Intelligent Active Force Controller for an Anti-lock Brake System Application

Transcription

1 Intelligent Active Force Controller for an Anti-lock Brake System Application MOHAMMED H. AL-MOLA, M. MAILAH, A.H. MUHAIMIN AND M.Y. ABDULLAH Department of System Dynamics and Control Faculty of Mechanical Engineering Universiti Teknologi Malaysia 8131 UTM Johor Bahru, Johor, MALAYSIA Abstract: - Antilock braking systems (ABS) are safety and control devices implemented in ground vehicles that prevent the wheel lock-up during panic braking. The existing ABS controls have the ability to regulate the level of pressure to optimally maintain the wheel slip within the vehicle stability range. However, the ABS shows strong nonlinear characteristics in which the vehicles equipped with the existing controllers can still have a tendency to oversteer and become unstable. In this paper, a new intelligent robust control method based on active force control (AFC) strategy is proposed via a simulation study. It is designed and implemented in a hybrid form by having the AFC loop directly cascaded in series with a fuzzy logic (FL) self-tuning proportional-integral-derivative (PID) control as the outermost loop position control for the effective overall performance. From the results, it is evident that FL-PID with AFC scheme shows faster and better response compared to the classic PID controller for the given loading and operating conditions. The incorporation of the AFC-based scheme into the ABS serves to provide enhanced performance that has great potentials to be implemented in real-time system. Key-Words: -Anti-lock brake system, AFC strategy, fuzzy logic, PID controller 1 Introduction Antilock brake systems (ABS) are common in today s passenger car, and feasible with the availability of low cost sensors and low cost microcomputers. The main components of an ABS are an electronic control unit, a brake force actuator, and wheel speed sensors. The function of an ABS is to prevent wheels from being totally locked during panic braking or braking on slippery road surface. The objective of an ABS is to achieve the shorter stopping distance and maintain a good steering stability during braking. As a mechanical system, the first ABS was developing for airplanes in 1947 [1]. For automotive fields, it was too expensive to design and develop an ABS at that time. In 1954 the first trial for automotive using ABS and was on a limited number which were fitted with an ABS from a French aircraft. In the late 6's, Ford, Chrysler, and Cadillac offered ABS on very few models. These very first systems used analogue computers and vacuum-actuated modulators [2]. At that time, it was not commercially successful [3]. The development of ABS was actually started in the 197s. Mercedes and BMW start to introduce (ECU) electronically-controlled ABS systems and that was in the late 7's. By 1985, Bosch ABS systems have been used by each of Audi, BMW [2]. The unknown parameters of the environment associating the vehicle and nonlinearity characteristics in its performance, made this mechanism as a nonlinear system. Many researchers used control strategies to hold this phenomenon one of them is fuzzy control.the other approach that is proposed in the design of the ABS controller is fuzzy PID control (FLPID) design method which is known as a hybrid control strategy and is the combination of fuzzy control and conventional PID control method. The main advantage of the FLPID is that is used fewer fuzzy rules than FC [4]. Yet another robust control scheme known as active force control (AFC) has emerged and has been shown to be far superior compared to the conventional PID control method in controlling various dynamical systems [5-1]. The principal objective of this study is to propose a hybrid controller, comprising a fuzzy logic with PID controller and a new robust active force controller applied to an ABS. The behaviour of the ABS with classic PID controller is deemed not appropriate, because when the vehicle tries to follow or track the slip ratio, it takes a longer time to reach the reference input slip. To overcome this problem, ISBN:

2 a fuzzy logic controller is designed specifically for tuning the PID gains. This configuration together with the AFC strategy provides a means of robust control so that the overall performance in emergency braking manoeuvre is considerably improved. 2 System Dynamics Fig. 1 shows the road coefficient of adhesions for various road conditions while Fig. 2 illustrates a free body diagram for a single wheel model. Based on this diagram, a simplified longitudinal vehicle model considering the rotational dynamics of the wheel and the linear vehicle dynamic can be accordingly derived. Fig. 1: The road conditions [11] Rotational dynamic of the wheel The rotational dynamics of the wheel is modeled by the following equation: J ω T R F R F 7 To simplify the model, the relationship between caliper pressure and the braking torque is assumed to be linear: 8 All the variables and parameters used in equations (1)-(8) are described as follows: : the total mass of vehicle (kg), N : normal load of the tire (N), ω: wheel angular speed (rad/s), V: vehicle linear speed (m/s), :Aerodynamic drag force (N), : Rolling resistance force(n), : longitudinal weight transfer load due to braking(n), : brake torque (N/m), : radius of the wheel, : Moment of inertia of wheel (kg. m ), : wheel base (m), ρ: Air density (kg/m ), : Center of gravity height (m), : Aerodynamic drag coefficient, : frontal area of the vehicle (m ), : specific torque constant, : output hydraulic pressure (kpa), : basic coefficient, : speed effect coefficient, : scale factor between (m/s) and mile per hour (mph), ( =2.237), 3 Controller Design The design of the fuzzy-self tuning PID and AFC schemes are presented. Fig. 2: Dynamic model for the single wheel 2.1 Linear dynamic of the wheel The linear dynamics of the wheel is derived using the standard Newtonian equations of motion and is formulated as follows: Fuzzy Self-Tuning PID Control The proposed fuzzy self-tuning PID control scheme is introduced. It uses the first order Takagi-Sugeno (T-S) fuzzy system as the tuning-tool for each of the PID control modules. In this way, the proposed scheme can be devised for any linear or nonlinear system in a straight forward manner [4]. Three decoupled fuzzy systems constitute the proposed self-tuning system; each corresponds to the individual PID parameters, i.e., K P, K I and K D as described by the following PID controller equation: (9) ISBN:

3 In designing the proposed fuzzy based systems, the error and change in error are initially used as the behavior-recognizers of the closed-loop performance. They are available signals in the closed loop system of the ABS and do not require extra hardware. The self-tuner can be expressed as:,,, 1 The fuzzy module is connected in parallel to the actual PID elements to generate the resultant controller signal as shown in Fig If (e is PB) and (de/dt is ZE) THEN (K P is PB)(K I is PS)(K D is PS) 2. If (e is ZE) and (de/dt is NB) THEN (K P is NS)(K I is PS)(K D is PM) 3. If (e is NB) and (de/dt is ZE) THEN (K P is NB)(K I is PS)(K D is PS) 4. If (e is ZE) and (de/dt is PB) THEN (K P is PS)(K I is PM)(K D is PM) Table 1: The linguistic output values for the linguistic variables, and, de/dt NB ZE PB e K P K I K D K P K I K D K P K I K D NB NB PS PS ZE NS PS PM PS PM PM PB PB PS PS 3.2 Active Force Control Hewit and Burdess (1981) proposed the idea of AFC which is derived from the Newton s second law of motion such as for a rotating mass, we have: 11 Fig. 3: Self-tuning fuzzy PID controller The module is trying to recognize when the corresponding parameter is not properly tuned and then seeks to adjust it to obtain the desired improved performance. A T-S type fuzzy system is used to synthesize each module. A typical rule has the following form: IF x1 IS A AND x2 IS B THEN z1 = f(x1, x2), z2 = f(x1, x2) and z3 = f(x1, x2) Where A and B are fuzzy sets in the antecedent, while z1=f(x1, x2), z2=f(x1, x2) and z3=f(x1, x2) are crisp function in the consequent. With this form, the fuzzy system can be characterized as two-input three-output fuzzy systems. In the proposed selftuner, the inputs, i.e., e and are normalized using three Gaussian membership functions; negative N, zero Z, and positive P so that the four rules constitute the rule base for each module as illustrated in Table 1. In this fuzzy controller, it is obvious that it contains two inputs that correspond to the error and the change of it and three outputs that are directly related to the three PID controller gains. Fuzzy rules have been developed as follows: Where T is the sum of all torques acting on the body, is the moment of inertia, and α is the angular acceleration. The objective of this control scheme is to control the dynamic system in order to ensure the system will remain stable and robust in the presence of known and unknown disturbances. For the ABS that will be embedded with the AFC scheme, the equation of motion becomes: Fig. 4: AFC concept applied to an ABS 12 Where T is the brake torque, Q is the disturbance torque, is the road friction torque, is the wheel radius, J is the moment of inertia of the wheel. Fig. ISBN:

4 3 illustrates the principle of the AFC applied to the ABS. The physical quantities need to be measured directly from the system are the actuating force and the vehicle acceleration which could be done by using some sensing elements. The estimated disturbance torque Q can be computed by the equation: V 13 Where E m is the estimated mass which can be tuned using intelligent method as proposed in this study, V is the vehicle acceleration, R represents the radius of the single wheel and T b is the brake torque. The brake torque is a function of the brake pressure that is generated by the non-linear hydraulic actuator. The aim of this control scheme is to control the dynamic system in order to ensure the system will remain stable and robust in the presence of known and unknown disturbances. In this work, AFC method was applied to ABS via a numerical study and comparison was made to the other closed-loop controllers for benchmarking the proposed system performance. 4 Simulation Study The performance of the proposed AFC-based controller was investigated and the results are compared between the proposed hybrid controller and the self-tuning fuzzy PID controller using MATLAB software. The single wheel parameters used in the simulation study are shown in Table 2. Table 2: Vehicle parameters kg.326 m J 1.7 kg. m.5 m ρ 1.23 kg/m.5 m m g 9.81 m/s It is assumed that vehicle is moving in a straightline at 9 km/h. All tests are run for a 1ms sampling period and the maximum braking torque is limited to 25 Nm. In the first simulation, the fuzzy selftuning PID is experimented and its performance is compared with the classic PID controller in terms of the vehicle speed, stopping distance, single wheel slip ratio and braking torque. Besides the road surface is assumed to be in dry condition. Fig. 5 (a) shows the typical trend in the vehicle and wheel speeds during braking under self-tuning fuzzy PID control scheme. The time response of the braking torque for the three proposed controllers is shown in Fig. 5 (b). It is very evident that the proposed AFCbased strategy produces the fastest response with the intelligent PID trailing very closely. S p e e d ( m /s ) B r a k i n g T o r q u e ( N. m ) Wheel speed Vehicle speed Time (s) (a) 5 PID FLPID FLPID-AFC Time (s) (b) Fig. 5: (a) Vehicle and wheel speed during the braking in dry road condition (b) Braking torque characteristics for the three control schemes S l ip PID FLPID FLPID-AFC (a) ISBN:

5 14 12 S t o p p i n g D i s t a n c e ( m ) PID 2 FLPID FLPID-AFC Time (s) (b) Fig. 6: (a) Wheel slip during braking (b) Stopping distance during the braking in dry road condition It is shown in Fig. 6 (a) that the wheel starts to track the desert slip reference upon initiating the braking process for each of the controller considered after a short period of time. The self-tuning PID and the proposed hybrid AFC controllers are observed to have the faster time response to reach the slip reference as depicted in Table 3, indicating the vehicle produces good stability and steerability. The AFC-based technique is shown to produce the fastest stopping time and least stopping distance (see Fig. 6(b)). Table 3 Stopping distance of the proposed controllers Dry road condition for (9 km/h) ABS controller Distance (m) Time (sec) PID FL-PID FL-PID+AFC Conclusion A self-tuning PID controller has been designed and implemented to the ABS via two different schemes. Initially, a self-tuning PID controller for ABS under dry road condition has been considered in which the PID gains have been appropriately tuned using the fuzzy rules. In the second scheme, a novel hybrid AFC controller has been proposed and compared to the PID controller with fuzzy logic. It is observed that the oscillations in the ABS with hybrid controller are much lesser than that of the conventional PID controller. In addition, it has a much faster response. It thereby implies that the vehicle has adequate lateral stability and good steerability in dry road conditions via the former X: Y: X: Y: 1.46 X: Y: 1.34 controller. Future work may consider the implementation of the proposed AFC-based technique to a real-world ABS application. Acknowledgements The authors would like to gratefully acknowledge the Universiti Teknologi Malaysia (UTM) for their full support of this research through a research university grant (Vote No.: 13J38) References: [1] C. Altrock, Fuzzy Logic Technologies in Automotive Engineering, Wescon 94, Idea/Microelectronics Conference Record, September 27-29, [2] I. Petersen, Wheel Slip Control in ABS Brakes Using Gain Scheduled Optimal Control with Constraints, Norwegian University of Science and Technology: Ph.D. Thesis, 23. [3] P.E. Wellstead, N. Pettit, Analysis and Redesign of an Antilock Brake System Controller, Procs. of the IEE Conference on Control Theory Application, 1997, pp [4] A.B. Sharkawy, Genetic Fuzzy Self-tuning PID Controller for Antilock Braking Systems, Engineering Applications of Artificial Intelligence, Vol. 23, No. 7, 21, pp [5] J.R. Hewit, J.S. Burdess, Fast Dynamic Decoupled Control for Robotics using Active Force Control, Mechanism and Machine Theory, Vol. 16, No. 5, 1981, pp [6] M. Mailah, A Simulation Study on the Intelligent Active Force Control of Robot Arm Using Neural Network, Jurnal Teknologi, Vol. 3, 1999, pp [7] S.B. Hussein, H. Jamaluddin, M. Mailah, A Hybrid Intelligent Active Force Controller for Robot Arms using Evolutionary Neural Networks, Procs. of the IEEE International Conference on Intelligent Systems and Technologies, 2, Kuala Lumpur. [8] G. Priyandoko, M. Mailah, Controller Design for an Active Suspension of a Quarter Car Model Using Fuzzy Logic Active Force Control, Procs. of the 2 nd International Conference on Mechatronics, Kuala Lumpur: 25, pp [9] R. Varatharajoo, C.T. Wooi, M. Mailah, Two Degree-of-freedom Spacecraft Attitude Controller, Advances in Space Research, Vol. 47, No. 4, 211, pp ISBN:

6 [1] M.H. Al-Mola, M. Mailah, S. Kazi, A.H. Muhaimin, M.Y. Abdullah, Robust Active Force Controller for an Automotive Brake System, Procs. of the 3 rd Conference on Intelligent Systems, Modeling and Simulation, Kota Kinabalu, Sabah, 212. [11] F. Tianku, Modeling and Performance Analysis of ABS Systems with Nonlinear Control, Master Thesis, Concordia University, 2. ISBN: