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Using the lead vehicle as previewsensor in convoy vehicle activesuspension controlMustafizur Rahman a & Geoff Rideout aa Faculty of Engineering and Applied Science, Memorial Universityof Newfoundland, St. John's, Canada

Version of record first published: 27 Jul 2012

To cite this article: Mustafizur Rahman & Geoff Rideout (2012): Using the lead vehicle as previewsensor in convoy vehicle active suspension control, Vehicle System Dynamics: International Journalof Vehicle Mechanics and Mobility, DOI:10.1080/00423114.2012.707801

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Vehicle System Dynamics2012, 1–26, iFirst

Using the lead vehicle as preview sensor in convoy vehicleactive suspension control

Mustafizur Rahman* and Geoff Rideout

Faculty of Engineering and Applied Science, Memorial University of Newfoundland,St. John’s, Canada

(Received 9 April 2012; final version received 22 June 2012 )

Both ride quality and roadholding of actively suspended vehicles can be improved by sensing theroad ahead of the vehicle and using this information in a preview controller. Previous applicationshave used look-ahead sensors mounted on the front bumper to measure terrain beneath. Such sensorsare vulnerable, potentially confused by water, snow, or other soft obstacles and offer a fixed previewtime. For convoy vehicle applications, this paper proposes using the overall response of the precedingvehicle(s) to generate preview controller information for follower vehicles.A robust observer is used toestimate the states of a quarter-car vehicle model, from which road profile is estimated and passed on tothe follower vehicle(s) to generate a preview function. The preview-active suspension, implementedin discrete time using a shift register approach to improve simulation time, reduces sprung massacceleration and dynamic tyre deflection peaks by more than 50% and 40%, respectively. Terraincan change from one vehicle to the next if a loose obstacle is dislodged, or if the vehicle paths aresufficiently different so that one vehicle misses a discrete road event. The resulting spurious previewinformation can give suspension performance worse than that of a passive or conventional activesystem. In this paper, each vehicle can effectively estimate the road profile based on its own statetrajectory. By comparing its own road estimate with the preview information, preview errors canbe detected and suspension control quickly switched from preview to conventional active control topreserve performance improvements compared to passive suspensions.

Keywords: active suspension; preview control; state observer; convoy vehicle; Kalman filter

1. Introduction

The performance of a vehicle suspension system is generally assessed in terms of the compet-ing objectives of sprung mass acceleration (ride quality), suspension deflection (rattle space),and tyre deflection (roadholding) [1]. Active suspension systems can manage these tradeoffsbetter than a passive suspension system, and even further improvements can be attained bythe use of preview of the road input [2–5]. Preview-active systems suffer from the practicaldifficulties involved in measuring the road surfaces by a body-mounted road sensor, since thecontrol law needs information on the road input some distance ahead of the vehicle. Look-ahead sensors on the front bumper, for example, ultrasonic or laser-based distance sensors,

*Corresponding author. Email: [email protected]

ISSN 0042-3114 print/ISSN 1744-5159 online© 2012 Taylor & Francishttp://dx.doi.org/10.1080/00423114.2012.707801http://www.tandfonline.com

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2 M. Rahman and G. Rideout

suffer from several limitations such as vulnerability to damage and spurious bump detection.For example, a heap of leaves could be shown as a serious obstacle, whereas a pothole filledwith water may not be detected at all [6,7]. Furthermore, these sensors may not be cost-effective, and mounting them at a fixed distance ahead of the wheel means that the optimalpreview time [8,9] can only be achieved at a single vehicle speed. Wheelbase preview controlhas also been studied [7,10,11] where the rear wheel road input is considered to be the sameas the front wheel road input and assumed to be a delayed version of that of the front. Rearsuspension performance can be improved through wheelbase preview even if no look-aheadsensors are used; however, front suspension performance is not improved and preview timelimitations persist. A convoy, or platoon, of vehicles provides a unique opportunity for pre-view control of the individual vehicle suspensions. The vehicles travel in close proximity ona similar path, meaning that each should see the same road profile. A scheme is proposed in[12] where the lead vehicle’s dynamic responses are used to estimate the road input, whichis sent to the follower vehicles in a convoy as the preview information for their suspensioncontrollers. The approach in [12] eliminates the use of look-ahead sensors for vehicles fol-lowing each other closely. In the military, convoys are used to carry soldiers, weapons, andsupplies. Many military drivers are young and inexperienced, and driver error has causedmany fatal accidents in both peacetime and wartime. Also, the development of an IntelligentVehicle Highway System with autonomous vehicle platoons remains an active research area.Improving ride quality of closely spaced vehicles will reduce vibration-related driver fatigueand injury, and improving roadholding and handling during evasive manoeuvres will preventaccidents. This paper reviews the system originally proposed in [12] and presents a new andimproved estimator to reconstruct road profiles with a wide range of discrete bumps. Theestimator works for vehicles with passive, active, or preview-active suspensions. Any vehiclein the platoon, not just the leader, can estimate the road profile for use by vehicles behind.A given vehicle can then use preview information from the convoy leader, the vehicle imme-diately preceding it, or any combination of preceding vehicles. Multiple sources of previewinformation allow variation in effective preview time, while also increasing robustness tosensor malfunction on an individual vehicle, or to changes in terrain due to obstacles beingdislodged mid-convoy. If a vehicle compares its own terrain estimate to that from the previewinformation and detects discrepancy, then its suspension control can revert to conventionalactive and that vehicle can initiate new preview information for its followers. The followingsection reviews literature on preview control of active suspension and the estimation of theunknown terrain disturbance. Section 3 outlines the vehicle model and states and implementsthe plant and preview controller in discrete time using a shift register approach to achievesignificant increases in computational efficiency. The relative benefits of active and preview-active suspensions are shown for multiple preview times. The unknown road profile observeris designed in Section 4 and demonstrated for vehicles with active and preview-active sus-pensions. The observer requires only measurement of the sprung mass acceleration, unsprungmass acceleration, and suspension deflection. These measurements need not be integrated ordifferentiated during the estimation, making the observer less susceptible to drift or noiseamplification than many road profile observers in the literature. Section 5 gives simulationresults for a two-vehicle convoy in which

(i) faulty sensors provide incorrect preview information to the follower (terrain error);(ii) the correct preview information is provided, but with a time lead or lag (timing error);

(iii) a mid-convoy terrain change is detected by the follower, the suspension of which switchesfrom preview to active control.

