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1、An Application of Nonlinear PID Control to a Class of Truck ABS ProblemsFangjun JiangFord Motor Company, Product Development Center, GB-E65, MD 19920901 Oakwood Blvd. Dearborn, MI 48124Zhiqiang GaoThe Applied Control Research LaboratoryDepartment of Electrical and Computer EngineeringCleveland State
2、 University, Cleveland, Oh 44115Abstract: A new NPID (Nonlinear Proportional-Integral-Differential) control algorithm is applied to a class of truck ABS (Anti-lock Brake System) problems. The NPID algorithm combines the advantages of robust control and easy tuning. Simulation results at various situ
3、ations using TruckSim show that NPID controller has shorter stopping distance and better velocity performance than the conventional PID controller and a loop-shaping controller.Keywords: Nonlinear, PID, ABS.1. IntroductionABS for commercial vehicles appeared on the market in 1960s and began to grow
4、fast in 1970s with the technologies of microcomputers and electronics 1. ABS is recognized as an important contribution to road safety. It is now available in almost all types of vehicles. The automotive industry is continuously developing new generations of ABS. The technologies of ABS are also app
5、lied in TCS (Traction Control System) and VDSC (Vehicle Dynamic Stability Control) It is well known that wheels will slip and lockup during severe braking or when braking on a slippery road surface (wet, icy, etc.). This usually causes a long stopping distance and sometimes the vehicle will lose ste
6、ering stability. The objective of ABS is to prevent wheels from lockup and achieve minimum stopping distance while maintaining good steering stability during braking.The wheel slip is defined as: （1.1）where S, , R and V denote the wheel slip, the wheel angular velocity, the wheel rolling radius, and
7、 the vehicle forward velocity, respectively.In normal driving conditions, V R therefore S 0. In severe braking, it is common to have = 0 while V 0 , or S = 1, which is called wheel lockup. Wheel lockup is undesirable since it prolongs the stopping distance and causes the loss of direction control.1.
8、1 A Class of Truck ABS ProblemsThe objective of ABS is to manipulate the wheel slip so that a maximum friction force is obtained and the steering stability (also known as the lateral stability) is maintained. That is, to make the vehicle stop in the shortest distance possible while maintaining the d
9、irectional control. It is well known that the friction coefficient, , is a nonlinear function of the slip, S. The ideal goal for the control design is to regulate the wheel velocity, , such that an optimal slip, which corresponds to the maximum friction, is obtained. For the sake of simplicity, howe
10、ver, it is very common in industry to set a desired slip to .2. Given the vehicle velocity, V, and the wheel radius R, the ABS control problem becomes regulating such that the slip in (1.1) reaches a desired value, such as .2In this paper, the control design is focused on a class of truck ABS proble
11、ms, which pose a few unique challenges, different from passenger cars.1. The actuator of the truck ABS is a pneumatic brake system, which is typically slower in response and harder to control than a hydraulic brake system. The control action of the brake system is discrete. The brake pressure is con
12、trolled by discrete valves (open or close). The brake pressure can be controlled to increase, hold constant or decrease. Through PWM (Pulse Width Modulation), the actions of the discrete valves are mapped into a continues analog control signal ranging from 1 to +1, where 1 means fully exhausting pre
