Anti-roll moment distribution active suspension

A system for controlling a suspension of a vehicle includes a plurality of sensors, an anti-roll moment module configured to determine a front-to-total anti-roll moment distribution based on at least a first operating parameter of the vehicle, at least one suspension actuator, and a suspension control module configured to control the at least one suspension actuator based on the determined front-to-total anti-roll moment distribution. A method of producing an anti-roll moment distribution module for a vehicle includes determining understeer characteristics of the vehicle, determining a maximum lateral acceleration of the vehicle, adjusting the understeer characteristics based on the determined maximum lateral acceleration, determining reference understeer characteristics, determining a plurality of reference yaw rates and a plurality of feedforward contributions using a non-linear quasi-static model of the vehicle, storing the reference yaw rates in a first look-up table, and storing the feedforward contributions in a second look-up table.

FIELD

The present disclosure relates to vehicle control systems and more particularly to systems and methods for vehicle suspension control.

BACKGROUND

In general, the anti-roll moment of a vehicle is a moment about the roll axis of the vehicle that counter acts a rotation of the vehicle body about the same axis, for example, a rotation caused by the lateral acceleration of the vehicle during cornering. The variation of the anti-roll moment distribution among the front and rear axles of a vehicle has an impact on the cornering response, especially at lateral acceleration levels close to the cornering limit. This is caused by the nonlinear behavior of typical automotive tires, characterized by an increase of the lateral force, (Fy), which is less than proportional to the increase of the vertical load (Fz) for a given value of slip angle. In cornering conditions, the load transfer (ΔFz) caused by the lateral acceleration of the vehicle, increases the vertical load on the outer wheel of the axle, and decreases the vertical load on the inner wheel. When two tires of the same axle are considered, the overall effect is a reduction of the total axle lateral force with ΔFz, or an increase of the slip angle value required for generating a given level of lateral axle force. In a first approximation, the sum of the load transfers on the front and rear axles in cornering is approximately constant with any suspension set-up, since it mainly depends on the geometric and inertial parameters of the vehicle. However, the load transfer distribution among the front and rear axles of a vehicle can be regulated through a controllable suspension system, which varies the front-to-total anti-roll moment distribution.

An increase of the anti-roll moment, and thus the load transfer, on the front suspension system of a vehicle increases the understeer of a vehicle. Conversely, an increase of the anti-roll moment on the rear suspension system of a vehicle reduces the understeer of the vehicle. Since control of vehicle understeer implies a variation of the yaw rate of the vehicle for a given steering input and vehicle speed, the control of the front-to-total anti-roll moment distribution can be adopted for vehicle yaw rate control. Thus, a controllable suspension system can be used for tracking a reference yaw rate.

Accordingly, a need exists for systems and methods for yaw rate control through the variation of a front-to-total suspension anti-roll moment distribution.

SUMMARY

A system for controlling a suspension of a vehicle is disclosed. The system includes a plurality of sensors. Each sensor of the plurality of sensors is configured to measure an operating parameter of the vehicle. The system further includes an anti-roll moment module configured to determine a front-to-total anti-roll moment distribution based on at least a first operating parameter of the vehicle measured by a first sensor of the plurality of sensors, at least one suspension actuator, and a suspension control module configured to control the at least one suspension actuator based on the determined front-to-total anti-roll moment distribution.

In other features, the anti-roll moment module includes a feedforward module configured to determine a feedforward contribution based on at least the first operating parameter of the vehicle. The front-to-total anti-roll moment distribution is based on the determined feedforward contribution.

In further features, the feedforward module includes a first look-up table. The first look-up table includes a first plurality of entries and each entry of the first plurality of entries includes a feedforward contribution value based on a non-linear quasi-static model of the vehicle. The feedforward module is further configured to (i) select a first entry of the first plurality of entries of the first look-up table based on the first operating parameter and (ii) determine the feedforward contribution based on the first entry of the first plurality of entries.

In other features, the anti-roll moment module includes a yaw rate module configured to determine a reference yaw rate based on at least the first operating parameter of the vehicle. The front-to-total anti-roll moment distribution is based on the determined reference yaw rate.

In further features, the yaw rate module includes a second look-up table. The second look-up table includes a second plurality of entries and each entry of the second plurality of entries includes a reference yaw rate value based on the non-linear quasi-static model of the vehicle. The yaw rate module is further configured to (i) select a first entry of the second plurality of entries of the second look-up table and (ii) determine the reference yaw rate based on the first entry of the second plurality of entries.

In other features, the anti-roll moment module includes an error module configured to determine a yaw rate error based on (i) the reference yaw rate and (ii) a second operating parameter of the vehicle measured by a second sensor of the plurality of sensors and a feedback module configured to determine a feedback contribution based on the yaw rate error. The second operating parameter is a yaw rate of the vehicle. The feedback module is configured to determine the feedback contribution by applying a correction to the yaw rate error based on proportional, integral, and derivative terms. In further features, the anti-roll module includes a front-to-total module configured to determine the front-to-total anti-roll moment distribution based on the feedforward contribution and the feedback contribution.

