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Improvement of ride comfort by unsprung negative skyhook damper control using in-wheel motors.

ABSTRACT

Vehicles equipped with in-wheel motors (IWMs) are capable of independent control of the driving force at each wheel. These vehicles can also control the motion of the sprung mass by driving force distribution using the suspension reaction force generated by IWM drive. However, one disadvantage of IWMs is an increase in unsprung mass. This has the effect of increasing vibrations in the 4 to 8 Hz range, which is reported to be uncomfortable to vehicle occupants, thereby reducing ride comfort. This research aimed to improve ride comfort through driving force control. Skyhook damper control is a typical ride comfort control method. Although this control is generally capable of reducing vibration around the resonance frequency of the sprung mass, it also has the trade-off effect of worsening vibration in the targeted mid-frequency 4 to 8 Hz range. This research aimed to improve mid-frequency vibration by identifying the cause of this adverse effect through the equations of motion. As a result, a method was derived by analysis that reduced vibration over a wide mid-frequency range by a control that applies unsprung vertical velocity in the direction that enhances that velocity (i.e., a negatively signed skyhook damper control called unsprung negative skyhook damper control). This control was then incorporated into a vehicle equipped with IWMs and the improvement effect on ride comfort was verified.

CITATION: Katsuyama, E. and Omae, A., "Improvement of Ride Comfort by Unsprung Negative Skyhook Damper Control Using In-Wheel Motors," SAE Int. J. Alt. Power. 5(1):2016.

INTRODUCTION

Vehicles equipped with in-wheel motors (IWMs) are capable of independently controlling the driving force at each wheel. Therefore, in addition to yaw control, IWMs can also control the roll and pitch of the sprung mass [1]. However, IWMs may also have an adverse effect on ride comfort due to the increased unsprung mass. Figure 1 compares simulated power spectral density (PSD) results for vertical acceleration of a vehicle body driven at 60 km/h (37 mph) over a rough road with and without a 25% increase in unsprung mass (same total vehicle weight) using a 4-wheel full-vehicle model. The increase in the unsprung mass caused vibration to increase, particularly around the 3 to 9 Hz range. Since vibration in the 4 to 8 Hz range is reported to be uncomfortable to vehicle occupants [2], this confirms that increasing the unsprung mass is not desirable for maintaining ride comfort. Therefore, this research examined a method of reducing uncomfortable vibrations using IWM driving force control.

RIDE COMFORT CONTROLS TARGETING ROAD SURFACE DISTURBANCES

Conventional Controls

Before being applied to vehicles, active suspension research originally began as a branch of rail vehicle engineering [3]. Skyhook damper control is typical well-established ride comfort control method [4] that has been applied to vehicle suspension controls [5], although various suspension control concepts have been proposed [6]. First, to confirm the effect of skyhook damper control, a simulation was carried out using a full-vehicle model equipped with IWMs, which was driven over a rough road at 60 km/h. Skyhook damper control was used to distribute the driving force. Figure 2 shows the PSD results for the vertical acceleration of the vehicle. Although the control was clearly effective in reducing vibration around the sprung mass resonance frequency, it had a slightly adverse effect on the 4 to 8 Hz range targeted in this research (vibration in this frequency range is referred to as "mid-frequency vibration" in this paper). When adopted in an actual vehicle, although the control suppressed major movements, fine hard vibrations were noticeable.

The reasons for the adverse effect of the skyhook damper control on mid-frequency vibration were examined theoretically. Figure 3 defines the quarter-car 2-degree-of-freedom (DOF) model used for this purpose. Equations (1) and (2) show the equations of motion for the sprung and unsprung mass, respectively. Here, [m.sub.1] and [m.sub.2] are the unsprung and sprung mass, [k.sub.s] and [c.sub.s] are the spring constant and damping factor of the suspension, and [k.sub.t] is the spring constant of the tire. [F.sub.c] is the acting force of the suspension due to the control, and reaction force is a positive value. [z.sub.0], [z.sub.1] and [z.sub.2] are the vertical displacements of the road surface, unsprung mass, and sprung mass, respectively, s is the Laplace operator. [c.sub.sh] in Equation (3) is delayed by the damping factor of the skyhook damper and acts in accordance with the transfer function D(s). Table 1 shows the values used for calculation with this model.

