Obtaining Desired Vehicle Dynamics Characteristics with Independently Controlled In-Wheel Motors: State of Art Review.
Decreasing oil resources and increasing environmental problems have stimulated the need for research in alternative energy sources for automobiles. Electric vehicles have come up as a strong contender among all other alternate vehicles (Ruther. et al., 2015). They run on renewable energy source and are tail-pipe emission free. With ever increasing fuel prices and health impacts of internal combustion engines there is a demand for the eco-friendly means of transportation (Ji. et al., 2012: Rezvani, et al.,2015; Wideberg. et al., 2014). Unlike conventional vehicles, which were driven by an engine connected to a powertrain, the EVs are generally driven by individual wheel motors. The advantage of individual motor control is enhanced safety, comfort and improved handling dynamics.
There have been various vehicle dynamics control and torque vectoring algorithms available in literature. We analysed most relevant research that underwent in this area in order to develop a guideline to be followed while designing such a control system. As the torques can be controlled independently, direct yaw moment control and side slip control has come out as one of the most widely used technology for pro-actively preventing accidents.
In 1996, the world's first vehicle with a right-and-left torque vectoring type direct yaw moment control system was developed (Sawase & Sano., 1999). The focus is to develop a controller which can control Couple traction/braking ([T.sub.i] i= FL/FR/RL/RR) of the four in-wheel motors, from basic driving slogans, that are, steering angle, position of the accelerator and brake pedal as shown in Figure 1. Generally, all vehicle dynamics control (VDC) algorithms are based on a hierarchical structure, where, from the slogan of driving and vehicle information the vehicle's response (FOX vehicle in our case) is identified. This structure arises in several levels as shown in Figure 2.
Generally, the variables used by VDC algorithms to monitor the dynamic behavior of vehicle are:
r: - Yaw rate; [beta]: - Slip angle
The system identifies whether the desired dynamics for the driver is within the range of operation of the vehicle. This further determines maximum grip between tires and ground. In case of detecting a discrepancy of the actual dynamics and the desired (and adjusted according to the maximum obtainable performance), a directional control is set to adjustr and [beta] to the desired values.
This directional control of the vehicle involves injection of a moment ([M.sub.z]) which is generated by traction/braking force difference in left-right wheels. Finally, longitudinal forces on each of the wheels are restricted to the maximum allowable value based on friction limit. There are three main control operation levels, namely,
1. Supervisory Controller
2. Upper-level Controller
3. Lower-level Controller
These control levels described in detail in the adjoining sections.
2.1. Steps in Developing a Controller
In order to develop an algorithm for torque allocation the following steps are to be carried out.
1. Characterization of the Desired Dynamic Response
This can be done in either two ways.
This is based on the mathematical model of the vehicle developed in any of the vehicle dynamics simulation interface like, Adams-Car, CarSim, Matlab, etc. The vehicle is tested against a standard handling maneuver (for example: ISO 3888 Double lane change (Kanchwala, et al., 2014)).
b. Field Testing
The vehicle can be tested according to the test criterion of a handling test (National Highway Traffic Safety Administration, Department of Transportation, April 6, 2007) along with a set of sensors mounted in order to get various response characteristics. The desired dynamics can be presented in several ways. Formulas from a simplified model can be represented as:
[[[r.sub.desired] = [f.sub.1] ([delta], [V.sub.x])]; [[[beta].sub.desired] = [f.sub.2] ([delta], [V.sub.x])]]
2. Deciding the Control Type and Layout
Series of works are needed to be carried out for developing the controller, namely,
a. Control of Yaw Rate and Side Slip Angle
Sliding mode, PID, Optimal LQ control, Fuzzy, etc.
b. Torque Allocation
Torque vectoring and wheel traction limits to be studied.
c. Control of Wheel Dynamics
Controlling the longitudinal slip of different wheels.
d. Characterization of the Electric Motors
This allows for sharing of pairs of traction / braking to optimize both efficiency/consumption and the dynamic response of the vehicle.
2.2. Vehicle Dynamics Control - VDC
VDC and stability control systems (Wang & Longoria, June, 20061 have attracted considerable attention from both academic and industry researchers. Main objective of VDC is to make the vehicle respond as intended by the driver (especially in adverse conditions) and to alleviate driver workload. This can be achieved by coordinating the actuation resources (tires) to expand the system operational envelope.
While cornering at high lateral acceleration, tire forces approach to or are at the physical limit, i.e. road adhesion. The vehicle side-slip angle grows and the effectiveness of vehicle steering angle in generating yaw moment reduces significantly because of tire force saturation. This fact is first illustrated by the so-called [beta]-method (Shibahata, et al., 1993).The decrease of restoring yaw moment generated by tire lateral force at high side-slip is the main cause of vehicle unstable motion. By the addition of an external yaw moment the vehicle stability can be recovered. Generally, the number of actuation inputs (slip and slip angles of four tires) is more than the number of control variables (longitudinal, lateral velocities and yaw rate). Therefore, a hierarchically coordinated control structure with control allocation provides a suitable approach (Fredriksson, et al., 2004: Wang & Longoria, June, 2006).