In yet other features, the anti-roll moment module includes an adjusting module configured to determine an adjusted feedforward contribution based on (i) the feedforward contribution and (ii) at least one of the yaw rate error or a slip angle of a rear axle of the vehicle. The anti-roll module also includes a front-to-total module configured to determine the front-to-total anti-roll moment distribution based on the adjusted feedforward contribution and the feedback contribution.

A method of controlling a suspension of a vehicle is disclosed. The method includes obtaining a plurality of operating parameters of the vehicle, determining a front-to-total anti-roll moment distribution based on at least a first operating parameter of the plurality of operating parameters of the vehicle, and adjusting at least one controllable suspension actuator of the vehicle based on the determined front-to-total anti-roll moment distribution.

In yet other features, the method includes determining a feedforward contribution based on at least the first operating parameter of the vehicle. The front-to-total anti-roll moment distribution is based on the determined feedforward contribution.

In further features, determining the feedforward contribution includes selecting a first entry from a first look-up table. The first look-up table includes a first plurality of entries and each entry of the first plurality of entries includes a feedforward contribution value that is based on a non-linear quasi-static model of the vehicle.

In other features, the method includes determining a reference yaw rate based on at least the first operating parameter of the vehicle. The front-to-total anti-roll moment distribution is based on the determined reference yaw rate.

In further features, determining the reference yaw rate includes selecting a first entry from a second look-up table. The second look-up table includes a second plurality of entries and each entry of the second plurality of entries includes a reference yaw rate value that is based on the non-linear quasi-static model of the vehicle.

In other features, the method includes determining a yaw rate error based on (i) the reference yaw rate and (ii) a second operating parameter of the plurality of operating parameters of the vehicle. The second operating parameter is a yaw rate of the vehicle. The method further includes applying a correction to the yaw rate error based on proportional, integral, and derivative terms to determine a feedback contribution. In further features, determining the front-to-total anti-roll moment distribution includes adding the feedforward contribution to the feedback contribution.

In yet other features, the method includes determining an adjusted feedforward contribution based on (i) the feedforward contribution and (ii) at least one of the yaw rate error or a slip angle of a rear axle of the vehicle. Determining the front-to-total anti-roll moment distribution includes adding the adjusted feedforward contribution to the feedback contribution.

A method of producing an anti-roll moment distribution module for a vehicle is disclosed. The method includes determining understeer characteristics of the vehicle, determining a maximum lateral acceleration of the vehicle, adjusting the understeer characteristics of the vehicle based on the determined maximum lateral acceleration, determining reference understeer characteristics, determining a plurality of reference yaw rates based on (i) the maximum lateral acceleration and (ii) the reference understeer characteristics using a non-linear quasi-static model of the vehicle, storing the plurality of reference yaw rates in a first look-up table in the anti-roll moment distribution module, and determining a plurality of feedforward contributions using the non-linear quasi-static model of the vehicle. Each feedforward contribution of the plurality of feedforward contributions can be used to determine a front-to-total anti-roll moment distribution for the vehicle. The method further includes storing the plurality of feedforward contributions in a second look-up table in the anti-roll moment distribution module.

In other features, the non-linear quasi-static model of the vehicle includes a set of equations and inequalities. Determining the understeer characteristics includes starting to solve the set of equations and inequalities using (i) increasing lateral acceleration values and (ii) constant velocity values and stopping in response to being unable to find a valid solution to the set of equations and inequalities.

In yet other features, determining the maximum lateral acceleration of the vehicle includes performing a minimization procedure on a cost function. In further features, determining the plurality of reference yaw rates and determining the plurality of feedforward contributions includes solving the set of equations and inequalities without using forward time integration.

DETAILED DESCRIPTION

The following description is merely exemplary in nature and is not intended to limit the present disclosure, application, or uses.FIG. 1shows a vehicle100incorporating an anti-roll moment distribution system. The vehicle100includes a body102, a suspension control module110configured to set and/or adjust controllable suspension components of the vehicle, and an anti-roll moment distribution module120configured to determine a front-to-total anti-roll moment distribution based on operating parameters of the vehicle100. The vehicle100also includes sensors130configured to measure the operating parameters of the vehicle100. In some implementations, the sensors130include a steering wheel angle sensor, a velocity sensor, a longitudinal acceleration sensor, and a yaw rate sensor. In other implementations, the sensors130may include additional or different sensors. While the vehicle100has been depicted as a passenger car, the anti-roll moment distribution system described herein may be suitably incorporated as part of other types of vehicles and/or in other types of applications, such as vehicles incorporating independent front and/or independent rear suspension systems.

The vehicle100includes a first front wheel140. The first front wheel140includes a first front controllable suspension actuator145. The suspension control module110is connected to the first front controllable suspension actuator145. The suspension control module110is configured to set and/or adjust vertical force applied by the first front controllable suspension actuator145to the first front wheel140.

Further, the vehicle100includes a second front wheel150. The second front wheel150includes a second front controllable suspension actuator155. The suspension control module110is connected to the second front controllable suspension actuator155. The suspension control module110is configured to set and/or adjust vertical force applied by the second front controllable suspension actuator155to the second front wheel150.

