WO2022262362A1 - 一种多质点车辆队列行驶系统的迭代学习控制方法 - Google Patents
一种多质点车辆队列行驶系统的迭代学习控制方法 Download PDFInfo
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B61—RAILWAYS
- B61L—GUIDING RAILWAY TRAFFIC; ENSURING THE SAFETY OF RAILWAY TRAFFIC
- B61L25/00—Recording or indicating positions or identities of vehicles or trains or setting of track apparatus
- B61L25/02—Indicating or recording positions or identities of vehicles or trains
- B61L25/021—Measuring and recording of train speed
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B61—RAILWAYS
- B61L—GUIDING RAILWAY TRAFFIC; ENSURING THE SAFETY OF RAILWAY TRAFFIC
- B61L15/00—Indicators provided on the vehicle or train for signalling purposes
- B61L15/0072—On-board train data handling
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
- G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
- G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B60—VEHICLES IN GENERAL
- B60L—PROPULSION OF ELECTRICALLY-PROPELLED VEHICLES; SUPPLYING ELECTRIC POWER FOR AUXILIARY EQUIPMENT OF ELECTRICALLY-PROPELLED VEHICLES; ELECTRODYNAMIC BRAKE SYSTEMS FOR VEHICLES IN GENERAL; MAGNETIC SUSPENSION OR LEVITATION FOR VEHICLES; MONITORING OPERATING VARIABLES OF ELECTRICALLY-PROPELLED VEHICLES; ELECTRIC SAFETY DEVICES FOR ELECTRICALLY-PROPELLED VEHICLES
- B60L15/00—Methods, circuits, or devices for controlling the traction-motor speed of electrically-propelled vehicles
- B60L15/32—Control or regulation of multiple-unit electrically-propelled vehicles
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B60—VEHICLES IN GENERAL
- B60L—PROPULSION OF ELECTRICALLY-PROPELLED VEHICLES; SUPPLYING ELECTRIC POWER FOR AUXILIARY EQUIPMENT OF ELECTRICALLY-PROPELLED VEHICLES; ELECTRODYNAMIC BRAKE SYSTEMS FOR VEHICLES IN GENERAL; MAGNETIC SUSPENSION OR LEVITATION FOR VEHICLES; MONITORING OPERATING VARIABLES OF ELECTRICALLY-PROPELLED VEHICLES; ELECTRIC SAFETY DEVICES FOR ELECTRICALLY-PROPELLED VEHICLES
- B60L15/00—Methods, circuits, or devices for controlling the traction-motor speed of electrically-propelled vehicles
- B60L15/32—Control or regulation of multiple-unit electrically-propelled vehicles
- B60L15/38—Control or regulation of multiple-unit electrically-propelled vehicles with automatic control
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B60—VEHICLES IN GENERAL
- B60L—PROPULSION OF ELECTRICALLY-PROPELLED VEHICLES; SUPPLYING ELECTRIC POWER FOR AUXILIARY EQUIPMENT OF ELECTRICALLY-PROPELLED VEHICLES; ELECTRODYNAMIC BRAKE SYSTEMS FOR VEHICLES IN GENERAL; MAGNETIC SUSPENSION OR LEVITATION FOR VEHICLES; MONITORING OPERATING VARIABLES OF ELECTRICALLY-PROPELLED VEHICLES; ELECTRIC SAFETY DEVICES FOR ELECTRICALLY-PROPELLED VEHICLES
- B60L50/00—Electric propulsion with power supplied within the vehicle
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B61—RAILWAYS
- B61L—GUIDING RAILWAY TRAFFIC; ENSURING THE SAFETY OF RAILWAY TRAFFIC
- B61L15/00—Indicators provided on the vehicle or train for signalling purposes
- B61L15/0058—On-board optimisation of vehicle or vehicle train operation
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
- G05B13/0265—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric the criterion being a learning criterion
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B61—RAILWAYS
- B61L—GUIDING RAILWAY TRAFFIC; ENSURING THE SAFETY OF RAILWAY TRAFFIC
- B61L2201/00—Control methods
Definitions
- the invention relates to the field of iterative learning control, in particular to an iterative learning control method for a multi-mass vehicle platooning system, aiming at a class of multi-mass vehicle platooning systems with structural uncertainty and input time lag.
- the multi-particle vehicle platooning system is a kind of spatial interconnection system composed of multiple train carriages coupled with each other, which has the characteristics of time-space coupling, large number of variables, and high dimensionality.