From vehicle dynamics point of view, yaw rate and side slip angle are closely related with vehicle maneuverability and lateral stability (Cho, et al.,2006). Based on driver steering input, desired yaw rate is determined, and correspondingly the desired yaw moment for this yaw rate is obtained. In coordinated VDC systems, reference model provides vehicle reference motions based on driver commands. The higher-level controller produces the generalized control efforts such as imposed forces and moments required to meet desired vehicle states. Control allocation optimally distributes the slip ratio and slip angle of each tire to simultaneously induce desired longitudinal and lateral forces (Li, et al.,2008: Li, et al., 2009). The task of a combined tire slip and slip angle tracking (Tire forces controller) controller is to manipulate driving/braking torque and steering angle of all wheels, independent of vehicle state. Corresponding vehicle states are fed back to higher level controller to close the loop. External yaw moment, independent of lateral forces and steering angle, is generated by the transverse distribution of vehicle braking force between left and right wheels. It is known as differential braking and is achieved using the main parts of anti-lock braking system (Van Zanten, et al., 1998). Longitudinal (braking and driving) forces for implementing VDC systems gives quick control action and is possible to integrate relevant hardware with existing anti-lock/spin systems (Van Zanten, 2000).
2.3. State of Art: Control Law and Strategies
The key point in the strategy of yaw stability control law is to find required corrective yaw moment. Control laws, defined by the researchers in previous research, have the likeness of using yaw rate and vehicle slip angle as control variables. They differ in control strategies, which are addressed below.
A fuzzy logic based direct yaw control for all wheel drive (AWD) EV is proposed in (Tahami, et al., 2003) which is taken as Case 1 (Figure 3) for discussion. A novel strategy is adopted where yaw rate and wheel slip ratio is controlled in the control loop. Separate fuzzy logic based controllers for yaw rate and wheels' slip ratio are used, where the yaw rate controller is determining the required torque. Corrective torque from yaw controller can saturate the tire force, to avoid this a slip controller is used to keep the slip ratio within the stable region. In yaw rate controller, reference yaw rate is generated by neural-network. It generates the reference yaw based on the vehicle speed and steering.
In case 2, (Figure 4), controller is designed to calculate the desire yaw moment from yaw rate error and vehicle slip angle error (Li, et al., 2008). Desired wheels' slip ratios are calculated based on desired yaw moment using fuzzy logic. It is assumed that ABS/TCS is available to manipulate braking or wheel traction. The key points in this paper realized are, the controller has used yaw rate and slip angle to find yaw moment and it is responsible for controlling the individual wheel sleep.
In Case 3, (Figure 5), for more robustness an active front steering controller is used. This controller is based on sliding mode control which provides the corrective steering angle (Zhao, et al., 2009). Rest of control architecture is same as Case 2. Use of steering control along with fuzzy controller is a novel strategy.
A PID controller for lateral acceleration error, a sliding mode controller for yaw rate error and another PID controller for wheel sleep error is used by (Kim & Kim, 2006: Kim & Kim, 2007) which is taken as Case 6 (Figure 6). Corrective wheel torques, generated by these three controllers, is then combined and used as total corrective torque to control the yaw rate of the vehicle.
From the above discussion, one can notice different strategies of torque based ESC for EVs. Several controllers like fuzzy, sliding mode control and neural network to control the system.
Direct yaw moment control (DYC) introduced vehicle directional stability control under emergency situations (Mirzaei, 2010). It is shown that DYC is the most effective method of motion control compared with the other conventional control systems such as four wheel steering (4WS) (Abe, 1999: Selby, et al., 2001). The 4WS control, which depends on the relation between tire lateral force and the steer angle as a control command. It is efficient at small values of lateral acceleration, as the steer input has negligible effect on yaw moment when wheel force saturates. Despite the high efficiency of DYC in a wide range of operation, the external yaw moment (control input), should be kept as low as possible because of its some undesirable effects. It slows down the vehicle as corrective yaw moment is applied through the brakes. This effect must be kept to a minimum so that the driver can feel supported rather than overruled. Limiting excessive use of external yaw moment by integrating DYC and 4WS is studied by (Selby, et al., 2001).
Depending on which variable is controlled, different control types of DYC have been proposed. The yaw rate control by DYC has been studied frequently (Esmailzadeh, et al., 2003: Mokhiamar & Abe, 2002: Mokhiamar & Abe, 2006). Some researchers have used the side-slip control type of DYC (Abe, 1999: Abe, et al., 2001). However, both variables have been controlled simultaneously by DYC (Park, et al., 2001: Ghoneim, et al., 2000).
