by each suspension/frame linkage with the objective of globally controlling road noise inside the cabin. Within this approach, the number of error sensors is justified by the number of suspension/chassis transmission paths. To optimize the active control configuration, an experimental model of a McPherson suspension (using the test bench) was realized on which an optimization algorithm was used to select the best locations and orientations of the two control actuators.

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Fig. 7. Experimental setup for secondary FRF measurements. (a) Locations of candidate control forces for secondary FRF measurements. (b) An example of secondary FRF measurement on the test bench using an inertial actuator.

5.1. Experimental model of the quarter-car suspension To find the best configuration (location, orientation) of control actuators, a database of experimental FRFs on the test bench was built. This database contains:

 45 primary FRFs (three directions of primary disturbance force  5 linkages  3 directions of force at each linkage) between the wheel hub primary disturbance forces and transmitted forces on the various suspension/frame linkages.

 540 secondary FRFs (three directions of secondary control force  12 positions of secondary control actuator  5 linkages  3 directions of force measurements at each linkage) between the secondary control force injected along three directions at 12 locations chosen on the suspension (see Fig. 7 (a)) and transmitted forces on the various suspension/ frame linkages. To measure the secondary FRFs, an inertial actuator was placed successively at each of 12 locations on the suspension with the help of a coupling part and was oriented successively along the X, Y and Z-axis. The choice of the secondary excitation locations was realized according to physical constraints of the actuator positioning on the suspension. Fig. 7(b) presents the configuration used experimentally to measure the secondary FRFs using an ADD inertial actuator. This actuator was chosen for its small size (diameter: 32 mm, height: 37 mm) and its small weight (84 g), and is easy to install on the suspension without modifying its dynamics. All the primary and secondary FRFs measured on the test bench constitute the experimental model of the suspension, which was used for the optimization of the control actuator configuration. This was done with a genetic algorithm which uses the minimization of a cost function to provide the best control actuator configuration. 5.2. Optimal control For a given control actuator configuration, the least mean squares method is used to determine the optimal control forces that minimize the sum of squared forces transmitted at selected suspension/frame linkages. The optimal control force n  1 vector (where n is the number of control actuators) can be written [19] 1 H Fs ¼ ðHH Hs Hp Fp s Hs Þ

(8)

Fp , primary disturbance vector (3  1); Hs , matrix of secondary FRFs between control forces and transmitted forces at selected linkages j  n (where j is the number of error signals at selected linkages); Hp , matrix of primary FRFs between primary disturbance and transmitted forces for all selected linkages ((j  3)). The optimal input obtained in Eq. (8) is then used to determine the residual forces transmitted by each suspension/ frame linkage. The residual forces ðFt Þ can be written Ft ¼ Hs Fs þ Hp Fp

(9)

The residual forces ðFt Þ are used to build the cost functions which are minimized by the genetic algorithm to derive the best control actuator configurations. 5.3. Genetic algorithm for actuator configuration Genetic algorithms are commonly used in non quadratic optimization problems such as optimal actuator positioning in ASAC problems [20,21]. The combination of genetic algorithms and the quadratic minimization theory has already been

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Table 1 Gene description for single force genetic optimization. Parameter

Number of bits

Optimization space

Secondary force locations Force azimuth angle ðyact Þ Force elevation angle ðfact Þ Total (chromosome)

4 8 8 20

12 points in total 256 (resolution of 1.41) 256 (resolution of 1.41)

proposed for the optimization of active vibration control of road noise based on an analytical suspension model [13]. As the experimental model of the suspension is more realistic, it is used here in the genetic algorithm to obtain the best control actuator configuration. The Genetic Algorithm (GA) is a method for solving both constrained and unconstrained optimization problems that is based on natural selection, the process that drives biological evolution. In this work, the parameters which one seeks to optimize are the location and the orientation of the control actuators. The 12 candidate locations shown in Fig. 7 (a)) are considered (coded with 4 bits in the GA) whereas the spherical angles yact and fact used by the genetic algorithm to define the orientation of the control actuators were discretized using 8 bits. Table 1 presents the chromosomes of an individual optimization variable. The GA repeatedly modifies a population of individual solutions to find the actuator configuration which minimizes the following cost functions: JFall ¼