- On the premise of ensuring the safe operation of trains improving the speed and performance of trains running within a limited time and in batches has become the focus of attention.
- due to the complex operating environment of the train there are often uncertainties in the actual system.
- there is a phenomenon of interactive transmission of information in the control implementation which usually involves input time lag, which leads to a lag in the system output response and affects the stability and performance of the system.
- iterative learning control is used to solve the tracking problem of the multi-particle vehicle platooning system.
- Iterative Learning Control is a new type of intelligent control method, which can improve the tracking performance of the controlled system within a limited time by repeatedly learning from previous batches. Its most notable features are the small amount of calculation, low requirement for prior knowledge of system dynamics, and simplicity and ease of implementation.
- This application applies iterative learning control to the multi-mass vehicle platoon driving system with uncertainty and input time delay, which can improve the response speed and trajectory tracking accuracy of the system, and improve the control performance.
- the present inventor proposes an iterative learning control method for a multi-mass vehicle platoon driving system.
- the technical scheme of the present invention is as follows:
- An iterative learning control method for a multi-mass vehicle platooning system comprising the following steps:
- Step 1 Establish a spatially interconnected system model of the multi-mass vehicle platooning system
- t and s are the discrete time and the train number respectively, and the above formula is substituted into equation (1) to obtain the partial recurrence equation
- x 1 (t+1,s) x 1 (t,s)+Tx 2 (t,s)
- p(t,s) denotes the pseudo-input channel of structural uncertainty
- q(t,s) denotes the pseudo-output channel of structural uncertainty
- I rf is the identity matrix whose dimension is r f ;
- Step 2 Transform the spatial interconnection system model
- the model (3) is transformed into an equivalent one-dimensional dynamic model by using lifting technology, and the lifting vector is defined as follows:
- X(t) [x(t,1) T ,x(t,2) T ,...,x(t,n) T ] T
- V(t) [v(t,1) T ,v(t,2) T ,...,v(t,n) T ] T
- W(t) [w(t,1) T ,w(t,2) T ,...,w(t,n) T ] T
- Y(t) [y(t,1) T ,y(t,2) T ,...,y(t,n) T ] T
- model (6) contains interconnected variables, then the model (6) needs to be further simplified;
- n is a permutation matrix independent of time t
- V(t) ⁇ -1 A 21 X(t) (8)
- Step 3 Design an iterative learning law based on the state observer
- k+1 represents the current running batch of the system
- t ⁇ [0, ⁇ ] represents the limited working cycle of each batch of the system
- the input delay constant satisfies the condition ⁇ ;
- the current control signal U k+1 (t) is equal to the control signal U k (t) of the previous batch plus an update item r k+1 (t), and the update item r k+1 (t) is obtained from the previous batch
- the error information is calculated;
- the tracking error of the k+1 batch system is
- Y r (t) is the desired output trajectory
- K 1 , K 2 and K 3 are the learning gains to be designed
- the update item is composed of state feedback information and PD-type previous tracking error information.
- learning gain K 2 K 3
- formula (22) is simplified to P-type ILC;
- Step 4 Carry out systematic stability analysis and learning gain solution to the linear discrete repetitive process model
- V(k,t) V 1 (t,k)+V 2 (k,t)
- model (25) is stable along the batch, and the learning gain of the update item (22) and the gain of the state observer (20) are respectively
- Equation (32) is equivalent to
- Equation (31) the model (25) is robust and stable along the batch, and the learning gain of the update item (22) and the gain of the state observer (20) are given by Equation (31).
- the multi-particle train dynamics equation is discretized using the finite difference method to obtain a partial recurrence equation, and then Transform it into a spatial interconnection system model;
- the lifting technology to convert the spatial interconnection system model into an equivalent one-dimensional dynamic model to compensate for the input time lag; design an iterative learning law based on the state observer, and according to the designed iterative learning law will
- the controlled object is transformed into an equivalent discrete repetitive process, and the sufficient conditions for the stability of the system along the batch are obtained according to the stability theory of the repeated process, and the controller synthesis problem is transformed into a linear matrix inequality.
- the method is simple and easy to implement, solves the problem of output response lag caused by input time lag, and considers the structural uncertainty of the system, and has good control performance and robustness.
- Fig. 1 is a structural diagram of a multi-mass vehicle platoon driving system provided by the present application.
- Fig. 2 is a structural diagram of the spatial interconnection system model provided by the present application.
- Fig. 3 is the output curve of the first train particle under the nominal condition provided by the present application.
- Fig. 4 is the output curve of the second train particle under the nominal condition provided by the present application.
- Fig. 5 is the output curve of the third train particle under the nominal condition provided by the present application.
- Fig. 6 is the RMS comparison curve of the nominal system provided by the present application.
- Fig. 7 is the output curve of the first train mass point under uncertain conditions provided by the present application.
- Fig. 8 is the output curve of the second train particle under the uncertain condition provided by the present application.
- Fig. 9 is the output curve of the third train particle under the uncertain situation provided by the present application.
- Fig. 10 is the RMS comparison curve of the uncertain system provided by the present application.
- Figure 2 is the structural diagram of the spatial interconnection system model, and each parameter matrix of model (3) is
- the working cycle is 20s, and the speed reference trajectory of each vehicle is
- the reference track signal is given by a waveform generator.
- the learning gain and the corresponding observer gain of the P-type ILC are the same.
- the above-mentioned iterative learning controller is realized by a STM32F103RCT6 chip.
- the input signal of the chip is collected by BENTLY 74712 speed sensor.
- the input signal enters the stm32 chip through the conditioning circuit for storage and calculation, and is used to construct an iterative learning update law.
- the signal obtained after CPU calculation is used as the control signal U k+1 (t) of the current batch.
- the control signal acts on the stepper motor DM3622 through the D/A conversion circuit, which is used to update the speed of the train particle until it tracks the given reference speed trajectory.
- Figure 3 is the output curve of the mass point of the first train under the nominal condition
- Figure 4 is the output curve of the mass point of the second train under the nominal condition
- Figure 5 is the output curve of the mass point of the third train under the nominal condition.
- Figure 6 is the RMS comparison curve of the nominal system. It can be seen that in the case of a constant input time delay, the state after the ⁇ step of the system estimated by the state observer is used as feedback, so that the system output responds in advance, and the input time delay is realized. compensation. With the increase of the number of iterations, the control signal is constantly updated, and the output of each train gradually tracks the expected speed trajectory, which verifies the effectiveness of the method of the present invention. In addition, compared with P-type ILC, PD-type ILC utilizes more tracking error information, and the root mean square error converges faster along the batch, which can achieve more perfect tracking performance.
- Figure 7 is the output curve of the mass point of the first train under uncertain conditions
- Figure 8 is the output curve of the mass points of the second train under uncertain conditions
- Figure 9 is the output curve of the mass points of the third train under uncertain conditions
- Figure 10 Represents the RMS contrast curve for an uncertain system.
- the state observer is used to estimate the future state of the system and form a feedback to act on the system, so that the system outputs a timely response after the time delay ⁇ , which improves the control process.
- the output of each train asymptotically tracks the desired velocity trajectory, and the tracking error converges along the batches, demonstrating the effectiveness of the proposed method and its robustness to the structural uncertainty of the system.
- PD-type ILC requires almost 7 batches to achieve perfect tracking. Compared with P-type ILC, the convergence time is shorter, the convergence speed is faster, and the tracking performance is better.
