Int. J. Vehicle Systems Modelling and Testing, Vol. 2, No. 4, 2007 411 Modular design and testing for anti-lock brake actuation and control using a scaled vehicle system Chinmaya B. Patil and Raul G. Longoria* Mechanical Engineering Department, The University of Texas at Austin, University Station, C2200, Austin, Texas 78712-0292, USA E-mail: chinmaya@mail.utexas.edu E-mail: r.longoria@mail.utexas.edu *Corresponding author Abstract: A unique decoupling feature in frictional disk brake mechanisms, derived through kinematic analysis, enables modularised design of an Anti-lock Braking System (ABS) into a sliding mode system that specifies reference brake torque and a tracking brake actuator controller. Modelling of brake actuation, vehicle dynamics, and control design are described for a scaled vehicle system. The overall control scheme is evaluated by hardware-in-theloop testing of the electromechanical brake system, and experimental results for two braking scenarios illustrate the benefits of the modular control design scheme and its impact on practical hardware-in-the-loop implementation. Keywords: anti-lock braking; hardware-in-the-loop; brake actuation. Reference to this paper should be made as follows: Patil, C.B. and Longoria, R.G. (2007) Modular design and testing for anti-lock brake actuation and control using a scaled vehicle system, Int. J. Vehicle Systems Modelling and Testing, Vol. 2, No. 4, pp.411 427. Biographical notes: Chinmaya Baburao Patil is a Doctoral Candidate in Mechanical Engineering at The University of Texas at Austin. He received the Master of Science Degree in August 2003 under the supervision of Dr. Raul G. Longoria, also in Mechanical Engineering. He graduated with the Bachelor of Engineering Degree from the Karnataka Regional Engineering College (now, National Institute of Technology) Surathkal, in 2000, receiving a Gold Medal from the Mangalore University in the discipline of Mechanical Engineering. His current research interests include modelling, design and control of dynamics systems in the presence of uncertainty. Raul G. Longoria received the BSME and PhD in Mechanical Engineering from the University of Texas at Austin in 1985 and 1989, respectively, and is currently Associate Professor at The University of Texas at Austin. He is a registered Professional Engineer in the State of Texas, with research and teaching emphasis in dynamic system modelling and testing and vehicle system dynamics and controls. Current research and development projects focus on ground robotics evaluation and on medical device design/development. He received a 2001 Ralph R. Teetor Educational Award from the Society of Automotive Engineers (SAE). Copyright 2007 Inderscience Enterprises Ltd.
412 C.B. Patil and R.G. Longoria 1 Introduction Antilock braking systems are a standard component of vehicle safety systems on modern road vehicles. A principal requirement of an ABS is to prevent wheel lock-up during braking regardless of road conditions, thereby maintaining steering response and yaw stability (Bauer, 1999). ABS seeks to extract as much traction from the tire/pavement interaction as possible, relying on a closed loop control system to modulate brake torque applied to the wheels (Wong, 2001). The nonlinear force interaction between the tire and pavement depends on many factors, including normal load on the contact patch, tread characteristics, vehicle speed, and other disturbances induced by road surfaces characterised by uncertainty and variability (e.g., presence of water, etc.) (Kulakowski and Chi, 1992). These circumstances can make the design and tuning of an ABS control system particularly challenging. Many different ABS control schemes have been proposed in the literature, including nonlinear PID (Jiang and Gao, 2001), sliding mode (Unsal and Kachroo, 1999; Will et al., 1998; Choi and Cho, 2001), adaptive control (Voit et al., 1995), neural networks (Lee and Zak, 2002) and fuzzy logic (Klein and Eichfeld, 1996). In order to ensure reliability, these controllers have to be rigorously tested in a wide variety of driving conditions. Control prototyping and hardware-in-the-loop testing plays a significant role in the early stages of the control design and testing. This paper describes a dynamic systems approach for modular design of the brake actuation and control subsystems of an ABS, and hardware-in-the-loop testing of the controllers using a one-fifth scaled test vehicle setup. The modular approach is enabled due to the decoupling of the brake actuator dynamics from that of the wheel dynamics in a vehicle equipped with disk brake system. This decoupling is highly desirable as a basis for designing an ABS system as a