Discussion and conclusions are provided in Section 6.

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Vehicle System Dynamics 3

2. Literature review

Bender [3], followed by many others, such as Hac [2], Louam et al. [5], and Huisman et al.[7], showed significant improvements in ride quality (as indicated by body acceleration) whenusing a preview of the upcoming terrain in the suspension controller design. Hac [2] reportedreduction in tyre deflection and suggested that a primary benefit of preview suspension couldbe in reducing dynamic tyre deflection as the suspension anticipates upcoming discrete roadevents. Papers by Hac [2] and Louam et al. [5] report the presence of an optimal preview time.More recent works on preview control such as [9,13–17] report performance improvements inthe three competing suspension control objectives mentioned in Section 1. Actuator dynamicsprovide a practical limitation on preview suspension performance. El Madany et al. [18] andPilbeam and Sharp [8] studied slow active suspension systems with preview, with El Madanyet al. [18] showing that good performance can be achieved using low-bandwidth actuation.Pilbeam and Sharp [8] also observed an optimal preview time and showed that lower bandwidthrequires more preview time but uses less energy than that of higher bandwidth systems.Papers by Muijderman [6], Langlois and Anderson [19], Kitching et al. [20], and Nagiri [21]showed that the use of preview can effectively overcome actuator delay, thereby improvingperformance. Al Akbari et al. [15] compared different preview control methods. Vahidi andEskandarian [22] studied the effect of uncertainties in a preview-active suspension system,showing limits on preview uncertainty beyond which the benefits of preview are negated. Typesof uncertainties studied by Vahidi and Eskandarian [22] are preview sensor noise and presenceof false objects on the road. The issue of preview information timing was not considered.This paper does a small parametric study of the effect of timing errors, as such errors areunique to the proposed convoy implementation where look-ahead sensors are not mounted toeach vehicle. Power consumption is an important consideration when considering practicalfeasibility of preview suspensions. Hac [2] and Marzbanrad et al. [14] showed lower powerconsumption for preview-active suspensions compared with conventional active suspensions.

Despite the theoretical benefits of preview, practical implementation has been limited. Hard-ware implementations of preview are given in [20,23,24], with [20] describing wheelbasepreview in a half-car rig with a hardware-in-the-loop simulation. Improvements in root-mean-square body acceleration at the drive axle were 15.4%, 18.2%, and 16.2% for motorway,principal, and minor roads, respectively. Akbari et al. [24] implemented multi-objectiveH∞/GH2 preview control on an experimental quarter-car setup and showed an improvementof 22% in ride comfort. Langlois et al. [23] implemented preview-controlled active suspen-sion in an off-road vehicle with ultrasonic look-ahead sensors in front of the vehicle. Resultsfrom [23] showed 15% improvement in ride quality over passive suspension and 4% overactive suspension without preview. The small improvement over active suspension was likelydue to a simplified controller that could be implemented without significant modifications totheir existing hardware. Preview has not infiltrated the automotive industry as much as conven-tional active or semi-active suspension, despite the industry’s potential use of custom-designedhardware, due to aforementioned challenges such as sensor cost, durability, and accuracy. Itis desirable to replace look-ahead sensors with road estimators as in [7,12] to generate thepreview information.

A number of methods can be found in the literature to estimate an unknown input [25–28].These methods typically require an assumed dynamic model of the unknown disturbance,which is not feasible for deterministic bumps of varying shape and spatial frequency. Theseunknown disturbance observers also require the differentiation of measurements, which posesserious challenges to maintaining an acceptable signal-to-noise ratio. Pure integration ofmeasurements such as accelerations requires elimination of drift. In [12], a continuous timeKalman–Bucy observer is designed where a virtual lead car with active suspension generates

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the road profile and estimates the vehicle states based on its dynamic motion and feeds itto a preview-controlled follower car. The implementation in [12] required differentiating theroad estimate, and the continuous-time Matlab simulation was prohibitively slow. To sum-marise, prior research motivates the use of preview suspension if practical implementationissues could be resolved. A road estimator that requires only practically available measure-ments, and no differentiation or integration thereof, is developed and applied to a simulatedconvoy scenario in this paper. The estimator replaces the look-ahead sensor. To improve thecomputational efficiency of the continuous time preview function from [2], as implementedin [12], a discrete-time model with a shift register algorithm for preview function generationis formulated. Such preview, without look-ahead sensors and with robustness to mid-convoyterrain changes, would have potential safety benefits to the military and to automated highwaysystems. Eventual improvements in vehicle-to-vehicle communication, active cruise control,and global positioning systems could allow discrete road events estimated through vehicledynamic response to be useful as preview information for following vehicles even if they werenot part of a formal convoy or fully automated highway. Preview control of active suspensionfor convoys not only improves the performance of individual vehicle but can also increasethe fuel efficiency of the convoy system. Al Alam et al. [29] showed that the use of previewinformation for adaptive cruise control system can reduce fuel consumption by 3.8–7.7%depending on the vehicle weight.

In this paper a quarter-car representation is used as the model for simulating the convoyvehicle preview scenario. The quarter car reduces the dimension of the optimal control problemcompared to a half or full car. Quarter-car-based optimal suspension controllers can effectivelycontrol pitch and roll in half cars [23,30]. The following section gives details of the modeland state variables used in this paper and develops and demonstrates the discrete-time previewcontroller.

