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Compensation Control of Bus Air Brake System in Under-pressure State [Sensors & Transducers (Canada)](Sensors & Transducers (Canada) Via Acquire Media NewsEdge) Abstract: The paper researched on bus driving stability control by yaw moment using differential braking, based on bus dynamic model in under-pressure condition. In the process of yaw moment control, under-pressure compensation control strategy of bus air brake system was proposed, its mathematical model was built and relevant controller was designed. Finally, simulation was carried out and the result shows control effect is good. Copyright © 2014 IFSA Publishing, S. L. Keywords: Differential braking, Driving stability, Under-pressure state, Under-pressure compensation control, Modeling, Simulation. (ProQuest: ... denotes formulae omitted.) 1. Introduction Driving stability is an important part of research field in automotive engineering, driving stability control is a kind of regulation technology against driving attitude and trajectory of the car in a variety of complex driving conditions, in order to ensure the safety, which belongs to vehicle active safety category [1]. Differential braking is one kind of most widely used and successful control methods in the active safety technology field, which imposes different pressure on the each wheel separately by brake system to generate yaw moment in the opposite direction of undesired lateral movement, in order to rectify or partially rectify the undesired movement trend [2]. All the time, the domestic and foreign automobile manufacturers and research departments has been a lot of research and made a lot of achievements direct at brake system [3, 4]. These studies all aimed at the vehicle worked on normal state and the lack of pressure caused by leakage is ignored. Due to improper installation, poor sealing properties, vibration in the process of driving and other factors, A small amount of leakage are often exist in the brake pipe, especially in the passenger cars and trucks which used air brake system [5]. The core of driving stability control using differential braking is controlling brake pressure of each wheel, lack of brake pressure caused by leakage will affect the control effect. Bus is the main tool of public traffic, its driving safety problem is the prominent problem, the paper takes the bus as the object of study, researches the control strategy against the state lack of pressure caused by leakage (called under-pressure state in this paper), designs the corresponding controller, to achieve driving stability control on underpressure state. 2. Under-pressure Compensation Control Strategy for Bus Air Brake System Brake is carried out in the process of driving straight, if the pressure in brake chambers of wheels are all in under-pressure state, braking distance of the bus will increase, duration of braking will prolonged. If the pressure of one of the wheels is smaller than other wheels, or pressure transfer time is longer, the phenomenon of drift or sideslip will occur, as shown in Fig. 1. Driver's expected travel route in the process of swerve is realized by the driver's operation on the steering wheel, but the operation often have difference corresponding to the expected travel route, when bus is driving in the road with high or low adhesion coefficient, oversteer or understeer is prone to occur. Currently, the active safety systems, such as ESP, can rectify the travel trajectory of oversteer or understeer in a large extent, and the rectification actions are implemented by the respective brake pressure operated on each wheel which generate a yaw moment in the opposite direction to deviation from the target track. If under-pressure is exist in one of wheels at the same time, the yaw moment required to rectify the travel trajectory will be insufficient, so that the rectification effect of active safety systems such as ESP will be failure or not ideal, as shown in Fig. 2. Based on the analysis above, pressure compensation control strategy of bus air brake system in under-pressure state is divided into two parts. At first, in order to rectify the deviation between actually traveling trajectory and desired travel path, differential braking is carried out to get the desired yaw moment. Secondly, in order to get the desired yaw moment, it is necessary to give some pressure compensation to bake system in under-pressure state. The combination of both above can achieve effective control goal aimed at traveling trajectory. The compensation of brake pressure can achieve by controlling solenoid valve, changing the duty cycle of solenoid valve to obtain a higher output pressure than normal state, the diagram as shown in Fig. 3, in which the pressure transfer relationship between various parts of the brake circuit get from reference 2 written by the same author [5]. 3. Structure of Compensation Control System in Under-pressure State for Bus Air Brake System According to under-pressure compensation control strategy of bus air brake system, the ultimate goal of control is to track the expected trajectory in the process of driving by control the parameters consist of yaw rate, lateral acceleration and sideslip angle. The direct objects controlled are solenoid valves in air brake system, the indirect object is brake pressure in the brake chambers. According to the control strategy described above, the paper uses the hierarchical control structure as shown in Fig. 4. Control system is mainly divided into two parts which are the upper controller and the lower controller. The upper controller is divided into two modules according to function, the module of vehicle motion state measures the status parameters of wheel speed sensors mounted on four wheels, lateral acceleration sensor, steering angle sensor and yaw rate sensor mounted on bus body, obtains and outputs the desired yaw moment using the measured parameter value. On the same time, the module of brake circuit pressure state collects pressure parameters of four solenoid valves and brake chambers, obtains and outputs the brake pressure compensation which brakes circuit and the chamber needed in under-pressure state by analysis and calculation. The lower controller gets the excepted yaw moment and pressure compensation outputted by the upper controller, and adjusts the brake pressure of each wheel in real-time according to instantaneous parameter of wheel speed and brake pressure feedbacked from the sensors, in order to obtain the desired effect on recitying the bus driving trajectory. 