The vehicle100also includes a first rear wheel160. The first rear wheel160includes a first rear controllable suspension actuator165. The suspension control module110is connected to the first rear controllable suspension actuator165. The suspension control module110is configured to set and/or adjust vertical force applied by the first rear controllable suspension actuator165to the first rear wheel160.

Further still, the vehicle100includes a second rear wheel170. The second rear wheel170includes a second rear controllable suspension actuator175. The suspension control module110is connected to the second rear controllable suspension actuator175. The suspension control module110is configured to set and/or adjust vertical force applied by the second rear controllable suspension actuator175to the second rear wheel170.

The anti-roll moment distribution module120generates a front-to-total signal. The value of the front-to-total signal represents the front-to-total anti-roll moment distribution (f) required to maintain a specific cornering behavior of the vehicle100. The front-to-total anti-roll moment distribution (f) may be expressed as a ratio of the front controllable anti-roll moment contribution (MAR,F,Act) of the vehicle100—e.g., the anti-roll moment contribution from the first front controllable suspension actuator145and the second front controllable suspension actuator155—to the total anti-roll moment contribution (MAR,Act,tot) of the vehicle100—e.g., the anti-roll moment contribution from the first front controllable suspension actuator145, the second front controllable suspension actuator155, the first rear controllable suspension actuator165, and the second rear controllable suspension actuator175. For example, the following formula may be used to express the front-to-total anti-roll moment distribution (f):

The suspension control module110sets and/or adjusts the controllable suspension components of the vehicle100—e.g., the first front controllable suspension actuator145, the second front controllable suspension actuator155, the first rear controllable suspension actuator165, the second rear controllable suspension actuator175—based on the front-to-total signal generated by the anti-roll moment distribution module120. For example, the suspension control module110may control the first front controllable suspension actuator145and the second front controllable suspension actuator155based on the following formula:
MAR,F,Act=fMAR,Act,tot

MAR,F,Actrepresents the front controllable anti-roll moment contribution of the vehicle100—e.g., the anti-roll moment contribution from the first front controllable suspension actuator145and the second front controllable suspension actuator155.

The suspension control module may control the first rear controllable suspension actuator165and the second rear controllable suspension actuator175using the following formula:
MAR,R,Act=(1−f)MAR,Act,tot

MAR,R,Actrepresents the rear controllable anti-roll moment contribution of the vehicle100—e.g., the anti-roll moment contribution from the first rear controllable suspension actuator165and the second rear controllable suspension actuator175.

While the vehicle100has been depicted as including controllable suspension actuators located on each vehicle corner, the anti-roll moment distribution system described herein may be suitably incorporated as part of other types of vehicles and/or in other types of applications. For example, the anti-roll moment distribution system described herein may be suitably incorporated into vehicles with controllable suspension actuators located only on the front or rear corners, a vehicle with controllable anti-roll bars—i.e., stabilizer bars—on either the front axles, the rear axle, or both axles, or vehicles with any other system capable of controlling the vertical load on the wheels of at least one axle of the vehicle100.

FIG. 2is a functional block diagram of the anti-roll moment distribution module120. The anti-roll moment distribution module120includes a feedforward module220, a reference yaw rate module230, a yaw rate error module240, a proportional-integral-derivative (PID) feedback module250, and a front-to-total distribution module260. In some implementations, the anti-roll moment distribution module120also includes an adjusting module265. The feedforward module220and the reference yaw rate module230receive signals from various vehicle sensors—such as, sensors130—that represent different operating parameters associated with the vehicle100. The signals may include a steering wheel angle signal270, a velocity signal272, and an acceleration signal274. The steering wheel angle signal270represents the current angle of the front wheels of the vehicle100. The velocity signal272and the acceleration signal274represent the current velocity and longitudinal acceleration of the vehicle100, respectively.

The feedforward module220generates a feedforward signal based on the values of the sensor signals. The feedforward signal represents a feedforward contribution to the front-to-total anti-roll moment distribution that is associated with the current operating parameters of the vehicle100—i.e., the values of the received sensor signals. The feedforward module220includes a look-up table that stores a plurality of feedforward contribution values. Each stored feedforward contribution value is associated with a unique set of vehicle parameters. For example, each feedforward contribution value may be associated with a steering wheel angle, a velocity, and a longitudinal acceleration. Each feedforward contribution value may also be associated with different or additional vehicle parameters—such as, a tire-road friction coefficient (μ). The stored feedforward contribution values and associated vehicle operating parameters are based on a non-linear quasi-static model of the vehicle100. The feedforward module220compares the values of the received sensor signals to the stored values in the look-up table. For example, the feedforward module220selects a stored feedforward value associated with vehicle parameters that match the values of the steering wheel angle signal270, the velocity signal272, and the acceleration signal274. The feedforward module220generates the feedforward signal based on the selected feedforward value and then outputs the generated signal. For example, if the anti-roll moment distribution module120includes the adjusting module265, the feedforward signal is outputted to the adjusting module265. Otherwise, the feedforward module220outputs the feedforward signal to the front-to-total distribution module260.