3. System model

The objective of this section is to implement the discrete-time preview problem and comparethe simulation results for preview-active, active, and passive suspension systems, assumingthat perfect knowledge of the road profile is available. Estimation of the road profile is donein Section 4.

Figure 1. Two degrees of freedom quarter-car model.

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A continuous approach to the preview problem will be shown before discretising the system.Figure 1 shows the quarter car with active suspension. The actuator is placed in parallel withthe passive damper and the spring. Equations of motion are

mszs + ks(zs − zu) + bs(zs − zu) − u = 0, (1)

muzu + ks(zu − zs) + kt(zu − zr) + bs(zs − zu) + u = 0. (2)

These equations can be written in a state-space form

x(t) = Ax(t) + Bu(t) + Fzr(t), (3)

where the state vector is x(t) = [zs zs zu zu]T and A, B, and F matrices are given by

A =

⎡⎢⎢⎢⎢⎢⎢⎣

0 1 0 0

− ks

ms− bs

ms

ks

ms

bs

ms

1 0 0 0ks

mu

bs

mu− (ks + kt)

mu− bs

mu

⎤⎥⎥⎥⎥⎥⎥⎦

, B =

⎡⎢⎢⎢⎢⎢⎢⎣

01

ms

0

− 1

ms

⎤⎥⎥⎥⎥⎥⎥⎦

, F =

⎡⎢⎢⎢⎣

000kt

mu

⎤⎥⎥⎥⎦ .

Equation (3) is a continuous-time state-space representation of the system. The optimal con-trol problem is to optimise the suspension system with respect to roadholding, ride comfort,and suspension working space. In addition, the magnitude of the control force must be con-strained to the limits of the actuator. A performance index can be defined based on the aboveparameters [2],

J = limT→∞

1

2T

∫ T

0E[z2

s + μ1{zs(t) − zu(t)}2 + μ2{zu(t) − zr(t)}2 + μ3u(t)2] dt, (4)

where E is the expectation, and constants μx are the weighting parameters selected by thedesigner. Equation (4) can be represented in a matrix form upon substitution of Equations (1)and (2),

J = limT→∞

1

2T

∫ T

0E[xTQ1x + 2xTNu + uTRu + 2xTQ12zr + zT

r Q2zr] dt, (5)

where

Q1 =

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

k2s

m2s

+ μ1bsks

m2s

− k2s

m2s

− μ1 −bsks

m2s

bsks

m2s

b2s

m2s

−bsks

m2s

− b2s

m2s

− k2s

m2s

− μ1 −bsks

m2s

μ1 + μ2 + k2s

m2s

bsks

m2s

−bsks

m2s

− b2s

m2s

bsks

m2s

b2s

m2s

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

,

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R = 1

m2s

+ μ3, N =

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

− k2s

m2s

− bs

m2s

k2s

m2s

bs

m2s

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

,

and

Q12 = [0 0 − μ2 0]T, Q2 = μ2.

The last term of the performance index can be neglected because of the fact that the controlinput does not affect the road irregularities. The objective of linear optimal preview control isto find a control force, u, so that the performance equation is minimised for an entire class ofstochastic inputs zr(t). The control force u(t) must contain a feedback term which takes thecurrent states using optimal linear quadratic regulator (LQR) theory and a feed-forward termfrom the knowledge of road ahead.

For the linear time-invariant system given by Equation (3), the measurement equation canbe written as

y = Cx + Du + v, (6)

where v is the measurement noise from the sensors. Here, the measured quantities are thestates x(t). Suppose the road profile is available up to time τp into the future, that is, zr(τ ) isavailable, where τ ∈ [t, t + τp], and all the states at time t are present. Then, the solution ofthe linear deterministic optimal preview control is given as [2]

uo(t) = −R−1[(NT + BTP)x(t) + BTr(t)], (7)

where P is the solution of the algebraic Riccati equation given by

PAn + ATn P + PBR−1BTP + Qn = 0, (8)

and the preview function is

r(t) =∫ Tp

0eAT

c σ (PF + Q12)zr(t + σ) dσ , (9)

where

An = A − BR−1NT and Qn = Q1 − NR−1NT.

The feedback part of Equation (7) is

ufbo(t) = −R−1(NT + BTP)x(t). (10)

The feedback gains can be found from the solution of the LQR problem that minimises theperformance index J. The feed-forward term is

uffo(t) = −R−1BTr(t). (11)

The vector r(t) ∈ Rn uses all the available future information about the road input zr. Toimprove simulation time, the continuous preview function has been discretised by the use ofexponential functions (see Appendix 3) and a variable shift register algorithm implemented,with discretisation done using MATLAB.

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3.1. Discretisation of continuous system

Consider again the continuous system (3)

x(t) = Ax(t) + Bu(t) + Fzr(t)

with measurements

y = Cx(t) + Du(t) + v(t),

where v(t) is a white noise process with variance Q. We will consider the road profile to bean input to the system which is unknown at this point and will be estimated. The estimatorswill be optimal for random inputs, but we will also consider deterministic road inputs such astraffic humps, potholes, etc. The continuous system time response is given by Franklin et al.[31] and Lewis [32],

x(t) = eA(t−t0)x(t0) +∫ t

t0

eA(t−t0)Bu(τ ) dτ +∫ t

t0

eA(t−t0)Fzr(τ ) dτ . (12)

Let t0 = kT and t = (k + 1)T for an integer k. Defining the sampled state function as xk �x(kT), we can write

xk+1 = eAT xk +∫ (k+1)T

kTeA[(k+1)t−τ ]Bu(τ ) dτ +

∫ (k+1)T

kTeA[(k+1)t−τ ]Fzr(τ ) dτ . (13)

