非完整机械控制系统的模型参考变结构控制_英文_
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[2]
Caplygin non2holonomic mechanical system ( i . e . , a non2holonomic system with certain symmetry proper2 ties ) . A so2called normal form is introduced to model the dynamics completely. Based on the normal form ,a feed2 back control strategy to perform input/ output decoupling is proposed by You and Chen Wang
T
B ( q) τ + J ( q) λ + d1 , J ( q) q = d2
n
( 1) ( 2)
0
∈
=
R n ×m , E2
Im J 12 ( q) In ( ) m
= . So
0
In m
∈
R n× n(
m)
, T ( q)
where the variable q ∈R denotes the generalized coor2 dinate and determines the geometric configuration of the mechanical system. The time derivative q ∈ R n is the generalized velocity. M : R
第 16 卷第 3 期 1999 年 6 月
控制理论与应用
CON TROL THEORY AND APPLICA TIONS
Vol . 16 ,No. 3 J un. , 1999
源自文库
M odel Ref e r e nce Va ri a bl e St r uct u r e Cont r ol f or 3 Non2Hol onomic M ec ha nical Cont r ol S ys yt e ms
n
0
where
→R
n× n
represents the gen2
q12 = J 12 ( q) q22 + F ( q2 , q2 ) q2 + ω 2
( )
( 5)
eralized moment of inertia , assumed to be a symmetric and positive definite matrix. τ ∈R is the control input . B : R n →R n ×r denotes the input matrix with full column rank , and B ( q) τ ∈ R is known as a nonconservative generalized force along the direction of its corresponding generalized coordinate q. G ( q) denotes the gravitational forces and the term C ( q , q ) q includes centrifugal and Coriolis forces ( even the frictional forces ) , J : R
2 M ai n r es ults
Consider the following non2holonomic mechanical system with parametric perturbation and external distur2
bance M ( q) q
( 2)
q2 +
0
=
( 4)
T ( q) E2 q2 + ω 1 where the matrices E1 and E2 are defined to be partitions of the identity matrix I n = ( E1 E2 ) as E1 = Im
+ C ( q , q ) q + G ( q) =
A bs t ract : A variable structure model reference tracking controller for non2holonomic mechanical systems is designed un2 der parametric perturbation and external disturbance. A design procedure with three2stage control is developed to solve the track2 ing problem for perturbed non2holonomic mechanical control systems based on a proper matrix decomposition ,the concept of in2 put/ output decoupling in nonlinear control theory , and the theory of variable structure control . Finally , a typical non2holonomic example — — — a vertical wheel moving on a given plane — — — is given with computer simulation to illustrate the significant ad2 vantage of the proposed method. Ke y wor ds : non2holonomic mechanical system ; decoupling ; tracking ; variable stucture control
the passive position variable ,and q2 ∈R n constraint J ( q) q = d2 becomes
-1 q1 = J 12 ( q) q2 + J 1 ( q) d2 -1
is regarded
as the active position variable . Then , the independent ( 3)
Wen Xiangcai
( Centre of Information ,State Environmental Protection Administration ・ Beijing , 100029 , P. R. China)
Liu Yongqing
(Department of Automation ,South China University of Technology ・ Guangzhou , 510640 , P. R. China)
Guo Qingfu
( Computation Center , Henan Financial and Ecology College ・ Zhengzhou , 450000 , P. R. China)
Guo Shujuan
(Department of Mathematics , Xinxiang Teacher College ・ Xinxiang , 453000 , P. R. China)
非完整机械控制系统的模型参考变结构控制
( 河南财经学院计算机中心・ 郑州 , 450000) ( 新乡师范专科学校数学系・ 新乡 , 453000) ( 国家环境保护总局信息中心・ 北京 , 100029) ( 华南理工大学电子与信息学院・ 广州 , 510640)
郭清傅
郭淑娟
温香彩
刘永清
摘要 : 在参数扰动和外部干扰情况下 , 对非完整机械控制系统设计了变结构模型参考跟踪控制器 . 基于适当的 矩阵分解 、 非线性控制理论中的输入2输出解耦概念及变结构控制理论 , 为解决干扰非完整机械控制系统的跟踪问 题提出了三级控制设计过程 . 最后通过一非完整机械控制系统的例子 ( 在给定平面上运动的垂直轮 ) 的计算机仿真 说明了提出方法的优越性 . 关键词 : 非完整机械系统 ; 解耦 ; 跟踪 ; 变结构控制
where J 12 ( q) = - J 1 ( q) J 2 ( q) . In terms of the above non2holonomic constraint , the velocity q is expressed in the form q = J 12 ( q) In m -1 J 1 ( q) d 2
[1 ] [3]
. McClamroch and
considered the holonomic case . In these de2
signs ,the dynamic models are assumed to be perfect ,ex2 actly known ,and free of external disturbances . However , in many practical situations , the system parameters may be perturbed due to unmodelled dynamics , model trunca2
