非线性控制理论在防滑刹车系统中的应用研究
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摘要
防滑刹车系统是重要的机载设备，对飞机的起飞、着陆安全性有重要
影响。因防滑刹车系统发生故障威胁飞机安全的事故时有发生。从公开发
表的文献看，研究飞机防滑刹车系统的报道不多见，研究工作也不深入，
特别是应用控制理论的新成果研究防滑刹车系统的工作做得比较少。飞机
防滑刹车系统包含比较多的非线性因素，特别是对系统性能有很大影响的
结合系数最大值是一个在一定范围内变化的不确定参数。因此，应用参数
不确定非线性系统控制理论研究飞机防滑刹车系统的控制问题是有意义
的。同时，它也是本文的研究主题。
文中总结了参数不确定非线性系统控制理论的研究成果，特别注意到
基于反馈线性化理论的控制方法是参数不确定非线性系统控制理论的一个
重要组成部分。在对该领域研究进展分析的基础上，针对满足三角形条件
和反馈线性化条件的非线性参数化不确定系统提出了一种鲁棒控制器设计
方法，并针对非线性参数化不确定系统提出了基于参数识别的鲁棒输出跟
踪器的设计方法。后者是本文为飞机防滑刹车系统设计输出跟踪器的理论
基础，同时也是本文的创新点之一。
在对结合力产生本质讨论的基础上，分析了滑水现象产生的原因和预
防措施。并分析了各类防滑刹车系统的原理与其性能的关系，以及低摩擦
系数跑道上系统性能恶化的原因及解决方法。通常用刹车效率衡量飞机防
滑刹车系统的性能，它与惯用的控制系统性能指标没有直接联系。通过研
究，得出了刹车效率与控制精度之间的关系，为直接利用刹车效率设计防
滑刹车系统提供了方便。这是本文的创新点之二。针对一种常用的描述结
合系数和滑移率函数关系的表达式，研究了最佳滑移率、结合系数最大值
和机轮抱死时的结合系数与该关系式中三个参数取值范围之间的联系，细
化了这些参数的取值范围，减轻了应用迭代法求参数具体值的计算工作
量。利用试验数据研究了最佳滑移率、结合系数最大值和机轮抱死时的结
合系数随飞机速度的变化规律。两者联系在一起，便得到了结合系数随飞
机速度和滑移率的变化规律。它是本文的创新点之三。
针对一种参数以非线性形式存在的描述结合系数与滑移率之间函数
关系的表达式，提出了一种在线识别表达式中参数的方法。利用基于受刹
机轮动态方程推算的结合系数以及结合系数与待估参数增量之间的一阶
Taylor展开式，可以识别关系式中参数的增量。在此基础上，就得到了待
估计参数的值。这是本文的创新点之四。
应用反馈线性化理论和作者提出的基于参数识别的鲁棒输出跟踪器设
计方法为防滑刹车系统设计了控制律，对飞机在多种跑道上的着陆刹车过
程进行了仿真计算，并分析了影响防滑刹车系统性能的因素。通过选取适
当的加权阵来设计跟踪器，能保证系统具有比较满意的性能。仿真结果表
明，本文提出的参数识别方法和控制器设计方法对于飞机防滑刹车系统是
有效的。跟踪器设计时所选择的权阵对湿跑道和冰跑道上刹车系统的性能
有较大的影响。增加对跟踪误差变化率以及跟踪误差对时间的二阶导数的
权重，能增加系统阻尼，提高系统性能。由于干跑道能提供较大的结合力
矩，飞机在干跑道刹车的性能通常比较好。仿真结果还表明，阻力伞能有
效地缩短飞机在各种跑道上的刹车距离和刹车时间。
For modern aircraft, the antiskid braking system is one of the key
airborne equipment and plays a very important role in safe takeoff and landing.
While accidents and incidents involving aircraft overrun and loss of
directional control due to antiskid braking system remain an important concern,
the researches on the system, especially on application of the latest
achivement of modern control theory to aircraft antiskid braking system, are
not so satisfactory that it can insure safe ground handling operation under
adverse conditions. There are many nonlinearities and uncertainties in aircraft
braking system,espacially the maximum friction coefficient can vary in a
certain range, and will affect the performance of system seriously. Therefor, it
is meaningful to improve the performance of antiskid braking systems by
means of parametric uncertainty nonlinear control theory, and it is the topic of
this dissertation.