In both side-slip control and yaw rate control by DYC, the desired (reference) models of these variables are established according to driver steering commands. Several researchers have used the steady-state behavior of linear vehicle model during a cornering maneuver as a desired model for the yaw rate with zero side slip (Esmailzadeh, et al., 2003: Geng, et al., 2009).
These models do not include the transient response for vehicle motions and therefore make large tracking errors at the beginning of maneuvers. Some researchers have used linear 2-DOF vehicle plane model (bicycle model) to be followed by the controller (Mokhiamar &Abe, 2006: Kanchwala, et al., 2015). Although the linear bicycle model shows a stable motion, it is unable to predict the tire/road conditions. It is desirable to develop a linear 2-DOF model with tire/road conditions.
There are several control methods to achieve the desired vehicle behavior using DYC in the literature. Ghoneim, et al., 2000 introduced a feedback control using yaw rate with proportional-derivative (PD) structure, while Geng, et al., 2009 used PID structure. Sliding mode control method has been also employed in finding the yaw moment control law (Abe, et al., 2001). In these methods, the optimization is not used as a main procedure in finding the control laws. A predictive optimal yaw stability controller based on a linearized vehicle model was by (Yamakawa & Watanabe, 2006). Some researchers have developed the well-known LQ theory to improve vehicle handling and stability using on-line numerical computations in optimization, but are not suitable for real-time implementation (Tark, et al., 2001). Esmailzadeh, et al., 2003 have presented an analytical solution for LQ problem, but the controller is based on tracking only reference yaw rate obtained from steady-state behavior of vehicle during cornering. In (Mirzaei, 2010), a complete LQ optimal problem is formulated to track the proposed desired model for both yaw rate and side-slip angle. The derived control law is developed in an analytical closed form which is easy to solve and implement. Also, different control forms are examined and effect of weighting factors on system performance is seen.
Apart from these control architectures researchers have also used model predictive control for direct yaw control (Kanchwala & Bordons, 2015). The wheel torques are independently controlled by using direct yaw moment and side slip control method to pro-actively improving vehicle handling. At high value of side slip the steering is no more capable of generating yaw moment and vehicle becomes laterally unstable. By unequal torque distribution a restoring yaw moment is generated and vehicle stability is ensured. The MPC monitors the Couple traction/braking torque of the four in-wheel motors, from basic driving slogans, which are, steering angle and desired speed. The model predictive control architecture has also been used to make the vehicle follow a desired path such as in the case of autonomous drive (Kanchwala & Ogai, 2016).
3. REVIEW ON THREE MAJOR CONTROLLERS
As discussed in Section 1, there are three major levels of control operation namely,
1. Supervisory controller
2. Upper-level controller
3. Lower-level controller
Supervisory controller (Kang, et al., 2011) determines the control mode and dynamics for vehicle stability based on an admissible control region which is the relationship between the vehicle speed and the maximum curvature of the vehicle considering steering, sideslip, and rollover constraints (Yoon, et al., 2007: Cho, et al., 2010). Upper level controller computes the traction force input and the yaw moment input to track the desired dynamics (Baffet et al., 2006). Finally, the lower level controller is designed to obtain actual actuator commands (front and rear driving motor torques and independent brake torques), to apply upper level control inputs (Tahami, et al, 2004).
3.1. Supervisory Controller
The Supervisory controller mainly determines the admissible control region.
Admissible Control Region
The admissible control region can be computed using the steering and sideslip constraints. These are described below:
1. Steering Constraint
The steering constraint describes the limitation imposed by kinematic steering and handling properties on the attainable manoeuvre. The steering constraint can be obtained from a two degrees of freedom (2-DOF) bicycle model and the definition of slip angle.
2. Sideslip Constraint
It describes the maximum curvature of the vehicle for lateral stability. Although some sideslip is expected and likely unavoidable, substantial slip causes large heading or trajectory tracking errors. Vehicle begins to skid when lateral traction force is equal to tire-road friction limit.
In unified chassis control (UCC) (Yoon, et al., 2010), the improvement of maneuverability and lateral stability is achieved by reducing the yaw rate error between actual and reference yaw rate (driver's steering input). Two types of reference yaw rates are derived according to control mode, i.e., the maneuverability mode, ESC-y (Electronic Stability Control) and lateral stability mode ESC-p. Each control mode generates a control yaw moment and longitudinal tyre force. The switching among control modes is performed based on the thresholds. For small sideslip angle, the controller is in the maneuverability mode, ESC-y and vice versa. The activation condition of the stability mode is determined by a phase plane analysis on the sideslip angle and sideslip angle rate. In ESC-y, a target yaw rate is generated based on the driver's steering input for maneuverability while in ESC-P, it is generated to reduce excessive sideslip angle for lateral stability.
