INTRODUCTION
Nowadays, the Electric Vehicle (EV) is an important way to solve the problem
of environmental pollution because of its low noise, nonpollution, diversification
of energy sources and high energy efficiency (Jeong and
Lee, 2011; Moriya et al., 2002). With the
rapid increasing of vehicle number in Chinese major cities, the road congestion
is becoming more and more serious, especially on the overpass. Many Internal
Combustion Engine (ICE) vehicle drivers will be inclined to stall when starting
on hill and even slip due to lack of experience (Haifeng
et al., 2007). Same problem exists for electric vehicle and the EV
also requires the hill starting process could adapt to the changes of the external
driving conditions (Xiusheng et al., 2010),
so, it is very important to study the hill starting process of electric vehicle.
The road slope is an important parameter to the starting control process, the
correct identification of the road slope has an important significance to develop
the starting control strategy. Jin et al. (2002)
presented a road slope recognition technology based on the longitudinal dynamic.
It calculated the road slope according to the acceleration changes with the
gradient resistance at the same vehicle speed and throttle opening. This is
a kind of numerical model method which needs plenty of experience. And it is
also limited by different vehicle types. Yang et al.
(2002) used an acceleration sensor which could identify the road slope by
analyzing the signals, such as the vehicle acceleration and the axle speed.
The cost of the sensor also limited its application.
In studies about starting control of electric vehicle (Delvecchio
et al., 2009) designed a Hill Start Assistance system for commercial
vehicles to make the starting process smooth. Wang et
al. (2009), the combined simulation model of the vehicle and the motor
was built in the acceleration process of EV. By using the speed and current
doubleclosedloop control strategy, the motor could obtain a good mechanical
property and realize the starting control in the motor level. However, the driver’s
intention was less reflected. Other studies about hill starting mainly focused
on ICE vehicle and most of them made the hill starting control strategy based
on the Hillstart Assist System (HAS) system in the AMT vehicle.
Considering the starting resistance and the clutch work conditions (Haifeng
et al., 2007) accurately judged the Hill Starting Aid (HSA) valve
releasing time by adding torque sensor in the HAS system, but the extra cost
brought by torque sensor limited the wide application of this system. Ge
et al. (1998) formulated the AMT vehicle’s hill starting strategy
and had achieved good effects by test. Chen and Kong (2011)
satisfies the requirements of starting process via controlling the clutch, so
there is no reference value to the EV which hasn’t clutch.
In general, the smooth starting of ICE vehicle was realized mainly by the clutch
or the torque converter but the electric vehicle which studied on in this study
is a fixed gear ratio EV, it means that the motor is directly connected to the
drive shaft with a fixed gear ratio reducer. So, the starting control strategy
is greatly different from ICE vehicle because the clutch has been canceled and
the smooth starting of EV was realized by controlling the motor torque adapting
to the vehicle driving condition. Therefore, this study will design a Luenberger
observer based on the vehicle longitudinal dynamics equation to recognize the
road slope online. The vehicle starting resistance would also be calculated
on this basis so as to solve the function trigger and HSA valve control problem
of the HAS system.
METHOD OF ROAD SLOPE RECOGNITION
Hill driving force analysis of electric vehicle: The hill driving force
of electric vehicle is shown in Fig. 1.
These forces include the vehicle driving force F_{t}, the rolling resistance
F_{f}, the air resistance F_{w} and the slope resistance F_{i}.
The acceleration resistance could be ignored during hill driving, so according
to the vehicle dynamics and the Newton’s
second law, the equation of hill driving can be obtained, as:
where, T_{t} is the vehicle driving torque; T is the motor output torque;
i is the speed ratio of driveline; η is the efficiency of driveline; G
is the gravity of vehicle; f is the rolling resistance coefficient; γ is
the road slope; C_{D} is the coefficient of air resistance; A is the
windward area of vehicle; v is the vehicle speed; m is the quality of vehicle;
r is the rolling radius of driving wheel.
Equation of system state space: The following liner processing on Eq.
1 is to reduce the complexity of the model:
• 
The maximum climbable gradient of electric vehicle is less
than 25% in this study, so sin γ≈γ, cos γ≈1;
2. Set up F_{S} = F_{t}F_{f}F_{w}, so,
the Eq. 1 could change into: 