The reference yaw rate module230generates a reference yaw rate signal based on the values of the sensor signals. The reference yaw rate signal represents a yaw rate associated with the current operating parameters of the vehicle100—for example, values of the signals from the sensors. The reference yaw rate module230includes a look-up table that stores a plurality of yaw rates. Each yaw rate in the look-up table is associated with a set of vehicle operating parameters. For example, each yaw rate may be associated with a steering wheel angle, a velocity, and a longitudinal acceleration. Each yaw rate value may also be associated with other vehicle operating parameters—such as, a tire-road friction coefficient (μ). Similar to the feedforward values stored in the feedforward module220, the stored yaw rates and associated vehicle parameters are based on the non-linear quasi-static model of the vehicle100. The reference yaw rate module230matches the current values of the steering wheel angle signal270, the velocity signal272, and the acceleration signal274to a stored yaw rate and then outputs a signal that represents the stored yaw rate.

In various implementations, the feedforward module220and the reference yaw rate module230may use a torque demand in traction and braking of the vehicle100or accelerator and brake pedal inputs in place of the velocity signal272and/or the acceleration signal274. The feedforward module220and the reference yaw rate module230may also receive an estimated current tire-road friction coefficient (μ). In other implementations, the feedforward module220and the reference yaw rate module230may receive a signal that represents the average steering angle of the front wheels of the vehicle100in place of the steering wheel angle signal270. In some implementations, the feedforward module220and the reference yaw rate module230may use alternative and/or additional signals to generate the feedforward signal and the reference yaw rate signal, respectively.

The yaw rate error module240is configured to generate a yaw rate error signal. The yaw rate error module240receives the reference yaw rate signal generated by the reference yaw rate module230. The yaw rate error module240also receives a yaw rate signal242that represents the current yaw rate of the vehicle100. The yaw rate error module240compares the reference yaw rate to the current yaw rate of the vehicle100and outputs a yaw rate error signal that represents the difference between the value of the reference yaw rate and the value of the current yaw rate of the vehicle100. The yaw rate error module240outputs the yaw rate error signal to the PID feedback module250. The yaw rate error module240may also output the yaw rate error signal to the adjusting module265.

The PID feedback module250is configured to receive the yaw rate error signal and output a feedback contribution signal. For example, the PID feedback module250applies a correction to the yaw rate error signal based on proportional, integral, and derivative terms. The PID feedback module250then outputs the results of the correction as the feedback contribution signal.

The adjusting module265is configured to output an adjusted feedforward contribution signal. In some implementations, the adjusting module265receives a slip angle signal267that represents an estimation of the slip angle of a rear axle (βR) of the vehicle100. To prevent undesired system responses in extreme conditions, a progressive deactivation algorithm is apply to the feedforward contribution—i.e., the value of the feedforward signal received from the feedforward module220. For example, the adjusting module265may use the following equation to determine an adjusted feedforward contribution:
fFFW=wFFW(|Δr|,|βR|)fFFW,SSTF+(1−wFFW(|Δr|,|βR|)fnominal

wFFWis a weighting whose value is 1 during normal vehicle operation and progressively decreases to zero in cases of significant yaw error rates (Δr) or rear axle sideslip angles (βR). fnominalrepresents a front-to-total anti-roll moment of the vehicle100without the anti-roll moment distribution module120. fFFW,ssrepresents the feedforward contribution determined by the feedforward module220, and fFFWrepresents the adjusted feedforward contribution. The adjusting module265outputs a signal that represents the adjusted feedforward contribution.

In some implementations, the adjusting module265includes a 2 dimensional look-up table that is used to determine the value of wFFW(|Δr|,|βR|). In other implementations, the value of wFFW(|Δr|,|βR|) may be determined as a product of two factors. For example, the value of wFFW(|Δr|,|βR|) may be calculated using the following formula:
wFFW(|Δr|,|βR|)=wFFW,ΔrwFFW,βR

The first factor (wFFW,Δr) may be determined using the following formula:

Δractis a yaw error rate activation threshold and Δrthis a yaw error rate upper threshold. The yaw rate of the vehicle100changes relative to both the speed of the vehicle100and the lateral acceleration of the vehicle100. As a result, the yaw error rate activation threshold (Δract) and the yaw error rate upper threshold (Δrth) change dynamically based on the speed of the vehicle100and the lateral acceleration of the vehicle100. For example, the following formulas may be used to determine the yaw error rate activation threshold (Δract) and the yaw error rate upper threshold (Δrth):

V is the speed of the vehicle100. ay,actis a predetermined lateral acceleration activation threshold. In various implementations, the predetermined lateral acceleration activation threshold (ay,act) may be 3 m/s2to 5 m/s2. ay,this a predetermined lateral acceleration upper threshold. The predetermined lateral acceleration upper threshold (ay,th) may be any value greater than the value of the predetermined lateral acceleration activation threshold (ay,act).

The second factor (wFFW,βR) may be determined using the following formula:

βactis a predetermined rear axle sideslip angle activation threshold. In some implementations, the rear axle sideslip angle activation threshold (βact) may be 3 degrees to 5 degrees. βthis a predetermined rear axle sideslip angle upper threshold. The rear axle sideslip angle upper threshold (βth) may be any value greater than the value of the rear axle sideslip angle activation threshold (βact). In some implementations, the rear axle sideslip angle upper threshold (βth) may be 5 degrees to 8 degrees.

