WO2024169527A1 - Method for controlling train speed on basis of fractional-order sliding mode and kalman filtering - Google Patents

Method for controlling train speed on basis of fractional-order sliding mode and kalman filtering Download PDF

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WO2024169527A1
WO2024169527A1 PCT/CN2024/073296 CN2024073296W WO2024169527A1 WO 2024169527 A1 WO2024169527 A1 WO 2024169527A1 CN 2024073296 W CN2024073296 W CN 2024073296W WO 2024169527 A1 WO2024169527 A1 WO 2024169527A1
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train
speed
time
sliding mode
fractional
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PCT/CN2024/073296
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French (fr)
Chinese (zh)
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黄盼
梁化典
漆林
卢昱昊
汤连桥
黄万杰
张伟
熊钢
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中车南京浦镇车辆有限公司
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Publication of WO2024169527A1 publication Critical patent/WO2024169527A1/en

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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
    • 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
    • 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
    • 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
    • B61L25/028—Determination of vehicle position and orientation within a train consist, e.g. serialisation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • G06F17/13—Differential equations
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/15—Correlation function computation including computation of convolution operations
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T10/00—Road transport of goods or passengers
    • Y02T10/60—Other road transportation technologies with climate change mitigation effect
    • Y02T10/72—Electric energy management in electromobility

Definitions

  • the present invention relates to the technical field of train control, and in particular to a train speed control method based on fractional order sliding mode and Kalman filtering.
  • the ATO (automatic train driving) system is mainly responsible for ensuring automatic train driving, providing automatic train control and adjustment, and assisting the driver in driving. It is one of the core systems of the rail transit CBTC system, among which speed control is the core function of the ATO system.
  • speed control is the core function of the ATO system.
  • many scholars have proposed different solutions, which are mainly divided into physical modeling and system identification. Among them, physical modeling has high control accuracy, but the mathematical model is complex. System identification simplifies the model complexity, but lacks real-time performance.
  • control algorithms for train applications mainly include fuzzy control, predictive control, adaptive control, neural network control or a combination of multiple control theories, but these algorithm models are highly dependent, and none of them take into account the errors in the real-time speed and position state obtained due to the noise of the previous sensors.
  • the existing train speed control algorithm has problems such as unprocessed early measurement noise, complex controller and low control accuracy.
  • the present invention provides a train speed control method based on fractional-order sliding mode and Kalman filtering, which can solve the problems pointed out in the background technology.
  • a train speed control method based on fractional order sliding mode and Kalman filtering comprises the following steps:
  • Step 1 Establish a train dynamics model
  • Step 2 Based on the train dynamics model, establish the train operation state space equation
  • Step 3 Calibrate the wheel axle speed sensor error through the Kalman filter algorithm
  • Step 4 Establish a sliding mode controller and introduce fractional-order calculus to achieve tracking control of the train reference speed and reference position.
  • the train power car model in step 1 is as follows:
  • x displacement
  • t running time
  • v the real-time speed of the train
  • u the traction/braking force on the train
  • w the basic resistance on the train
  • a, b, c are the rolling mechanical resistance coefficient, friction resistance coefficient, and air resistance coefficient of the train respectively
  • a c is the actual acceleration of the train
  • ⁇ is the train acceleration coefficient
  • ⁇ is the wheel rotation mass coefficient of the train.
  • m is the mass of the train
  • v(t) is the real-time speed of the train
  • x(t) is the real-time position of the train
  • f(t) is the traction/braking force of the train
  • w(t) is the real-time basic resistance
  • d(t) is the additional resistance and external disturbance
  • the method for calibrating the wheel axle speed sensor error by using the Kalman filter algorithm in step 3 is as follows:
  • d k is the compensation value when the train is running for k cycles
  • v k is the speed measurement value including the measurement error when the train is running for k cycles
  • v is the actual speed of the train
  • a c a k + ⁇ k #(4)
  • ⁇ k is the k-cycle train acceleration measurement error compensation value
  • a k is the accelerometer measurement value
  • a c is the actual train acceleration
  • ⁇ k is the combined error of acceleration and speed
  • a k t is (no explanation required)
  • v k is the speed measurement value containing measurement error during the k-cycle train operation
  • v k+1 is the speed value at the next moment;
  • Dk is the error disturbance caused by the accuracy error of the wheel axle speed sensor itself within k cycles, that is, the observation noise
  • xk is the displacement measurement value within k cycles
  • X is the actual amount of displacement
  • X(k+1) is the k+1 period speed state quantity
  • B are system parameters
  • X(k) is the k-period velocity state quantity
  • A(k) is the k-period system control matrix
  • ⁇ W(k) is Gaussian noise
  • Y(k) is the displacement observation
  • H is the parameter of the measurement system
  • V(k) is the observation noise
  • k-1) is the covariance prediction of time k-1 to time k
  • k-1) is The optimal covariance at time k-1
  • Q(k-1) is the covariance of the system process at time k-1;
  • K(k) is the filter gain
  • k-1) is the covariance prediction of time k at time k-1
  • HT is the transposed matrix of H
  • R(k) is the Gaussian noise at time k
  • k-1) is the predicted state at time k at time k-1
  • K(k) is the filter gain at time k
  • V(k) is the observation noise
  • k) is the optimal covariance at time k
  • k-1) is the covariance prediction at time k-1 for time k
  • I is the identity matrix
  • the estimated value of the Kalman filter is calculated through the above recursive steps
  • the fractional calculus is introduced in step 4 as follows:
  • d m /dt m is the traditional differential, where m is the smallest integer not less than the fractional order a, t is time, ⁇ is the integral variable, and when ⁇ 0, is a fractional differential, when ⁇ >0, it is a fractional integral; ⁇ (x) is a gamma function, m is a fractional order limiting integer;
  • the sliding surface introduced into the fractional calculus in step 4 is:
  • the sliding mode controller established in step 4 is:
  • k 2 sgn(S)d is the nonlinear switching control term of the system, which is used to deal with external disturbances and uncertain factors; k 1 and k 2 are control gains, where k 1 >0, k 2 >0; S is the sliding mode switching function.
  • the tracking error is obtained through the sliding mode controller and the input is output to the train ATO system until the train reaches the destination.
  • the present invention has the following beneficial effects:
  • the present invention proposes a Kalman filter algorithm based on fractional-order sliding mode control.
  • Kalman filtering can not only eliminate the measurement error caused by the previous system noise, but also reduce the chattering phenomenon caused by the sliding mode control, considering that the sliding mode of the sliding mode controller is independent of the parameters and disturbances of the system, it is proposed to adopt an improved Kalman filter control algorithm based on sliding mode control, and at the same time introduce fractional-order calculus into the sliding mode switching function to further suppress the chattering phenomenon;
  • the present invention effectively suppresses the early sensor data measurement error in the train speed control algorithm, thereby improving the actual control accuracy, while also maintaining a faster response speed and weak model dependence effect.
  • Fig. 1 is a flow chart of the present invention
  • FIG. 2 is a structural block diagram of the present invention.
  • a train speed control method based on fractional-order sliding mode and Kalman filtering includes the following steps:
  • Step 1 Establish a train dynamics model
  • Step 2 Based on the train dynamics model, establish the train operation state space equation
  • Step 3 Calibrate the wheel axle speed sensor error through the Kalman filter algorithm
  • Step 4 Establish a sliding mode controller and introduce fractional calculus to achieve tracking control of the train reference speed and reference position;
  • the control object of the present invention is a single-track high-speed train.
