AN OVER-VIEW OF NEXT GENERATION ANTILOCK BRAKE SYSTEM CONTROLLER S. John Department of Mechanical Engineering The Polytechnic of Namibia, P. Bag 13388, Windhoek, Namibia,
[email protected],
Keywords: Anti-lock braking system, vehicle dynamics, friction, slip, PID, SMC, fuzzy logic, neural network Abstract Anti-lock braking system has been in existence for a while, however the controlling modes have moved from a simple table rule to more complicated modes. Recent research focuses on slip control using adaptive control, fuzzy logic and neural networks employing genetic algorithms. This is mainly due to the non-linear nature of the dynamic problems. This paper reviews four famous ABS controller designs proposed by researchers. The conclusion of this review is the proposal of possible hybrid control systems for optimum performance of the ABS on different road terrains. 1
Introduction
Hard braking of vehicles during an emergency leads to the locking of wheels. When wheels lock they lose frictional contact with the road and this causes the vehicle to skid. This situation leads to the driver losing control of the vehicle, the consequence of which could be devastating. In this situation, experienced drivers pump the brakes rapidly and carefully in order to avoid sliding of the car, thereby maximizing the grip between the tyre and the road. The antilock braking system (ABS) is a device that senses when the wheels of a car are about to lock, while braking and it controls the pressure supply to the brakes of the individual wheels to avoid locking of the wheels. This reduces the braking distance and enhances steerability while braking. ABS has been applied to locomotive vehicle since 1943 while the first application of ABS to aircraft was in the late 1940s’ to early 1950s’ [1]. ABS was first installed in cars in the late 1970s’ [2]. Most commercial ABS has an algorithm that is based on complicated logic rules, which attempt to capture all possible operating scenarios and conditions. These are, road conditions, straight line braking, manoeuvring and braking operation, to mention just a few. These rules are executed by means of a control computer that switches on and off solenoid valves to ensure the right pressures are delivered to the wheels while avoiding slippage [3]. ABS is now available on most modern cars as a standard component [4]. However, the controller employed requires extensive field testing to tune it. In the event of migrating an already tuned controller to another vehicle, this will require a repeat of the tuning process allover again. In addition the wheel slip tends to oscillate around its optimal point; this hampers
1
the performance of the system. In view of this, several ambitious controller algorithms have been proposed in the literature of recent. There are several control challenges which researchers must address in tackling the next generation ABS. These include but are not limited to the following: first, noise attenuation, this problem is common with the table rule control method commonly used by the automobile industry, which introduces chattering due to the on/off nature of the solenoid valves. Secondly, the controller should be robust with regard to vehicle dynamics, road conditions and disturbance that might affect the control performance. Thirdly, the accuracy in slip tracking should be achieved. The final consideration this paper also seeks to present in favour of hybrid ABS control is the implementation aspect; this should be cost effective and kept as simple as possible. The overall goal of the ABS is to provide ride comfort and control in an emergency braking situation by being able to shorten the braking distance and provide the driver with the control of the vehicle steering. It is the goal of this paper to make a case for hybrid systems based on results presented in the literature. To do this, we would review some key ABS controller designs proposed in the literature. These are PID, sliding mode control (SMC), fuzzy logic, and neural network control methods. By comparison of these control methods, we would show that a hybrid system controller will be the preferred ABS control method for the future. 2
The Controller Challenges
To appreciate the problem researchers are trying to tackle, it will be appropriate to present the major challenges posed by the control problem. The problem is simplified by starting with the quarter-car model shown in Figure 1, to develop the mathematical model of the vehicle dynamics. This model has been adopted due to its extensive use by researchers in their works due to the fact that the mathematical model is further simplified by this model.