cascade of two closed-loop control systems, a high-level vehicle controller and a low-level brake actuator controller, as illustrated in Figure 1. The implied modularisation of the ABS control system design is shown to have several significant advantages. Firstly, the design of the high-level vehicle controller need not include the dynamics of the brake actuator, and is thus simplified by virtue of the reduced complexity of the plant model. This can be important for implementation of advanced control algorithms. Secondly, the decoupled dynamics enables a simplified hardware-in-the-loop implementation of the ABS system. With the brake actuator as the hardware component, and by including the critical interaction between the tire and the road surface in software, performance of the brake actuator system under a variety of braking scenarios can be quickly evaluated early on in the design stage which is valuable in the development of the ABS system. Finally, since any modifications to the brake actuator design will have no effect on the high-level controller, and vice-versa, many different control algorithms can be tested with different brake actuator designs with minimal modifications. This adds much value to the ABS test setup. Figure 1 Block diagram of the modular ABS control design
Modular design and testing for anti-lock brake actuation and control 413 The paper is organised as follows. The scaled vehicle test setup is briefly described, followed by kinematic and dynamic modelling of the brake actuator system. Design of a compensator to improve the bandwidth of the brake actuator is presented, followed by vehicle modelling for design of an antilock braking sliding mode controller. The details of hardware-in-the-loop implementation of the ABS controller are presented, and the results of controller performance testing for two panic braking scenarios are described. 2 Scaled vehicle test setup description Scaled vehicles have been used to investigate various vehicle control systems performance, including vehicle stability control (Brennan and Alleyne, 2000), automated highway control systems (Kachroo et al., 1995), etc. Figure 2 shows the one-fifth scale test vehicle used in this study for demonstrating antilock-brake system control design and operation. The vehicle includes encoders to measure wheel speeds, and an electromechanical brake system on the two front wheels. The vehicle is part of a test setup that includes a National Instruments PXI real-time controller, with requisite counter/timer(s) and general purpose Data Acquisition (DAQ) cards for sensing and control. Communication between the vehicle and the real-time controller takes place over an umbilical cable, which provides power to the electromechanical brake actuator system, and signals from the encoders and to the actuator system. The test platform is more fully described by Patil (2003). A description and modelling of the electromechanical brake actuator system is provided in the next section. Figure 2 One-fifth scale test vehicle, with electromechanical disk brakes 3 Brake actuator system modelling The test vehicle features electromechanically-actuated front disk brakes illustrated schematically in Figure 3. The DC motor (a modified RC-type servo) is operated by a current amplifier driven by a computer-generated voltage signal. A cable-lever-cam mechanism transforms the motor torque into the braking force at the brake pads. The floating brake pad forces the brake disk (rotationally coupled to the wheel) against a fixed brake pad. The return spring keeps the two brake pads disengaged when no brake
414 C.B. Patil and R.G. Longoria force is applied. The force induced by the brake pads directly modulates the effective braking torque applied to rotating disk/wheel system. Figure 3 Schematic representation of the brake system 3.1 Kinematic modelling and demonstration of decoupling The frictional contact between the brake pads and the disk contribute to the decoupling of the dynamics of the wheel and the brake actuator. In order to verify the decoupling, it is sufficient to demonstrate that the velocity of the brake pad is kinematically decoupled from that of the wheel. This is discussed here. A schematic representation of a wheel with a brake disk mounted on its axle is shown in Figure 4. For clarity the brake pads are not shown, but the point of application of the average brake force on the disk is shown as P. A fixed reference frame OXYZ is chosen with the origin O at the centre of the disk, the Z-axis aligned with the wheel axle, with the X and Y axes lying in the plane of the wheel. The wheel and the disk are rotating about the Z-axis with angular velocity, ω. An intermediate