13、ssure, +1 means fully building uppressure and 0 means holding pressure as constant.2. The measurement of the brake pressure is not available, which makes the control of the pneumatic brake system even more difficult. The ABS controller must deal with the brake dynamics and the wheel dynamics as a wh
14、ole plant.3. The measurement of the vehicle velocity or vehicle acceleration is not available. The only feedback signals are two or four channels of wheel angular velocity. It poses a challenging problem for the vehicle velocity estimation since the vehicle velocity is necessary to set the wheel ref
15、erence velocity. A separate study was carried out to resolve this issue in 2.4. The complex dynamics of the tractor/trailer system and the large variations of the truck operation condition set a very stringent requirement for the ABS controller. The tuning and testing of a truck ABS are also much mo
16、re difficult than an ABS for passenger cars.1.2 Current TechnologyVarious control strategies have been implemented in real ABS products or discussed in publications. Since the technologies used in commercial ABS products are usually kept as trade secrets, it is very difficult to determine their deta
17、iled control algorithms. From the literature available 3, 4, 5, 6, a few algorithms use an approach similar to bang-bang control. They usually have two or more threshold values for the wheel deceleration or the wheel slip. Once the calculated wheel deceleration or wheel slip is over one of the thres
18、hold values, the brake pressure is commanded to increase, hold constant or decrease. This algorithm will result in a peak-seeking strategy in the slip curve or forcing the wheel deceleration/slip to be within a particular range.Finite state machine methods are also widely applied in the industry. Ba
19、sed upon the measured signals such s wheel velocity, vehicle deceleration and/or brake pressure, the operation of the vehicle is characterized by a set of different states, such as normal driving, lockup, free rolling ,etc. The rake pressure is then controlled to increase, hold constant or decrease
20、based on the state the vehicle is in and other design logic.These two methods heavily rely on the experience of the designers and drivers. It is fairly difficult to analyze the controllers performance during the design stage. The tuning of the controller is done purely on trial and error basis. The
21、needs for a systematic design approach for the development are quite evident in this industry. Such needs motivated the research efforts that result in 9.In particular, the truck ABS problems are reformulated as a closed-loop control problem. A cascade loop structure, as shown in Figure 1, as well a
22、s various control algorithms are proposed. The outer loop, which includes the vehicle velocity estimation and desired slip calculation, provides the command signal, Vwd , for the inner wheel velocity loop. The separation of the outer and inner loop designs, similar to the separation principle in lin
23、ear system theory, are only made possible in the framework of Figure 1.Figure 1: A Cascade Structure for ABSThe vehicle velocity estimation and the wheel velocity controller are the key design issues. A nonlinear filter approach, based on the work in 10, to vehicle velocity estimation problems was d
24、eveloped and proved to be quite effective 2,9. For inner loop control, three methods were explored in 9, including the PID, the loop-shaping, and the NPID algorithms. The PID is easy to design and tune but is also limited in performance. The loop-shaping controller, designed based on the linear mode
25、l of the plant and frequency response loop-shaping concepts, is quite capable in simulation. The drawback is the difficulty of tuning such controllers on a real industrial simulator, where the controller must be adjusted for nonlinearities and disturbances uncounted for in the modelSimilar tuning di