TF is a first-order low pass filter. The value of TF may be determined using the following formula:

fc,Wrepresents the cutoff frequency of the low pass filter. In some implementations, TF may have a cutoff frequency of 5 Hz—i.e., fc,Wis equal to 5. In other implementations, TF may have a cutoff frequency of 1 Hz. In yet other implementations, TF may have a cutoff frequency between 1 Hz and 5 Hz.

The front-to-total distribution module260receives the feedback contribution signal generated by the PID feedback module250and either the feedforward signal generated by the feedforward module220or the adjusted feedforward signal from the adjusting module265. The front-to-total distribution module260adds the feedforward signal, or the adjusted feedforward signal, to the feedback contribution signal to generate a front-to-total signal276. The front-to-total distribution module260then outputs the front-to-total signal276—for example, to the suspension control module110.

The feedforward contribution values stored in the feedforward module220and reference yaw rates stored in the reference yaw rate module230are based on the non-linear quasi-static model of the vehicle100. The quasi-static model is used to calculate the understeer characteristics of the vehicle100for non-zero values of longitudinal acceleration at a given speed. Such a calculation is not a trivial task in case of a simulation model in the time domain, as it requires a careful set-up of multiple maneuvers. This property makes the quasi-static model ideal for the design of non-linear feedforward contributions. To track a generic steady-state reference yaw rate, the corresponding steady-state front-to-total anti-roll moment distribution is a non-linear function of the driver inputs and vehicle operating conditions—i.e., the vehicle operating parameters. In various implementations, the quasi-static model has eight degrees of freedom—for example, the longitudinal, lateral, roll, and yaw motions of the vehicle100and the rotation of each wheel of the vehicle100. In some implementations, the quasi-static model may have seven or fewer degrees of freedom. In other implementations, the quasi-static model may have nine or more degrees of freedom.

In practice, given the complexity of the cornering behavior of the vehicle100, a realistic steady-state front-to-total anti-roll moment distribution cannot be determined through a single open formula. Moreover, the reference yaw rate and feedforward contribution values used must be consistent with each other, and compatible with both the achievable cornering response and the actuator limitations of the vehicle100. Therefore, the reference yaw rates and the feedforward contributions are determined based on the non-linear quasi-static vehicle model of the vehicle100offline and stored in the respective look-up tables. The look-up tables enable the anti-roll moment distribution module120to determine feedforward contributions and the reference yaw rates that correspond to the operating parameters of the vehicle100in real-time, while ensuring that the determined values are consistent with each other, and compatible with both the achievable cornering response and the actuator limitations of the vehicle100.

The look-up tables in the feedforward module220and the reference yaw rate module230are generated offline using the quasi-static model to calculate the necessary values for the steady-state feedforward front-to-total anti-roll moment distribution—fFFW,ss(δsw, V, ax)—and the steady-state reference yaw rate—rref,ss(δsw, V, ax). The time derivatives of vehicle sideslip angle (β), roll angle (φ), and wheel slip ratios (σi) are assumed to be zero. In this way, the quasi-static model results in a set of algebraic equations that can be solved for different operating conditions of the vehicle, without requiring forward time integration.

FIGS. 3A and 3Bdepict various variables associated with the non-linear quasi-static model of the vehicle100.FIG. 3Ais a top view of the vehicle100andFIG. 3Bis a rear view of the vehicle100. With reference toFIGS. 3A and 3B, in the resulting set of algebraic equations: m is the mass of the vehicle100; CG is the center of gravity of the vehicle100; u is the component of the velocity vector at the center of gravity along the longitudinal axis of the vehicle reference system; v is the component of the velocity vector at the center of gravity along the lateral axis of the vehicle reference system; r is the vehicle yaw rate; Fx,iis the longitudinal force of the i-th tire; Fy,iis the lateral force of the i-th tire; δiis the steering angle of the i-th wheel; Fdragis the aerodynamic drag force; xiis the longitudinal coordinate of the i-th wheel with respect to the vehicle center of gravity; yiis the lateral coordinate of the i-th wheel with respect to the vehicle center of gravity; Mz,iis the self-alignment moment of the i-th tire; hCGis the height of the vehicle center of gravity; dFis the front suspension roll center height; dRis the rear suspension roll center height; MAR,Fis the front suspension anti-roll moment; and MAR,Ris the rear suspension anti-roll moment.

In some implementations, the longitudinal force balance of the vehicle100may be calculated using the following formula:

The lateral force balance of the vehicle100may be calculated using the following formula:

The yaw moment balance of the vehicle100may be calculated using the following formula:

The roll moment balance of the vehicle100may be calculated using the following formula:

Further, the moment balance for the i-th wheel of the vehicle100may be calculated using the following formula:
Tdr,i−Tb,i−Fx,iRl,i−My,i−Jw,i{dot over (ω)}i=0

Tdr,iis the i-th drivetrain torque, referred to the i-th wheel; Tb,iis the braking torque at the i-th corner; Jw,iis the mass moment of inertia of the i-th wheel, including the relevant drivetrain contributions depending on the drivetrain architecture; {dot over (ω)}iis the angular acceleration of the i-th wheel. In some implementations, mathematical conditions may be imposed on Tdr,iand Tb,ito emulate the behavior of different drivetrain or braking system architectures, or the intervention of a chassis control system based on direct yaw moment control.