  • the biggest control difficulty for the controller is the accurate tracking of the speed curve.
  • the complexity of the entire line resource environment determines that the train speed position state data must have noise and measurement errors. Therefore, if the controller itself has a good disturbance suppression ability, the tracking accuracy during the operation process will be guaranteed, and it will be beneficial to realize the state of the train.
  • the Kalman filter model is designed at the beginning to eliminate noise and data measurement errors.
  • the designed controller should have good robustness, so that it can overcome the unknown external interference of the system and the uncertainty of the measurement data, so as to achieve fast and stable online control, and ensure that the train can achieve high-precision speed tracking during the tracking operation, as well as smooth control input and other requirements;
  • the train power car model in step 1 is as follows:
  • x displacement
  • t running time
  • v the real-time speed of the train
  • u the traction/braking force on the train
  • w the basic resistance on the train
  • a, b, c are the rolling mechanical resistance coefficient, friction resistance coefficient, and air resistance coefficient of the train respectively
  • a c is the actual acceleration of the train
  • ⁇ is the train acceleration coefficient
  • ⁇ is the wheel rotation mass coefficient of the train
  • the resistance of the train consists of additional resistance and basic resistance.
  • the basic resistance is affected by the train speed and mechanical wear, but the additional resistance only appears in the fixed part of the line. This paper combines the additional resistance with the uncertain disturbance part.
  • m is the mass of the train
  • v(t) is the real-time speed of the train
  • x(t) is the real-time position of the train
  • f(t) is the traction/braking force of the train
  • w(t) is the real-time basic resistance
  • d(t) is the additional resistance and external disturbance, is the velocity derivative
  • the basic running resistance of trains is affected by environmental factors, such as wind speed and track surface conditions. Various coefficients are obtained through multiple test fittings in the project. Therefore, the formula used in the model is inevitably caused by external environmental factors during the actual operation of the train.
  • axle speed sensors can reduce the burden of data processing and communication, but there are errors such as idling, slipping, and measurement errors during train operation;
  • the method for calibrating the wheel axle speed sensor error by using the Kalman filter algorithm in step 3 is as follows:
  • d k is the compensation value when the train is running for k cycles
  • v k is the true value of the speed without measurement error when the train is running for k cycles
  • v is the actual speed of the train
  • a c a k + ⁇ k #(4)
  • ⁇ k is the k-cycle train acceleration measurement error compensation value
  • a k is the accelerometer measurement value
  • a c is the actual train acceleration
  • ⁇ k is the combined error of acceleration and speed
  • a k t is (no explanation required)
  • v k is the speed measurement value containing measurement error during the k-cycle train operation
  • v k+1 is the speed value at the next moment;
  • Dk is the error disturbance caused by the accuracy error of the wheel axle speed sensor itself within k cycles, that is, the observation noise
  • xk is the measured displacement of k cycles
  • X is the actual amount of displacement
  • X(k+1) is the k+1 period speed state quantity
  • B are system parameters
  • X(k) is the K-period velocity state quantity
  • A(k) is the k-period system control matrix
  • ⁇ W(k) is Gaussian noise
  • Y(k) is the displacement observation
  • H is the parameter of the measurement system
  • V(k) is the observation noise
  • k-1) is the covariance prediction of time k at time k
  • k-1) is the optimal covariance at time k-1
  • Q(k-1) is the covariance of the system process at time k-1;
  • K(k) is the filter gain
  • k-1) is the covariance prediction of time k at time k-1
  • HT is the transposed matrix of H
  • R(k) is the Gaussian noise at time k
  • k-1) is the predicted state at time k at time k-1
  • K(k) is the filter gain at time k
  • V(k) is the observation noise
  • k) is the optimal covariance at time k
  • k-1) is the covariance prediction at time k-1 for time k
  • I is the identity matrix
  • the estimated value of the Kalman filter is calculated through the above recursive steps
  • the estimated value of the Kalman filter can be calculated through the above recursive steps In the above steps, I represents the identity matrix.
  • the covariance matrix Q is determined by ⁇ W(k), and the covariance matrix R is determined by V(k). V(k) represents the observation noise;
  • Sliding mode control has strong robustness, which can make the system state converge to the desired running trajectory within a limited time. It also has strong parameter adaptive processing function, ensuring that the system will not have discontinuous switching when there is parameter uncertainty, avoiding adverse effects on the system;
  • fractional-order calculus Since the switching phenomenon is inevitable in sliding mode control, in order to suppress the chattering caused by it, fractional-order calculus is introduced to improve this problem. Based on the advantages of fractional-order calculus in softening the discontinuous switching problem, the Caputo form of fractional-order calculus used in the present invention is defined as follows:
  • step 4 fractional calculus is introduced as follows:
  • d m /dt m is the traditional differential, where m is the smallest integer not less than the fractional order a, t is time, ⁇ is the integral variable, and when ⁇ 0, is a fractional differential, when ⁇ >0, it is a fractional integral; ⁇ (x) is a gamma function, m is a fractional order limiting integer;
  • Fractional-order sliding mode control can make the error system converge faster, improve control accuracy, and make the control process smoother.
  • the performance of the regulation process is different under different fractional orders.
  • the appropriate fractional-order calculus operator is selected to make the system meet different dynamic and static performances. Because integer-order differentials are special cases, compared with integer orders, fractional-order calculus parameters have a wider range of adaptability and more flexibility in object selection, and have better dynamic processing effects;
  • the designed sliding hyperplane needs to introduce the train position error e i and the train speed error To ensure the rapid synchronous convergence of the error; the sliding surface of the fractional calculus introduced in step 4 is:
  • the sliding mode controller established in step 4 is:
  • k 2 sgn(S)d is the nonlinear switching control of the system The term is used to deal with external disturbances and uncertain factors.
  • k 1 and k 2 are control gains, where k 1 >0 and k 2 >0.
  • S is the sliding mode switching function.
  • the tracking error obtained by the sliding mode controller is output as input to the train ATO system until the train reaches the destination;
  • the present invention adopts the Kalman filter algorithm to eliminate various mutation data, observation noise and measurement errors from the front end, thereby inputting an optimized control data into the controller;