5 3 250 X X X

F tmk ðf Þ  F ntmk ðf Þ

(10)

m ¼ 1 k ¼ 1 f ¼ 20

JFB1B3BH ¼

X

3 250 X X

F tmk ðf Þ  F ntmk ðf Þ

(11)

m ¼ 1;3,5 k ¼ 1 f ¼ 20

where Ftmk is the residual force transmitted by linkage m along direction k. The first cost function JFall (Eq. (10)) aims at minimizing all the forces transmitted to the frame and the second function cost JFB1B3BH (Eq. (11)) aims at minimizing the forces transmitted to the frame through B1, B3 and BH linkages. The choice of the criterion JFB1B3BH was dictated by the available equipment. Indeed, the strut tower (BH) was equipped with a set of three single-axis force sensors to measure the three-dimensional force transmitted at BH. As only two tri-axis force sensors were available, it was necessary to choose only two linkages among B1, B2, B3 and B4. Knowing that (B1, B2) and (B3, B4) are pairs of linkages on the same viscoelastic bushing, the choice was directed towards the linkage points which transmit the most vibratory energy, according to Fig. 6. This explains the choice of B1 and B3. The maximum force amplitude delivered by the ADD inertial actuator (3 N) is taken into account in the optimization algorithm as a constraint (calculated control forces whose amplitude is larger than 3 N are automatically set to 3 N). Therefore, the optimized configuration takes into account the force limitation of the actuators. However, after the optimal configuration has been found, optimal control results were obtained without limiting the force generated by the actuators. 5.3.1. Configuration for minimization of JFall for tri-axis road excitation In this case, the optimization algorithm aims at minimizing the overall force transmissibility using two control actuators. Here, the equivalent three-dimensional road force calculated in Section 3 is used as the primary disturbance. Fig. 8(a) displays the optimized actuator configuration: the first actuator is located on the lower A-arm close to the B3 and B4 linkages which transmit most of the energy for realistic road excitation. The second actuator is placed on the steering rod side close to the primary disturbance. As seen in Fig. 8(b), this actuator configuration lends to a reduction of the JFall criterion of 8 dB between 20 and 250 Hz. The required control effort is relatively small between 100 and 250 Hz, as the average control force is 0.3 N in this frequency range. However below 100 Hz, the control forces shown in by Fig. 8(c) and (d) exceed the force limitations of ADD inertial actuators. 5.3.2. Configuration for minimization of JFall and JFB1B3BH for Z-axis road excitation only To simplify the implementation of the active control system on the test bench, it was chosen to inject the primary disturbance on the suspension only along the vertical axis. Consequently, the optimization of the control actuator configuration was repeated using only the FZ component of the road equivalent force previously identified. Fig. 9(a) shows the best actuators control configuration using JFall as the cost function in the GA. Fig. 9(b) shows the best control actuator configuration found by the GA using J FB1B3BH as the cost function. To evaluate the impact of the choice of the error sensor locations on the optimal actuator locations, Fig. 9(c) presents the residual value of JFall for the following cases: no control; with JFall used as the criterion for actuator optimization; with J FB1B3BH used as the criterion for actuator optimization. When using JFall as the optimization criterion, the reduction of this criterion is 10.7 dB between 20 and 250 Hz. The use of J FB1B3BH as the optimization criterion gives a reduction of 8.6 dB on JFall over the same frequency band. These results

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30 No control Optimal control

Z 20

Y

Actuator 2

Criteria magnitude (dB)

10

X

0

10

10

9

9

8

8

7

7 Amplitude (N)

Amplitude (N)

Actuator 1

6 5 4

100

150 Frequency (Hz)

200

250

50

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150 Frequency (Hz)

200

250

6 5 4

3

3

2

2

1

1

0

50

0 50

100

150 Frequency (Hz)

200

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Fig. 8. Best control actuator configuration to minimize JFall for tri-axis road excitation. (a) Actuator positions and orientations. The orientations of ! ! ! ! ! ! ! ! actuator 1 and actuator 2 are respectively: U act1 ¼ 0:81 X 0:25 Y þ 0:53 Z and U act2 ¼ 0:15 X þ 0:55 Y 0:82 Z . (b) Value of the minimization criterion before and after control. (c) Control force amplitude for actuator 1. (d) Control force amplitude for actuator 2.