Assuming that the control input u(t) is reconstructed from the discrete control sequence uk

by using a zero-order hold and also that the unknown road input zr(t) is reconstructed from adiscrete measurement sequence zrk using a zero-order hold, u(τ ) and zr(τ ) have constant valuesof u(kT) = uk and zr(kT) = zrk , respectively, over the integration interval. The discrete-timeequation becomes

xk+1 = eAT xk +∫ (k+1)T

kTeA[(k+1)t−τ ]B dτ · uk +

∫ (k+1)T

kTeA[(k+1)t−τ ]F dτ · zrk . (14)

On changing the variables twice (λ = τ − kT and then τ = T − λ), the above equation canbe written as

xk+1 = eAT xk +∫ T

0eAτ B dτ · uk +

∫ T

0eAτ F dτ · zrk . (15)

The equivalent discrete form of the system is then

xk+1 = �xk + �uk + �zrk , (16)

where

� = eAT = I + AT + A2T 2

2! + · · · ,

� =∫ T

0eAτ B dτ = BT + ABT 2

2! + · · · ,

� =∫ T

0eAτ F dτ = FT + AFT 2

2! + · · · .

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Discretisation of the measurement equation is straightforward since it has no dynamics:

zk = Cxk + Duk + vk . (17)

The covariance R of vk in terms of the given covariance Q can be found easily from

R = QT

.

For the current analysis, the steady-state LQR gains from the continuous system are used forthe feedback part of the actuator force given by Equation (10). The feed-forward part givenby Equation (11) contains the preview function

r(t) =∫ Tp

0eAT

c σ (PF + Q12)zr(t + σ) dσ .

This must also be discretised. The discrete preview function at any step can be found from thepreview function value calculated at the previous step and is given by (see Appendix 3)

rk+1 = F−1rk − F−1zrk M�t + Fnzrk+n+1M�t, (18)

where

F = eATc �t ,

M = PF + Q12, Tp = n�t.

Here, �t can be the same as the discretisation time step T . A more general form of the previewfunction calculation (variable shift register approach) can be written as (see Appendix 3)

rk+p = F−(p+q)rk−q − S1 + S2, (19)

where the preview information at rk+p is to be determined given that the preview informationat rk−q is known and

S1 =1,p+q−1∑

i=p+q,j=0

F−izrk−q+j M�t,

S2 =1,p+q−1∑

i=p+q,j=0

Fn−i+1zrk+n+j M�t,

where p + q < n. Vehicle and performance index parameters of the quarter-car model used inthe study are shown in Table 1.

The results for the case of perfect measurements are given below. The road input consideredhere is a single half-sinusoidal bump expressed using the following equation [2]:

zr(t) ={

c[1 − cos 40π(t − 3)], t ∈ [3, 3.05],0, otherwise,

where 2c is the height of the bump in metres and t is the time in seconds. A bump height of10 cm has been considered for simulation with vehicle velocity 20 m/s. Figure 2(a) shows thevertical position of the wheel zu (unsprung mass displacement) along with the road elevationzr. Figure 2(b) shows the vertical acceleration of the vehicle body zs for passive, active, and

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Table 1. Quarter-car model parameters.

Symbol Description Value

ms Sprung mass 250 kgmu Unsprung mass 45 kgks Suspension stiffness 16 000 N/mkt Tyre stiffness 160 000 N/mbs Damping coefficient 1000 Ns/mT Sampling frequency 1250 HzTp Preview time 0.2 s

Figure 2. (a) Wheel displacement (zu), (b) sprung mass acceleration (zs), (c) tyre deflection (zu − zr), and (d)suspension deflection (zs − zu) for passive, active, and preview-active suspension systems (preview time 0.2 s).

preview-active suspensions. For active and preview-active suspensions, the weights of theperformance index are μ1 = 103, μ2 = 105, and μ3 = 0 which puts emphasis on roadholdingmore than ride comfort. The force actuator has been saturated by clipping the force at ±4000 N,that is, u ∈ [−4000 N, 4000 N]. A preview time of 0.2 s has been used. Figure 2(c) showstyre deflection (zu − zr) along with the road elevation zr, and Figure 2(d) shows suspensiondeflection (zs − zu) along with the road elevation zr.

From the results, it is evident that preview-active control is better compared with con-ventional active and passive suspension systems (Table 2). Figure 2(c) shows better roadtracking, with improvements of 46.47% and 23.37% in positive and negative peak mag-nitudes, respectively, compared with a passive system and 42.47% and 23.78% compared

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Table 2. Improvements in performance compared with passive and active systems forroadholding weighting factors.

Preview Improvements (Ip, In)% Improvements (Ip, In)%time (s) Description (passive system) (active system)

0.1 Suspension deflection (46.17,41.64) (40.93,36.05)Roadholding (43.75,21.85) (39.55,22.27)Ride quality (−2.30,32.39) (14.69,38.48)

0.2 Suspension deflection (51.12,41.89) (46.36,36.32)Roadholding (46.47,23.37) (42.47,23.78)Ride quality (3.48,35.45) (19.51,41.27)


with an active system. Comparison of suspension deflection (Figure 2(d)) shows 51.12%and 41.89% improvement over the passive system and 46.36% and 36.32% over the activesystem. Relatively less but still significant improvement in ride comfort has been observedfrom Figure 2(b), which is justified given that the chosen gain parameters emphasise road-holding. Weighting factors that put more emphasis on ride comfort (μ1 = 0.5, μ2 = 104,and μ3 = 0.000001) show greater reductions in sprung mass acceleration while maintainingsignificant roadholding improvements as shown in Table 3.

The effect of preview time is investigated by quantifying the improvement in peak magni-tudes of sprung mass acceleration, suspension deflection, and tyre deflection for three previewtimes: 0.1, 0.2 and 0.3 s. Improvement for any particular state xi compared with passive andactive systems has been calculated using the following relationship:

Ip = max(xi,passive/active) − max(xi,preview)

max(xi,passive/active)× 100%, (20)

In = min(xi,passive/active) − min(xi,preview)

min(xi,passive/active)× 100%, (21)

where Ip and In are the performance improvements in the positive and the negative peak,respectively.