Figure 4 shows a Bode plot of the sprung mass acceleration that occurs in response to road surface displacement input, as calculated by the model. The first order lag shown in Equation (4) was substituted for D(s), 5.3 Hz was used as the cutoff frequency [f.sub.c] and 40% of [c.sub.s] was substituted into the control damping factor [c.sub.sh]. In addition, the input amplitude was multiplied by 1/f, which is the reciprocal of the input frequency f As a result, applying the skyhook damper control reduced vibration around the sprung mass resonance frequency and slightly worsened mid-frequency vibration. These results reproduce the same trends calculated using the full-vehicle model. However, when there was no lag, mid-frequency vibration did not worsen. In other words, the worsening of mid-frequency vibration is not an inherent characteristic of IWMs, but a characteristic of skyhook damper control containing lag.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

The mechanism by which the control worsened mid-frequency vibration was analyzed by calculating sprung mass displacement [z.sub.2] with respect to unsprung mass displacement [z.sub.1] rather than road surface displacement [z.sub.0]. Equation (5) was used for this purpose.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)

This equation can be used to identify the following points. The suspension damping factor [c.sub.s] is contained in the velocity terms of both the numerator and denominator of the transfer function shown in Equation (5). However, the skyhook coefficient [c.sub.sh] is only included in the denominator. In other words, although convergence improves as the suspension damping factor increases, it also has the trade-off effect of worsening input from the unsprung mass. In contrast, it also explains that a skyhook damper enhances the suppression of the sprung mass without worsening the input from the unsprung mass. However, since a control lag is applied to the [c.sub.sh] term, it is not impossible to increase the equivalent damping factor of the denominator with respect to fast frequency inputs, thereby affecting the sprung mass control.

Proposed Control

First, the research examined ways of eliminating the control lag D(s) in the denominator. The first order term of s in the numerator and denominator both contain the suspension damping factor [c.sub.s]. In skyhook damper control theory, the coefficient of the first order term of s in the denominator is larger than the coefficient of the first order term in the numerator. However, to eliminate the lag in the denominator while maintaining this magnitude relationship, [c.sub.s] can be reduced by software control rather than through the hardware. In other words, as shown in Equation (6), in addition to the sprung mass skyhook control force shown in the first term on the right side, a control force should be applied that is proportional to the suspension stroke velocity of the second term on the right side. It should be noted that the sign of the control force [F.sub.c] is positive in the direction of the rebound of the suspension control actuator (i.e., the extension direction).

[F.sub.c] = [-[c.sub.sh][z.sub.2]s - [c.sub.sc]([z.sub.1] - [z.sub.2])s]D(s) (6)

In this equation, although [c.sub.sc] is the amount of decrease in suspension damping caused by the control, Equation (7) can be obtained from Equation (6) by applying a value equal to the sprung mass skyhook damper damping factor [c.sub.sh]. By substituting this into Equation (5), the sprung mass displacement with respect to the unsprung mass displacement can be expressed using Equation (8)

[F.sub.c] = - [C.sub.sh][Z.sub.1]SD(s) (7)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (8)

Based on Equation (8), the control lag of the denominator is eliminated and the first order term of s in the denominator satisfies the condition that it should be larger than the first order term of the numerator. In addition, as shown in Equation (7), one distinguishing feature of the proposed control is that the command value does not require information about the sprung motion and that the control is performed using only the vertical velocity of the unsprung mass. The direction of this control force is opposite to the skyhook damper and enhances the absolute vertical velocity of the unsprung mass. Therefore, this control is called the unsprung negative skyhook damper control. This control can be explained in physical terms as follows. When a wheel travels over a bump, the unsprung mass possesses velocity in the upward direction. This control raises the unsprung mass and, simultaneously, the reaction force lowers the sprung mass. This has the effect of holding down the sprung mass, which should inherently rise up, while restricting an increase in the contact load. When the wheel moves down after the bump, the opposite action occurs and the same sprung mass motion suppression effect occurs. Ultimately, this control acts to actively move the tires to follow the road surface profile.

The effect of the conventional and proposed controls was confirmed and compared using a 2-DOF model simulation. The control lag D(s) was set as the same first order lag as described above. Figure 5 shows the results. Although the conventional sprung skyhook damper control increased the mid-frequency vibration that is a source of discomfort for vehicle occupants, the proposed control enabled a substantial improvement. Figures 6 and 7 compare the unsprung vertical acceleration and contact load of the controls. Unsprung vertical acceleration appears to worsen around the unsprung resonance frequency. Although fluctuations in contact load also worsen around the unsprung resonance frequency, a substantial reduction is achieved around 3 Hz.

These simulation results suggested a major improvement effect. However, Equation (8) contains a lag term in the numerator. Since the reason why this does not have an adverse impact on sprung acceleration could not be explained, this research then focused on analyzing this phenomenon.

EXAMINATION OF SPRUNG AND UNSPRUNG SKYHOOK DAMPER MECHANISMS

As described in the previous section, both sprung and unsprung skyhook damper controls that contain no lag have the effect of simply increasing or decreasing the damping term (i.e., the first order coefficient of s in the denominator and numerator). The effect of these terms on the sprung acceleration was investigated.

Figures 8 and 9 show the magnitudes of the Bode plots for sprung acceleration with the respective damping terms [c.sub.s] of the denominator and numerator increased or decreased between a range of 0.1 to 3.0 times. The results show that the damping factor of the denominator only has an effect around the sprung mass resonance frequency. This is because the damping factor of the denominator is proportional to the sprung velocity, which decreases as the frequency increases. In contrast, the damping factor of the numerator has an effect over a wide frequency range. This is because the damping factor of the numerator is proportional to the unsprung velocity, which has a tracking trend even with fast inputs. These results indicate that the sprung skyhook damper control does not have an adverse effect on the frequency range at 3 Hz and above, even when the control lag causes a reversal in the control gain and the damping factor decreases. In other words, the adverse effect around the 3 to 8 Hz range caused by the sprung skyhook damper control lag is not due to a decrease in the equivalent damping factor of the denominator. Based on this analysis, it should be possible to express the actual output values of the sprung skyhook damper control containing a control lag as synthesized values weighted by the sprung and unsprung vertical velocities, respectively. This research then examined this method.

First, the command waveform Y of the control with lag was defined as the sine function in Equation (9). Here, [omega] is the input frequency.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (9)

The unsprung vertical velocity [U.sub.l] and sprung vertical velocity [U.sub.2] are defined by Equations (10) and (11), respectively.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (10)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (11)

The weighting functions [w.sub.1] and [w.sub.2] are calculated based on the fact that the synthesized waveform created by applying [w.sub.1] and [w.sub.2] to [U.sub.1] and [U.sub.2] is equal to Y, as shown in Equation (12).

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (12)

Using the addition theorem of sine waves, the right side of Equation (12) can be changed as follows, defining that part as a and b.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (13)

Using the definition in Equation (14). Equation (13) can be converted into Equation (15).

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (14)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (15)

Here, since Equation (16) is true, [[theta].sub.d] that satisfies Equation (17) exists.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (16)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (17)

Therefore, Equation (15) can be converted into Equation (18).

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (18)

Further in accordance with addition theorem, Equation (18) becomes Equation (19) and r and [[theta].sub.d] correspond to [g.sub.c] and [[theta].sub.c] in Equation (9).

Y = r sin([omega]t + [[theta].sub.d]) (19)

Based on the calculations described above, [w.sub.1] and [w.sub.2] can be calculated as shown in Equation (20).

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (20)

First, using this result, the weighting functions [w.sub.1] and [w.sub.2] were calculated with the command waveforms of the sprung skyhook damper control containing control lag expressed using the sprung and unsprung velocities. Here, the frequency transfer functions of the unsprung and sprung velocities [v.sub.z1] and [v.sub.z2] with respect to the road surface input [z.sub.0] as calculated by the quarter-car 2-DOF model simulation are defined as [G.sub.1](j[omega]) and [G.sub.2](j[omega]), respectively. As shown in Equation (21), the magnitudes of [G.sub.1](j[omega]) and [G.sub.2](j[omega]) are defined as [g.sub.1] and [g.sub.2], and the phase angles are defined as [[theta].sub.1] and [[theta].sub.2] In addition, the value obtained by multiplying the sprung velocity magnitude with the control lag magnitude and the control damping factor is defined as [g.sub.c], and the value obtained by adding the control lag phase angle to the phase angle of the sprung velocity is defined as [[theta].sub.c]. It should be noted that the sign of the control force is positive in the direction of the rebound force of the suspension control actuator (i.e., the direction in which the sprung mass is pushed up). These values were substituted into Equations (9), (10), and (11). In addition, [w.sub.l] and [w.sub.2] were normalized using the control damping factor [c.sub.sh]. Then, since the sign for the positive skyhook damper is positive, the normalized weighting functions [w.sub.1 n] and [w.sub.2 n] were defined as Equations (22) and (23). By expressing these values as +1 or -1, a positive or negative skyhook damper is produced, respectively, in which [c.sub.sh] is the damping factor. Additionally, as the control lag, D(j[omega]) was given first order lag characteristics as shown in Equation (24) and the same cutoff frequency as described above was adopted.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (21)

[w.sub.1n] = [w.sub.1]/[c.sub.sh] (22)

[w.sub.2n] = - [w.sub.2]/[c.sub.sh] (23)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (24)

Figure 10 shows the normalized weighting functions [w.sub.1 n] and [w.sub.2 n] for the input frequencies calculated as above. Due to the effect of control lag, the sprung skyhook damper control is composed of the unsprung positive skyhook damper control added to the sprung positive skyhook damper control. Since the effect of the sprung positive skyhook damper control is dominant around the sprung mass resonance frequency, it offsets the adverse effect of the unsprung positive skyhook damper control. However, since the sprung positive skyhook damper control has little effect at 3 Hz and above, the effect of the unsprung positive skyhook damper control is dominant, causing mid-frequency vibration to worsen.

Next, the weighting for the sprung and unsprung velocities was calculated in the same way for the unsprung negative skyhook damper control. Equation (25) is substituted into each magnitude and phase shown in Equations (9), (10), and (11). Again, it should be noted that the control sign is positive in the direction of the rebound force of the suspension control actuator (i.e., the direction in which the unsprung mass is pushed down), in the same way as described above.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (25)

Figure 11 shows the results. Unsprung negative skyhook damper control containing control lag acts as an unsprung negative skyhook damper over a wide range around 2 Hz. At the same time, the effect of the sprung positive skyhook damper is also applied. Both act to reduce vibration and, since there are no adverse elements, a vibration damping effect as shown in Fig. 5 is achieved over a wide range from low to mid-frequencies.

In contrast, Equation (26) shows the effect of incorporating the dead time (i.e., assuming communication and calculation delay as the control delay). As shown in Fig. 12, although the sprung acceleration is virtually unchanged for the sprung positive skyhook damper control, it worsens at and above 7 Hz for the unsprung negative skyhook damper control. Here, the cutoff frequency [f.sub.c] was set to 16 Hz and the dead time tm was set to 0.02 sec.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (26)

Figure 13 shows the normalized weightings for these results. When dead time is included, the sign of the unsprung skyhook damper control reverses from negative to positive at the 7 Hz boundary. This is thought to be the cause of the adverse effect shown in Fig. 12, which should be improved by reducing the dead time.