The angular acceleration of the i-th wheel ({dot over (ω)}i) may be calculated using the following formula:

Rl,iis the laden radius of the i-th wheel characterized by a rolling radius Re,iand σiis the slip ratio of the i-th tire.

The vertical tire load (Fz) of the first front wheel140(Fz,1) and the second front wheel150(Fz,2) may be calculated using the following formula and inequality:

Flift,Fis the aerodynamic lift force of the front of the vehicle100and l is the wheelbase of the vehicle100. b represents the rear semi-wheelbase of the vehicle100—i.e., the distance between the center of gravity of the vehicle100(CG) and the rear axle. For example, with continued reference toFIG. 3A, b may be equal to either x3or x4.

The vertical tire load (Fz) of the first rear wheel160(Fz,3) and the second rear wheel170(Fz,4) may be calculated using the following formula and inequality:

Flift,Ris the aerodynamic lift force of the rear of the vehicle100. a represents the front semi-wheelbase of the vehicle100—i.e., the distance between the center of gravity of the vehicle100(CG) and the front axle. For example, with continued reference toFIG. 3A, a may be equal to either x1or x2.

With respect to calculating the vertical tire load (Fz), the inequalities are necessary to express the fact that if a wheel lifts from the road surface, the respective vertical tire load cannot become negative. In such a condition, the vertical load on the opposite wheel of the axle cannot exceed the total vertical load on the axle, which is expressed by the right-hand term of each inequality.

The front anti-roll moment (MAR,F) of the vehicle100may be calculated using the following formula:
MAR,F=MAR,F,Pass+MAR,F,Act

MAR,F,Passrepresents the front passive anti-roll moment contribution of the vehicle100. MAR,F,Actrepresents the front controllable anti-roll moment contribution of the vehicle100—e.g., the anti-roll moment contribution from the first front controllable suspension actuator145and the second front controllable suspension actuator155.

Similarly, the rear anti-roll moment (MAR,R) of the vehicle100may be calculated using the following formula:
MAR,R=MAR,R,Pass+MAR,R,Act

MAR,R,Passrepresents the rear passive anti-roll moment contribution of the vehicle100. MAR,R,Actrepresents the rear controllable anti-roll moment contribution of the vehicle100—e.g., the anti-roll moment contribution from the first rear controllable suspension actuator165and the second rear controllable suspension actuator175.

The total anti-roll moment of all of the controllable suspension actuators of the vehicle100(MAR,Act,tot) may be calculated using various methods. For example, the desired roll angle characteristic of the vehicle100may be determined as a function of lateral acceleration of the vehicle100. Alternatively, the desired roll characteristic of the vehicle100may be determined as a function of the steering wheel angle and velocity of the vehicle100. The quasi-static model of the vehicle100includes considerations of the actuation ratio limitations of the controllable suspension actuators of the vehicle100.

The equations of the quasi-static model of the vehicle100are solved without forward integration in the time domain. In various implementations, the non-linear system of equalities and inequalities of the quasi-static model of the vehicle100may be solved using the Matlab nonlinear optimization function fmincon. While fminconis an optimization function, it may also be used as a solver by adopting a zero objective function. For example, the quasi-static model equations may be imposed as equality constraints and the physical vehicle and controllable suspension actuator limitations may be imposed as inequality constraints. In the event of multiple valid solutions—e.g., the vehicle100includes other active systems providing actuation redundancy—an objective function is defined and fminconis used to minimize the objective function while ensuring that the constraints are respected. In other implementations, an alternative optimization function and/or software package may be used to solve the equations of the quasi-static model of the vehicle100.

InFIG. 4, a flowchart shows an example method of producing an anti-roll moment distribution module for a vehicle—such as the anti-roll moment distribution module120of the vehicle100. The method begins at410with the computation of the understeer characteristics of a passive vehicle—i.e., the vehicle100without an anti-roll moment distribution system. The non-linear quasi-static model of the passive vehicle is solved for increasing values of lateral acceleration (ay) and constant values of velocity (V), and optionally for longitudinal acceleration (ax) or another relevant vehicle parameters (Θ)—such as, an estimated tire-road friction coefficient (μ). The calculations stop once a valid solution to the quasi-static model cannot be found. The calculations are run with a nominal value of the front-to-total anti-roll moment distribution parameter (fnominal). The nominal value corresponds to the front-to-total anti-roll moment of the vehicle without an anti-roll moment distribution system. The result of the solution to the quasi-static model using fnominalrepresents the understeer characteristics of the vehicle without the anti-roll moment distribution system—δdyn(ay). More specifically, one understeer characteristic (δdyn(ay)) is obtained for each velocity (V) and set of optional vehicle parameters (Θ)—such as, axand μ. δdynis the dynamic steering angle at the wheel—i.e., the difference between the actual steering angle and the kinematic steering angle, where the latter is the average steering angle of the front wheels required to make the vehicle travel on the considered trajectory radius at nearly zero speed. Alternatively, δdynmay refer to the steering wheel of the vehicle, and the understeer characteristic can be expressed as δSW,dyn(ay).