The vehicle velocity considered for simulation is 20 m/s. A preview time of 0.3 s gives thebest overall performance; however, the point of the tables is that the ability to vary preview time

Table 3. Improvements in performance compared with passive and active systems for ridequality weighting factors.

Preview Improvements (Ip, In)% Improvements (Ip, In)%time (s) Description (passive system) (active system)

0.1 Suspension deflection (9.17,6.91) (32.71,24.14)Roadholding (15.16,9.75) (27.70,15.91)Ride quality (48.99,56.92) (−2.21,29.04)



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is advantageous. The method of this paper allows preview information from different possiblelead vehicles to be used, allowing preview time to be varied in an actual implementation.Different forward speeds will have different optimal preview times, again motivating thedeparture from fixed look-ahead sensors for which a single preview time is associated with agiven vehicle velocity. It has also been found in our simulations that there exists a trend in theperformance improvement such that if the vehicle speed is increased over a limited range forthe same single bump, then preview suspension performance increases.

4. Observer design

The preceding section showed significant improvements from using a preview-active suspen-sion system. Noise-free sensors and perfectly measured preview information were assumed.However, in practice, it is not possible to measure all the states. Sensors are not noise-freeand sensor data may require integration or differentiation to get the system states. Integra-tion introduces drift and differentiation amplifies the error and causes instability. In general,the available measurements in a vehicle active suspension system are the sprung mass accel-eration, unsprung mass acceleration, and suspension deflection. Therefore, to implement apreview-active control system for the model defined by the state space (3), it is necessary todesign an observer. Additionally, the preview information must also be generated from thelead vehicle suspension response. The designed observer must

(i) observe the states that cannot be measured from the available sensors;(ii) estimate the road profile from the vehicle and suspension response of any vehicle, whether

lead or follower, with either passive-, active-, or preview-controlled suspension.

4.1. Observer design background

Let us consider a system given by (with noise added to the road)

x(t) = Ax(t) + Bu(t) + F[zr(t) + ξ(t)]with the measurement equation

y = Cx(t) + v(t),

where ξ(t) and v(t) are the process and measurement noise, respectively. An optimal Kalmanestimator can be constructed following [33]

˙x(t) = Ax(t) + Bu(t) + L(y − y), (22)

where

y = Cx(t) + Du(t) [D = 0]and L is the optimal gain matrix given by

L = PCTV−1.

P is the solution of the algebraic Riccati equation

AP + PAT − PCTV−1CP + FWFT = 0,

where W = E{ξ(t)ξ(t)T} and V = E{v(t)v(t)T} are the process and measurement noise inten-sity matrices. The noises considered are white with zero mean, that is, E{ξ(t)} = E{v(t)} = 0.

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4.2. Development of the proposed observer

Recall the quarter-car model in Figure 1 with state-space form given by Equation (3),

x = Ax + Bu + Fzr.

Let us define the measurement equation as

y = Cx + Du + Gzr + v,

where

y =⎡⎣zs − zu

zs

zu

⎤⎦ and C =

⎡⎢⎢⎢⎢⎣

1 0 −1 0

− ks

ms− bs

ms

ks

ms

bs

ms

ks

mu

bs

mu− (ks + kt)

mu− bs

mu

⎤⎥⎥⎥⎥⎦ ,

D =

⎡⎢⎢⎢⎢⎣

01

ms

− 1

mu

⎤⎥⎥⎥⎥⎦ and G =

⎡⎢⎣

00

− kt

mu

⎤⎥⎦ .

Let us reconstruct the observer including the unknown road profile as an input as

ˆx = Ax + Bu + Fzr + L(y − y) (23)

and define the observed measurements as

y = Cx + Du + Gzr. (24)

The inclusion of road profile as an unknown input presents a challenge, as we wish to estimateroad profiles for which no mathematical model can be assumed. Subtracting Equation (1) fromEquation (2), we can write

mszs + muzu + kt(zu − zr) = 0.

Rewrite in terms of the road input:

zr = zu + ms

ktzs + mu

ktzu (25)

and express the road profile in terms of observer states and measurements:

zr = �x + �y, (26)

where � = [0 0 1 0] and � = [0 ms/kt mu/kt].At any time, the road profile may be estimated by using Equation (26) where unsprung

mass deflection is one of the output states from the observer, and sprung and unsprung massaccelerations are the output measurements at that particular time. The intermediately estimatedroad profile can then be fed back into the observer model as an input. Substituting zr inEquation (23), we get

ˆx = (A + F� − BK)x + F�y + L(y − y). (27)

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Figure 3. Schematic representation of the proposed observer.

A schematic diagram of the observer is shown in Figure 3. Here, K is the optimal previewcontrol gain as shown in Section 4, and L is the optimal observer gain matrix equal to

L = (PCT + FW)V−1

and P is the solution of the following algebraic Riccati equation (see Appendix 2):

AP + PAT − PCTV−1CP + FVFT = 0, (28)

where

A = A − FWV−1C,

V = W − WV−1WT,

V = V + GWGT + GVGT − XGT − GXT,

W = WGT,

where

W = E{zr(t)zr(t)T},

V = E{v(t)v(t)T},X = E{v(t)zr(t)

T},V = E{zr(t)zr(t)

T}.W and V are the process and measurement noise intensity matrices. The noises considered arewhite with zero mean, that is, E{ξ(t)} = E{v(t)} = 0. Though it has been considered that theroad profile be a white noise process while designing the observer, the observer works wellfor other profiles as will be shown by simulation results.