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Abstract
本发明公开了一种多质点车辆队列行驶系统的迭代学习控制方法，涉及迭代学习控制领域，该方法包括：首先利用有限差分法对多质点列车动力学方程进行离散化得到偏递推方程，然后将其转化为空间互联系统模型；其次，使用提升技术将空间互联系统模型转换为等价的一维动态模型，为补偿输入时滞，基于状态观测器设计迭代学习律；再次，根据迭代学习律将被控对象转化为等价的离散重复过程，基于重复过程的稳定性分析将控制器综合问题转换成线性矩阵不等式。该方法简单易于实现，解决了输入时滞引起的系统输出响应滞后的问题，并且考虑了系统的结构不确定性，具有良好的控制性能与鲁棒性。
Description
本发明涉及迭代学习控制领域，尤其是一种多质点车辆队列行驶系统的迭代学习控制方法，针对一类具有结构不确定性和输入时滞的多质点车辆队列行驶系统。
近年来，随着铁路的飞速发展，列车的高效出行方式深受人们的欢迎。多质点车辆队列行驶系统是一类由多个列车车厢相互耦合构成的空间互联系统，具有时空耦合、变量数目多、维数高的特性。在保证列车安全运行的前提下，提高列车有限时间和批次内运行的速度和性能成为了关注的重点。然而，由于列车复杂的运行环境，实际系统往往存在不确定性。此外，在控制实施中存在信息交互传输的现象，通常会涉及到输入时滞，导致系统输出响应滞后，影响系统的稳定和性能。针对上述多质点车辆队列行驶系统的运行特点，迭代学习控制被用于解决多质点车辆队列行驶系统的跟踪问题。
迭代学习控制(Iterative Learning Control，ILC)是一种新型的智能控制方法，通过从先前的批次中重复学习，能在有限时间内提高被控系统的跟踪性能。它最显著的特点是计算量小，对系统动力学的先验知识要求低，简单易于实现。本申请将迭代学习控制应用于具有不确定性和输入时滞的多质点车辆队列行驶系统可以提高系统的响应速度和轨迹跟踪精度，改善控制性能。
发明内容
本发明人针对上述问题及技术需求，提出了一种多质点车辆队列行驶系统的迭代学习控制方法，本发明的技术方案如下：
一种多质点车辆队列行驶系统的迭代学习控制方法，包括如下步骤：
第一步：建立多质点车辆队列行驶系统的空间互联系统模型
所述多质点车辆队列行驶系统的动力学方程描述为
其中，
表示第i辆车的位置，
是控制输入，表示列车的牵引力，τ是由信号传输所引起的时滞常量，
是测量输出，表示列车的速度；m表示每辆列车质量，其变化范围是
k是弹簧系数，其变化范围是
选择采样时间T，利用有限差分法对方程(1)进行近似离散化，即
其中，t和s分别为离散时间和列车序号，将上述公式代入方程(1)得到偏递推方程
x
1(t+1,s)＝x
1(t,s)+Tx
2(t,s)
y(t,s)＝x
2(t,s)
设车辆间互相传递的信息为各自的位置信息，即令互联变量w
+(t,s)＝w
-(t,s)＝x
1(t,s)，v
+(t,s)＝x
1(t,s-1)，v
-(t,s)＝x
1(t,s+1)，输出变量y(t,s)＝x
2(t,s)，将方程(2)转化为不确定空间互联系统模型，即
其中，
上式x(t,s)∈R
n、u(t,s)∈R
q和y(t,s)∈R
m分别表示第s个子系统的状态、输入和输出变量；τ(0<τ<α)表示时滞常量；
和
表示相邻子系统间的互联作用，且满足
其边界条件为v
+(1)＝w
-(1)＝0，v
-(n)＝w
+(n)＝0，n为子系统数目；
p(t,s)表示结构不确定性的伪输入通道，q(t,s)表示结构不确定性的伪输出通道，且
p(t,s)＝θ
sq(t,s) (5)
其中，不确定块
δ
i∈R,|δ
i|≤1,i＝1,…,f，δ
i描述了系统动力学参数的变化，I
rf为维度为r
f的单位矩阵；
第二步：对空间互联系统模型进行转换
利用提升技术将模型(3)转化为等价的一维动态模型，定义提升向量如下：
X(t)＝[x(t,1)
T,x(t,2)
T,…,x(t,n)
T]
T
V(t)＝[v(t,1)
T,v(t,2)
T,…,v(t,n)
T]
T
W(t)＝[w(t,1)
T,w(t,2)
T,…,w(t,n)
T]
T
P(t)＝[p(t,1)
T,p(t,2)
T,…,p(t,n)
T]
T
Q(t)＝[q(t,1)
T,q(t,2)
T,…,q(t,n)
T]
T
U(t-τ)＝[u(t-τ,1)
T,u(t-τ,2)
T,…,u(t-τ,n)
T]
T
Y(t)＝[y(t,1)
