Sensors & Transducers Vol. 7 Issue 6 June 04 pp. 7-3 Sensors & Transducers 04 by ISA Publishing S. L. http://www.sensorsportal.com Compensation Control of Bus Air Brake System in Under-pressure State Zhishen WANG Gangyan LI College of Engineering Zhejiang Normal University No. 688 Yingbin Road Jinhua City Zhejiang Province 3004 China School of Mechanical & Electronic Engineering Wuhan University of Technology No. Luoshi Road Wuhan City Hubei Province 430070 China E-mail: wzs@zjnu.cn Received: 8 April 04 /Accepted: 30 May 04 /Published: 30 June 04 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 igned. inally simulation was carried out and the result shows control effect is good. Copyright 04 ISA Publishing S. L. Keywords: Differential braking Driving stability Under-pressure state Under-pressure compensation control Modeling Simulation.. 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 []. 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 unired lateral movement in order to rectify or partially rectify the unired movement trend []. 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) igns the corresponding controller to achieve driving stability control on underpressure state. http://www.sensorsportal.com/html/digest/p_7.htm 7
Sensors & Transducers Vol. 7 Issue 6 June 04 pp. 7-3. 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 silip will occur as shown in ig.. ig.. Effect of under-pressure brake in steering. ig.. Effect of under-pressure brake in driving straight. 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 get 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 ig.. 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 ired travel path differential braking is carried out to get the ired yaw moment. Secondly in order to get the ired 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 ig. 3 in which the pressure transfer relationship between various parts of the brake circuit get from reference written by the same author [5]. Δp ig. 3. Compensation for under-pressure state. 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 silip 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 cribed above the paper uses the hierarchical control structure as shown in ig. 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 ired 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 8
Sensors & Transducers Vol. 7 Issue 6 June 04 pp. 7-3 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 ired effect on recitying the bus driving trajectory. ig. 4. Structure of compensation control system. 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 ired additional yaw moment in order to make the bus traveling along the ired trajectory. The transverse component of running track for bus can measured by silip angle and yaw rate so the purpose of obtaining the ired yaw moment is to produce the silip angle and yaw rate expected. The second task is to obtain ired brake pressure timely in under-pressure state in order to meet the control requirements of ired 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 e the z switching function of sliding mode control is: S S S x x x y y y z z z. () 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 e p the switching function of sliding mode control is: S S q q q p p p () where λx λy λz λq and λp are the positive real adjustment factor. To keep the control system on the sliding surface timely the switching function of sliding mode need meet: lim SS 0. (3) s 0 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 9
Sensors & Transducers Vol. 7 Issue 6 June 04 pp. 7-3 a single track in the process of analyzing on the lateral movement of bus that is so-called singletrack model as shown in ig. 5. x y ( ) ( ) xmax + = (7) ymax O R R v f α f Inertial coordinate system β δ A v x O αr v r l f l r According to vehicle dynamics theory of R. Rajamani [3] it can be derived that the value of yaw rate θ is restrained as follows: θ μg θmax = 0.85 vx (8) Thus the get of control for yaw rate is as follows: ig. 5. Single-track model for driving bus. B θ θ θ θ = θmax sgn( θ ) θ > θ max max (9) According to the geometric model the simplified formula for slip angle of each wheel is: v y + l fθ α = α = α f = δ tan v x. v y l rθ α3 = α4 = αr = tan v x (4) where α f l f α r and l r 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 written by the same author [] yaw rate and silip angle expected can be derived: vx δ θ = mv x ( lrcαr l fcα f) lf + lr + Cα fcαr( lf + lr) Cαrlflr+ Cαrlr mvxlf β = δss lc r αr lfc α f Cα r( lf + lr) lf + lr + mv x Cα fcαr( lf + lr) (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 ired yaw torque can t increase indefinitely so the value of yaw rate and silip angle expected will have limited boundaries. If the ired 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]: In addition for the control requirements if the value of silip 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] silip angle can be limited using the following formula: β vx βmax = 0 7 40 (0) Thus the get of control for silip angle is as follows: β β β β = max βmax sgn( β ) β > βmax 6. Compensation Controller Design for Bus Air Brake System () As shown in ig. 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 ired yaw rate and silip angle according to the reduction in reference written by the same author [] in order to get the ired yaw rate and silip angle the yaw moment required is: ( θ λ0( β β ) η0( θ θ λ( β β ))) 3 My = Iz + ( 3δ + ) T ( y y) δ lfδ( ( y + y ) ( x + x ) ) lr( y 3+ y 4) () 0