Figure 4 shows a representative block diagram of the proposed observer model. No inte-gration or differentiation of the measurements is needed to generate the state estimates unlike

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Figure 4. Block diagram of the observer.

Figure 5. Actual versus estimated (a) wheel displacement (zu), (b) sprung mass acceleration (zs), (c) tyre deflection(zu − zr), and (d) suspension deflection (zs − zu) with preview (0.2s).

many other methods in the literature [10,34,35]. Based on the observer model given by Equa-tions (27), (24), and (26), simulation has been carried out in MATLAB and the performanceof the observer is shown below. The estimated road using this observer will be transferred to

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Figure 6. Road observation for the designed observer for (a) rounded pulse and (b) two consecutive bumps.

Table 4. Model uncertainty study.

Level Sprung mass (kg) Tyre stiffness (N/m)

High/high 400 240 000High/low 400 100 000Low/high 200 240 000Low/low 200 100 000

the follower vehicle to use as preview information. The road input considered is the same asin the previous section. Velocity of the vehicle for simulation is the same as in the previoussection, that is, 20 m/s with a preview time of 0.2 s. Figure 5(a) shows the estimated versusactual sprung mass acceleration. Figure 5(b) and (c) shows the estimated tyre and suspensiondeflection versus the actual tyre and suspension deflection. Figure 6 shows the estimated roadprofile versus the actual road profile for different types of road input.

4.3. Uncertainty analysis

The observer model has been studied for sensitivity to vehicle parameter changes. Usingthe controller designed with the nominal design parameters indicated in Table 1 and noise

Figure 7. Estimated road with vehicle parameter variation: (a) high sprung mass/high tyre pressure and (b) lowsprung mass/low tyre pressure.

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intensities listed in Appendix 1, prediction sensitivity has been done for perturbed sprungmass and tyre pressure (tyre stiffness). Four different possible sprung mass and tyre stiffnesscombinations have been studied as indicated in Table 4. The estimated results are shown inFigure 7. Only the estimated road profiles for the high/high and low/low configurations havebeen shown. The results show that even though the parameter deviation is as high as 50%, theestimated road profile is close to actual road estimate.

5. Convoy preview with active/preview switching

In this section, the difficulties encountered by an ideal preview-controlled convoy systemare discussed and the performance of the convoy system is simulated for several realisticscenarios. A convoy system working on preview may encounter several difficulties whichcould be due to

(1) faulty sensors in individual vehicles,(2) mid-convoy terrain changes,(3) communication error (preview information out of phase with road).

If the lead vehicle sensor is damaged, or if the lead vehicle hits a bump (thereby generating pre-view information for the followers) but dislodges it, then preview information will be incorrect.The performance of the followers’ preview-controlled suspensions may be reduced signifi-cantly. This section simulates these situations and proposes a method to stop the propagationof error throughout the convoy system. Consider the following scenarios.

5.1. Scenario 1: Presence of faulty sensors in lead vehicle

Consider the hypothetical case where the amplitude of the generated information from the leadvehicle is half of that of the actual road. Figure 8(a) and (b) compares the resulting sprungmass accelerations and the tyre deflection of the follower vehicle, respectively. Figure 8 showsthat the performance decreases in the presence of erroneous preview information.

5.2. Scenario 2: Mid-convoy terrain changes

Suppose the lead vehicle dislodges a bump. The follower vehicle expects to hit it but does not,and its preview-controlled suspension reacts so the follower vehicle will undergo a transient

Figure 8. (a) Ride quality (zs) and (b) tyre deflection (zu − zr) of the follower vehicle using correct and erroneouspreview information.

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Figure 9. (a) Ride quality (zs) and (b) tyre deflection (zu − zr) of the follower vehicle due to spurious previewinformation (no actual bump).

Figure 10. Preview information by the lead vehicle lagging by (a) 0.005 and (b) 0.025 s.

response due to the spurious active suspension input. Figure 9 shows the responses due to thespurious information received by the preview controller of the follower vehicle.

5.3. Scenario 3: Lag/lead in the preview information

Suppose the lead vehicle can generate the preview information correctly but the informationhas a lag/lead when the first follower receives it. Two scenarios are considered as shown inFigure 10.

5.3.1. Small time lag (0.005 s)

Suppose the follower vehicle will hit the bump 0.005 s earlier than the calculated previewinformation (Figure 10(a)).

Figure 11(a) and (b) shows the performance of the preview controller under this situation.Results show that the lag in the information by a small amount of time decreases the ride quality.Minor reduction in roadholding performance is noted for the positive peak but improvements inthe negative peak can be observed (Figure 11(b)). Minor deterioration in suspension deflectionin both positive and negative peaks was observed.

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Figure 11. (a) Ride quality (zs) and (b) tyre deflection (zu − zr) of the follower vehicle due to small lag in previewinformation (lag time 0.005 s).

Figure 12. (a) Ride quality (zs) and (b) tyre deflection (zu − zr) of the follower vehicle due to large lag in previewinformation (lag time 0.025 s).

5.3.2. Larger time lag (0.025 s)

Let us consider that there is a relatively larger lag of 0.025 s (Figure 10(b)). Ride qualityperformance under this condition significantly decreases for the follower vehicle as can beobserved from Figure 12(a). Roadholding performance and suspension deflection have alsodecreased significantly when the lag is higher with roadholding shown in Figure 12(b). Peaksuspension deflection increases from 5 to 10 cm.

5.3.3. Small lead time (0.005 s)

Now consider that there is a small lead of 0.005 s, that is, the follower vehicle will hit thebump 0.005 s later than the calculated preview information. Figure 13(a) and (b) shows theperformance of the preview controller under this situation. Interestingly, the ride quality androadholding performance have been increased when the preview information is leading by asmall amount of time. Suspension working space requirements remain the same as before anddo not show any deterioration. As for the unsprung mass displacement, the performance isslightly increased because of the fact that the actuator reacts earlier and pulls the unsprungmass before it can hit the bump.