T,y(t,2)
T,…,y(t,n)
T]
T
则整个不确定空间互联系统模型由以下模型等价描述
其中，
模型(6)中包含互联变量，则需对所述模型(6)进一步简化；
利用式(4)的互联特性及其边界条件，得到互联变量间的等式关系
W(t)＝ηV(t) (7)
其中，η是与时间t无关的置换矩阵；
将式(7)代入(6)中，得到
V(t)＝η
-1A
21X(t) (8)
然后将式(8)代入(6)，消去互联变量W(t)和V(t)，得到以下等价的不确定模型
其中，
根据式(5)得到
P(t)＝θQ(t) (10)
其中不确定性块θ＝diag{θ
1,…,θ
n},θ
i≤I,i＝1,…,n；
将式(10)代入(9)，得到
然后将式(11)代入(9)，利用消元法消去不确定变量P(t)和Q(t)，得到一般形式的状态空间模型
其中，
ΔB＝B
11θ(I-D
11θ)
-1D
12
第三步：基于状态观测器设计迭代学习律
将状态空间模型(12)描述为ILC结构形式
其中k+1表示系统当前运行批次，t∈[0,α]表示系统每一批次的有限工作周期，输入时滞常量满足条件τ<α；
则所述迭代学习律表示为
U
k+1(t)＝U
k(t)+r
k+1(t) (14)
当前控制信号U
k+1(t)等于前一批次的控制信号U
k(t)加上一个更新项r
k+1(t)，所述更新项r
k+1(t)由前次误差信息计算得到；
第k+1批次系统的跟踪误差为
e
k+1(t)＝Y
r(t)-Y
k+1(t) (15)
其中，Y
r(t)为期望输出轨迹；
考虑到输出响应存在滞后，因此将所述跟踪误差重新描述为
e
k+1(t)＝Y
r(t-τ)-Y
k+1(t) (16)
引入状态误差向量
假设Y
r(0)＝Y
k(0)＝CX
k(0)和
即系统每一批次都返回至相同初始状态，则
且
为了补偿输入时滞，利用当前批次的输出信息构造了如下的状态观测器
其中，
是状态
的τ步超前预测，即
是
的估计值；L是待设计的观测器增益；
定义观测误差为
设学习律(14)中的更新项为
其中，K
1、K
2和K
3是待设计的学习增益；
所述更新项由状态反馈信息和PD型前次跟踪误差信息构成，当学习增益K
2＝K
3时，式(22)简化为P型ILC；
将(22)代入(20)，得到
并且
令
K＝K
2-K
3，得到以下具有时滞的线性离散重复过程模型
其中，
第四步：对所述线性离散重复过程模型进行系统的稳定性分析和学习增益求解
选取李雅普诺夫函数为
V(k,t)＝V
1(t,k)+V
2(k,t)
其中，S＝diag{S
1,S
2}>0，Q＝diag{Q
1,Q
2}>0，P
2>P
1>0；V
1(t,k)表示沿一个批次的能量变化，V
2(k,t)表示批次间的能量变化；各子函数增量为
其中，
总的函数增量为
其中，
如果对任意的k和t，ΔV(k,t)<0都成立，则模型(25)沿批次稳定，其等价条件为Π<0；对Π<0使用Schur补引理，在不等式两边分别左乘和右乘
并且作变量代换，令
得到以下结论：
对于式(25)所描述的具有时滞的标称线性离散重复过程模型，若存在矩阵W＝diag{W
1,W
2}>0，X＝diag{X
1,X
2}>0，Z
1>0，Z
2>0和矩阵R、R
1、R
2、R
3使得下列线性矩阵不等式成立
则模型(25)沿批次稳定，更新项(22)的学习增益和状态观测器(20)的增益分别为
当考虑系统存在结构不确定性时，对Π<0使用Schur补引理，并在不等式两边分别左乘和右乘
并且作变量代换，令
得到
Ξ
1+MΘN+N
TΘ
TM
T<0 (32)
其中，
Θ＝θ(I-D
11θ)
-1,θ
Tθ≤I
式(32)等价于
其中ε＞0；
根据Schur补引理，式(33)描述为
对上式分别左乘和右乘diag{I,εI,εI}，并用ε替换ε
2，得出以下结论：
对于式(25)所描述的具有时滞的不确定线性离散重复过程模型，若存在矩阵W＝diag{W
1,W
2}>0，X＝diag{X
1,X
2}>0，Z
1>0，Z
2>0和矩阵R、R
1、R
2、R
3使得下列线性矩阵不等式成立
其中，
则模型(25)沿批次鲁棒稳定，更新项(22)的学习增益和状态观测器(20)的增益由式(31)给出。
本发明的有益技术效果是：