Sensors & Transducers Vol. 7 Issue 6 June 04 pp. 7-3 RT p η p p = q + λ+ λη q ( ) ( ) (8) c c c leak Vc ig. 6. Brake pressure compensation in under-pressure state. or the control of brake pressure compensation the paper adopts the method of sliding mode control the switching function of sliding mode control is defined: s = p p + λ ( q q ) (3) c c According to the stability conditions of sliding mode control: pc = pc λ( q q ) η + ( p p λ ( q q )) c c (4) where λ and η are the positive real adjustment coefficients. The of brake circuit in the leakage condition in reference 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 q = q then the mass flow into brake chamber in leakage condition is q = q q leak. Therefore the equation (4) can be changed to: ( ) p = p λq η p p + λq c c leak c c leak (5) Meanwhile ignoring the change of temperature the change of pressure and flow in brake chamber is: dpc p c = = ( RT( q qleak )) (6) dt V Differentiating the above equation: c pc = ( RT( q q leak) ) (7) V c By equation (5) and (7) it can be obtained: 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 q 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: ( p / p) b q = Cρ a p b qleak = Cleak ρa p Differentiating the above equation: Cleak ρart qlaek = Cleakρa p = q VL p b C ρ RT p = C ρ p -( ) b leak a a VL C ρ p p q = ( b)( - b) a b p C ρ p p + [ ] p p p p [ ( b) ] [ ] p p p 3 a ( b)( b) b p (9) (0) () Combining formula (8) (0) and () 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 p c can be controlled through controlling the pressure p 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: x = KBpc / R () x = KBpc / R
Sensors & Transducers Vol. 7 Issue 6 June 04 pp. 7-3 When the ired yaw moment is positive in order to obtain it the braking pressure compensations required are: M ytr pc = a M ytr pc ( a) = (3) If it is not in under-pressure condition caused by leakage the pressure control valve as shown in equation (3) so it need to increase the compensation if a leakage is present the pressures output by control valve are: M ytr p = p0 + pz a M ytr p = p0 + pz + ( a) (4) can not exceed the maximum pressure provided by bus air brake system. If the ired value exceeds the upper limit the upper limit is provided only that is: p p p max p (or p )= p max p > p max (6) where p is the ired control value in accordance with the formula (4) and (5) p max 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-turn 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 ig. 7 to ig. 9. where p 0 is the pressure current supplied by control valve p z and p z are the pressure compensations in under-pressure state. Similarly when the ired yaw moment is negative the pressures supplied by control valve are: M ytr p = p0 + pz ( a) M ytr p = p0 + pz + a (5) ig. 7. Yaw rate response. 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. urther 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. or 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 ired control get. In addition it should be noted that the control pressure of control valve has an upper limit which ig. 8. Slip angle response. ig. 0. Lateral acceleration response.
Sensors & Transducers Vol. 7 Issue 6 June 04 pp. 7-3 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 ired 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 ired 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 igned and simulation is carried out in J-turn driving conditionthe simulation result shows that the effect of control is good. Acknowledgment References []. Wang Zhishen Li Gangyan Anti-silip differential brake control for bus aimed at the state of leakage from brake pipeline Advances in Information Sciences and Service Sciences Vol. 4 Issue 0 pp. 00-008. []. 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 7 th World Congress of the International ederation of Automatic Control Seoul Korea 008. [3]. D.. Chu G. Y. Li X. Y. Lu J. K. Hedrick Rollover prevention or vehicles with elevated CG using active control in Proceedings of the 0 th International Symposium on Advanced Vehicle Control (AVEC'0) Loughborough UK 00. [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 008 pp. 73-8. [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. 57-58 0 pp. 608-6. The authors greatly acknowledge the support of Research und for the Doctoral Program of Zhejiang Normal University. 04 Copyright International requency Sensor Association (ISA) Publishing S. L. All rights reserved. (http://www.sensorsportal.com) 3