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Figure 13. (a) Ride quality (zs) and (b) tyre deflection (zu − zr) of the follower vehicle due to small lead in previewinformation (lead time 0.005 s).

Figure 14. (a) Ride quality (zs) and (b) tyre deflection (zu − zr) of the follower vehicle due to larger lead in previewinformation (lead time 0.025 s).

5.3.4. Larger lead time (0.025 s)

The performance of the follower vehicle under this situation can be observed from Figure 14(a)and (b). Ride quality and roadholding performance degrade significantly. The suspensiondeflection is unchanged, and the unsprung mass deflection increases significantly.

Simulation for extended lead/lag time when the preview information is half or fully outof phase has also been studied (50 and 100 ms, respectively). In each case, the performancedeteriorates significantly. In summary, while the preview-controlled suspension is somewhatrobust to small lead times in the receipt of preview information, the correct timing of thepreview information is important and will be a practical challenge to the convoy previewsuspension scheme proposed herein.

5.4. Convoy preview control

Given the implications of preview information error as described in the previous section,a means of preventing the error from propagating through the convoy is essential. This isfeasible if each vehicle can estimate the road profile correctly even if its preview information

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Figure 15. Concept of robust preview (∗if available).

is erroneous. Erroneous information can be rejected using the following steps:

(1) A vehicle’s ongoing road profile estimation can be compared with recent previewinformation.

(2) If comparison shows a large disparity then the vehicle could switch to a wheelbase previewsystem (outside the scope of this paper but the subject of ongoing work) where its frontwheel would work in active mode and the rear wheel in preview mode.

(3) For the next follower vehicle, the correct information (estimated road profile) would besent. If wheelbase preview is not available, the vehicle would switch to active control.

(4) If the disparity of the estimation is not large then an average estimate of the road profilescould be sent to the followers, thereby filtering out small errors from one vehicle.

This preview concept is shown in Figure 15. The proposed observer can estimate the roadprofile accurately even when the preview information is incorrect, making the concept shownabove implementable. In each of the erroneous preview information cases discussed previously,the observer estimates the true road very accurately. Estimated road profile by the observer forscenario 1 (amplitude error) and scenario 2 (non-existent road event) are shown in Figure 16(a)and (b). When erroneous preview information is present then the propagation of error can bestopped immediately and the follower vehicle then can act as a lead vehicle. In additionto the scenarios discussed above, there might be another possible scenario where the localprediction of the follower vehicle is faulty. If the local prediction of a vehicle is incorrectthen the suspension performance of the vehicle may deteriorate if it selects to rely on itsown estimation. In this case, the vehicle should act on preview-active suspension (consideringthat the preview information is correct). In addition, the vehicles can receive the previewinformation from multiple lead vehicles. If any vehicle observes the same road profile fromtwo or more leading vehicles but not with its own estimation, then it could rely only on thepreview information and assume that its local estimation was faulty. To conclude, there canbe multiple algorithms to make the control system robust and to maximise the performancein a real world situation. This is an issue of ongoing research.

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Figure 16. Estimated road profile by preview-controlled follower vehicle with incorrect preview information for(a) scenario 1 and (b) scenario 2.

5.5. Preview-active to active switching

If the follower vehicle can change its control system from preview-active to active modequickly enough, the effects of preview error can be minimised. Simulated results follow, withswitching initiated when the discrepancy between the live estimate and the preview informationexceeds 2 cm.

Figure 17. (a) Ride quality (zs), (b) unsprung mass deflection (zu), (c) suspension deflection (zs − zu), and (d) tyredeflection (zu − zr) of the follower vehicle when switched from preview-active to active suspension mode.

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Figure 17(a)–(d) shows the performance of the switched-suspension follower vehicle whenworking on an incorrect preview information. Roadholding and unsprung mass deflectionperformance recover after switching to active suspension mode. Suspension deflection of thefollower is increased by the switch to active mode.

To summarise, this switching method in conjunction with the proposed observer has thefollowing benefits:

(1) Follower vehicle can discard erroneous preview information from the lead vehicle andswitch to active suspension or wheelbase preview mode to maximise performance.

(2) Follower vehicle can act as a lead vehicle thereby generating the correct preview infor-mation for the next follower vehicle and ceasing the propagation of the error throughoutthe convoy.

6. Conclusion

A new approach to preview control of convoy vehicles has been presented. Rather than usingpotentially unreliable look-ahead sensors that restrict preview time, this method uses theresponses of lead vehicles to estimate the road profile and generate preview informationthereby. A new vehicle state observer has been designed, in which the road profile is accuratelyestimated despite being an unknown disturbance with no assumed mathematical description.Discrete bumps are estimated very accurately, and it is such bumps for which preview suspen-sion is anticipated to have the most practical benefit. The observer requires three practicallyavailable measurements: sprung mass acceleration, unsprung mass acceleration, and suspen-sion deflection. No differentiation or integration of the measurements is required. The previewcontrol has been implemented for linear quarter-car models using a computationally efficientdiscrete-time formulation, with the preview function computed using a shift register approach.Preview control gave significant improvements over active suspension in terms of ride qualityand roadholding. Challenging aspects of convoy preview are timely communication of previewinformation, possible suspension sensor malfunction, and mid-convoy terrain changes due todislodged obstacles or path variation. Simulation results show some robustness to small errorsin preview information communication timing, especially when the preview information leadsthe actual bump. The proposed observer can estimate the road profile very accurately evenin the presence of incorrect preview information from the preceding vehicle. As a result ofeach vehicle being able to perform its own road estimation and compare it with the previewinformation, its suspension can be switched from preview to conventional active control ifdiscrepancies are significant. Preview errors can therefore be attenuated and not passed backthrough the entire string of vehicles. Future work will implement the proposed observer inhardware using a quarter-car test bench. Extension of the vehicle model to a half car willallow the use of wheelbase preview as well. Full-car models with lateral dynamics and drivermodels will be used to study robustness to path variation, which will be related to followingdistance. While obvious applications of such convoy preview control are military deploymentsand automated highway systems, future advances in vehicle-to-vehicle communication andglobal positioning system technology would make road preview from leading vehicles usefuland accessible to the general motoring public.

Acknowledgements

The authors gratefully acknowledge the support of the Natural Sciences and Engineering Research Council underits Discovery Grant programme, along with the support of the Auto21 Network of Centres of Excellence, ProjectE301-EHV ‘Hybrid Vehicle Active Safety Systems and Grid Interfacing’.

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Appendix 1. Symbols and matrices

zs Sprung mass displacement (m)zs Sprung mass velocity (m/s)zu Unsprung mass displacement (m)zu Unsprung mass velocity (m/s)zr Road profile (m)(zs − zu) Suspension working space (m)(zu − zr) Dynamic tyre deflection (m)ξ(t) Process noisev(t) Measurement noiseJ LQG cost functionL Steady-state Kalman observer gain matrixW Process noise intensity matrixV Measurement noise intensity matrixNominal process and measurement noise intensity values: W = 2 × 10−4,

V =⎡⎣9.1 × 10−9 0 0

0 1.6 × 10−5 00 0 3.6 × 10−3

⎤⎦ .

Appendix 2. Optimal Kalman observer gain

Consider the system

x = Ax + Bu + Fzr

with measurement equation

y = Cx + Du + Gzr + v.

The observer for the system is given by

ˆx = Ax + Bu + Fzr + L(y − y),

ˆx = Ax + Bu + Fzr + L(y − Cx − Du − Gzr).

From the above expressions, we can write

e = x − ˆxexpanding the matrix equations

e = (A − LC)e + Fzr − L(Du + Gzr + v − Du − Gzr)

= (A − LC)e + Fzr − LGzr − Lv + LGzr

= (A − LC)e + (F − LG)zr + LGzr − Lv

= (A − LC)e + Fzr + LGzr − Lv

= (A − LC)e + Fzr + K zr − Lv

= (A − LC)e + ζ ,

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where K = LG, F = F − LG, and ζ = Fzr + K zr − Lv. The objective is to minimise the square of the error. Now,

E{ζ ζT} = FE{zrzrT}FT + LE{vvT}LT − LE{vzT

r }KT − KE{zrvT}LT + KE{zr z

Tr }KT

= FWFT + LVLT − LXKT − KXTLT + KVKT

= (F − LG)W(F − LG)T + LVLT − LX(LG)T − LGXTLT + LGVGTLT

= FWFT − FWGTLT − LGWFT + LGWGTLT + LVLT − LXGTLT − LGXTLT + LVLT

= FWFT + L(V + GWGT + GVGT − XGT − GXT)LT − LWTFT − FWLT

= FWFT + LVLT − LWTFT − FWLT,

where

V = V + GWGT + GVGT − XGT − GXT,

W = WGTW = E{zr(t)zr(t)T},

V = E{v(t)v(t)T},X = E{v(t)zr(t)

T},V = E{zr(t)zr(t)

T}.

Appendix 3. Discretisation of preview function

The vector r(t) is given by Hac [2] as

r(t) =∫ Tp

0eAT

c σ (PF + Q12)zr(t + σ) dσ . (A1)

In a discrete form

r(t) =n∑

i=0

eATc ·i·�t(PF + Q12)zr(t + i�t)�t, (A2)

where Tp = n · �t. Let k be the current time index calculated from k = t/�t, F = eATc �t and M = PF + Q12, then

we get

r(k) =n∑

i=0

F iMzr(k + i)�t. (A3)

Expand

r(k) = [F 0zr(k + 0) + F 1zr(k + 1) + · · · + F n−1zr(k + (n − 1)) + F nzr(k + n)]M�t, (A4)

at time index k + 1,

r(k + 1) = [F 0zr(k + 1) + F 1zr(k + 2) + · · · + F n−1zr(k + n) + F nzr(k + 1 + n)]M�t. (A5)

From Equations (A4) and (A5), we can write

r(k)

FM�t= r(k + 1)

M�t− [F nzr(k + 1 + n)] + F−1zr(k)

re-arranging

r(k + 1) = F−1r(k) − F−1zr(k)M�t + F nzr(k + n + 1)M�t. (A6)

Equation (A6) shows the discrete value of the preview function at any time t = (k + 1)�t given the preview value atprevious time step. Similarly, the value at any point of time t = (k + 2)�t can be found easily given the value at any

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earlier point of time t = (k − 1)�t as

r(k + 2) = F−3r(k − 1) − [F−3zr(k − 1) + F−2zr(k) + F−1zr(k + 1)]M�t

+ [F n−2zr(k + n) + F n−1zr(k + n + 1) + F nzr(k + n + 2)]M�t,

r(k + 2) = F−3r(k − 1) −1,2∑

i=3,j=0

F−izr(k − 1 + j)M�t +1,2∑

i=3,j=0

F n−i+1zr(k + n + j)M�t.

Similarly, a more general form of the equation for the preview value at time t = (k + p)�t given the value of previewfunction at t = (k − q)�t can be written as

r(k + p) = F−(p+q)r(k − q) −1,p+q−1∑

i=p+q,j=0

F−izr(k − q + j)M�t +1,p+q−1∑

i=p+q,j=0

F n−i+1zr(k + n + j)M�t

or

r(k + p) = F−(p+q)r(k − q) − S1 + S2, (A7)

where

S1 =1,p+q−1∑

i=p+q,j=0

F−izr(k − q + j)M�t,

S2 =1,2∑

i=3,j=0

F n−i+1zr(k + n + j)M�t,

and p + q < n.

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