The thresholds, [[gamma].sub.e,th] and [[beta.sub.th] are to be carefully determined. There have been several methods to determine the threshold for the sideslip angle. The most relevant method is to use the phase plane analysis (Chung and Yi, 2006). However, it requires the sideslip angle rate, which is difficult to measure or estimate. Hence, threshold value [[beta].sub.th] is used in the work of Yoon et al., 2010, and the value is set to 3[degrees] under the assumption of [micro] = 0.35 (Rajamani, et al., 2012). The threshold of yaw rate error [[gamma].sub.e,th] is set as 0.08 rad/s considering a case when vehicle undergoes a lane change at 60 kmph.
3.2. Upper Level Controller
The upper level controller is designed to compute the desired traction force input [F.sub.x_des] and desired yaw moment input [M.sub.z_des] for desired dynamics tracked by Supervisory controller. Upper-controller systems are widely discussed (Tseng, et al., 1999: Yi, et al., 2003: Rajamani, et al., 2012). It mainly consists of three main parts, a traction force calculator, a speed controller, and a yaw rate controller (Kang, et al., 2011). The traction force calculator determines the traction force corresponding to the human driver's input, [F.sub.x_Human] (Accelerator/Brake pedal signal: APS/BPS, Figure 7). The upper level controller is further sub-divided into two parts, namely,
1. Speed controller
2. Yaw rate controller
It follows the desired speed determined by the supervisory controller. The desired traction force is determined by traction force calculator or speed controller according to the control mode. It is designed based on sliding-mode control (SMC) method to obtain traction force
Yaw Rate Controller
The yaw rate controller computes the yaw moment input to track the desired yaw rate. It computes yaw moment input to reduce the yaw rate error again using SMC.
It is important to discuss to identify what are the required control parameters. If the controller is designed using only yaw rate as the control variable it would fail to stabilize the vehicle on the road where tire road adhesion is low (Al Emran Hasan, et al. 2013). At low friction vehicle slip angle increases rapidly without influencing lateral force, yaw rate and lateral acceleration. The controller should take both of the yaw velocity and slip angle as controller parameters else the vehicle would not achieve stability in critical situation (Kost, et al., Robert Bosch GmbH. 1996; Gutierrez, et al., 2011).
The Yaw Rate and Side slip controllers are discussed below.
3.2.1. Yaw Rate Controller
To compensate the loss of vehicle stability in emergency situations due to nonlinear characteristics of tire forces, a linear 2DOF (Figure 8) vehicle plane model (bicycle model) with appropriate physical constraints is proposed as a desired model to be followed by the controller. The governing equations for the linear vehicle model, in the state space form, are expressed as (Wong. J.Y., 2008):
[mathematical expression not reproducible] (1)
[mathematical expression not reproducible] (2)
In the above equations, the vehicle side-slip angle [beta] and the yaw rate r are the two state variables. The front wheel steering angle d is considered as the driver input. Other parameters are:
[C.sub.af], [C.sub.ar]: Cornering stiffness of the front and rear tires; [l.sub.1] [l.sub.2]: Distances of CG from front and rear axles; m: Vehicle mass; [I.sub.2]: Moment of inertia about vertical axis; [V.sub.x]. Longitudinal velocity.
The steady-state vehicle yaw rate and side slip during a constant cornering maneuver is obtained as,
[mathematical expression not reproducible] (3)
[mathematical expression not reproducible] (4)
The steady-state value of vehicle side-slip angle in terms of yaw rate is given by,
[mathematical expression not reproducible] (5)
Referring to the vehicle dynamics model, the term of lateral acceleration is defined as:
[mathematical expression not reproducible] (6)
where, [V.sub.y] is the lateral velocity. Therefore, steady-state value of yaw rate is defines as,
[mathematical expression not reproducible] (7)
Since the lateral acceleration of the vehicle in terms of 'g' units and it cannot exceed the maximum road coefficient of friction (Cho. et al., 2008) the maximum steady-state value of yaw rate [r.sub.ss] must be limited to,
[mathematical expression not reproducible] (8)
The measured lateral acceleration a can be taken instead of [mu]g. Now, the constraint |[r.sub.ss|max] can be easily applied to the linear vehicle model. In this way, combination of the following condition with previous equations makes limits the desired yaw rate to a value compatible with tire/road conditions.