Fz = mg
ωx
Tb
vx
Fx = µ Fz Figure 1: Free-body diagram of a quarter car model From Newton’s laws of motion we develop the following equations:
mvx = − Fx J ω = rFx − Tb sign(ω )
(1)
2
Where m is the mass of the quarter car, vx is the longitudinal velocity of the vehicle, J is the rotational inertia of the wheel, r is the radius of the tyre, ω is the angular velocity of the wheel, Fx is the friction force between the tyre and the road, and Tb is the applied torque or braking torque. Current research focuses on slip control, and the goal of the controller is to follow a predetermined trajectory of the slip, based on road conditions and other dynamics. The longitudinal wheel slip λx is defined by the equation:
λx =
( vx − ω r )
(2)
vx
One of the challenges introduced by (2) is the fact that it is not easy to measure the vehicle velocity ( vx ). Next we consider the friction force which is given by the equation:
Fx = Fz µ ( λx , µ H , α )
(3)
Where µ H is the optimum friction coefficient, α is the slip angle of the wheel, and Fz is the normal force. The friction coefficient µ , is dependent on the road condition and has a non-linear relationship with the slip as shown in Figure 2 below. Differentiating equation (2) with respect to time and substituting (1) will yield the slip rate:
λx = −
1 vx
r 1 r2 1 − + λ µ Fz + ( ) x m J vx J
Tb
(4)
From (1) and (4) it can be seen that as vx → 0 the slip rate, λ → ∞ this is a case of tyre lockup, which is undesirable as steerability, directional stability and the general control of the vehicle will be greatly hampered. Therefore the slip controller should be switched off at low velocities; in this case at speeds of 0.8 m s [1]. Also the following could be shown; if v(0) > 0 and Tb ≥ 0 then λx (t ) ∈ [0,1] ∀t and vx (t ) ≤ 0 ∀t where v(t ) > 0 . This is the case of deceleration. The major challenge of the ABS controller is to take advantage of the optimum friction coefficient, µ H in order to reduce the braking distance, irrespective of the road conditions. Different friction models exist in the literature, a famous one is the so-called ‘magic formula’ presented in [5]. Reviews of the various models are presented in [6], [7].
3
3
Controller Review
In this section of the paper, we will review the control method of commercially available ABS and the current research trend in the development of new control methods.
3.1 Current ABS Controllers Mass production of ABS commenced in 1978 [2], and the basic concept is illustrated in Figure 2 below.
Electronic Control Unit (ECU) Compares actual slip to the desired slip
Acting on the braking pressure
Hydraulic Modulator with solenoid valves Builds-up the braking pressure
Petal force Speed sensors Wheel brake cylinder (manipulated variable)
Road Condition
Figure 2: Closed loop ABS schematic
It consists of an electronic control unit (ECU), speed sensors located at the wheels and a modulator that regulates the solenoid valves. The speed sensors send speed signals to the ECU, which decides when to increase, or decrease the braking pressure at the wheels on the application of the brakes by the driver. The ECU computes the deceleration of the vehicle and compares it with the actual speed sensor to determine if the slippage is becoming excessive. Another method is for the ECU to monitor the deceleration rate of the wheels and determine when it is about to lock. Any of this combination of sensing the wheels lock-up is used by various ABS designs [2]. On the determination of a wheel lock-up point, the solenoid valves releases the pressure on the wheels momentarily thereby maximizing the friction/slip relations, by staying within the control region as shown in Figure 3. Most commercially available ABS still implements braking using hydraulic brakes.
4
80
Friction coefficient (mu) [%]
70 60 50 40
Shaded area shows the control region
30 20 10 0
0
10
20
30
40
50 Slip [%]
60
70
80
90
100
Figure 3: Friction curves for different road conditions
The controller method explained above utilises rule-based technique with an exhaustive tables for different road conditions [1], tuning is accomplished by trial and error and extensive field testing. With the solenoid valves opening and closing, chattering effect cannot be avoided and hence the problem of stability is introduced. Migration of the ABS to another vehicle will require a whole session of tuning all over. These are some of the reasons for a search for a more effective and robust controller for the ABS.
3.2 Current Research Trend Current ABS control cycle entails monitoring the deceleration of the wheels, and as soon as the deceleration rate goes below a certain set- threshold, the pressure modulator activates to hold the braking pressure at the wheels; otherwise it releases the pressure. However, future ABS will have to track predetermined slip values for various road conditions. Hence, the future ABS controllers will be required to be more intelligent as they must be able to determine the road conditions, and determine which set slip it must track. It should also be able to switch between slip values when road conditions change suddenly. This demands speed and efficiency on the controller.