4. Compensation Control Method in Under-pressure State for Bus Air Brake System In the process of under-pressure compensation control on bus air brake system, the first task is to obtain the desired additional yaw moment, in order to make the bus traveling along the desired trajectory. The transverse component of running track for bus can measured by sideslip angle and yaw rate, so the purpose of obtaining the desired yaw moment is to produce the sideslip angle and yaw rate expected. The second task is to obtain desired brake pressure timely in under-pressure state, in order to meet the control requirements of desired yaw moment, that is, to provide a compensation for the reduced brake pressure even if in under-pressure state. Aimed at the control objectives, the paper adopts sliding mode control algorithm as control foundation for under-pressure compensation control of bus air brake system. According to the defined coordinate system, error for movement control can be defined as the error in X, Y and Z directions, that is e = [ex,ey,ez], the switching function of sliding mode control is: ... (1) According to the pressure-flow equation, error for pressure control can be defined as the error of the mass flow which flow into brake chambers and the pressure in brake chambers, that is e = [eq, ep J, the switching function of sliding mode control is: ...(2) where Ax, Ay, Az, Aq and Ap are the positive real adjustment factor. To keep the control system on the sliding surface timely, the switching function of sliding mode need meet: ...(3) 5. Under-pressure Compensation Control Model for Bus Air Brake System According to Ackerman Steering Geometry, the curvature of driving path is not equal between outside wheels with inside wheels in the process of steering, that is, the difference of steering angle between outside wheels with inside wheels always exists, but it can be compensated by the steering mechanism [3]. Therefore, the traveling trajectory bus can be seen as a single track in the process of analyzing on the lateral movement of bus, that is, so-called singletrack model, as shown in Fig. 5. According to the geometric model, the simplified formula for slip angle of each wheel is: ...(4) where (Xf, Ij., Of. and lr are the slip angle of front wheels, the distance between the front wheels and the center of gravity respectively. According to the vehicle dynamics model get from reference 1 written by the same author [1], yaw rate and sideslip angle expected can be derived: ...(5) ...(6) In the condition of ignoring the force of wind, the force on driving bus is only given by the ground, so the force which the tires get is the only external source. Due to the restrictions by road conditions and other factors, the desired yaw torque can't increase indefinitely, so the value of yaw rate and sideslip angle expected will have limited boundaries. If the desired lateral parameters exceed the limited value defined, the tire force saturated, the amount given by control system can only output the boundary value. When the bus is in ultimate state, the longitudinal force and lateral force wheels suffered meet the relationship as follows [3]: ...(7) According to vehicle dynamics theory of R. Rajamani [3], it can be derived that the value of yaw rate 6 is restrained as follows: ...(8) Thus the target of control for yaw rate is as follows: ...(9) In addition, for the control requirements, if the value of sideslip angle is too large, the tires will work in non-linear region, the control precision will reduce, according to the theory of U. Kiencke and L. Nielsen's [3], sideslip angle can be limited using the following formula: ...(10) Thus the target of control for sideslip angle is as follows: ...(11) 6. Compensation Controller Design for Bus Air Brake System As shown in Fig. 6, the under-pressure compensation controller of bus air brake system is divided into two layers: the upper controller and the lower controller. The upper controller gets state parameters required by the lateral acceleration sensor, the steering angle sensor, the yaw rate sensor, the wheel speed sensor and the pressure sensors, calculates the expected travel trajectory and the compensation required of brake pressure, and outputs to the lower controller. The expected travel trajectory is achieved by the desired yaw rate and sideslip angle, according to the reduction in reference 1 written by the same author [1], in order to get the desired yaw rate and sideslip angle, the yaw moment required is: ...(12) For the control of brake pressure compensation, the paper adopts the method of sliding mode control, the switching function of sliding mode control is defined: ... (13) According to the stability conditions of sliding mode control: ... (14) where ? and vx are the positive real adjustment coefficients. The of brake circuit in the leakage condition in reference 2 written by the same author[5], but the mode of pressure-flow characteristics need to be simplified for control. Assuming it is equal between the mass flow into brake pipe with that flow into brake chamber in normal state, that is qx =q2 , then the mass flow into brake chamber in leakage condition is ^2=^i -«leak. Therefore, the equation (14) can be changed to: ... (15) Meanwhile, ignoring the change of temperature, the change of pressure and flow in brake chamber is: ... (16) Differentiating the above equation: ... (17) By equation (15) and (17), it can be obtained: ... (18) In addition, when the leakage of brake pipe is large, the brake system will issue a warning signal, and the research object of the paper is the case when the leakage is small. Therefore, in the process of braking, the difference between pressure inside the pipe with pressure in the outlet of solenoid valve is not too much, the ratio between the pressures in these two points will be more than the critical pressure ratio. The calculation of ?i should choose the formula in the condition of subsonic flow. The ratio between atmospheric pressure with the pressure in the brake pipe is very small, so the calculation of leakage mass flow should choose the formula in the condition of sonic flow, that is: ...(19) Differentiating the above equation: ...(20) ... (21) Combining formula (18), (20) and (21), control function of brake pressure compensation can be obtained, and it just relate to the pressure in the brake circuit which can be collected in real-time by pressure sensor. According to the control function, pressure pc can be controlled through controlling the pressure A used solenoid valve. After obtained expected pressure compensation and yaw moment by the upper controller, the lower controller adjusts brake pressure in real-time according to the parameters of wheel speed and brake pressure gotten from corresponding sensors. The longitudinal forces in the steering wheels generated by braking respective are: ...(22) When the desired yaw moment is positive, in order to obtain it the braking pressure compensations required are: ... (23) If it is not in under-pressure condition caused by leakage, the pressure control valve as shown in equation (23), so it need to increase the compensation if a leakage is present, the pressures output by control valve are: ... (24) where P\q is the pressure current supplied by control valve, pz\ and pz2 are the pressure compensations in under-pressure state. Similarly, when the desired yaw moment is negative, the pressures supplied by control valve are: ... (25) There is a certain ratio between the brake pressure of rear wheels with the brake pressure of front wheels and it can be obtained by the same approach. The paper adopts sliding mode control as the control method for under-pressure compensation control of bus air brake system. In practical engineering problems, inaccuracy of model and external disturbance is always exist, the control objectives would slide back and forth near the sliding surface, high-frequency control input is required which will cause harm to control object and make the control cannot be carried. Further, since there are pressure fluctuations in the process of pressure transferring, and it can be seen according to the curve of the air chamber charging, the pressure rises very slowly when which is about to reach a maximum value, this will bring difficulty for the realtime control. For these two reasons, the paper defines a boundary layer with the width of 5 kPa for the sliding surface, that is, input of control will stop when the pressure achieves the range of plus or minus 5 kPa near the desired control target. In addition, it should be noted that the control pressure of control valve has an upper limit, which can not exceed the maximum pressure provided by bus air brake system. If the desired value exceeds the upper limit, the upper limit is provided only, that is: ... (26) where Pdes is the desired control value in accordance with the formula (24) and (25), Pmax is the maximum pressure provided by bus air brake system. 7. Simulation and Analysis Based on the above analysis and the model established, the paper simulated the model using MATLAB / Simulink in J-tum driving condition. In simulation, the paper assumed that the initial speed of the vehicle is 80 km/h, and the pipes for left wheel braking were in under-pressure state, simulation results as shown in Fig. 7 to Fig. 9. It can be seen from the above diagrams, in the absence of any control, bus movement curve disappears at about 7 s which means a rollover occurred. The rollover is prevented through the desired yaw moment control, and the control has a certain effect. Meanwhile, if in the process of controlling, under-pressure compensation control obviously optimized control effect due to the influence of the under-pressure is considered. 8. Conclusions The paper aimed at the problem in brake stability control of bus air brake system in under-pressure condition, based on the differential braking, carried out stability control by desired yaw moment. In this paper, pressure compensation control strategy in under-pressure state is presented, the mathematical model is built, under-pressure compensation controller of bus air brake system is designed, and simulation is carried out in J-tum driving condition, the simulation result shows that the effect of control is good. Acknowledgment The authors greatly acknowledge the support of "Research Fund for the Doctoral Program of Zhejiang Normal University". References [1] . Wang Zhishen, Li Gangyan, Anti-sideslip differential brake control for bus aimed at the state of leakage from brake pipeline, Advances in Information Sciences and Service Sciences, Vol. 4, Issue 2, 2012, pp. 200-2008. [2] . E. Dincmen, T. Acarman, Active coordination of the individually actuated wheel braking and steering to enhance vehicle lateral stability and handling, in Proceedings of the 17th World Congress of the International Federation of Automatic Control, Seoul, Korea, 2008. [3] . D. F. Chu, G. Y. Li, X. Y. Lu, J. K. Hedrick, Rollover prevention or vehicles with elevated CG using active control, in Proceedings of the 10th International Symposium on Advanced Vehicle Control (AVEC 10), Loughborough, UK, 2010. [4] . S. J. An, K. Yi, G. Jung, K. I. Lee, Y. W. Kim, Design yaw rate and steering control method during cornering for a six-wheeled vehicle, International Journal of Automotive Technology, Vol. 4, Issue 2, 2008, pp. 173-181. [5] . Zhishen Wang, Gangyan Li, Qiqiao Wu, Jun Xu, Research on pressure characteristics of vehicle air braking system with leakage from pipeline, Applied Mechanics and Materials, Vol. 157-158, 2012, pp. 608-611. 1 Zhishen WANG,2 Gangyan LI 1 College of Engineering, Zhejiang Normal University, No. 688, Yingbin Road, Jinhua City, Zhejiang Province, 320014, China 2 School of Mechanical & Electronic Engineering, Wuhan University of Technology, No. 122, Luoshi Road, Wuhan City, Hubei Province, 430070, China, 1 E-mail: [email protected] Received: 8 April 2014 /Accepted: 30 May 2014 /Published: 30 June 2014 (c) 2014 IFSA Publishing, S.L. |