[mathematical expression not reproducible] (9)
To increase the vehicle stability limit, an intentional modification of yaw rate response from second to first order model has been proposed (Mokhiamar & Abe, 2002). This modification is due to the fact that when side-slip angle converges to zero, yaw rate can be reduced to a first-order lag. As a result, the proposed yaw rate (dynamic response) by keeping its steady-state value is given by,
[mathematical expression not reproducible] (10)
The yaw-rate error is,
[[DELTA]r = [r - [r.sub.des]]] (11)
Feedback of yaw-rate error is used to demand a desired yaw-rate torque from the lower controller. The moment command is generated based on the yaw rate error, where desired yaw rate is inferred from driver commanded steer angle rate (Hallowell & Ray, 2003). The moment is approximated as,
[M = K[I.sub.zz]([r.sub.des] - r)] (12)
Where, K is the gain factor, [r.sub.des] is the desired yaw acceleration, and r is the actual yaw command.
For a real-time controller an actual yaw rate of a vehicle is measured directly using electronic yaw rate sensors. But for simulation actual yaw rate is found from vehicle model. Desired yaw rate is determined from steady state relation between steering angle and vehicle trajectory. In Unified chassis controller (Yoon, et al., 2010). ESC-[gamma] is designed to force vehicle to track a reference yaw rate generated by a driver's steering input. The dynamic equation of yaw rate can be presented as,
[mathematical expression not reproducible] (13)
Tyre cornering stiffness ([C.sub.[alpha]f], [C.sub.[alpha]r]) is influenced by vertical load, slip angle and wheel slip. Since the tyre cornering stiffness has inherent nonlinearity and uncertainty, the sliding mode control (SMC) method has been used for the design of the desired yaw moment in order to incorporate directly the uncertainties in control design stage. Cornering stiffness deviation from actual value is bounded as,
[|[C.sub.]alpha]i] - [C.sub.[alpha]i]| [less than or equal to] [F.sub.i] (i = f, r)] (14)
Where '[C.sub.[alpha]i]' indicates the best estimate of the actual value, of [C.sub.[alpha]i]. Defining a sliding surface, [S.sub.1] as
[[[S.sub.1] = r - [r.sub.des]]; differentiating gives [[S.sub.1] = r - [r.sub.des]]] (15)
Substituting Equation (15) in (13) yields,
[mathematical expression not reproducible] (16)
The equivalent control input that would achieve [S.sub.1] = 0 is given by,
[mathematical expression not reproducible] (17)
In above equation the second discontinuous term is introduced to satisfy sliding condition regardless of model uncertainty ([C.sub.[alpha]f], [C.sub.[alpha]r]). Substituting Equation (17) into sliding condition ([S.sub.1][S.sub.1] [less than or equal to] [[eta].sub.1]|[S.sub.1]|), gives gain [k.sub.1],
[mathematical expression not reproducible] (18)
where, [[eta].sub.1] is a positive constant. In (Yoon et al.. 2010), [[eta].sub.1] is set as 10.
3.2.2. Vehicle Side Slip Angle Controller
Vehicle body side slip angle is one of the most significant parameters in vehicle stability (Al Emran Hasan, et al., 2013). It is the angle between vehicle longitudinal axis and direction of velocity at CG
[[beta] = [[V.sub.y]/[V.sub.x]]] (19)
Side slip angle cannot be measured using any commercially available sensor. In real time, using lateral accelerometer along with a yaw rate sensor is used to estimate the side slip angle of the vehicle. Desired side slip angle [[beta].sub.des] can be obtained from steady state steering angle by equation (4). The measured side slip angle is compared with desired side slip angle and the error between them is fed to the control law of ESC-[beta] Using 2D bicycle model, vehicle lateral dynamics is expressed as,
[m[V.sub.y] = -m[V.sub.x]r + 2[F.sub.yf]cos[delta] + 2[F.sub.yr]] (20)
From Equation (20). assuming that [V.sub.x] [approximately equal to] 0, the sideslip angle dynamics can be arranged as follows:
[mathematical expression not reproducible] (21)
If the reference yaw rate for the lateral stability is defined as,
[mathematical expression not reproducible] (22)
Then, body sideslip angle changes into a stable dynamics as shown in previous Equations, which implies that the body sideslip angle asymptotically converges to zero.
[mathematical expression not reproducible] (23)
Where, [K.sub.[beta]] is a design parameter which is strictly positive. In this study, [K.sub.[beta]] is set to 3.
Some researchers have used both Yaw rate error and side slip error to generate restoring yaw moment (Geng. et al.. 2009; Mirzaei. 2010; Al Emran Hasan, et al., 2013). The linear quadratic (LQ) method is considered as a suitable tool for solving such problem (Mirzaei. et al., 2008). In order to formulate a complete LQ problem, a performance index that penalizes the tracking errors and control expenditure is first considered in the following form:
[mathematical expression not reproducible] (24)
where, [w.sub.b], [w.sub.r] and [w.sub.u] are weighting factors indicating relative importance of corresponding terms. [M.sub.z] is the external yaw moment which must be determined from control law. The subscript d denotes the desired response. Minimizing J improve tracking accuracy with minimum external yaw moment.