treats a special system , the
3 This work is supported by National Science Foundation ( 69874010) and Postdoctoral Foundation of China .
Manuscript received Sep . 25 , 1996 ,revised Oct . 20 , 1997 .
386
CON TROL THEORY AND APPLICA TIONS
Vol . 16
m
tion , uncertainty in friction force and load , flexibility of the mechanical body and deformation of the constrained surface ,etc . In addition ,external disturbance due to vari2 ations of environment and load may also occur. Hence ,a control design for control systems to achieve the purpose of robust tracking under parametric perturbation and ex2 ternal disturbance is important for practical application. This paper considers the problem.
1 I nt r o d ucti o n
Problems associated with the tracking ,stabilization and
stability of control systems with non2holonomic con2 straints ( i . e , control systems with non2integrable con2 straints ) have become increasingly important during the past decade and have consequently received the attention of many investigators . This system has extensive practical background ,such as mobile robots , automatic pilot vehi2 cles , a knife edge moving in point contact on a plane surface , a vertical wheel rolling without slipping on a plane surface . Bloch et al
Caplygin non2holonomic mechanical system ( i . e . , a non2holonomic system with certain symmetry proper2 ties ) . A so2called normal form is introduced to model the dynamics completely. Based on the normal form ,a feed2 back control strategy to perform input/ output decoupling is proposed by You and Chen Wang
T
B ( q) τ + J ( q) λ + d1 , J ( q) q = d2
n
( 1) ( 2)
0
∈
=
R n ×m , E2
Im J 12 ( q) In ( ) m
= . So
0
In m
∈
R n× n(
m)
, T ( q)
where the variable q ∈R denotes the generalized coor2 dinate and determines the geometric configuration of the mechanical system. The time derivative q ∈ R n is the generalized velocity. M : R
第 16 卷第 3 期 1999 年 6 月
控制理论与应用
CON TROL THEORY AND APPLICA TIONS
Vol . 16 ,No. 3 J un. , 1999
源自文库
M odel Ref e r e nce Va ri a bl e St r uct u r e Cont r ol f or 3 Non2Hol onomic M ec ha nical Cont r ol S ys yt e ms
n
0
where
→R
n× n
represents the gen2
q12 = J 12 ( q) q22 + F ( q2 , q2 ) q2 + ω 2
( )
( 5)
eralized moment of inertia , assumed to be a symmetric and positive definite matrix. τ ∈R is the control input . B : R n →R n ×r denotes the input matrix with full column rank , and B ( q) τ ∈ R is known as a nonconservative generalized force along the direction of its corresponding generalized coordinate q. G ( q) denotes the gravitational forces and the term C ( q , q ) q includes centrifugal and Coriolis forces ( even the frictional forces ) , J : R
2 M ai n r es ults
Consider the following non2holonomic mechanical system with parametric perturbation and external distur2
bance M ( q) q
( 2)
q2 +
0
=
( 4)
T ( q) E2 q2 + ω 1 where the matrices E1 and E2 are defined to be partitions of the identity matrix I n = ( E1 E2 ) as E1 = Im
+ C ( q , q ) q + G ( q) =