The sections above have proposed a method of equivalently expressing a synthesis of sprung and unsprung positive and negative skyhook dampers by expressing control lag using both sprung and unsprung velocity components. As a result, it was understood that the worsening effect of sprung skyhook damper control on mid-frequency vibration is due to the effects of the unsprung positive skyhook damper control. In addition, as the inverse effect, the capability of unsprung negative skyhook damper control to improve mid-frequency vibration was also confirmed from these results.

APPLICATION TO VEHICLE EQUIPPED WITH IWMS AND VERIFICATION OF CONTROL EFFECT

Full-Vehicle Simulation

This control method was applied to a vehicle equipped with IWMs. Vehicles equipped with IWMs use the suspension reaction force generated by motor drive as a form of active suspension control [1].

This control, which was studied above using a quarter-car model, was then applied to independent control of each wheel. However, generally, the vertical component of suspension reaction force generated by braking is much larger at the rear wheels than the front wheels. The test vehicle equipped with IWMs in this research is no different. In addition, since a longitudinal force occurs to generate the vertical force, this control was applied only to the left and right rear wheels and the generated longitudinal force was canceled at the left and right front wheels, respectively. If the unsprung vertical velocities at the left and right rear wheels are defined as [v.sub.zrl] and [v.sub.zrr], the driving force control command value for each wheel is expressed by Equation (27). It should be noted that, as shown in Fig. 14, [-c.sub.sh] is the damping factor of the unsprung negative skyhook damper and [[theta].sub.r] is the angle of the line drawn from the contact point of the rear wheels to the instantaneous center of the rear suspension with respect to the horizontal plane.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (27)

As shown in the quarter-car model simulation results above, if the unsprung negative skyhook damper control contains dead time, the control has an adverse effect above a certain frequency. Dead time occurs in an actual control system due to communication and calculation delay. However, since the control is only applied to the rear wheels, the lag can be compensated by using the unsprung vertical velocity [v.sub.zf] detected by the front wheels as the estimated unsprung vertical velocity [[??].sub.zr] of the rear wheels, as shown in Equation (28). Here, [l/v.sub.x], which corresponds to the wheelbase divided by the vehicle velocity, is the lag time created by the passage of the wheelbase, and [t.sub.d] is the lag time created by the control. In addition, since Figs. 6 and 7 show that the sprung and unsprung acceleration and contact load fluctuations worsen around the unsprung mass resonance frequency due to the control, a low pass filter with a cutoff frequency of 10 Hz was applied to the control command values. This also includes the lag time [t.sub.d] Unlike the sprung skyhook damper control, the proposed control can be applied to each wheel. One distinguishing feature of this control is its capability to make this type of lag compensation.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (28)

Vehicle behavior was simulated on a rough road at 60 km/h. The characteristics of the simulated vehicle were, weight: 1,950 kg, wheelbase: 2.7 m, front/rear track: 1.54/1.55 m, and tires: 235/45R18. Figure 15 shows the results. The same improvement in mid-frequency sprung pitch, heave, and roll as the quarter-car model was confirmed. In the frequency range below 2 Hz, pitch worsened while heave improved. This was because the control was only applied to the rear wheels, which meant that pitch and heave could not be independently controlled. In addition, the PSD trough generated by wheelbase filtering [7] also worsened compared to the state without control. However, this is because the control was operating using information from the two rear wheels only.

In addition to vehicles equipped with IWMs, this control is also applicable to any vehicle with suspension controls. If the vertical force can be controlled independently for all four wheels, it should be possible to obtain an additional control effect for the front wheels and to avoid the trough in the PSD frequency results. Based on these assumptions, a substantially improved control effect was presumed.