reference frame OX D Y D Z D is fixed on to the disk with point O as its origin, the Z D axis normal to the plane of the disk, with the X D and Y D axes in the plane of the disk. The Z D axis makes an arbitrary angle θ with the Z-axis of the fixed reference frame (i.e., the wheel and the brake disk are not parallel to each other). A third reference frame PX P Y P Z P is fixed on to the brake pads at point P, and is always aligned with the fixed reference frame. The distance OP represents the effective radius of the brake disk, denoted by R b. In order to establish the decoupled nature of the dynamics of the disk brake and the wheel, an expression for the velocity of the brake pad (point P) is obtained in terms of the wheel angular velocity and is shown to be independent of it when the brake disk and the wheel are aligned parallel to each other. The position and velocity vectors of point P in OX D Y D Z D reference frame are given by, Rb cos( γ) Rb γ { sin( γ)} r R sin( γ) =, V = R γ {cos( γ)}. (1) 0 0 D P b D P b
Modular design and testing for anti-lock brake actuation and control 415 Figure 4 Kinematics of disk brake mechanism It is clear that γ = DωP, the angular velocity of frame PX P Y P Z P with respect to frame OX D Y D Z D. Using the relation, OωP = DωP + OωD, and since O ω P is a null vector, DωP = OωD, which implies that γ = ω. Now, the velocity vector of point P in the fixed reference frame OXYZ is be obtained as, OVP = VO + DVP + OωD DrP. (2) Here, V O is a null vector, D r P and D V P are given by equation (1), and OωD, which represents the angular velocity of OX D Y D Z D with respect to OXYZ, is given by, ω sin( θ) cos{ φ} ωd = ω sin( θ) sin( φ). ω cos( θ) O All the vectors are expressed in terms of unit vectors in the OX D Y D Z D reference frame. Substituting in equation (2) and simplifying yields the velocity of the brake pads as, V Rb ω sin( γ){1 cos( θ)} = R ω { cos( γ)} {1 cos( θ)}. R b ω {sin( γ) cos( φ) cos( γ) sin( φ)} sin( θ ) O P b Substituting the value of angle θ as zero, which is the nominal value of the disk brake system design, in equation (4) reduces each component of the velocity vector O V P to zero. Thus, the velocity of the brake pad is zero, and is independent of the velocity of the wheel under normal operation. As such, the dynamics of the disk brake actuation system are decoupled from those of the brake-disk/wheel. Another approach to demonstrate the decoupled dynamics is to use spatial kinematics and 6-dimensional vectors or screw vectors (Davidson and Hunt, 2004) to represent the brake actuating force and wheel velocity. It can be shown that the two are reciprocal to each other, thus indicating that the power transmitted by the brake force itself to the (3) (4)
416 C.B. Patil and R.G. Longoria wheel is zero. It is the frictional contact between the two that does the work required to slow the wheel velocity. 3.2 Dynamic modelling The brake actuator dynamics relating the force induced by the brake pad (or equivalently the applied braking torque) to the control voltage command are of primary interest. Critical metrics such as the gain, response time, etc., directly influence the ABS performance. Experimental modelling based on frequency response testing was carried out on the brake actuator system, as described in the following. To estimate an input-output relationship for the brake actuation system, a force sensor was mounted flush with the brake pad to measure the dynamic brake force. Swept-sine frequency response testing was conducted (changes in amplitude showed insignificant changes for the purposes of this application). The frequency of the input voltage signal was varied over the range of (1.25 rad/s, 62.5 rad/s) in discrete steps of 1.25 rad/s. Beyond 62.5 rad/s, the signal-to-noise ratio diminished rapidly. The magnitude of the output force was found to vary linearly with the input voltage up until 5 V, beyond which saturation occurred. During actual operation, the brakes were never operated in the saturation region, as a level of 3.5 V was sufficient to generate enough braking torque to completely lock the wheels. The signal generation and DAQ were carried out at a sampling rate of 1 khz (sufficiently high for the application). Figure 5 shows graphs of the input and output signals for two input frequency values. Figure 5 Input and output signals from frequency response testing of brake actuator testing The magnitude and phase shift information was extracted from the input sinusoidal voltage signal applied to the motor and the measured output force sensor voltage signal, to obtain an approximate linear frequency response function model of the electromechanical brake system dynamics. The braking torque generated by the actuator is determined from the force at the pad (given an estimated brake pad coefficient of friction, µ b, and effective radius, R b, for force application; e.g., T b = R b µ b F b ). It was found that the cable-lever-cam transmission mechanism of the brake actuator system exhibited significant dead-zone and saturation nonlinearities. By using a describing function technique (Ogata, 1990) in conjunction with frequency response testing, a linear approximation to the brake actuator system was formulated. This model takes the form of a transfer function relating output brake torque, T b, to the input voltage, V in,