5
Therefore, current research trend by leading researchers from academic and industry in the development of ABS is model-based design [1]. With available software like Matlab/Simulink, simulations on proposed models can be performed, improved upon before the actual building of a prototype. All of the above may sound very complex; however, with current developments in autoelectronics this can be achieved. Some of these developments include the current braking methods like the brake-by-wire, which delivers the braking pressure using electro-hydraulic or electro-mechanical systems [8]. These methods deliver more accurate braking pressure than the hydraulic brakes. The introduction of the ‘Electronic Stability Programme’ (ESP), has given rise to several possibilities to improve on the ABS performance s well. In summary, the current research trend is to have a threshold slip for different road conditions. The objective of the controller is to maintain a braking torque that regulates the slip, λ to the pre-set threshold slip value ( λ0 ) depending on the road condition. In the following sections, four controller methods that have received a lot of attention from researchers will be reviewed. These are; PID, Fuzzy logic, sliding mode and neural network control methods.
3.2.1 PID ABS Controller The PID controller has been in used for decades and has become famous due to its ease of design and tuning [9]. The linear PID controller can be represented by the equation;
(
u = K P e + TI ∫ e + TD e
)
(5)
Where e, ∫ e and e represent the error, the time integral of the error and the time derivative of the error respectively. K P is the proportional gain, TI is the integral time constant and TD is the derivative time constant. u is the controlled output. Solyom [1] proposed a model based approach, in which the design objective is for each wheel to follow a reference trajectory for the longitudinal wheel slip. The quarter-car model was used for the analysis. A gain scheduled PI(D) controller was implemented for his design. Braking from an initial speed of 30 m s the vehicle achieved a stopping distance of between 36m to 41m , which is a considerable improvement to currently available ABS. Secondly, tuning of the controller did not take as long as commercial ABS. However, the transient condition was slightly unstable. One of the major advantages in Solyom’s work, was exploring the accuracy and ease of tuning of the PID controller. The PID control method has been known to behave poorly when systems are highly nonlinear and hence Jiang and Gao [9] have proposed a ‘nonlinear PID’ (NPID). This so called NPID is represented by the equation;
6
u = K NP f ( e, α p , δ p ) + TNI f
( ∫ e, α , δ ) + T p
p
ND
f ( e, α D , δ D )
(6)
Where K NP , TNI and TND are parameters with similar meaning to K P , TI and TD in the linear PID and f (*) is a non linear function, while the subscripts p and D represents proportional and derivative respectively. The method of gain scheduling implemented for the NPID is same for the linear PID. A comparison between the two controls methods revealed that NPID has a better robustness to linear PID when tested on ABS stopping distance, road conditions and tyre conditions. The NPID performance was on the average 25% improvement over the linear PID. Another development is reported in [10] where a PID ABS controller with a sliding modebased optimizer was proposed. The optimizer determines the optimal slip that corresponds to the maximum deceleration of the vehicle and tract it. The tracking is done by regulating the brake torque of the vehicle. Only simulation examples were provided.
3.2.2 Sliding Mode Control (SMC) The challenge in developing an ideal mathematical vehicle dynamics model for the ABS is one of the major motivations for the introduction of the sliding mode control (SMC) and others, to be discussed later. A simplified structure of SMC ABS is illustrated in Figure 4 below. It contains a robust controller, an equivalent controller and a sliding surface estimator. The robust controller compensates for broad range of uncertainties while the equivalent controller does the actual tracking of the desired slip. The robustness of the SMC is its main strength as an ABS controller. Sliding Surface
λc
Referenc e Model
λd λ
λe
Sliding Mode Control System
Robust Controller
urb
ueq +
Equiv Controller
+
+
usm
ABS Model
λ
Limiter
Figure 4: Block diagram of SMC ABS However, two major problems identified with SMC are the introduction of chattering effect and steady-state error. In solving the chattering effect, a saturation function is employed in place of the sign function for switching control for different road conditions. The introduction of the saturation function further introduces steady state error [11] [12]. 3.2.3 Fuzzy logic ABS controller Another method of tackling the difficulties in developing a comprehensive mathematical model, incorporating as many important vehicle braking dynamics as possible, has led to the development of fuzzy logic ABS controllers. The fuzzy logic control has the advantage of adaptation to complex changes in the vehicle operational conditions, such as the nonlinearity of the vehicle tyre and suspension systems. This gives it a good robust performance [13]. In
7
their work, Yu et-al [13] developed a fuzzy logic controller with the objective of tracking an optimal slip ratio in real time, to obtain a shorter stopping distance while enhancing side slip stability. An 8-degree of freedom vehicle model was used. The fuzzy logic controller consisted of 25 fuzzy rules and the triangular membership functions were used for fuzzification of the input and output variables. Typical triangular functions, known as ‘linguistic functions’ are shown in Figure 5 below.