The coefficient [w.sub.[beta]] (0 [less than or equal to] [w.sub.[beta]] [less than or equal to] 1) is introduced in the performance index as a weighting factor on [beta] deviation by Geng, 2009. It is defined as,
[w.sub.b] = [q.sup.2][w.sub.[beta]] and [w.sub.r] = [q.sup.](1 - [w.sub.[beta]]) where,
[mathematical expression not reproducible] (25)
where, [[beta].sub.0] is a threshold value which has been set as 10[degrees] (Geng. et al., 2009).
A sliding mode based control law has been chosen with the weighted combination of yaw rate error and slip angle error (Al Emran Hasan, et al., 2013). The control law is described below, where is the sliding surface, is the yaw rate, is the controller variable and is the actual side-slip of the vehicle.
[S = r - [r.sub.des] + [epsilon]([beta] - [[beta].sub.des])] (26)
Controller determines amount of required torque at each wheels to generate a corrective yaw moment to meet the targeted yaw rate determined desired value generator. From wheel torques rotational velocity of the wheel or tires is determined and then a lower controller can track the wheels' rotations. Simulations have been performed with the popular sine with dwell maneuver which has been used by transport authorities around the world for stability testing (Picot. et al., 2011).
3.3. Lower Level Controller
The lower controller ensures that the yaw or side slip-mitigation correction commands of upper controller can be obtained from the torque-management devices. It is designed to obtain actual actuator commands, front and rear driving motor torques and independent brake torques. An optimization based control allocation strategy is used to map control inputs to actual actuator commands (Kang. et al., 2011). Lower level controller has to control speed and wheel slip (Traction control), perform torque estimation, allocate torques to the individual wheels. In addition to these it should take motor characteristics into account by precise motor modeling. A detailed state of the art survey is been given about lower level controller design and the method of operation in this section.
These are the four main steps to be followed while designing the lower level controller. These steps are briefly discussed below.
3.3.1. Wheel Slip Control
First role of the lower level controller iswheel slip control. A wheel slip controller is essentially a traction control system. It is designed to keep the wheel slip ratio [i.sub.x] of each wheel below [i.sub.x_max]. It is only activated when the magnitude of the wheel slip ratio is larger than [i.sub.x_max]. It determines the net torque command of wheel so that actual wheel speed tracks desired wheel speed for slip limitation.
Traction control is developed to ensure the effectiveness of the torque output. It is necessarily an anti-slip control (Yin et al., 2009). In general traction control systems utilize the non-driven wheel velocities to provide an approximate vehicle velocity. However, this method is not applicable when the vehicle is accelerated by 4WD systems or decelerated by brakes. For this reason, the accelerometer measurement is used to calculate the velocity, but it cannot avoid offset and error issues. Other sensors, e.g., optical sensors (Turner & Austin, 2000), magnetic markers Tee & Tomizuka, 1996: Lee &
Tomizuka, 2003: Suryanarayanan & and Tomizuka, 2007), etc., can also obtain the chassis velocity. However, they are too expensive to be applied for an actual vehicle real-time control.
(Tahami, et al., 2004) used a data fusion method for this purpose. The wheel linear speeds are used as pseudo sources of vehicle speed. Via integration of the acceleration another estimate for vehicle velocity is made available. For this purpose, an additional accelerometer is embedded in the vehicle in order to measure the vehicle longitudinal acceleration. The inputs are all fed into an estimator, where a Fuzzy logic determines which input is more reliable. Inputs are weighted and averaged to give the estimated speed. Figure 9 shows the block diagram of the estimator and it consists of two stages. In first stage preprocessing occurs, the wheel slips are calculated using the previous estimated vehicle speed and the measured wheel speeds. In next stage, wheel linear speeds and vehicle speed obtained by integration are weighted using Fuzzy rules.
The weighted values are averaged to give vehicle speed. Rule sets, which are used for weights are:
1. In cruise driving, the integral of the vehicle acceleration is not reliable, since the accelerometer signal is comparable to offset and noise of the measuring circuit.