Modular design and testing for anti-lock brake actuation and control 417 T () s 778. 4 Gp () s = =. V s s s s b 2 in ( ) (0. 2 + 1)( + 35. 3 + 555. 2) (5) From this model, the system bandwidth for the existing brake actuation system is approximately 22.5 rad/s. It is noted here that, a physics-based model of the brake actuator system also revealed the third order dynamics evident in equation (5) (Patil, 2003). For the sake of brevity, details of the physical modelling are not included here. 3.3 Compensator design A compensator is designed to cancel the dominant brake system pole (at s = 5), and to provide a sufficiently fast response while ensuring that the brake actuator does not saturate; a suitable compensator transfer function was found as, 0125. s + 1 Gc () s = 3. 001. s + 1 The Bode plot for the resulting closed loop brake actuation system including the compensator indicates a bandwidth of 55 rad/s as shown in Figure 6. It was determined that further improvement in the brake system bandwidth would require physical redesign of the cable-lever-cam transmission mechanism. In the following section, a demonstration is presented of the effectiveness of a controlled ABS using this compensated braking actuation system. (6) Figure 6 Closed-loop bode plot of brake system with compensator
418 C.B. Patil and R.G. Longoria 4 Vehicle modelling In order to study the behaviour of the vehicle during simultaneous braking and turning, a 2-D bicycle model (Wong, 2001) encompassing both the longitudinal and the lateral dynamics of the vehicle is used in this study. Figure 7 shows the schematic of the bicycle model. For the condition of braking, the model equations are given by, M V x = Fxf cos( δ) Fyf sin( δ), (7) M V y = Fyf cos( δ) + Fyr Fxf sin( δ) ωz M Vx (8) where, V x is the longitudinal velocity, V y is the lateral velocity, ω z is the yaw velocity, and δ is the steering angle measured at the wheels. The symbol F represents forces on the wheels due to tire-surface interaction, with the subscripts having the following meaning: x is along the longitudinal direction, y is along the lateral direction, f is the front wheel and r is the rear wheel. The weight transfer between the front and the rear axles due to deceleration while braking, the aerodynamic drag effects, and the rolling resistance on the wheels were not significant in the scaled vehicle test setup. Figure 7 Bicycle model schematic The rotational dynamics of the front wheels subjected to braking torque T b is given by, J ω = F R T (9) xf b where, ω is the angular wheel speed, J is the rotational inertia of the front wheels, and R is the wheel radius. The longitudinal and lateral forces acting on the wheels from the road surface depend on the longitudinal wheel slip, and are modelled as,
Modular design and testing for anti-lock brake actuation and control 419 F = N µ ( λ) x F = N αλ ( ) y (10) where, N represents the normal load on the wheels, µ(λ) is the longitudinal coefficient of friction, and α(λ) is the lateral coefficient of friction between the wheel and the road surface. The longitudinal wheel slip is defined to include the effect of the steering angle input as, Vx R ω cos( δ) λ =. (11) V x Note that because a real-time mode is used here to estimate slip, it is not necessary to utilise the type of real-time estimation techniques demonstrated in recent studies literature (Wang et al., 2004). Also, the values of the actual system parameters have been determined for the scaled vehicle test setup, and are summarised in Table 1 (Patil, 2003). These values are used in the hardware-in-the-loop implementation of ABS control. The design of this control is described in Section 5. Table 1 Vehicle parameters Parameter Description Value Units M Mass of the vehicle 8.8 kg L Wheel base 0.460 m Wf Weight on front axle 36.3 N Wr Weight on rear axle 50 N Jz Moment of inertia of vehicle about Z-axis 0.237 kg-m 2 J Moment of inertia of individual wheel 0.001 kg-m 2 R Wheel radius 0.061 m 5 ABS control design The requirement of an ABS controller is