The method continues with420where the maximum achievable value of lateral acceleration (ay) and limit understeer characteristics of the vehicle100are determined. For a set of parameters, the limit understeer characteristic is considered as an extreme case that should not be exceeded when determining the reference vehicle cornering response. For example, since passenger cars are normally understeering, an understeer characteristic as close as possible to the neutral steering behavior and compatible with the specific actuator limitations may be considered as a limit understeer characteristic. The neutral steering behavior corresponds to a zero value of the dynamic steering angle (δdyn). The limit understeer characteristics are calculated with an optimization procedure. This minimizes a cost function (Jay,max). In one implementation, when the limit understeer characteristic is the neutral steering behavior. The cost function may be expressed as the absolute value of the dynamic steering angle. For example, the following formula may be used to calculate Jay,max:
Jay,max=wdyn|δdyn|

The optimization uses the non-linear quasi-static model formulation as a set of equality and inequality constraints. In other implementations, alternative cost function formulations may be used. For example, if a limit cornering response different from the neutral steering one is required, the term wdyn|δdyn| may be replaced with the expression wdyn|δdyn−δdyn,ref,lim|, where δdyn,ref,limmay be expressed as a function of lateral acceleration of the vehicle100. For example, the following formula may be used to determine δdyn,ref,lim:

δdyn,refrepresents δdyn,ref,lim, kusis the understeer gradient of the linear part of the characteristic, a*yis the upper limit of the linear part of the characteristic; and ay,maxis the maximum achievable lateral acceleration.

The optimization is run for increasing values of ay, for each velocity V and set of optional vehicle parameters (Θ). The optimization stops when the constraints can no longer be satisfied. This occurs when the maximum achievable lateral acceleration (ay,max) is reached. The additional outputs of this step are plots of δdyn,ref,lim(ay) and δlim(ay), for each velocity (V) and set of optional vehicle parameters (Θ). δdyn,ref,lim(ay) and δlim(ay) plots may be considered as the limit understeer characteristics of the vehicle—i.e., the most extreme understeer characteristics to be evaluated in the design of the vehicle cornering response. In some implementations, δlimis the actual steering angle at the wheels of the vehicle—average steering angle at the front axle—including the kinematic and dynamic contributions. In other implementations, δlimmay refer to the angle of the steering wheel of the vehicle100.

The method continues with430, where reference understeer characteristics necessary to achieve the desired vehicle cornering response are defined. For example, the desired vehicle response could be less understeering than that of the passive vehicle. The reference understeer characteristics should not conflict with the maximum achievable lateral acceleration and limit understeer characteristics determined in420. The reference understeer characteristics can be expressed as an analytical function of lateral acceleration (ay) with three parameters, kus, a*y, and ay,max. For example, the formula above for determining δdyn,refmay be used.

A visualization—for example, through a graphical user interface of a computer—of a plot of the understeer characteristics of the passive vehicle, the limit understeer characteristic, and the reference understeer characteristic may be presented. The reference understeer characteristics in terms of the actual steering angle—δref(ay)—is then calculated. For example, the following formula may be used to calculate δref(ay):

The wheelbase of the vehicle is represented by l. In other implementations, the steering wheel angle, rather than the steering angle at the wheels, may be used to define the reference understeer characteristics.

The method continues with440, where the reference yaw rate design is determined. In430, the steering angle of the reference understeer characteristics was calculated as a function of lateral acceleration (ay) for different values of V and Θ (to be used as breakpoints of the look-up tables). At440, interpolation is performed to calculate the reference lateral acceleration (ay,ref) as a function of the calculated steering angle values (also to be used as breakpoints of the look-up tables). Hence, the computation of the look-up tables of the steady-state value of the reference yaw rate—rref,ss(δ, V, Θ)—is achieved from the δref(ay) characteristics calculated at430. The look-up table may be stored in the reference yaw rate module230of the anti-roll moment distribution module120. The following formula may be used to calculate the reference yaw rates:

δay,maxrepresents the minimum value of steering angle for which ay,ref,maxis achieved. In some implementations, each reference yaw rate (rref,SS) may be determined with respect to the angle of the steering wheel (δSW) of the vehicle100rather than the steering angle of the wheels of the vehicle100. For example, rref,SS(δSW, V, Θ) may be calculated based on the determined values of rref,SS(δ, V, Θ) and an appropriate steering ratio.

The method continues with450. At450, feedforward contribution values of the front-to-total anti-roll moment distribution are determined. The quasi-static model is solved to determine the required front-to-total anti-roll moment ratio required to achieve the reference understeer characteristic. In some implementations, rref,SS(δ, V, Θ) is imposed as an equality constraint while solving the quasi-static model. In other implementations, rref,SS(δSW, V, Θ) is imposed as an equality constraint while solving the quasi-static model. A look-up table of feedforward contribution values as a function of steering angle (δ), velocity (V), and optional vehicle operating parameters (Θ) is generated. For example, the look-up table of feedforward values may be stored in the feedforward module220of the anti-roll moment distribution module120.

