CN110361965B - 线性Luenberger观测器的构建方法 - Google Patents

线性Luenberger观测器的构建方法 Download PDF

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CN110361965B
CN110361965B CN201910419584.9A CN201910419584A CN110361965B CN 110361965 B CN110361965 B CN 110361965B CN 201910419584 A CN201910419584 A CN 201910419584A CN 110361965 B CN110361965 B CN 110361965B
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刘辉
沈宏继
李胜利
张晓瑜
冯晓霞
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Beijing Institute of Technology BIT
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Abstract

本发明公开了一种线性Luenberger观测器的构建方法，包括以下步骤：步骤1，建立车辆驱动***的状态空间方程，判断驱动***的能观性；步骤2，对驱动***的状态做分块划分，重构驱动***状态分量，得到改写后的驱动***状态观测方程；步骤3，在改写的驱动***状态方程中引入变换，获得Luenberger观测器的表达方程和误差方程；本发明构建的线性Luenberger观测器的实现难度降低，减小了转速传感器输出信号中的高频噪音，使得观测器的观测结果更加逼近驱动***实际状态，观测结果准确、及时。

Description

线性Luenberger观测器的构建方法
技术领域
本发明属于车辆控制技术领域，特别是涉及一种线性Luenberger观测器的构建方法。
背景技术
出于成本、可靠性和安装条件等方面的考虑，现有的产品级车辆中很少安装转矩传感器对驱动轴转矩进行直接测定，驱动轴转矩只能通过现有可测信息间接获取；与转矩传感器相比，转速传感器成本低廉，应用光电码盘等转速传感器，可对动力传动***各处的转速状态进行监测。
而现有的检测方法在实际应用中，会受到车轮转速传感器、电机B旋变误差的影响，再利用积分方法检测时，传感器信号噪音、外界干扰等因素会因为积分作用在估计结果了累加，使得估计值与实际值产生较大的误差，特别是当估计初始值与实际初始值存在误差时，估计误差增大，在实际中应用难度大。
发明内容
本发明的目的在于提供一种线性Luenberger观测器的构建方法，利用实际可测量进行反馈，对估计结果实时矫正，使得估计值能很好的跟踪实际值，并能够抵挡外界的干扰，使估计值与实际值的误差减小，适于实际应用。
本发明所采用的技术方案是，线性Luenberger观测器的构建方法具体包括以下步骤：
步骤1，建立车辆驱动***的状态空间方程，判断驱动***的能观性，
以
Figure BDA0002065574440000011
Ts为状态变量、
Figure BDA0002065574440000012
和
Figure BDA0002065574440000013
为驱动***输出、TP和Tv为驱动***输入，建立驱动***状态方程，驱动***的状态空间方程如式(1)所示：
Figure BDA0002065574440000014
其中，x是状态空间方程的输入，y为状态空间方程输出，
Figure BDA0002065574440000015
Figure BDA0002065574440000021
Figure BDA0002065574440000022
是电机B的转角，
Figure BDA0002065574440000023
是车轮的转角，θB为电机转速，θv为车轮转速，
Figure BDA0002065574440000024
是通过对转速θB、θv积分获得，Ts是驱动轴转矩，Ct为减速器阻尼，JP即为电机B转子惯量，ir为主减速器传动比，Cv为车轮阻尼，Jv为车体等效到车轮的等效惯量和车轮惯量之和，ks为驱动轴刚度，Cs为驱动轴阻尼，i指的是主减速器的传动比，TP为驱动***输出轴转矩，Tv为车辆阻力矩；
驱动***的能观性矩阵
Figure BDA0002065574440000025
能观性矩阵N的秩为3，驱动***可观；
步骤2，对驱动***的状态做分块划分，重构驱动***状态分量，得到改写后的驱动***状态观测方程；
步骤3，在改写的驱动***状态方程中引入变换，获得Luenberger观测器的表达式和误差方程。
进一步的，步骤2的具体过程如下：
两个可测的状态变量即为驱动***输出：
Figure BDA0002065574440000026
状态变量Ts需要观测记作x2＝[Ts]，由于矩阵C的秩为2，驱动***的状态空间方程改写为：
Figure BDA0002065574440000027
其中，
Figure BDA0002065574440000028
Figure BDA0002065574440000031
I为单位矩阵；
驱动***划分为两个子***Λ1和Λ2，两个子***Λ1和Λ2相互耦合，子***Λ1状态方程为：
Figure BDA0002065574440000032
子***Λ2状态方程为：
x2＝A21x1+A22x2+B2u
对子***Λ2的***状态x2＝[Ts]进行重构，***状态x2的输入和输出分别为：
Figure BDA0002065574440000033
将输出误差反馈项
Figure BDA0002065574440000034
引入子***Λ2状态方程中，得到驱动***的观测器方程为：
Figure BDA0002065574440000035
其中G为反馈增益矩阵，G＝[g1g2]，g1为两个可测状态变量的反馈增益，g2为状态变量Ts的反馈增益。
进一步的，步骤3中在改写的驱动***观测器方程中引入变换
Figure BDA0002065574440000036
Luenberger观测器的表达方程和误差方程：
Figure BDA0002065574440000037
Figure BDA0002065574440000038
本发明的有益效果是：本发明利用车辆运行中的实际可测量，对观测器进行反馈，降低了估计结果与实际值的误差；本发明对***状态进行重构，使得***状态可观性良好，通过引入变换，降低积分作用对观测结果的影响，使得观测器的实现难度降低，观测误差减小，适于实用。
附图说明
为了更清楚地说明本发明实施例或现有技术中的技术方案，下面将对实施例或现有技术描述中所需要使用的附图作简单地介绍，显而易见地，下面描述中的附图仅仅是本发明的一些实施例，对于本领域普通技术人员来讲，在不付出创造性劳动的前提下，还可以根据这些附图获得其他的附图。
图1是线性Luenberger观测器结构图。
具体实施方式
下面将结合本发明实施例中的附图，对本发明实施例中的技术方案进行清楚、完整地描述，显然，所描述的实施例仅仅是本发明一部分实施例，而不是全部的实施例。基于本发明中的实施例，本领域普通技术人员在没有做出创造性劳动前提下所获得的所有其他实施例，都属于本发明保护的范围。
混合动力车辆有三个动力源，分别是发动机、电机A和电机B，发动机和电机A耦合对车辆前轮进行驱动，电机B对车量后轮进行驱动，电机A与电机B之间电气连接有动力电池，车辆直驶时所受外力与车辆的运动状态、整车重量、地面性质、地面坡度等因素有关，车辆在直驶过程中直驶方向上所受外力主要有牵引力、滚动阻力、空气阻力、坡度阻力、加速阻力等，将车辆直驶方向上所受外力转化为车轮所受力矩，可知驱动***的动力学方程如下所示：
Figure BDA0002065574440000041
其中
Figure BDA0002065574440000042
是电机B的转角，
Figure BDA0002065574440000043
是车轮的转角，θB为电机转速，θv为车轮转速，
Figure BDA0002065574440000044
是通过对转速θB、θv积分获得，JP即为电机B转子惯量，TP为驱动***输出轴转矩，Ct为减速器阻尼，ir为主减速器传动比，Jv为车体等效到车轮的等效惯量和车轮惯量之和，Cv为车轮阻尼，Cs为驱动轴阻尼，ks为驱动轴刚度，Tv为车辆阻力矩，以此对驱动轴转矩Ts建立状态观测器进行观测，
Figure BDA0002065574440000045
是电机B的转角加速度、
Figure BDA0002065574440000046
是车轮的转角加速度。
线性Luenberger观测器的构建方法，包括以下步骤：
步骤1，建立车辆驱动***的状态空间方程，判断驱动***的能观性；
以
Figure BDA0002065574440000051
Ts为状态变量、
Figure BDA0002065574440000052
和
Figure BDA0002065574440000053
为驱动***输出、TP和Tv为驱动***输入，建立驱动***状态方程，驱动***的状态空间方程如式(1)所示：
Figure BDA0002065574440000054
其中，
Figure BDA0002065574440000055
Figure BDA0002065574440000056
i指的是主减速器的传动比，x是状态空间方程的输入，y为状态空间方程输出；则驱动***的能观性矩阵
Figure BDA0002065574440000057
将公式(1)代入能观性矩阵中可得：
Figure BDA0002065574440000058
驱动***能观性矩阵的秩rank(N)＝3，则驱动***可观；
步骤2，根据驱动***的状态空间方程对驱动***状态做分块划分，重构驱动***状态分量，得到改写后的驱动***观测器方程；
由于状态变量
Figure BDA0002065574440000059
能直接测量得到，所以仅需建立一维的降维观测器对Ts进行重构，以建立动态性能良好、鲁棒性较强且能稳定运行的***，提高***的可观性；
两个可测的状态变量即为驱动***输出：
Figure BDA00020655744400000510
状态变量Ts需要观测记作x2＝[Ts]，由于rank(C)＝2，对驱动***的驱动轴转矩状态作分块划分，驱动***可改写为：
Figure BDA0002065574440000061
其中，
Figure BDA0002065574440000062
Figure BDA0002065574440000063
I为单位矩阵；
改写后驱动***的状态空间方程为：
Figure BDA0002065574440000064
根据驱动***的状态空间方程可知，驱动***被划分为两个子***Λ1和Λ2，两个子***Λ1和Λ2相互耦合，子***Λ1状态方程为：
Figure BDA0002065574440000065
子***Λ2状态方程为：
x2＝A21x1+A22x2+B2u
对子***Λ2的***状态x2＝[Ts]进行重构，***状态x2的输入和输出分别为：
Figure BDA0002065574440000066
将输出误差反馈项
Figure BDA0002065574440000067
引入子***Λ2状态方程中，其中G为反馈增益矩阵，G＝[g1 g2]，g1为两个可测状态变量的反馈增益，g2为状态变量Ts的反馈增益，可得驱动***观测器方程为：
Figure BDA0002065574440000071
步骤3，在改写的驱动***状态方程中引入变换，对驱动***状态方程进行矫正，得到线性Luenberger观测器方程及结构；
由于改写的驱动***观测器方程中存在驱动***输出量y的微分，使得状态变量观测的实现难度增大，还会将转速传感器输出信号中的高频噪音放大，使得观测误差增大，为了消除微分对观测结果的影响，在改写的驱动***观测器方程中引入变换
Figure BDA0002065574440000072
将改写的驱动***观测器方程变换为：
Figure BDA0002065574440000073
根据步骤3的驱动***观测器方程实现对驱动轴转矩Ts的观测；
驱动***状态估计误差方程为：
Figure BDA0002065574440000074
采用极点配置法配置(A22-GA12)的极点，使得估计误差
Figure BDA0002065574440000075
快速衰减到零，进而促使估计误差
Figure BDA0002065574440000076
快速衰减到零；将驱动***的状态空间方程代入上式，可得线性Luenberger观测器表达式和状态观测误差表达式为：
Figure BDA0002065574440000077
Figure BDA0002065574440000078
其中
Figure BDA0002065574440000079
完成了线性Luenberger观测器的设计，线性Luenberger观测器结构如图1所示。
本说明书中的各个实施例均采用相关的方式描述，各个实施例之间相同相似的部分互相参见即可，每个实施例重点说明的都是与其他实施例的不同之处。尤其，对于***实施例而言，由于其基本相似于方法实施例，所以描述的比较简单，相关之处参见方法实施例的部分说明即可。
以上所述仅为本发明的较佳实施例而已，并非用于限定本发明的保护范围。凡在本发明的精神和原则之内所作的任何修改、等同替换、改进等，均包含在本发明的保护范围内。