2. In braking situation all wheel speeds are weighted low, because of large wheel slips.
The focus is on the development of a core traction control system based on the maximum transmissible torque estimation (MTTE) that requires neither chassis velocity nor information about tire-road conditions. In this system, only the torque reference and the wheel rotation speed is used to estimate the maximum transmissible torque. The differential equations for the calculation of longitudinal motion of the vehicle are described as:
[[J.sub.w][omega] = T-r[F.sub.d]] (27)
[m[V.sub.x] = [[F.sub.d] - [F.sub.dr]]] (28)
[[V.sub.w] = r[omega]] (29)
[[F.sub.d] ([i.sub.x]) = [mu]N] (30)
Where: [J.sub.w]: Wheel inertia; [V.sub.w]: Wheel velocity; [omega]: Wheel rotation speed; T: Driving Torque; r: Wheel radius; [F.sub.d]. Friction Force (Driving force); m: Vehicle Mass; N: Normal load; [V.sub.x]. Chassis Velocity (Vehicle velocity); [F.sub.dr] Driving resistance; [i.sub.x]. Slip ratio and [mu] Friction coefficient. The relation between slip ratio and friction coefficient can be described by various formulas. (Yin, et al., 20091 used widely used magic formula based tyre model (Pacejka & Bakker, 1992) to build a vehicle model for the simulations.
3.3.2. Torque Estimation: MTTE (Maximum Transmissible Torque Estimation)
To avoid complicated [mu] - [i.sub.x] relation, only dynamic relation between tire and chassis is considered based on below considerations, which transform anti-slip control to max transmissible torque control.
1. Kinematic relationship between wheel-chassis is fixed and known independent of road type.
2. During acceleration, considering stability and tire slip, a well-managed control of difference of velocity between wheel and chassis is more important than mere pursuit of max acceleration.
3. If wheel and chassis accelerations are well controlled, then the difference between wheel and chassis velocities, i.e., the slip, is also well controlled.
The driving force, i.e., the friction force between the tire and the road surface, can be calculated as (Kanchwala & Wideberg, 2016):
[mathematical expression not reproducible] (31)
In normal road conditions, [F.sub.d] is less than the maximum friction force from the road. However, when slip occurs, [F.sub.d] equals the maximum friction force that the tire-road relation can provide and cannot increase with T. The difference between wheel and chassis velocities becomes more, i.e., the acceleration of wheel is more than that of chassis. Therefore, for slip not to start or become severe, the acceleration of the wheel must be close to that of the chassis. Moreover, considering [mu] - [i.sub.x] relation described in Magic Formula, appropriate difference between chassis velocity and wheel velocity is necessary to generate friction force. Accordingly, a relaxation factor, a is introduced as an approximation between chassis and wheel acceleration, given by,
[mathematical expression not reproducible] (32)
For no or limited slip, [alpha] should be close to one. With a designed [alpha], when the vehicle enters a slippery road, [T.sub.max] must be reduced adaptively following the decrease of [F.sub.d] to satisfy, the no-slip condition. Since the friction force from road is available, the maximum transmissible torque [T.sub.max] is.
[mathematical expression not reproducible] (33)
This formula allows a certain maximum torque output from the wheel (for given [F.sub.d]) so as not to increase the slip. Finally, the proposed controller uses [T.sub.max] to constrain torque reference if necessary. In lower level controller, optimal distribution algorithm is designed to generate actuator commands for efficient driving, minimization of the allocation error, and slip limitation. To distribute the actuator commands, the LQ constrained problem is formulated as a weighted least-squares (WLS).
3.3.3. Torque Allocation
In torque controller (Figure 10), the limiter with a variable saturation value controls the torque output according to the dynamic situation. Under normal conditions, the torque reference pass through the controller without any effect, but on a slippery road, the controller constrains the torque output close to [T.sub.max]. At first, the estimator uses commanded torque into inverter and rotation speed of wheel to calculate friction force, and it then estimates maximum transmissible torque. Finally, it utilizes estimated torque value as a saturation value to limit the torque output.
It causes a phase shift, due to low resolution of the shaft encoder installed in wheel, a low-pass filter (LPF) with time constant of [[tau].sub.1] is introduced to smooth digital signal [V.sub.w] fed to the differentiator. In order to keep the filtered signals in phase, another LPF with a time constant of [x.sub.2] is also added.
In (Yamakawa. et al., 2007). a method of torque allocation and control for electric off-road vehicles based on a PD control is proposed. In order to examine optimal wheel torque distribution to the front and rear wheels on rough ground, a numerical vehicle model was constructed for the pitch plane.
For wheel torque distribution with the vehicle model, the following two methods are employed,
A. Determining the torque on each wheel to control the speed of individual wheels; and
B. Determining the torque on each wheel based on vertical load on wheel to control vehicle speed.
In order to compare efficiency, both numerical models drive the vehicle at same speed using speed feedback control. Motor torque is determined by the following feedback system with PI control.
[mathematical expression not reproducible] (34)
Where, [K.sub.p] and [K.sub.i]: proportional and integral gains, [V.sup.T]: target velocity, and [V.sup.R]: wheel velocity. The integral control in the second term is added to reduce the system's steady-state error. Fig. 11 shows the block diagrams for the feedback systems A and B respectively. System A uses wheel speed feedback while System B applies feedback based on the vehicle's center of mass velocity to estimate the necessary total torque on the vehicle, and then allocates torque to each wheel based on the ratio of vertical loads. If wheel torque computed by the loop exceeds maximum torque available at each wheel, a block followed by PI blocks saturates (limits) wheel torque using the following algorithm.