A bs t ract : A variable structure model reference tracking controller for non2holonomic mechanical systems is designed un2 der parametric perturbation and external disturbance. A design procedure with three2stage control is developed to solve the track2 ing problem for perturbed non2holonomic mechanical control systems based on a proper matrix decomposition ,the concept of in2 put/ output decoupling in nonlinear control theory , and the theory of variable structure control . Finally , a typical non2holonomic example — — — a vertical wheel moving on a given plane — — — is given with computer simulation to illustrate the significant ad2 vantage of the proposed method. Ke y wor ds : non2holonomic mechanical system ; decoupling ; tracking ; variable stucture control
the passive position variable ,and q2 ∈R n constraint J ( q) q = d2 becomes
-1 q1 = J 12 ( q) q2 + J 1 ( q) d2 -1
is regarded
as the active position variable . Then , the independent ( 3)
Wen Xiangcai
( Centre of Information ,State Environmental Protection Administration ・ Beijing , 100029 , P. R. China)
Liu Yongqing
(Department of Automation ,South China University of Technology ・ Guangzhou , 510640 , P. R. China)
Guo Qingfu
( Computation Center , Henan Financial and Ecology College ・ Zhengzhou , 450000 , P. R. China)
Guo Shujuan
(Department of Mathematics , Xinxiang Teacher College ・ Xinxiang , 453000 , P. R. China)
非完整机械控制系统的模型参考变结构控制
( 河南财经学院计算机中心・ 郑州 , 450000) ( 新乡师范专科学校数学系・ 新乡 , 453000) ( 国家环境保护总局信息中心・ 北京 , 100029) ( 华南理工大学电子与信息学院・ 广州 , 510640)
郭清傅
郭淑娟
温香彩
刘永清
摘要 : 在参数扰动和外部干扰情况下 , 对非完整机械控制系统设计了变结构模型参考跟踪控制器 . 基于适当的 矩阵分解 、 非线性控制理论中的输入2输出解耦概念及变结构控制理论 , 为解决干扰非完整机械控制系统的跟踪问 题提出了三级控制设计过程 . 最后通过一非完整机械控制系统的例子 ( 在给定平面上运动的垂直轮 ) 的计算机仿真 说明了提出方法的优越性 . 关键词 : 非完整机械系统 ; 解耦 ; 跟踪 ; 变结构控制
where J 12 ( q) = - J 1 ( q) J 2 ( q) . In terms of the above non2holonomic constraint , the velocity q is expressed in the form q = J 12 ( q) In m -1 J 1 ( q) d 2
[1 ] [3]
. McClamroch and
considered the holonomic case . In these de2
signs ,the dynamic models are assumed to be perfect ,ex2 actly known ,and free of external disturbances . However , in many practical situations , the system parameters may be perturbed due to unmodelled dynamics , model trunca2
treats a special system , the
3 This work is supported by National Science Foundation ( 69874010) and Postdoctoral Foundation of China .
Manuscript received Sep . 25 , 1996 ,revised Oct . 20 , 1997 .
386
CON TROL THEORY AND APPLICA TIONS
Vol . 16
m
tion , uncertainty in friction force and load , flexibility of the mechanical body and deformation of the constrained surface ,etc . In addition ,external disturbance due to vari2 ations of environment and load may also occur. Hence ,a control design for control systems to achieve the purpose of robust tracking under parametric perturbation and ex2 ternal disturbance is important for practical application. This paper considers the problem.
1 I nt r o d ucti o n
Problems associated with the tracking ,stabilization and
stability of control systems with non2holonomic con2 straints ( i . e , control systems with non2integrable con2 straints ) have become increasingly important during the past decade and have consequently received the attention of many investigators . This system has extensive practical background ,such as mobile robots , automatic pilot vehi2 cles , a knife edge moving in point contact on a plane surface , a vertical wheel rolling without slipping on a plane surface . Bloch et al