Fig. 1: 
Force analyze when the vehicle driving on hill 
And the following is a discretization result of Eq. 2:
Where:
Because the Luenberger observer requirements the system has the observability,
so it means the matrix:
must be a full rank matrix. According to calculation, the rank of Q_{0}
is 2, so, the system is observable. Pole assignment method can be used to design
the observer (Liu, 2006).
Design of the Luenberger observer: The state equation of Luenberger
observer is shown as follow (Liu, 2006) :
where, x_{L} is the state of model; y_{L} is the output of
model; H is the feedback gain matrix of state observer; according to Eq.
3 and 4, the error vector can be shown as:
When xL(t_{0}) = x(t_{0}), the equation x_{L}(t) =
x(t) is correct, so the feedback of output doesn’t work, it only works
in the situation of x_{L}(t_{0})≠x(t_{0}). As long
as the eigenvalue of the matrix AHC has a negative real part, the error of
initial state vector will always attenuate by index law and the rate of attenuate
depends on the pole assignment of the matrix aHC to ensure the observables
converged to the actual value (Liu, 2006; Li
and Li, 2006). The structure of the designed Luenberger observer is shown
in Fig. 2.
Where, F_{S} and v are input signals, v is the signal of vehicle speed
sensor and the road slope γ can be estimated online.
The order of the system is 2 and it is necessary to configure the system’s
poles appropriately. The characteristic polynomial of the Luenberger observer
is shown as follow:

Fig. 2: 
Structure of the designed luenberger observer 
Set a and b as the eigenvalue of the matrix H, so the Eq. 6
changes into:
The two elements of the H matrix are shown as follow:
h_{1} = (a+b) h_{2} = ab 
The method of choosing the eigenvalue of H matrix is included (Barrho
et al., 2005):
• 
The value must be negative; otherwise the system will be unstable 
• 
If the distance between the eigenvalues and imaginary axis is too far,
the sensitivity of noise will increase 
• 
If the distance between the eigenvalues and imaginary axis is too near,
the response of system will be slow 
According to these restrictions, set a = b, b = 3, so:
Slope recognition precision analysis: In order to explain the precision
of Luenberger observer, this study built a MATLAB/simulink model shown in Fig.
3. According to the vehicle’s
driving conditions, the inputs of the model include the road slope (positive
means uphill, negative means downhill), the vehicle’s
weight m and vehicle speed and then F_{S} could be calculated. Finally,
comparing the observed and real road slope could analyze the Luenberger observer’s
precision.

Fig. 3: 
Simulation model of road slope recognition precision 
Table 1: 
Recognition results of the luenberger observer 

Table 1 shows the results of the Luenberger observer’s
precision. The results show that no matter the vehicle is on uphill or downhill,
the observer always has a high precision and the error is less than 1%.
STARTING CONTROL OF ELECTRIC VEHICLE BASED ON HAS
Structure and function of hill assist system (HAS) in electric vehicle:
The function of HAS is that even if the driver does not depress the brake pedal,
the vehicle can also keep braking force temporarily and doesn’t slip by
the control of ECU in state of hill starting or hill parking. When the vehicle
needs to start, it can release the braking force automatically to complete the
starting process successfully (Ge et al., 1998).
The basic structure and principle of the HAS are as follow: The vehicle can
maintain or release the braking force though ECU to control the ON/OFF which
is in the electromagnetic coil of solenoid valve, by installing solenoid valve
and check valve in the hydraulic circuit between the brake master cylinder and
wheel cylinder like Fig. 4. In general, the electromagnetic
coil is in the OFF state with no excitation, the HSA valve is opened, the brake
works normally. When the braking pressure needs to be kept during hill starting,
the electromagnetic coil is in the ON state, the HSA valve is closed to cut
off hydraulic loop between the brake wheel cylinder and the brake cylinder,
so the oil pressure in the wheel cylinder could be kept. If the driver feels
the braking force is not enough, he can depress the brake pedal to increase
the oil pressure through the check valve which is parallel with the HSA valve
and then, the braking force could be increased. During the hill starting process,
the electromagnetic coil will be in OFF state when the driving force is higher
than the starting resistance, so the oil cycle will be opened and the oil pressure
released. Then the braking state will be ended and it can avoid the vehicle
slipping and make the hill starting process smooth.
Hill starting integrated control of electric vehicle: The integrated
control of hill starting aims at achieving a safe and smooth starting process
according to the driver’s intention.