26、fficulties can also be seen in various other advanced control strategies such as fuzzy logic control, model reference control and neural network, which were also extensively discussed as possible candidates for ABS.In the development of an ABS controller, one of the major issues is testing. The ABS
27、controller needs to go through a series of software and hardware tests. Due to the complexity of the truck system and the large variations of operation conditions, on-site calibration or tuning of the controller is necessary. This requires the new control methods to be not only more powerful, but al
28、so easily tunable. The tuning of a fuzzy logic controller or model reference controller involves multiple rules or re-design of the controller. It is not convenient to be carried out on-site. The conventional PID controller is easy to tune but appears not to be adequate in performance.Based on the a
29、bove discussion, we propose a NPID control design strategy, based on the work of J. Han 11,12, that combines the advantages of robust performance and the ease of tuning. It is proved to be an effective controller for truck ABS.英语翻译 非线性PID控制在一系列卡车ABS问题中的应用蒋方军福特汽车公司产品开发中心，GB-E65,MD 19920901OAKWOOD BLV
30、D.DEARBORN,MI 48124高志强克利夫兰州立大学电子与计算机工程应用控制研究实验室，克利夫兰，OH44115摘要：一种新型的NPID（非线性比例-积分-微分）控制算法正应用于一系列卡车的ABS（制动防抱死系统）问题中。NPID算法不仅鲁棒性强，而且参数便于整定。使用仿真软件TRUCKSIM在各种情况下的仿真结果显示，相对于常规的PID控制器和回路整形控制器，NPID控制器具有更短的制动距离和更好的速度表现性。关键词：非线性，PID,ABS.1.引言商用车上配置ABS系统出现于上世纪60年代，随着微型计算机和电子技术的发展，ABS系统在70年代进入了一个高速发展的时期。ABS对于公路
31、交通安全做出了巨大贡献，几乎所有的汽车都配备了ABS系统。汽车工业也正在不断的开发更新一代的ABS系统，同时ABS技术也正被应用于TCS(牵引控制系统)和VDSC（车辆动态稳定性控制系统）。众所周知，车辆在紧急制动或在一些湿滑、结冰的路面上制动时，车轮将会滑动并锁死。这通常会导致一个较长的制动距离，某些时候汽车还将丧失转向稳定性。ABS的功能就是在汽车制动时防止车轮锁死，在保持较好的转向稳定性的同时获得最短的制动距离。车轮滑移率为： （1.1）式中S,w,R和V分别代表车轮的滑移率、角速度、滚动半径和车辆前进速度。在正常的驾驶状态下，VwR,因此S0。在紧急制动的情况下，w=0而V0,即S=1
32、,这种情况称为车轮锁死。我们不期望车轮锁死的情况发生，因为它延长了停车距离并将导致转向控制作用的丧失。1.1 卡车ABS的一系列问题ABS的目标是通过控制车轮滑移率以获得最大的摩擦力，并且能够维持转向稳定性，以使汽车在尽可能短的距离内停车，同时维持转向控制。大家知道，摩擦系数是滑移率S的非线性函数，控制器设计的理想目标是通过调节车轮转速w得到与最大摩擦力相对应的最优滑移率。为简化起见，工业上通常设定期望滑移率为0.2.给定汽车速度V和车轮半径R,ABS控制问题就转化成为通过调节车轮转速w以使得（1.1）式中的滑移率S达到期望值0.2.本文中设计的控制器主要是针对卡车的ABS问题，这类问题不同于
33、小型汽车，具有一定的特殊性。（1）卡车ABS执行器通常是气动系统，这类系统比液压制动系统响应更慢，更难以控制。制动压力的控制是通过离心阀的开启与关闭来完成的，受控的制动压力可以增大、保持或减小。通过PWM（脉宽调制），离心阀的输出可以用一个连续的模拟控制信号描述，其取值范围在-1+1之间，-1表示完全卸除压力，+1表示施加最大压力，0表示将压力维持在一个恒定的数值。（2）制动压力的检测通常是不能实现的，这将使得气动制动系统的控制更加困难。ABS控制器必须将制动动态过程和车轮动态过程看做一个整体的被控对象来处理。（3）汽车速度或加速度的测量也不能实现，仅有的反馈信号是两路或四路车轮的角速度。估算
34、汽车速度将是一个具有挑战性的问题，因为汽车速度对于设定车轮参考转速非常必要。一项解决这种问题的独立研究已经实现。（4）拖动系统复杂的动态过程和卡车工作条件的多变性对ABS控制器提出了十分苛刻的要求。卡车ABS系统整定与调试过程比小汽车的相应过程更加困难。1.2 技术现状在实际的ABS产品中使用了各种各样的控制策略，很多的著作论文中也谈到了这些控制策略。由于商业ABS产品所使用的技术通常作为行业秘密，很难搞清这些产品的详细控制算法。从已有的参考文献可以看出，一部分算法使用的方法类似于“棒-棒”控制。对于车轮的减速或滑移率，这些算法通常设定两个或两个以上的极限值，制动压力受控于增加、保持或减少状态
35、。这些算法将会在-S曲线上导致峰值搜寻策略，或者强迫车轮的减速/滑移率在一个特定的范围内。有限状态机构法在工业中被广泛应用。基于诸如车轮转速、车辆减速或制动压力这些被测信号，车辆的操控以一系列不同的状态为特征，如正常驾驶、锁死和空挡滑行。基于车辆所处的状态和其他的控制逻辑，受控的制动压力可以增大、保持或减小。这两种方法在很大程度上依赖于设计者和驾驶者的经验。在设计阶段，分析控制器的性能是非常困难的，控制器参数的整定完全是以试凑法为基础的。实际上，卡车ABS问题可以归咎为一个闭环控制问题。正如各种各样的控制算法所提出的一样，它是一个串级回环结构，如图1所示。外环包括车辆速度估算和期望滑移率计算，
36、为内环车轮转速提供了命令信号。将系统分为外环和内环的设计方法与线性系统的分割原理类似，只适用于框图化的理论分析。 图1.ABS的串级结构车轮速度估算与车轮速度控制器是设计的关键。基于文献【10】的工作所开发出的一种非线性滤波器方法对于车辆的速度估算是十分有效的。对于内环控制，文献【9】提供了三种方法，分别是PID算法、回路整形算法和NPID算法。PID算法容易设计、便于整定，但性能上受约束；基于被控对象和所设计的回路整形控制器的回路整形算法，在仿真时功能较为强大，但在真正的工业仿真器上，这样的控制器难以整定，因为控制器调整时必须面对模型中为数众多的非线性和干扰因素。相似的整定困难问题也出现在了
37、各种各样的先进的控制策略中，如模糊逻辑、参考模型和神经网络控制算法等，这些都曾作为ABS系统的控制算法在很多文献中都有讨论。ABS控制器开发面临的一个主要问题是测试的问题，它需要通过一系列的软硬件测试。由于卡车系统的复杂性和工作环境的多变性，需要现场的控制器校准或整定，这就要求新的控制方案不仅要功能强大，而且便于整定。模糊逻辑控制器和参考模型控制器涉及到了众多的规则，某些情况下还要对控制器进行重新设计，这在现场调试时都是不便于实施的。常规PID控制器便于调整，但其性能有一定的缺陷。基于以上的讨论，我们在文献【11】、【12】的基础上提出了一种NPID控制策略，它集合了具有鲁棒性和便于整定的优点，被认为是卡车ABS的一种有效的控制器。