to maximise the traction available from the road surface, thereby ensuring minimum stopping distance with stable steering operation. In order to guarantee good performance in the presence of substantial uncertainty in road surface conditions, vehicle occupancy, tire tread conditions etc., the ABS control must be robust. Sliding mode control is a well-known nonlinear control scheme that provides robustness to parametric uncertainties (Slotine and Li, 1991), motivating its selection for ABS control in this study. The sliding mode controller is designed for a simplified model of vehicle dynamics by neglecting the influence of steering angle. This is acceptable since the lateral tire forces induced during turning will improve the braking performance as long as they do not lock-up when the brake-torque is applied. With zero steering angle input, the longitudinal dynamics of the vehicle and the wheel can be expressed as, M V = N µλ ( ) (12) J ω = N µ ( λ) R Tb
420 C.B. Patil and R.G. Longoria and the wheel slip equation reduces to, V R ω λ =. (13) V The system model is reformulated using dimensionless parameters as, x = π µ ( λ) 1 2 L x = π π µ ( λ) u J L (14) x λ = x1 2 1, (15) where, x 1 = (V/g), x 2 = (ω R)/g, π L = (L r /L), π J = (1/2 M R 2 /J), u = T b R/( g J ) with g being the acceleration due to gravity. To assist in controller formulation, a functional approximation is assumed for the nonlinear relationship between the longitudinal friction coefficient between the wheel and road surface, µ, and the wheel slip, λ, as (Jiang and Gao, 2001), λ µλ ( ) = 2 µ p λp, 2 2 λp + λ where λ p is the wheel slip value at which the peak friction µ p occurs for the road surface. Figure 8 illustrates that this approximation corresponds well to µ λ data curves for two different surfaces obtained from literature (Wong, 2001) in the low slip region. Figure 8 Plot of coefficient of friction vs. wheel slip for typical surfaces (Wong, 2001) with functional approximation of equation (16) (16)
Modular design and testing for anti-lock brake actuation and control 421 In the present paper, in order to achieve the goal of maximising the road surface traction, the sliding mode controller is designed to maintain the longitudinal wheel slip λ at a value of 0.2, which defines a region where maximum friction coefficient µ occurs for nominal conditions in the scaled vehicle laboratory (based on measured µ λ curves (Patil, 2003)). The sliding surface for the ABS controller is chosen as, s = λ λ d, (17) where λ d is the desired (target) value for the wheel slip, and is assumed to be a constant. The sliding surface is of first order because the control input u appears in the first derivative of the output, λ; i.e., the relative order of the output is 1 (Slotine and Li, 1991). If the dynamics of the brake actuator were included in the design of the sliding mode controller (which would be required if the dynamics of the actuator and that of the wheel were coupled), the order of the sliding surface would be higher than 1, which would significantly complicate the design of the controller. The desired dynamics of the sliding surface is chosen as, s = η sat( s) η sgn( s) if s Φ = η ( s Φ ) otherwise, where η is a constant controller gain and sgn( ) is the signum function. The sat( ) function provides a mechanism to reduce chattering in the sliding mode control (Slotine and Li, 1991). The expression for the control input u is determined by substituting equations (14) (17) in equation (18), as, u = ˆ π ˆ µ ( ˆ λ){(1 ˆ λ) + ˆ π } xˆ η sat( s), (19) L J 1 where terms with ^ represent best estimates of the corresponding parameters considering uncertainties in the system. The value of the control gain η is estimated from Lyapunov analysis to ensure a stable attractive sliding surface (Slotine and Li, 1991). The actual value of the gain is chosen via simulations. (18) 6 Hardware-in-the-loop implementation The ABS control system is evaluated in a hardware-in-the-loop setting, with the physical brake actuator system, as shown in schematic in Figure 9. The vehicle bicycle model and wheel dynamics, the sliding mode controller and the brake system compensator are all implemented in software. The simulation code is developed using MATLAB/Simulink, compiled with MATLAB Real-Time Workshop, and used as a dynamically linked library in a test program built in LabVIEW. The test program includes DAQ code built around the vehicle dynamics model and the controllers. The entire program is transferred to a PXI real-time controller via TCP/IP network, and is executed from a host computer interface program inside LabVIEW. A control loop rate of 1 k samples per second was achieved by this approach.