justify the choice of the error sensors configuration (B1, B3, BH) since this configuration still provides a significant reduction of the vibrations which are transmitted to the frame by all the linkages and along all the directions. It is thus this control configuration which was implemented experimentally on the test bench. 6. Active control results on the quarter-car suspension On the test bench, tri-axis error force sensors (ICP PCB 260A01) were installed at B1 and B3. The data provided by these ¨ and Kjaer 8200) in BH were used to measure the J FB1B3BH criterion, sensors and the three single axis force sensors (Bruel which was minimized using the feedforward control structure presented in Fig. 10. A Multiple Input Multiple Output (MIMO) FX-LMS controller [19] was implemented on a dSPACE control prototyping system and the secondary transfer paths were identified offline with Finite Impulse Response (FIR) filters that were adapted using steepest descent algorithm. The active control system was tested for sinusoidal disturbances with a frequency varying between 50 Hz and 250 Hz with 5 Hz increment. For each single frequency disturbance, the 2 control filters and 18 identification filters were implemented with 4-tap FIR filters. The use of single frequency disturbance allowed to compensate for the low sensitivity of the tri-axis force sensors in B1 and B3 linkages by setting the primary force magnitude to have an adequate signal to noise ratio at error sensors without saturating the control actuators. The primary disturbance was injected by a suspended shaker which excited the wheel hub along the Z-axis. In the active control experiments, either the electrical input to the disturbance shaker or the force injected by the shaker (measured using an ICP PCB 208C04 force sensor) was tested as reference signals in the FX-LMS controller. The main

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Fig. 9. Best control actuator configuration to minimize JFall and J FB1B3BH for Z-axis road excitation. (a) Actuator positions and orientations for JFall ! ! ! ! ! ! ! ! minimization. The orientations of actuator 1 and actuator 2 are respectively: U act1 ¼ 0:83 X 0:18 Y 0:52 Z and U act2 ¼ 0:28 X 0:14 Y 0:95 Z . (b) Actuator positions and orientations for J FB1B3BH minimization. The orientations of actuator 1 and actuator 2 are respectively: ! ! ! ! ! ! ! ! U act1 ¼ 0:93 X þ 0:1 Y þ 0:34 Z and U act2 ¼ 0:64 X 0:35 Y þ 0:68 Z . (c) Impact of JFall and J FB1B3BH minimization on JFall criteria.

difference between these two signals is the possible feedback of the control actuators on the force injected by the primary shaker (whereas the shaker voltage is assumed independent of the control inputs). If not compensated in the control structure, such a feedback on the reference signal may affect the performance of the feedforward controller [19]. After this preliminary study conducted to observe a possible feedback on the reference signal, the force sensor placed in the primary dynamic shaker link is chosen as reference for active control. In a real system, this information is not available and wheel hub acceleration should be used as reference for the feedforward control system. Assuming that there is a linear function between the acceleration and the force injected on the wheel hub (as shown in previous works [16]), using force as the reference instead of acceleration should not have any effect on active control results when the primary disturbance is sinusoidal. The control actuator configuration derived using the GA using FZ as primary disturbance and JFB1B3BH as the optimization criterion (Fig. 9 (b)) was implemented on the test bench using two ADD inertial actuators. Each control actuator was equipped with a force sensor to monitor the injected control force. Each actuator was mounted on a small aluminium block which was bonded on the suspension at the location and in the orientation provided by the genetic algorithm (see Fig. 11 (a)).

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Fig. 10. Block diagram of the feedforward active vibration control system on the test bench.

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Fig. 11. Active control results on the test bench. (a) Experimental configuration of control actuators. (b) Comparison of optimal control and experimental control performance with either force reference input or electrical reference input.

The control results are presented in Fig. 11(b). The optimal control based on the experimental model of the suspension predicts a reduction of 7.9 dB between 50 and 250 Hz while the experimental reduction with the primary force as reference signal is 4.4 dB. In comparison, the experimental reduction using the electrical input to the primary shaker is 4.6 dB. These results demonstrate that the reference force sensor is not too much affected by the control actuator inputs. The experimental reduction of J FB1B3BH is smaller than that predicted from the experimental model. This difference can be explained by the resolution of the conditioning electronics associated with the error sensors, in particular, the triaxis force sensors in B1 and B3 linkages. Indeed, the primary force magnitude was set to maximize the forces on the suspension linkages without requiring excess control forces that would have saturated the control actuators. The realization of this trade-off is very difficult but active control was performed below the saturation limit of the control actuators. In these conditions, the coherence between the reference signal (force measurement or shaker electrical input) and forces measured at B1, B3 and BH linkages is above 0.95 at most frequencies. However, when the control is on, the forces at the various linkages are reduced and the resolution limit of the error sensors is reached before the control system has converged to the optimal solution. Fig. 11(b), at some frequencies (55, 105, 155, 160, 165 and 250 Hz), the reduction of the J FB1B3BH criterion is larger than that predicted by the experimental model. This might result from slight deviations on the orientation of the control actuators: in fact, the mounting of the control actuators was done with an orientation error of 7101 compared to the configuration obtained by the genetic algorithm.