Claims (1)

1.线性Luenberger观测器的构建方法，其特征在于，具体包括以下步骤：
步骤1，建立车辆驱动***的状态空间方程，判断驱动***的能观性；
以
Figure FDA0003246186500000011
Ts为状态变量、
Figure FDA0003246186500000012
和
Figure FDA0003246186500000013
为驱动***输出、TP和Tv为驱动***输入，建立驱动***状态方程，驱动***的状态空间方程如式(1)所示：
Figure FDA0003246186500000014
其中，x是状态空间方程的输入，y为状态空间方程输出，
Figure FDA0003246186500000015
Figure FDA0003246186500000016
Figure FDA0003246186500000017
是电机B的转角，
Figure FDA0003246186500000018
是车轮的转角，θB为电机转速，θv为车轮转速，
Figure FDA0003246186500000019
是通过对转速θB、θv积分获得，Ts是驱动轴转矩，Ct为减速器阻尼，JP为电机B转子惯量，ir为主减速器传动比，Cv为车轮阻尼，Jv为车体等效到车轮的等效惯量和车轮惯量之和，ks为驱动轴刚度，Cs为驱动轴阻尼，i指的是主减速器的传动比，TP为驱动***输出轴转矩，Tv为车辆阻力矩；
驱动***的能观性矩阵
Figure FDA00032461865000000110
能观性矩阵N的秩为3，驱动***可观；
步骤2，对驱动***的状态做分块划分，重构驱动***状态分量，得到改写后的驱动***状态观测方程；
两个可测的状态变量即为驱动***输出：
Figure FDA00032461865000000111
状态变量Ts需要观测记作x2＝[Ts]，由于矩阵C的秩为2，驱动***的状态空间方程改写为：
Figure FDA00032461865000000112
其中，
Figure FDA0003246186500000021
Figure FDA0003246186500000022
I为单位矩阵；
驱动***划分为两个子***Λ1和Λ2，两个子***Λ1和Λ2相互耦合，子***Λ1状态方程为：
Figure FDA0003246186500000023
子***Λ2状态方程为：
x2＝A21x1+A22x2+B2u
对子***Λ2的***状态x2＝[Ts]进行重构，***状态x2的输入和输出分别为：
Figure FDA0003246186500000024
将输出误差反馈项
Figure FDA0003246186500000025
引入子***Λ2状态方程中，得到驱动***的观测器方程为：
Figure FDA0003246186500000026
其中G为反馈增益矩阵，G＝[g1 g2]，g1为两个可测状态变量的反馈增益，g2为状态变量Ts的反馈增益；
步骤3，在改写的驱动***状态方程中引入变换
Figure FDA0003246186500000027
获得Luenberger观测器的表达式和误差方程：
Figure FDA0003246186500000028
Figure FDA0003246186500000029
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