422 Figure 9 C.B. Patil and R.G. Longoria Schematic of hardware-in-the-loop testing of ABS controller with the physical brake actuator During a typical test, the vehicle model states are initialised with values corresponding to a pre-defined initial vehicle velocity and wheel slip, and the braking action is started. The sliding mode controller decides the brake torque to be applied depending upon the actual and the desired wheel slip values. The compensator compares the desired brake torque with the torque applied in the previous sample time, and issues a control voltage signal to the DC motor amplifier driving circuit. A load cell measures the force at the brake pads, from which the actual applied brake torque is inferred and applied to the vehicle model. The HIL experimental setup is shown in Figure 10. Figure 10 Experimental setup for hardware-in-the-loop testing of ABS control with the physical brake actuator
Modular design and testing for anti-lock brake actuation and control 423 The current implementation is very different from the hardware-in-the-loop implementation of ABS systems found in literature (Ming-Chin and Ming-Chang, 2003; Kachroo and Ozbay, 1997), where brakes are applied to a wheel which is being driven by a drum (representing the vehicle) by friction contact which models the wheel-road surface interaction. Including the dynamics of the wheel in software, due to the decoupled nature of the brake actuator and wheel dynamics, greatly simplifies the test setup. Also, advanced models can be used to implement the wheel-road surface friction interaction (Canudas-de-Wit and Tsiotras, 1999) in software, thereby making the test setup more flexible with regards to evaluation of the ABS controller performance in different road surface conditions. 7 Experimental results Figures 11 and 12 show the results of hardware-in-the-loop testing of the modular ABS controller in the two test cases, namely, braking in straight line with road surface transition braking while steering. Figure 11 Hardware-in-the-loop testing of ABS with road surface transition at t = 0.75 s (peak friction dropping from 0.75 to 0.45)
424 C.B. Patil and R.G. Longoria Figure 12 Hardware-in-the-loop testing of ABS with steering The plots of the vehicle and peripheral wheel velocities, the wheel slip, and the brake torque are shown. For both the test cases, the initial vehicle velocity is chosen as 4.0 m/s (approximately corresponds to 7 body-lengths of the scaled vehicle per second, which translates to about 65 mph for a full sized vehicle) and initial wheel speed corresponding to wheel slip of 0.1. This is reasonable since ABS kicks in only under heavy braking when the value of slip increases much more than the nominal wheel slip value of 0.03 (3%) under normal driving conditions (Wong, 2001). The value chosen has no impact on the control performance, since the output of the sliding mode controller remains the same until the error in the wheel slip from the desired value falls within the saturation zone. Antilock braking is initiated at the start of the simulation and stopped when the vehicle speed reaches 1 m/s. The wheel and road surface interaction is modelled as a one dimensional look-up-table between the friction coefficient and the wheel slip (µ λ curve). In the straight line braking test case, a sudden transition in the road surface is initiated at time t = 0.75 s from the start of the test, with the peak friction coefficient of the surface dropping from 0.75 to 0.45. The sliding mode controller gain η is set at 75. The desired wheel slip is chosen as 0.2, and the sliding surface saturation function parameter φ is set at 0.05. As seen in Figure 11, the ABS controller maintains the wheel slip around the desired value even with the sudden change in the road surface and prevents wheel lock-up. The limited bandwidth of the electromechanical brake actuator on the scaled vehicle causes the sliding mode controller to operate in nearly bang-bang manner.
Modular design and testing for anti-lock brake actuation and control 425 Figure 12 shows the results of hardware-in-the-loop testing of ABS controller with a constant steering input of 8.5 (measured at the wheels) applied to the simulated bicycle model of the vehicle. The transition in the road surface is turned off, with the peak friction coefficient remaining at 0.75 during the entire test run (evident in the reduced time to slow the vehicle to 1 m/s from 1.6 s to 1.4 s). The desired wheel slip and controller gain values are not changed. Again, the sliding mode controller works in a switching manner, but maintains the wheel slip close to the desired value. The experimental results indicate that the brake actuator does not track the desired brake torque satisfactorily. This is due to overestimation of the brake actuator system bandwidth by the linearised approximate model obtained from the frequency response testing and describing function approach. A more detailed modelling of the system nonlinearities will enable better estimation of the system bandwidth, and therefore better tuning of the sliding mode controller. But more importantly, the results serve to show that different ABS test cases can be evaluated without any change to the hardware-in-the-loop test setup. Although it is not illustrated here, it is possible to conduct a batch experiment of alternate ABS control schemes with many different driving scenarios all in one test run, thereby making it possible to evaluate the performance of the different controllers and the brake actuator quickly and efficiently. This could potentially enable proper tuning of the ABS controller and the brake actuator via more economical bench-testing before it is fully evaluated in a prototype vehicle. 8 Conclusions The design and hardware-in-the-loop implementation of an ABS control for a one-fifth scale vehicle has been described in detail. The ABS controller is organised into two functional modules: a sliding mode controller which generates the desired brake torque to be applied based on the vehicle and the wheel dynamics, and a compensator for the brake actuation system to enable it to track a reference torque. It is argued that this is possible because the frictional interaction between the brake pads and the brake disk in disk brake mechanisms decouples the dynamics of the brake actuator from that of the wheel, which is verified by kinematical analysis of the disk brake mechanism. The modular design of the ABS control is shown to simplify the design of the sliding mode controller, due to the reduced order of the plant dynamics. Another significant benefit is seen in the HIL testing of the controller with the physical brake actuator. By implementing the wheel and vehicle dynamics, and the wheel-road surface interaction in software along with the two controllers, the antilock braking performance of the actuator and the control algorithm can be evaluated for emergency braking on a variety of road surfaces and driving conditions quickly, without any changes to the test setup. Hardware-in-the-loop test results in two panic braking scenarios are presented, braking in straight-line with surface change braking while turning. Although the ABS controller is unable to perfectly regulate the wheel slip at the desired value because of the bang-bang type operation (caused by the limited brake actuator bandwidth), the test results validate the modular design of the ABS control and its hardware-in-the-loop implementation.