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Fig. 12(a) and (b) presents the control forces Fact1 and Fact2 delivered by each control actuator normalized by the primary disturbance injected vertically on the wheel spindle. These ratios illustrate the required control actuator authority relative to the primary disturbance. Fig. 12(a) shows that the ratio F act1 =F Z obtained in experiments on the test bench follows the tendency predicted by the experimental model. However, the ratio F act2 =F Z remains lower than that predicted by the model. This result can explain the difference in the control performance between the optimal control and experimental control on the test bench. To analyze these results, we conducted a Singular Value Decomposition (SVD) of Hs , the matrix of secondary FRFs between the two control actuators and the nine force sensors at the B1, B3 and BH linkages. Hs is thus a 9  2 matrix whose SVD at each frequency is Hs ¼ U  S  VH

(12)

where V is a 2  2 matrix which contains a set of orthonormal input basis vector directions for Hs , U is a 9  9 matrix which contains a set of orthonormal output basis vector directions for Hs and S is a pseudo-diagonal 9  2 matrix which contains the singular values of Hs . The absolute value of matrix V components (V11, V12) are shown in Fig. 13(b) as a function of frequency. As the two columns of V are orthonormal: 9V 11 9 ¼ 9V 22 9 and 9V 12 9 ¼ 9V 21 9. The average for 9V ii 9 is 0.9 and the average for 9V ij 9 (for iaj) is 0.3 in the 50–250 Hz frequency range. This result shows that the transfer paths between one actuator and the set of error sensors are relatively independent of the transfer paths between the second actuator and the error sensors. As the singular value associated to the actuator 1 (S11) is significantly larger than that associated to the actuator 2 (S22) (see Fig. 13(a)), the

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Fig. 12. Theoretical and experimental control forces. (a) Ratio between the control force delivered by actuator 1 (Fact1) and the primary vertical disturbance (FZ). (b) Ratio between the control force delivered by actuator 2 (Fact2) and the primary vertical disturbance (FZ).

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Fig. 13. Singular Value Decomposition of the secondary plant matrix Hs. (a) Singular values S11 and S22. (b) Right singular matrix component Vij.

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action of the actuator 1 on the set of error sensors is larger than that of actuator 2. In the FX-LMS controller adaptation, the convergence of the control input to actuator 1 is thus reached much faster than the convergence of the control input to actuator 2. When the convergence of actuator 1 input is reached, the force error signals are reduced to the resolution limit of these sensors. Therefore the error signals are no longer correlated to the reference and actuator 2 does not provide any additional attenuation of error sensors. The SVD study provided insight into why the experimentally measured control force from actuator 2 was lower than predicted. It is postulated that this lower than expected force output produced less attenuation of the error signal than was expected based on the experimental model.

7. Conclusion In this paper, an experimental approach was proposed to optimize an active vibration control system for cancellation of road noise inside vehicles. First, the road noise disturbance was characterized as a 3D equivalent force applied to the wheel spindle on quarter-car test bench to reproduce the accelerations measured on the vehicle in real road conditions. Then, a transmission path analysis was conducted for each suspension/frame linkage using a 3D primary excitation on the wheel spindle. The results obtained from the transmission paths using the force transmissibility factors have revealed that the vibration energy is mainly transmitted through suspension/frame linkages along the vertical axis and the lateral axis. The proposed active control system is based on minimizing dynamic forces transmitted through suspension/frame linkages using force actuators on the wheel-suspension. To optimize the control actuator configuration, an experimental model was constructed using a large number of primary and secondary FRFs measured on the test bench. This experimental model of the suspension was then used in a genetic algorithm combined with the optimal control theory to obtain the best control actuator configuration (location and orientation). The active control system that was experimentally tested on the quarter-car test bench used two inertial control actuators and nine force sensors distributed at lower A-arm and suspension strut tower linkages. A 4.6 dB attenuation was measured in the 50–250 Hz range, thus proving the feasibility and the effectiveness of the active control approach on the suspension. However, this experimental attenuation is smaller than that predicted from the experimental model (7.9 dB). This performance difference is due to the sensors sensitivity and the control actuators authority. So, in future work, the sensors sensitivity will be improved and the control actuators will be chosen to deliver the required control force.

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