本申请研究了一种具有结构不确定性和输入时滞的多质点车辆队列行驶系统的鲁棒ILC方法，首先利用有限差分法对多质点列车动力学方程进行离散化得到偏递推方程，然后将其转化为空间互联系统模型；其次使用提升技术将空间互联系统模型转换为等价的一维动态模型，为补偿输入时滞；基于状态观测器设计迭代学习律，根据设计的迭代学习律将被控对象转化为等价的离散重复过程，根据重复过程稳定性理论得到系统沿批次稳定的充分条件，将控制器综合问题转换成线性矩阵不等式。该方法简单易于实现，解决了输入时滞引起的输出响应滞后问题，并且考虑了系统的结构不确定性，具有良好的控制性能与鲁棒性。
图1是本申请提供的多质点车辆队列行驶系统的结构图。
图2是本申请提供的空间互联系统模型的结构图。
图3是本申请提供的标称情况下第1个列车质点的输出曲线。
图4是本申请提供的标称情况下第2个列车质点的输出曲线。
图5是本申请提供的标称情况下第3个列车质点的输出曲线。
图6是本申请提供的标称系统的RMS对比曲线。
图7是本申请提供的不确定情况下第1个列车质点的输出曲线。
图8是本申请提供的不确定情况下第2个列车质点的输出曲线。
图9是本申请提供的不确定情况下第3个列车质点的输出曲线。
图10是本申请提供的不确定系统的RMS对比曲线。
下面结合附图对本发明的具体实施方式做进一步说明。
图1为多质点车辆队列行驶系统的结构图，对于其动力学方程(1)，取时滞常量τ＝4；每辆列车质量m＝2[kg]，变化范围
弹簧系数k＝2[N/m]，变化范围
采样时间T＝0.05[s]。
图2为空间互联系统模型的结构图，则模型(3)的各个参数矩阵为
考虑3辆列车互联的多质点车辆队列行驶系统，设系统初始条件为x
0(0,1)＝x
0(0,2)＝x
0(0,3)＝0，每一批次的有限工作周期为20s，每辆车的速度参考轨迹为
参考轨迹信号由波形发生器给出。
求解式(25)，得到标称系统PD型ILC的学习增益和观测器增益为
P型ILC的学习增益和相应的观测器增益为
上述迭代学习控制器的实现通过一块STM32F103RCT6芯片实现。芯片的输入信号由BENTLY 74712速度传感器采集得到。输入信号通过调理电路进入stm32芯片进行存储和计算，并用于构造迭代学习更新律，CPU计算后得到的信号作为当前批次的控制信号U
k+1(t)。控制信号通过D/A转换电路作用于步进电机DM3622，用于更新列车质点的速度，直到跟踪上给定的参考速度轨迹。
图3为标称情况下第1辆列车质点的输出曲线，图4为标称情况下第2辆列车质点的输出曲线，图5为标称情况下第3辆列车质点的输出曲线。为进一步评价系统跟踪性能，引入均方根误差性能指标
图6为标称系统的RMS对比曲线，可以看出在输入时滞常量的情况下，利用状态观测器估计的系统τ步以后的状态作为反馈，使系统输出提前响应，实现了对输入时滞的补偿。随着迭代次数的增加，控制信号不断更新，每辆列车的输出逐渐跟踪上期望的速度轨迹，验证了本发明方法的有效性。此外，相比于P型ILC，PD型ILC利用了更多的跟踪误差信息，均方根误差沿批次收敛 的速度更快，可以实现更完美的跟踪性能。
求解式(34)，得到不确定系统的PD型ILC的学习增益和观测器增益为
同理，P型ILC的学习增益和相应的观测器增益为
图7为不确定情况下第1辆列车质点的输出曲线，图8为不确定情况下第2辆列车质点的输出曲线，图9为不确定情况下第3辆列车质点的输出曲线，图10表示不确定系统的RMS对比曲线。
可以看出在时滞常量和结构不确定性同时存在的情况下，利用状态观测器对系统未来状态进行估计并构成反馈作用于系统，使得系统在经过时滞τ后输出及时响应，改善了控制过程。随着迭代次数的增加，每辆列车的输出渐近跟踪上期望的速度轨迹，跟踪误差沿批次收敛，说明了本发明方法的有效性，并且对系统的结构不确定性具有鲁棒性。另外，PD型ILC实现完美跟踪需要几乎7个批次，相比于P型ILC收敛时间更短，收敛速度更快，跟踪性能更好。
以上所述的仅是本申请的优选实施方式，本发明不限于以上实施例。可以理解，本领域技术人员在不脱离本发明的精神和构思的前提下直接导出或联想到的其他改进和变化，均应认为包含在本发明的保护范围之内。
Claims (1)
- 一种多质点车辆队列行驶系统的迭代学习控制方法，其特征在于，所述方法包括：第一步：建立多质点车辆队列行驶系统的空间互联系统模型所述多质点车辆队列行驶系统的动力学方程描述为
其中，表示第i辆车的位置，
是控制输入，表示列车的牵引力，τ是由信号传输所引起的时滞常量，
是测量输出，表示列车的速度；m表示每辆列车质量，其变化范围是
k是弹簧系数，其变化范围是
选择采样时间T，利用有限差分法对方程(1)进行近似离散化，即
其中，t和s分别为离散时间和列车序号，将上述公式代入方程(1)得到偏递推方程