NB
1
NS
ZO
PS
PB
NB
1
0.5
NS
ZO
PS
PB
0.5
0
0 -1.5
-1
-0.5
0
0.5
1
1.5
-1.5
Input variables
-1
-0.5
0
0.5
1
Output variables
Figure 5: Input/output membership linguistic functions In this case P stands for positive, N for negative, B for big, S for small and ZO for zero. Therefore PB will denote ‘positive big’, NB for ‘negative big’ etc. This study [13] utilised the Mamdani algorithm for the fuzzy logic operation and the Gravity algorithm for defuzzification. From typical simulation results presented, the proposed controller was found robust in that it was able to adapt to changes in road conditions. It also shortens further the stopping distance by 15% compared to a controller with a fixed slip ratio scheme. This proposed scheme could also find use in traction control as well. Klein [14] implemented antilock braking system controller using fuzzy logic for the vehicle speed estimation. The test vehicle was a BMW 328i, fitted with hydraulic braking system. The test was carried out on a dry asphalt pavement. The results showed that the deceleration level and steerability are comparable to commercially available ABS systems. However, good results were obtained only when optical or microwave sensors were employed. These are very expensive and might not be used in ABS commercially. The development and implementation time were shortened compared to the conventional ABS. Recent experiments on a prototype Fuzzy ABS have shown considerable improvement in performance against current ABS methods with as few as six-fuzzy logic rules. This prototype was tested on a test tract with alternating road conditions from snowy to wet asphalt [15].
3.2.4 Neural Network Approaches Neural Network has become a prefered alternative control technique particularly in nonlinear dynamic systems. In control systems, the commonly used neural network models are: Model predictive control, Nonlinear autoregressive-moving average (NARMA) and Model reference control. In each case, System identification is the first step after the development of an accurate dynamic model of the plant, or accurate data collection for systems that cannot be represented in a mathematical model form [16],[17]. In general, system identification is the method in
8
which a neural network model is trained to represent the feedforward dynamics of the plant. The predicted error between the plant model’s output and the neural network model’s output is used as the neural network training signal [16]. This is schematically represented in Figure 6 below.
Input
Plant
+ Neural Network Model
Error
Learning Algorithm
Figure 6: Neural Network plant approximation Neural network popularity for non-linear dynamic problems could be attributed to its ability to robustly model a system from raw or experimental data. This methodology has been applied successfully in the modelling and control of nonlinear dynamic systems, using the multi-layer perceptron approximator [11]. A hybrid control system of recurrent neural network (RNN) and a PID has been proposed by [11] for application in anti-lock braking system. The simulations on dry asphalt and icy roads were successfully conducted with good results. Parameters for the adaptation laws were derived using a Lyapunov function [11] to ensure the stability of the system. A more recent work in this field is by Pedro et-al [18], in this work, the proposed neural network based feedback linearization control method is known as NARMA L2 (Non-linear Autoregressive Moving Average). The main objective was to achieve maximum friction coefficient at optimal slip ratio, leading to a shorter stopping distance. This was done in comparison with PID control method. The ABS plant was in the form;
y (k + d ) = f [ y (k ), y (k − 1),..., y ( k − na + 1), u ( k ), u ( k − 1),..., u (k − nb + 1) ] ... + g[ y (k ), y (k − 1),..., y (k − na + 1), u (k ), u ( k − 1),..., u ( k − nb + 1)]u ( k )
(5)
Where f is a nonlinear function, na is the number of past outputs, nb is the number of past inputs, and d is the system delay. The controller was of the form:
9
u (k + 1) = { yr ( k + d ) − f [ y (k ),..., y (k − n + 1), u (k ),..., u ( k − n + 1)]}
(6)
× g[ y ( k ),..., y ( k − n + 1), u ( k ),..., u ( k − n + 1)]−1
of 30 m on dry s asphalt ( µ H = 0.9 and λ = 0.25 ) . Both the PID and NARMA L2 achieved a stopping time of Simulation
was
conducted
from
an
initial
vehicle
speed
about 3.2sec at a distance of about 43m . However, the NARMA L2 controller achieved these results with less controller effort about 7 times less than that of the PID; this demonstrated the superiority of the NARMA L2 over the PID control method. Both controllers performed much better than commercially available ABS with respect to control effort and stopping distance.