Based on the review of progress in parametric uncertainty nonlinear
system control theory, it is noticed that design methods based on feedback
linearization are the main parts and the author proposes a robust controller
design method for a nonlinear parametrization uncertain system satisfying
feedback linearization and triangularity conditions,and a robust output
tracking controller for a nonlinear parametrization uncertain system based on
the identification of uncertain parameters. The latter,which is the first creative
point,is the basis of robust controller design for aircraft antiskid braking
system in this dissertation.
Based on the analysis of mechanism of tire-runway friction force, the
author analyzes the aircraft hydroplaning and its provision, measures the
principles and performances of different types antiskid braking systems, the
performance degrading and its solutions. The braking efficiency is a main
performance index in aircraft antiskid braking systems, the author studies the
relationship between control accuracy and braking efficiency, so that we may
design antiskid braking systems by means of braking efficiency directly, and
this is the second creative point. The author also studies the relationship
between the maximum friction coefficient, optimum slip ratio, friction
coefficent with locked wheels and three parameters in friction coefficient
function of slip ratio, and three fit functions derived from experimental
analysis, maximum friction coeffient, optimum slip ratio and friction
coefficent v~ ith locked wheels, of aircraft speed. At last, the author proposes a
quantitative relationship between tire-runway friction coefficient, aircraft
speed and slip ratio, this is the third creative point.
The author proposes a new parameter online identification method for
nonlinear parameters in a common friction coefficient function of slip ratio.
On the basis of a derived friction coefficient from dynamics equation of
braked wheels and one step Taylor function between friction coefficient and
variable value of the parameters to be estimated, we can calculate the
estimated parameters This is the fourth creative point.
By the use of controllers derived from feedback linearizable principle and
output tracking method based on parameter identification, the author studies
the perfOrmance of a certaln alrcraft antlskld braklng system under dlfferent
kinds of runways, with or without landing parachute, and analyzes the factors
affecting the system perfOrmance. Aircraft antiskid braking system can meet
the performance indexes by means of a fit weighting matrix in controller
design. It is shown that both
影响。因防滑刹车系统发生故障威胁飞机安全的事故时有发生。从公开发
表的文献看，研究飞机防滑刹车系统的报道不多见，研究工作也不深入，
特别是应用控制理论的新成果研究防滑刹车系统的工作做得比较少。飞机
防滑刹车系统包含比较多的非线性因素，特别是对系统性能有很大影响的
结合系数最大值是一个在一定范围内变化的不确定参数。因此，应用参数
不确定非线性系统控制理论研究飞机防滑刹车系统的控制问题是有意义
的。同时，它也是本文的研究主题。
文中总结了参数不确定非线性系统控制理论的研究成果，特别注意到
基于反馈线性化理论的控制方法是参数不确定非线性系统控制理论的一个
重要组成部分。在对该领域研究进展分析的基础上，针对满足三角形条件
和反馈线性化条件的非线性参数化不确定系统提出了一种鲁棒控制器设计
方法，并针对非线性参数化不确定系统提出了基于参数识别的鲁棒输出跟
踪器的设计方法。后者是本文为飞机防滑刹车系统设计输出跟踪器的理论
基础，同时也是本文的创新点之一。
在对结合力产生本质讨论的基础上，分析了滑水现象产生的原因和预
防措施。并分析了各类防滑刹车系统的原理与其性能的关系，以及低摩擦
系数跑道上系统性能恶化的原因及解决方法。通常用刹车效率衡量飞机防
滑刹车系统的性能，它与惯用的控制系统性能指标没有直接联系。通过研
究，得出了刹车效率与控制精度之间的关系，为直接利用刹车效率设计防
滑刹车系统提供了方便。这是本文的创新点之二。针对一种常用的描述结
合系数和滑移率函数关系的表达式，研究了最佳滑移率、结合系数最大值
和机轮抱死时的结合系数与该关系式中三个参数取值范围之间的联系，细
化了这些参数的取值范围，减轻了应用迭代法求参数具体值的计算工作
量。利用试验数据研究了最佳滑移率、结合系数最大值和机轮抱死时的结
合系数随飞机速度的变化规律。两者联系在一起，便得到了结合系数随飞
机速度和滑移率的变化规律。它是本文的创新点之三。
针对一种参数以非线性形式存在的描述结合系数与滑移率之间函数
关系的表达式，提出了一种在线识别表达式中参数的方法。利用基于受刹
机轮动态方程推算的结合系数以及结合系数与待估参数增量之间的一阶
Taylor展开式，可以识别关系式中参数的增量。在此基础上，就得到了待
估计参数的值。这是本文的创新点之四。
应用反馈线性化理论和作者提出的基于参数识别的鲁棒输出跟踪器设
计方法为防滑刹车系统设计了控制律，对飞机在多种跑道上的着陆刹车过
程进行了仿真计算，并分析了影响防滑刹车系统性能的因素。通过选取适
当的加权阵来设计跟踪器，能保证系统具有比较满意的性能。仿真结果表
明，本文提出的参数识别方法和控制器设计方法对于飞机防滑刹车系统是