设车辆间互相传递的信息为各自的位置信息，即令互联变量w +(t,s)＝w -(t,s)＝x 1(t,s)，v +(t,s)＝x 1(t,s-1)，v -(t,s)＝x 1(t,s+1)，输出变量y(t,s)＝x 2(t,s)，将方程(2)转化为不确定空间互联系统模型，即
其中，
上式x(t,s)∈R n、u(t,s)∈R q和y(t,s)∈R m分别表示第s个子系统的状态、输入和输出变量；τ(0<τ<α)表示时滞常量；和
表示相邻子系统间的互联作用，且满足
其边界条件为v +(1)＝w -(1)＝0，v -(n)＝w +(n)＝0，n为子系统数目；p(t,s)表示结构不确定性的伪输入通道，q(t,s)表示结构不确定性的伪输出通道，且p(t,s)＝θ sq(t,s) (5)其中，不确定块δ i∈R，|δ i|≤1,i＝1,…,f，δ i描述了系统动力学参数的变化，
为维度为r f的单位矩阵；
第二步：对空间互联系统模型进行转换利用提升技术将模型(3)转化为等价的一维动态模型，定义提升向量如下：X(t)＝[x(t,1) T,x(t,2) T,…,x(t,n) T] TV(t)＝[v(t,1) T,v(t,2) T,…,v(t,n) T] TW(t)＝[w(t,1) T,w(t,2) T,…,w(t,n) T] TP(t)＝[p(t,1) T,p(t,2) T,…,p(t,n) T] TQ(t)＝[q(t,1) T,q(t,2) T,…,q(t,n) T] TU(t-τ)＝[u(t-τ,1) T,u(t-τ,2) T,…,u(t-τ,n) T] TY(t)＝[y(t,1) T,y(t,2) T,…,y(t,n) T] T则整个不确定空间互联系统模型由以下模型等价描述
其中，
模型(6)中包含互联变量，则需对所述模型(6)进一步简化；利用式(4)的互联特性及其边界条件，得到互联变量间的等式关系W(t)＝ηV(t) (7)其中，η是与时间t无关的置换矩阵；将式(7)代入(6)中，得到V(t)＝η -1A 21X(t) (8)然后将式(8)代入(6)，消去互联变量W(t)和V(t)，得到以下等价的不确定模型
其中，
根据式(5)得到P(t)＝θQ(t) (10)其中不确定性块θ＝diag{θ 1,…,θ n},θ i≤I,i＝1,…,n；将式(10)代入(9)，得到
然后将式(11)代入(9)，利用消元法消去不确定变量P(t)和Q(t)，得到一般形式的状态空间模型
其中，
ΔB＝B 11θ(I-D 11θ) -1D 12第三步：基于状态观测器设计迭代学习律将状态空间模型(12)描述为ILC结构形式
其中k+1表示系统当前运行批次，t∈[0,α]表示系统每一批次的有限工作周期，输入时滞常量满足条件τ<α；则所述迭代学习律表示为U k+1(t)＝U k(t)+r k+1(t) (14)当前控制信号U k+1(t)等于前一批次的控制信号U k(t)加上一个更新项r k+1(t)，所述 更新项r k+1(t)由前次误差信息计算得到；第k+1批次系统的跟踪误差为e k+1(t)＝Y r(t)-Y k+1(t) (15)其中，Y r(t)为期望输出轨迹；考虑到输出响应存在滞后，因此将所述跟踪误差重新描述为e k+1(t)＝Y r(t-τ)-Y k+1(t) (16)引入状态误差向量
假设Y r(0)＝Y k(0)＝CX k(0)和即系统每一批次都返回至相同初始状态，则
且
为了补偿输入时滞，利用当前批次的输出信息构造了如下的状态观测器
其中，是状态
的τ步超前预测，即
是
的估计值；L是待设计的观测器增益；
定义观测误差为
设学习律(14)中的更新项为
其中，K 1、K 2和K 3是待设计的学习增益；所述更新项由状态反馈信息和PD型前次跟踪误差信息构成，当学习增益K 2＝K 3时，式(22)简化为P型ILC；将(22)代入(20)，得到
并且
令K＝K 2-K 3，得到以下具有时滞的线性离散重复过程模型
其中，
第四步：对所述线性离散重复过程模型进行系统的稳定性分析和学习增益求解选取李雅普诺夫函数为
其中，S＝diag{S 1,S 2}>0，Q＝diag{Q 1,Q 2}>0，P 2>P 1>0；V 1(t,k)表示沿一个批次的能量变化，V 2(k,t)表示批次间的能量变化；各子函数增量为
其中，
总的函数增量为
其中，
如果对任意的k和t，ΔV(k,t)<0都成立，则模型(25)沿批次稳定，其等价条件为Π<0；对Π<0使用Schur补引理，在不等式两边分别左乘和右乘并且作变量代换，令