3.2.5 Hybrid ABS Controllers In order to compensate for the shortcomings of various ABS controller designs, hybrid controllers seem to be the way out. There are some proposals in the literature [19 &20]. By comparing the performances of four different control methods; threshold control, PID control, variable structure control and fuzzy logic control Jun [19] came to the conclusion that it is difficult for any single control method to provide optimal control, accuracy and robustness under all kinds of braking conditions. The quest for hybrid systems has been an area of focus by researchers, for example Assadian [20] investigated a mixed H ∞ and fuzzy logic controller. In the study, simulations provided showed that using fuzzy logic mapping to vary the commanded slip value based on the vehicle deceleration input provides optimal results with H ∞ as the main controller or regulator of the torque.
4
Summary
This paper reviewed current research trend for future ABS controllers; the following were examined; PID, Sliding mode, Fuzzy logic and Neural network methods. These methods were selected due to their popularity amongst researches. The PID control method has the advantages of accuracy and ease of tuning, however, the PID control method has the problem of robustness. There have been attempts to improve on this short-coming by introducing the so-called ‘Nonlinear PID’ (NPID) but not much has been done in this direction to warrant proposing it as a solution to the problem of robustness. More investigation is required on NPID. The introduction of the sliding mode controller seems to have solved the problems of the PID controller, by providing the required robustness and capability to track the desired slip accurately. However, a saturation problem seems to have been encountered. The introduction of a saturation function to tackle the chattering problem by some researchers [12] has led to the introduction of steady state error. Therefore the advantage of accuracy seems to have been compromised.
10
Next, is the ‘Fuzzy logic controller’ and from the name it may suggest a controller that is not precise as against a more precise one. An average person would rather want to have a more precise ABS controller rather than driving around with some kind of ‘fuzzy’ anti-lock braking system. But this control method has a lot of advantages and seems to provide solutions to most of the problems encountered with PID and SMC. One of its greatest strengths is definitely its robustness to handle un-modelled vehicle dynamics and external disturbances. Its major disadvantage however, is accuracy and cost of implementation. Neural network is relatively new to the world of ABS control, but its ability to train itself to adapt to various operating conditions as well as un-modelled vehicle dynamics has exhibited great potentials. In comparison with PID, the presenters of this paper have shown that it could improve on the control effort considerably [18]. However, more investigation is on-going on using different neural network model structures.
5
Conclusions
In conclusion, in order to achieve accuracy, stability and robustness, model based designs would have to develop models in several degrees of freedom to capture as much as possible the dynamics involved. This will consequently lead to a complex system and might introduce several other problems. One example of such a problem will be the time it would take to get the controller tuned. It will equally place more demand on the hardware in terms of sampling time and memory requirement. On the other hand, quasi mathematical model based systems like the fuzzy logic and neural network seems to provide the needed robustness with respect to un-modelled dynamics, but disadvantaged on accuracy. In the case of fuzzy solutions, it will equally be difficult to try to develop logic rules for all manoeuvring scenarios. The findings of this investigation therefore shows that for the development of ABS controller, for the future brake by wire vehicles, a hybrid controller incorporating modelled and fuzzy controller methodologies should be investigated and adopted.