有效的。跟踪器设计时所选择的权阵对湿跑道和冰跑道上刹车系统的性能
有较大的影响。增加对跟踪误差变化率以及跟踪误差对时间的二阶导数的
权重，能增加系统阻尼，提高系统性能。由于干跑道能提供较大的结合力
矩，飞机在干跑道刹车的性能通常比较好。仿真结果还表明，阻力伞能有
效地缩短飞机在各种跑道上的刹车距离和刹车时间。
For modern aircraft, the antiskid braking system is one of the key
airborne equipment and plays a very important role in safe takeoff and landing.
While accidents and incidents involving aircraft overrun and loss of
directional control due to antiskid braking system remain an important concern,
the researches on the system, especially on application of the latest
achivement of modern control theory to aircraft antiskid braking system, are
not so satisfactory that it can insure safe ground handling operation under
adverse conditions. There are many nonlinearities and uncertainties in aircraft
braking system,espacially the maximum friction coefficient can vary in a
certain range, and will affect the performance of system seriously. Therefor, it
is meaningful to improve the performance of antiskid braking systems by
means of parametric uncertainty nonlinear control theory, and it is the topic of
this dissertation.
Based on the review of progress in parametric uncertainty nonlinear
system control theory, it is noticed that design methods based on feedback
linearization are the main parts and the author proposes a robust controller
design method for a nonlinear parametrization uncertain system satisfying
feedback linearization and triangularity conditions,and a robust output
tracking controller for a nonlinear parametrization uncertain system based on
the identification of uncertain parameters. The latter,which is the first creative
point,is the basis of robust controller design for aircraft antiskid braking
system in this dissertation.
Based on the analysis of mechanism of tire-runway friction force, the
author analyzes the aircraft hydroplaning and its provision, measures the
principles and performances of different types antiskid braking systems, the
performance degrading and its solutions. The braking efficiency is a main
performance index in aircraft antiskid braking systems, the author studies the
relationship between control accuracy and braking efficiency, so that we may
design antiskid braking systems by means of braking efficiency directly, and
this is the second creative point. The author also studies the relationship
between the maximum friction coefficient, optimum slip ratio, friction
coefficent with locked wheels and three parameters in friction coefficient
function of slip ratio, and three fit functions derived from experimental
analysis, maximum friction coeffient, optimum slip ratio and friction
coefficent v~ ith locked wheels, of aircraft speed. At last, the author proposes a
quantitative relationship between tire-runway friction coefficient, aircraft
speed and slip ratio, this is the third creative point.
The author proposes a new parameter online identification method for
nonlinear parameters in a common friction coefficient function of slip ratio.
On the basis of a derived friction coefficient from dynamics equation of
braked wheels and one step Taylor function between friction coefficient and
variable value of the parameters to be estimated, we can calculate the
estimated parameters This is the fourth creative point.
By the use of controllers derived from feedback linearizable principle and
output tracking method based on parameter identification, the author studies
the perfOrmance of a certaln alrcraft antlskld braklng system under dlfferent
kinds of runways, with or without landing parachute, and analyzes the factors
affecting the system perfOrmance. Aircraft antiskid braking system can meet
the performance indexes by means of a fit weighting matrix in controller
design. It is shown that both
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