FIG. 5is a flowchart that depicts an example method of controlling the suspension of a vehicle based on pre-stored feedforward and reference yaw rate values. In various implementations, control may be performed by the suspension control module110and the anti-roll moment distribution module120. Control begins at510, where control obtains operating parameters of the vehicle100. For example, the steering angle of the wheels and the velocity and longitudinal acceleration of the vehicle are obtained. In some implementations, the angle of a steering wheel of the vehicle100is obtained rather than the actual steering angle of the wheels. Similarly, accelerator and brake pedal positions may be obtained in place of the vehicle's velocity and longitudinal acceleration. Control then continues with520.

At520, control determines a feedforward contribution to a front-to-total anti-roll moment distribution and a reference yaw rate of the vehicle100based on the obtained vehicle operating parameters. For example, the feedforward module220compares the obtained vehicle operating parameters to values stored in a first look-up table. The feedforward module220selects a stored feedforward value that is associated with the obtained vehicle parameters. The anti-roll moment distribution module120uses the selected feedforward value as the feedforward contribution.

Similarly, the reference yaw rate module230compares the obtained vehicle parameters to the values stored in a second look-up table. The reference yaw rate module230selects a stored reference yaw rate value that is associated with the obtained vehicle parameters. The anti-roll moment distribution module120uses the selected reference yaw rate value as the reference yaw rate. Control then progress to530.

At530, control obtains the actual yaw rate of the vehicle. For example, control may read the value of a signal from a yaw rate sensor located in the vehicle. Control then progresses to540, where a yaw rate error is determined. Control calculates the yaw rate error based on the determined reference yaw rate and the obtained actual yaw rate of the vehicle. Control continues with550.

At550, control determines a feedback contribution to the front-to-total anti-roll moment distribution of the vehicle. Control determines the value of the feedback contribution based on the determined yaw rate error. For example, control may apply a correction to the yaw rate error based on proportional, integral, and derivative terms. The result of the correction is the feedback contribution. In some implementations, control progresses to560—for example, when the anti-roll moment distribution module120includes the adjusting module265. In other implementations, control progresses to570.

At560, control adjusts the feedforward contribution determined at520. For example, the adjusting module265of the anti-roll moment distribution module120may apply a progressive deactivation algorithm to the feedforward contribution, to prevent undesired system responses in extreme conditions. The deactivation algorithm may include a transfer function that is applied to the feedforward contribution. In various implementations, the transfer function may be a first-order low pass filter. In some implementations, the transfer function may have a cutoff frequency of 5 Hz. In other implementations, the transfer function may have a cutoff frequency of 1 Hz. In yet other implementations, the transfer function may have a cutoff frequency between 1 Hz and 5 Hz Control then progresses to570.

At570, control determines a front-to-total anti-roll distribution ratio (f) based on the feedback contribution and either the feedforward contribution determined at520or the adjusted feedforward contribution determined at560. For example, control may add either the feedforward contribution or the adjusted feedforward contribution to the feedback contribution. The resulting sum is the front-to-total anti-roll moment distribution (f). Control sets and/or adjusts the controllable suspension actuators of the vehicle100based on the front-to-total anti-roll moment distribution. Control then returns to510.

Spatial and functional relationships between elements (for example, between modules, circuit elements, semiconductor layers, etc.) are described using various terms, including “connected,” “engaged,” “coupled,” “adjacent,” “next to,” “on top of,” “above,” “below,” and “disposed.” Unless explicitly described as being “direct,” when a relationship between first and second elements is described in the above disclosure, that relationship can be a direct relationship where no other intervening elements are present between the first and second elements, but can also be an indirect relationship where one or more intervening elements are present (either spatially or functionally) between the first and second elements.

As used herein, the phrase at least one of A, B, and C should be construed to mean a logical (A OR B OR C), using a non-exclusive logical OR, and should not be construed to mean “at least one of A, at least one of B, and at least one of C.” The term subset does not necessarily require a proper subset. In other words, a first subset of a first set may be coextensive with (equal to) the first set.

The module may include one or more interface circuits. In some examples, the interface circuit(s) may implement wired or wireless interfaces that connect to a local area network (LAN) or a wireless personal area network (WPAN). Examples of a LAN are Institute of Electrical and Electronics Engineers (IEEE) Standard 802.11-2016 (also known as the WIFI wireless networking standard) and IEEE Standard 802.3-2015 (also known as the ETHERNET wired networking standard). Examples of a WPAN are the BLUETOOTH wireless networking standard from the Bluetooth Special Interest Group and IEEE Standard 802.15.4.

Some or all hardware features of a module may be defined using a language for hardware description, such as IEEE Standard 1364-2005 (commonly called “Verilog”) and IEEE Standard 1076-2008 (commonly called “VHDL”). The hardware description language may be used to manufacture and/or program a hardware circuit. In some implementations, some or all features of a module may be defined by a language, such as IEEE 1666-2005 (commonly called “SystemC”), that encompasses both code, as described below, and hardware description.