得到以下结论：
对于式(25)所描述的具有时滞的标称线性离散重复过程模型，若存在矩阵W＝diag{W 1,W 2}>0，X＝diag{X 1,X 2}>0，Z 1>0，Z 2>0和矩阵R、R 1、R 2、R 3使得下列线性矩阵不等式成立
则模型(25)沿批次稳定，更新项(22)的学习增益和状态观测器(20)的增益分别为
当考虑系统存在结构不确定性时，对Π<0使用Schur补引理，并在不等式两边分别左乘和右乘并且作变量代换，令
得到
Ξ 1+MΘN+N TΘ TM T<0 (32)其中，
Θ＝θ(I-D 11θ) -1,θ Tθ≤I式(32)等价于
其中ε＞0；根据Schur补引理，式(33)描述为
对上式分别左乘和右乘diag{I,εI,εI}，并用ε替换ε 2，得出以下结论：对于式(25)所描述的具有时滞的不确定线性离散重复过程模型，若存在矩阵W＝diag{W 1,W 2}>0，X＝diag{X 1,X 2}>0，Z 1>0，Z 2>0和矩阵R、R 1、R 2、R 3使得下列线性矩阵不等式成立
其中，
则模型(25)沿批次鲁棒稳定，更新项(22)的学习增益和状态观测器(20)的增益由式(31)给出；第五步：给出所述多质点车辆队列行驶系统的具体参数，确定所述迭代学习律的学习增益及相应的观测器增益，对ILC状态空间模型施加本批次的控制信号，得到本批次的输出，然后通过所述迭代学习律的反复调节控制，使得车辆队列行驶系统每辆列车的输出渐近跟踪上期望的速度轨迹。
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| CN109031958A (zh) * | 2018-10-16 | 2018-12-18 | 廊坊师范学院 | 分数阶多智能体追踪一致性的迭代学习控制方法 |
| CN110032066A (zh) * | 2019-01-10 | 2019-07-19 | 廊坊师范学院 | 分数阶非线性系统轨迹跟踪的自适应迭代学习控制方法 |
| CN113341726A (zh) * | 2021-06-18 | 2021-09-03 | 江南大学 | 一种多质点车辆队列行驶系统的迭代学习控制方法 |
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| EP3798075B1 (en) * | 2019-09-25 | 2023-08-02 | Ningbo Geely Automobile Research & Development Co. Ltd. | A method for driving a vehicle platoon |
| EP3836111A1 (en) * | 2019-12-09 | 2021-06-16 | Ningbo Geely Automobile Research & Development Co. Ltd. | A method for operating a transportation system |
| CN111158349B (zh) * | 2020-01-15 | 2021-01-08 | 浙江大学 | 基于多步线性化策略的无人驾驶车辆模型预测控制方法 |
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| CN101846979A (zh) * | 2010-06-29 | 2010-09-29 | 北京航空航天大学 | 一种精确目标跟踪的超前迭代学习控制方法 |
| CN109031958A (zh) * | 2018-10-16 | 2018-12-18 | 廊坊师范学院 | 分数阶多智能体追踪一致性的迭代学习控制方法 |
| CN110032066A (zh) * | 2019-01-10 | 2019-07-19 | 廊坊师范学院 | 分数阶非线性系统轨迹跟踪的自适应迭代学习控制方法 |
| CN113341726A (zh) * | 2021-06-18 | 2021-09-03 | 江南大学 | 一种多质点车辆队列行驶系统的迭代学习控制方法 |
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| US20230078812A1 (en) | 2023-03-16 |
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