[mathematical expression not reproducible] (35)
The wheel torques obtained above have to be generated by the motor. Precise motor modelling is required to generate this torque. A permanent magnet motor model torque dynamics model is used in fZhao. et al., 2009) to provide demanded required torque by stability system of an all-wheel drive EV. A relatively similar second order motor torque dynamics model is used by (A1 Emran Hasan, et al., 2013) as.
[mathematical expression not reproducible] (36)
3.3.4. Handling Actuator Constraints
In the actuator constraints, actuator limits and the friction circle limit at each wheel should be considered. In most proposed model, the friction force is assumed to be determined by wheel slip. Let [F.sub.x] be longitudinal friction force and [F.sub.z] be vertical load. Then, tire/road friction coefficient is,
[[[mu].sub.x] = [[F.sub.x]/[F.sub.z]]] (37)
The longitudinal wheel slip [i.sub.x] can be defined as,
[mathematical expression not reproducible] (38)
Where, [r.sub.ef] is the effective wheel radius, [omega] is angular velocity. Normally, [[mu].sub.x] increases when vehicle velocity decreases or the road surface becomes rough. With given conditions, [[mu].sub.x] is a nonlinear function of [i.sub.x] with a distinct maximum (maximum of friction). The relationship of [[mu].sub.x] and [i.sub.x] can be clearly distinguished into two parts: the steady rising part of the [[mu].sub.x] - [i.sub.x] graph and the local sliding part in which [[mu].sub.x] gradually decreases to [[mu].sub.x_glide].
The method of individual motor torque control has been investigated in this paper. The aim of this literature survey was to develop a path which can be followed while developing a torque vectoring system. Next step is the development and experimental testing of these novel control algorithms on actual vehicle. We were able to develop a systematic guideline of various works involved in developing such a system.
The paper began with steps in developing the controller. For most of the control applications a mathematical model of the vehicle is developed. The virtual vehicle model must be validated by field test results to ensure model accuracy. Next step was to decide control type and layout. Various control types are available in literature but we have found that an optimal LQ controller is most suitable in automotive control applications. The reason is that it is robust and relatively less significant to system parameter variabilities which are often encountered in an automobile.
The process of control law development is broadly divided in three sub-sections namely, Supervisory control, Upper level control and Lower level control design.
Supervisory controller mainly determines the Admissible Control Region. For supervisory control, the unified chassis control (UCC) from (Yoon. et al., 2010) gives detailed explanation of setting the thresholds, [[gamma].sub.th] and [[beta].sub.th] for yaw rate and side slip errors. Upper level controller from (Kang, et al., 2011) is fairly detailed as it defines the relationship between the vehicle speed and the maximum curvature of the vehicle considering steering, sideslip, and rollover constraints. Finally, lower level controller is been discussed. There are the four main steps to be followed while designing the lower level controller. First step is longitudinal slip control design (traction control) for which the fuzzy logic based speed estimator of (Tahami, et al., 2004) is most appropriate for field applications as it is computationally very quick., torque allocation algorithm. Then comes the torque estimation algorithm which was discussed by maximum torque transmissibility equation. The torque allocation algorithm by (Yamakawa & Watanabe, 2006), proposes a method of torque allocation and control for electric off-road vehicles based on a PD control which is found to be most appropriate. Finally, motor torque characterisation and the process of doing the same is shown in section 3.3.4.
Yaw Rate and Side slip controller development methodology has also been discussed separately in a great detail. The mathematical model is been formulated and the equations are presented. Moreover, the wheel torque allocation based on the yaw rate and side slip controller is also been taken into account with the lower level controller model equations separately defined.
The works involved in development of a control system have been properly sub-divided in a logical fashion. From the vast amount of available literature, most relevant papers were selected and are discussed. We hope this guideline serves the needs of a vehicle control system designer.5.
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School of Aerospace, Transport and Manufacturing
Cranfield-MK43 0AL, United Kingdom
Department of Manufacturing and Engineering Construction
University of Oviedo
Department of Manufacturing and Engineering Construction
University of Oviedo
Department of Transportation Engineering
E.T.S.I. - University of Seville
National Automotive Testing, Research and Infrastructure Project
Pablo Luque Rodriguez and Daniel Alvarez Mantaras
University of Oviedo
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|Author:||Kanchwala, Husain; Rodriguez, Pablo Luque; Mantaras, Daniel Alvarez; Wideberg, Johan; Bendre, Sagar|
|Publication:||SAE International Journal of Passenger Cars - Mechanical Systems|
|Article Type:||Technical report|
|Date:||Jul 1, 2017|
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