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Journal of ZheJiang University (Engineering Science)  2021, Vol. 55 Issue (3): 462-471    DOI: 10.3785/j.issn.1008-973X.2021.03.006
    
Backstepping based precise control of brake cylinder pressure for train
Chi LEI(),Meng-ling WU
Institute of Rail Transit, Tongji University, Shanghai 201804, China
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Abstract  

A precise control method of brake cylinder pressure based on backstepping was proposed for the heavy-haul train equipped with electronically controlled pneumatic (ECP) brake system. A control model of ECP brake system with strict feedback form was established through equivalent continuous processing and linearization. By introducing the uncertainties with known upper bound, and adopting the sliding mode variable structure with exponential approach law, the local robustness of the system was achieved. A control law based on backstepping was designed by constructing error variables and Lyapunov function. A first-order filter was introduced to solve the problem of counting the derivative repeatedly in the control law. The performance of the controller was analyzed through hardware-in-loop test. Test results showed that, comparing with the traditional controller, the controller of brake cylinder pressure based on backstepping had a higher control accuracy, and its steady state control error was within the range of ±8 kPa without obviously overshoot in the pressure regulation process. In addition, the introduction of dead zone in the controller can significantly reduce the operation times of the AV/RV valve and improve the service life of the system.



Key wordselectronically controlled pneumatic brake system      equivalent continuous processing      backstepping controller      precise control      pressure     
Received: 26 February 2020      Published: 25 April 2021
CLC:  U 270.35  
Cite this article:

Chi LEI,Meng-ling WU. Backstepping based precise control of brake cylinder pressure for train. Journal of ZheJiang University (Engineering Science), 2021, 55(3): 462-471.

URL:

http://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2021.03.006     OR     http://www.zjujournals.com/eng/Y2021/V55/I3/462


基于反步法的列车制动缸压力精确控制

针对重载列车电控空气(ECP)制动系统,提出基于反步法的制动缸压力精确控制方法. 通过等效连续化处理和线性化处理,建立具有严格反馈方式的ECP制动系统控制模型;引入已知上界的不确定项,采用指数趋近律的滑模变结构,实现系统局部鲁棒性;基于反步法设计控制律,构造误差变量以及 Lyapunov函数;引入一阶滤波器,解决控制律中存在的“微分项数爆炸”问题. 硬件在环试验结果表明:与传统控制器相比,基于反步法的制动缸压力控制器具有更高的控制精度,其稳态控制误差在±8 kPa内,且调压过程无明显超调;在控制器中引入控制死区,可以大幅降低AV/RV阀的动作次数,提高系统使用寿命.


关键词: 电控空气制动系统,  等效连续化,  反步控制器,  精确控制,  压力 
Fig.1 Simplified model of ECP brake system
Fig.2 Average displacement characteristics of solenoid valve spool under three control methods
Fig.3 Flow chart of brake cylinder pressure controller design
Fig.4 Schematic diagram of ECP brake system (HIL) test bench
类别 tdo/ms tmo/ms tdc/ms tmc/ms d/ms xm/ms Cq2
AV阀 8 7 1 2 6 0.3 0.68
RV阀 5 6 2 4 10 0.25 0.6
Tab.1 AV/RV solenoid valve characteristic parameters
参数 符号 数值
不确定项上界 B1B2 0.5
误差变量自适应参数初值 σ10σ20 1×10?8,1×10?9
自适应变化率 ρ1ρ2 1×10?11
边界层厚度 ε 0.02
一阶滤波器 λ 0.005
Tab.2 AV/RV solenoid valve characteristic parameters
Fig.5 Step response of brake system
Fig.6 Duty cycle output signal of backstepping controller in step response
Fig.7 Frequency response of brake system(f=0.02 Hz)
Fig.9 Duty cycle output signal of backstepping controller in frequency response
Fig.8 Frequency response of brake system(f=0.05 Hz)
Fig.10 Brake cylinder pressure response characteristics with dead-time control
Fig.11 Duty cycle of PWM signal with dead-time control
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