Fig. 4: 
Electrohydraulic structure of HAS 
It contains motor control, resistance calculation and the control of HSA valve.
Figure 5 shows the schematic diagram of this integrated control.
Wherein, the motor control is mostly based on the drive torque corresponding
with the position of accelerator pedal. This study focuses on discussing the
calculation of the resistance during vehicle start on hill and the control of
HAS, it includes HAS function trigger and HSA valve control logic.
Starting resistance is an important parameter to starting control. Data show
that when the electric vehicle starts on hill, the road conditions are substantially
as same as the time before the driver depressed the brake pedal to stop the
vehicle (Ge et al., 1998). The air resistance
is proportional to the square of the vehicle speed, so it can be ignored for
the low vehicle speed during hill starting and the acceleration resistance also
could be ignored similarly. So, resisting torque T_{γ} during hill
starting primarily contains slope resistance T_{i} and rolling resistance
T_{f}:
where, m can be detected by vehicle weight sensor, g is a constant, r is the
vehicle structural parameter, γ has been identified by the observer and
the rolling resistance torque is related to the rolling resistance coefficient.
Road rolling resistance coefficient is generally determined by experiments,
it’s hard to identify this parameter of each road.

Fig. 5: 
Schematic diagram of hill starting integrated control 
In order to avoid vehicle slipping caused by HSA valve prematurely releasing
on bad road, this study properly amplifies the rolling resistance coefficient
by replacing it with the counterpart of potholes pebble road and the value is
about 0.04.
The mentioned function trigger of the HAS in this study belongs to an active
control strategy. It can be triggered automatically. Through the realtime tracking
of the road state recognition as mentioned in previous segment, each new result
has to replace the previous result to ensure the road slope saved in ECU accurately.
This process will last until the time when the brake pedal begins to work and
the value will be used to trigger the HAS function during the vehicle’s
next starting (Xiao, 2009; Yan, 2009).
The results of experiments show that when a vehicle on a hill which has a ramp
angle less than 2° with no braking force, it will not slide even the shift
lever is in neutral state. So, the HAS function can only be trigger when the
vehicle is on a hill which has a ramp angle more than 2° (Haifeng
et al., 2007).
The key issue of HAS control is the ON/OFF control of HSA valve, including
the start moment and release moment of the valve. The ECU collects the vehicle
running state data via sensors and some kinds of algorithms to decide ON/OFF
the HSA valve. Control signals input to ECU includes the following sections:
(1) Motor start signal, (2) Motor output torque, (3) Accelerator pedal signal,
(4) Input axis rotational speed signal, (5) Gear shifting signal, (6) Brake
pedal signal, (7) Parking brake signal (8) HAS disable switch signal (9) Recognition
result of starting resistance torque (10) Vechile weight signal.
If all the following conditions are satisfied, the HSA valve will be electrified
and shut down and the braking force will be maintained (Ge
et al., 1998; Xiao, 2009; Yan,
2009):
(1) Parking, (2) Motor starting, (3) Vehicle is in gear, (4) Braking pedal
is depressed, (5) The HAS function be triggered, (6) HAS disable switch is on
OFF state.
The parking state is judged by whether the input axis has a zero rotational
speed (the number of pulses is zero in 0.2 sec). Condition 1 is mandatory brake
when the driver didn’t make any
mistakes, conditions 2 and 3 are measures to avoid the HAS working when parking
braking, conditions 4, 5, 6 are the keys to run HAS control.
If any of the following conditions is satisfied, the HSA valve will be power
off and the braking force will be relieved (Ge et al.,
1998; Xiao, 2009; Yan, 2009):
• 
Accelerator pedal is depressed and motor output torque greater
than calculated starting resistance torque 
• 
Exist forward direction speed signal on input axis 
• 
Exist parking brake signal 
• 
HAS disable switch is in the ON state 
Condition 1 and 2 are the keys to relieve braking force and they are the key
points for a vehicle to start smoothly. In addition, parking brake will be done
when the driver hope to park the vehicle for a long time, in this situation,
the HSA valve should be power off. Condition 4 actually is a manual operation
from the drivers and it should be satisfied.
The above control logic show that the HAS adapts to vehicle hill starting but
can not work in parking situation for a long time, however, it can make the
system more stable.
SLOPE RECOGNITION AND HILL STARTING SIMULATION
Figure 6 shows the simulation results of the slope recognition,
this study assumes that the vehicle speed is a constant and then simulation
with different F_{S}.