Actual Vehicle Verification

Vehicle behavior was measured at 60 km/h on a rough road (the same conditions as the simulation). The unsprung vertical velocity used by the control adopted a high pass filter with a cutoff frequency of 0.1 Hz applied to the integral value of the G sensors attached to the unsprung mass. As a result, as shown in Fig. 16, mid-frequency pitch, heave, and roll all improved, verifying the same trends as the simulation. The results of a subjective evaluation by the test drivers found that the vehicle exhibited no fine uncomfortable movements and that no hard sensations were felt. The subjective evaluations also evaluated the ride comfort as refined, indicating that the adverse effect of the increased unsprung mass was eliminated and a further improvement effect was obtained.

CONCLUSION

* Conventional sprung skyhook damper control has an adverse effect on mid-frequency vibration. The reason for this was identified analytically from the equations of motion. A theory was then derived that mid-frequency vibration could be reduced through driving force control that applies force proportionally to the vertical velocity of the unsprung mass and in the direction that enhances that velocity (called the unsprung negative skyhook damper control).

* In addition, the improvement effect in the mid-frequency region of the above theory was verified by expressing control lag as weighted sprung and unsprung velocity components.

* The proposed control was applied to the rear wheels of a vehicle equipped with IWMs. Tests confirmed that the control reduced sprung mid-frequency vibration and improved actual ride comfort.

* One of the distinguishing characteristics of this control is that it functions using the unsprung vertical velocity only, without requiring detection or estimation of sprung mass movement. It is also applicable to suspension control devices other than IWMs and further control effects are expected by controlling the vertical force independently for all four wheels.

REFERENCES

[1.] Katsuyama, E., "Decoupled 3D Moment Control for Vehicle Motion Using In-Wheel Motors," SAE Int. J. Passeng. Cars - Mech. Syst. 6(1):137-146, 2013, doi:10.4271/2013-01-0679.

[2.] "Mechanical vibration and shock - Evaluation of human exposure to whole-body vibration - part 1," ISO Standard 2631-1,1997.

[3.] Hedrick, J.K., "Railway Vehicle Active Suspensions," Vehicle System Dynamics 10:267-283, 1981. doi:10.1080/00423118108968679.

[4.] Karnopp, D., "Active Damping in Road Vehicle Suspension System," Vehicle System Dynamics 12(6), 1983, doi :10.1080/00423118308968758.

[5.] Aoyama, Y., Kawabata, K., Hasegawa, S., Kobari, Y. et al., "Development of the Full Active Suspension by Nissan," SAE Technical Paper 901747, 1990, doi: 104271/901747.

[6.] Tseng, H., Hrovat, D., "State of the art survey: active and semi-active suspension control," Vehicle System Dynamics 53:7, 1034-1062, 2015, doi :10.1080/00423114.2015.1037313.

[7.] Gillespie, T, "Fundamentals of Vehicle Dynamics," (Warrendale, Society of Automotive Engineers, Inc., 1992), doi:10.4271/R-114.

CONTACT INFORMATION

KATSUYAMA, Etsuo

Toyota Motor Corporation

Phone:+81 50 3165 2589

etsuo_katsuyama@mail.toyota.co.jp

Etsuo Katsuyama and Ayana Omae

Toyota Motor Corporation

Table 1. Parameters for calculation.

Parameters           Symbol     Unit     Value

Sprung mass          [m.sub.2]  kg        500
Unsprung mass        [m.sub.1]  kg         80
Spring stiffness     [k.sub.s]  N/m        30e3
Damping coefficient  [c.sub.s]  N/(m/s)  2000
Tire stiffness       [k.sub.t]  N/m       300e3
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Author:Katsuyama, Etsuo; Omae, Ayana
Publication:SAE International Journal of Alternative Powertrains
Article Type:Report
Date:May 1, 2016
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