426 C.B. Patil and R.G. Longoria Acknowledgements Support from National Instruments Corporation is gratefully acknowledged. This project has also been partially supported by a grant from the National Science Foundation for the Industry/University Cooperative Research Center for Virtual Proving Ground Simulation: Mechanical and Electromechanical Systems (Grant No. EEC-9706083). References Bauer, H. (1999) Driving Safety Systems, 2nd ed., Robert Bosch, GmBH., Stuttgart. Brennan, S. and Alleyne, A. (2000) The Illinois roadway simulator: a mechatronic testbed for vehicle dynamics and control, IEEE/ASME Transactions on Mechatronics, Vol. 5, No. 4, pp.349 359. Canudas-de-Wit, C. and Tsiotras, P. (1999) Dynamic friction models for vehicle traction control, 38th IEEE Conference on Decision and Control, Phoenix, AZ, pp.3746 3751. Choi, S. and Cho, D. (2001) Design of nonlinear sliding mode controller with pulse width modulation for vehicular slip ratio control, Vehicle System Dynamics, Vol. 36, No. 1, pp.57 72. Davidson, J.K. and Hunt, K.H. (2004) Robots and Screw Theory, Oxford University Press, New York. Jiang, F. and Gao, Z. (2001) An application of nonlinear PID control to a class of truck ABS problems, Proceedings of the 40th IEEE Conference on Decision and Control, Vol. 1, pp.516 521. Kachroo, P. and Ozbay, K. (1997) Microprocessor controlled small scale vehicles for experiments in automated highway systems, Korean Transport Policy Review, Vol. 4, No. 3, pp.145 178. Kachroo, P., Ozbay, K., Leonard, R. and Unsal, C. (1995) Flexible low-cost automated scaled highway (FLASH) laboratory for studies on automated highway systems, IEEE International Conference on Systems, Man and Cybernetics, Intelligent Systems for the 21st Century, Vol. 1, pp.771 776. Klein, R. and Eichfeld, H. (1996) Antilock braking system and vehicle speed estimation using fuzzy logic, 1st Embedded Computing Conference, October, Paris, France. Kulakowski, B.T. and Chi, M. (1992) Measurement and modeling of truck tire traction characteristics, ASTM STP, Vol. 1164, pp.112 124. Lee, Y. and Zak, S.H. (2002) Designing a genetic neural fuzzy antilock brake system controller, IEEE Transactions on Evolutionary Computation, Vol. 6, No. 2, pp.198 211. Ming-Chin, W. and Ming-Chang, S. (2003) Simulated and experimental study of hydraulic antilock braking system using sliding-mode PWM control, Mechatronics, Vol. 13, pp.331 351. Ogata, K. (1990) Modern Control Engineering, 2nd ed., Prentice-Hall, Englewood Cliffs, NJ. Patil, C.B. (2003) Antilock Brake System Re-design and Control Prototyping using a One-fifth Scale Vehicle Experimental Test-bed, Master s Thesis, Department of Mechanical Engineering, The University of Texas at Austin, Austin, Texas. Slotine, J-J.E. and Li, W. (1991) Applied Nonlinear Control, Prentice-Hall, Englewood Cliffs, NJ. Unsal, C. and Kachroo, P. (1999) Sliding mode measurement feedback control for antilock braking systems, IEEE Transactions on Control Systems Technology, Vol. 7, No. 2, pp.271 281. Voit, M., Chamaillard, Y. and Gissinger, G.L. (1995) Methodology for the design of a new strategy in vehicle braking: simulation and comparison of algorithms, JSAE Review, Vol. 16, No. 2, pp.220 231.
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