Fig. 6(ad): 
Simulation results of slope recognition, (a) Curver of FS
changes with time, (b) Vehicle speed (c) Input signal of observer feedback
gain matrix changes with time and (d) Results of ramp recognition 

Fig. 7(ad): 
Starting simulation results on a 15% slope hill with full
load, (a) Pedal opening changes with time, (b) Control signal of HAS valve,
(c) Vehicle speed simulation results and (d) Jerk simulation results 
Table 2: 
Key technical parameters of electric vehicle 

As the system itself has the response time, so in the results, the observer
feedback matrix input signal Δv was larger in the first 2 sec and the road
slope obtained was 14.8% after 2 sec and then because the system input F_{S}
increased after 5 sec, the road slope increased to 20.4% accordingly. From this
result, the precision of the designed Luenberger observer is verified.
In the hill starting simulation, this study takes an electric vehicle which
is modified from an A0 level vehicle as the research object and Table
2 shows the key technical parameters of electric vehicle.
Figure 7 shows the simulation results of the hill starting
on a 15% ramp with full load. The curve indicates that the system trigger the
HAS function automatically via the slope recognition. When the driver depressed
the brake pedal, the HSA valve power off and the brake pressure will be held.
After 1 sec, the brake pedal was released but the HSA valve also on off state.
After 1.5 sec, the driver depressed the accelerator pedal and the motor driving
torque was greater than the starting resistance at 2.3 sec, then the HSA valve
power on, the braking force was released, then the vehicle start smoothly. Figure
7d indicates that the jerk during the starting process was less than 2.5
m sec^{3}, the ride comfort is very good. During the whole process,
the vehicle didn’t slip, the control effect is satisfactory.
CONCLUSION
• 
The longitudinal dynamics equation of the electric vehicle
hill starting had been analyzed; the state equation had been achieved by
linear process and the system’s observability had been determined based
on the equation; a Luenberger observer had been designed by configured the
pole of the system reasonably to recognize the road slope online 
• 
Hill starting integrated control of electric vehicle based on the HAS
had been proposed; the starting function trigger in HAS, calculation of
starting resistance and the control logic of HSA valve had been solved;
the simulation results showed that the proposed method could satisfy the
requirement of electric vehicle hill starting and there was no slip during
the starting process and the jerk was less than 2.5 m sec^{3},
the starting ride comfort is good 
ACKNOWLEDGMENT
The study is supported by Natural Science Foundation Project of CQ CSTC (CSTC,
No. 2011BA3019).