11
References S. Solyom ‘Synthesis of a Model-based tyre Slip Controller’. PhD Thesis. [1] Department of Automatic Control, Lund Institute of Technology, Lund Sweden. 2002. [2] K. Dietsche & M. Klingebiel, ‘Automotive Handbook’ 7th Edition, Robert Bosch GmbH, Plochingen, July 2007 pp 820 -849. Wellstead P.E and Pettit, N.B.O.L. (1997) ‘Analysis and redesign of antilock brake [3] system controller’ IEEE Proc. Control Theory Appl., Vol. 144, No. 5, pp 413-425. [4] D. K. Yoo, ‘Model based wheel slip control via constrained optimal algorithm’ M.Sc Thesis, School of Electrical and Computer Engineering, RMIT University, 2006. [5] E. Bakker, H.B. Pacejka and L. Lidner , ‘A New Tyre Model with an Application in Vehicle Dynamics Studies,’ SAE 890087, 1989 pp.83-95, 1989. S. John and J. Pedro ‘Review of Tyre/Road Friction Coefficient Estimation for ABS [6] Controller Design’ Fifth South African Conference on Computational and Applied Mechanics , 2006, pp 432 - 440 [7] J. Svendenius, ‘Tyre models for use in braking applications’ PhD Thesis. Department of Automatic Control, Lund Institute of Technology, Lund Sweden. 2003. [8] P. Yoon, H. Kang, I. Hwang, K. Huh and D. Hong, ‘Braking Status Monitoring for Brake-by-Wire Systems’, SAE Technical series No. 2004-01-0259, SAE World Congress, Detroit, Michigan, 2004. F. Jiang and Z. Gao, ‘An application of nonlinear PID control to a class of truck ABS [9] problems’ Proceedings of the 40th IEEE conference on decision and control, 2001, pp 516 521 [10] L. Austin and D. Morrey, ‘Recent advances in antilock braking systems and traction control systems’ Proceedings Institute of Mechanical Engineers, UK, Vol. 214, Part D, 2000, pp. 625 – 638. [11] C.M. Lin and C.F Hsu “Neural-Network Hybrid Control for Antilock Braking Systems” IEEE Trans. On Neural Networks, Vol.14, No. 2, 2003, pp 351 – 359. [12] K.R. Buckholtz, ‘Reference input wheel slip tracking using sliding mode control’, SAE Technical series No. 2002-01-0301, SAE World Congress, Detroit, Michigan, March, 2002. [13] F. Yu, J. Z. Feng and J. Li, ‘A fuzzy logic controller design for vehicle ABS with a on-line optimized target wheel slip ratio’ International Journal of Automotive Technology, 2002, Vol. 3, No. 4, pp165 – 170.
12
[14] R. Klein, ‘Antilock-Braking System and Vehicle Speed Estimation Using Fuzzy Logic’ 1st Embedded Computing Conference, October 1996, Paris. [15] C. V. Altrock, ‘Fuzzy logic in automotive engineering’, The computer applications journal, Circuit celler ink, Issue 88, 1997 [16] M.T. Hagan and H.B. Demuth ‘An Introduction to the use of Neural Networks in Control Systems,’ Int. Journal, Robust Nonlinear Control 2002; Vol. 12: pp 959 - 985. [17] M. Norgaard, O. Ravn, N.K. Poulsen and L.K. Hansen ‘Neural Networks for Modelling and Control of Dynamic Systems’- A Practitioner’s Handbook, Springer-Verlag London Limited, 2000. [18] J.O.Pedro, O.T.C. Nyandoro and S. John ‘Neural Network Based Feedback Linearisation Slip Control of an Anti-lock Braking System’- accepted conference paper , Asian Control Conference ASCC09, China 2009. [19] C. Jun, ‘The study of ABS control system with different control methods’ Proc. Of the 4th International Symposium on Advanced Vehicle Control, Nagoya, Japan 1998 [20] F. Assadian, ‘Mixed H ∞ and fuzzy logic controllers for the automobile ABS, SAE Technical paper series 2001-01-0594, World congress Detroit Michigan, March 2001.
13