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Abstract

A method for controlling a train speed on the basis of a fractional-order sliding mode and Kalman filtering, which method belongs to the technical field of train control. By means of Kalman filtering, not only can a measurement error caused by system noise at an earlier stage be eliminated, but chattering caused by sliding mode control can also be reduced. Considering that a sliding mode of a sliding mode controller is unrelated to parameters and disturbance of a system, an improved Kalman filtering control algorithm based on sliding mode control is proposed; moreover, fractional-order calculus is introduced into a sliding mode switching function, so as to further suppress chattering; and a measurement error of sensor data at the earlier stage in a train speed control algorithm is effectively suppressed, thereby improving the actual control precision, and also maintaining a relatively high response speed and a weak-model dependence effect.

Description

一种基于分数阶滑模以及卡尔曼滤波的列车速度控制方法A train speed control method based on fractional-order sliding mode and Kalman filtering 技术领域Technical Field
本发明涉及列车控制技术领域，特别涉及一种基于分数阶滑模以及卡尔曼滤波的列车速度控制方法。The present invention relates to the technical field of train control, and in particular to a train speed control method based on fractional order sliding mode and Kalman filtering.
背景技术Background Art
随着城市轨道交通的迅速发展，在高效率运营的同时对列车驾驶控制技术也提出了更高的要求。ATO(列车自动驾驶)系统主要负责保证列车自动驾驶，提供列车自动控制和调整并辅助司机驾驶等功能，是轨道交通CBTC系统的核心系统之一，其中速度控制是ATO系统最核心的功能，对于速度控制功能，很多学者提出不同的解决方案，主要分为物理建模和系统辨识，其中物理建模的控制精度高，但是数学模型复杂，系统辨识简化了了模型复杂度，但是缺乏实时性，目前针对列车应用的控制算法主要有模糊控制、预测控制、自适应控制、神经网络控制或多个控制理论的组合，但这些算法模型依赖性强，且都没有考虑到前期传感器噪声导致获取的实时速度位置状态存在误差。With the rapid development of urban rail transit, while operating efficiently, higher requirements are also put forward for train driving control technology. The ATO (automatic train driving) system is mainly responsible for ensuring automatic train driving, providing automatic train control and adjustment, and assisting the driver in driving. It is one of the core systems of the rail transit CBTC system, among which speed control is the core function of the ATO system. For the speed control function, many scholars have proposed different solutions, which are mainly divided into physical modeling and system identification. Among them, physical modeling has high control accuracy, but the mathematical model is complex. System identification simplifies the model complexity, but lacks real-time performance. At present, the control algorithms for train applications mainly include fuzzy control, predictive control, adaptive control, neural network control or a combination of multiple control theories, but these algorithm models are highly dependent, and none of them take into account the errors in the real-time speed and position state obtained due to the noise of the previous sensors.
综上所述，现有列车速度控制算法中存在前期测量噪声未处理、控制器复杂、控制精度低的问题。In summary, the existing train speed control algorithm has problems such as unprocessed early measurement noise, complex controller and low control accuracy.
发明内容Summary of the invention
本发明提供一种基于分数阶滑模以及卡尔曼滤波的列车速度控制方法，可以解决背景技术中所指出的问题。The present invention provides a train speed control method based on fractional-order sliding mode and Kalman filtering, which can solve the problems pointed out in the background technology.
一种基于分数阶滑模以及卡尔曼滤波的列车速度控制方法，包括如下步骤：A train speed control method based on fractional order sliding mode and Kalman filtering comprises the following steps:
步骤一：建立列车动力学模型；Step 1: Establish a train dynamics model;
步骤二：基于列车动力学模型，建立列车运行状态空间方程；Step 2: Based on the train dynamics model, establish the train operation state space equation;
步骤三：通过卡尔曼滤波算法校准轮轴速度传感器误差； Step 3: Calibrate the wheel axle speed sensor error through the Kalman filter algorithm;
步骤四：建立滑模控制器，并引入分数阶微积分，实现对列车参考速度和参考位置的跟踪控制。Step 4: Establish a sliding mode controller and introduce fractional-order calculus to achieve tracking control of the train reference speed and reference position.
所述步骤一中的列车动力车模型如下：
The train power car model in step 1 is as follows:
其中，式中:x为位移；t为运行时间；v为列车运行的实时速度；u为列车受到的牵引/制动力；w为列车所受基本阻力；a、b、c分别为列车滚动机械阻力系数、摩擦阻力系数、空气阻力系数；ac为列车实际加速度；为速度导数，即加速度；ξ为列车加速度系数；γ为列车的车轮回转质量系数。Wherein: x is displacement; t is running time; v is the real-time speed of the train; u is the traction/braking force on the train; w is the basic resistance on the train; a, b, c are the rolling mechanical resistance coefficient, friction resistance coefficient, and air resistance coefficient of the train respectively; a c is the actual acceleration of the train; is the velocity derivative, i.e. acceleration; ξ is the train acceleration coefficient; γ is the wheel rotation mass coefficient of the train.
根据步骤一中的列车动力学模型建立如下列车运行状态空间方程：
According to the train dynamics model in step 1, the following train operation state space equation is established:
其中，m为列车的质量，v(t)为列车的实时速度，x(t)为列车的实时位置，f(t)为列车的牵引/制动力，w(t)为所受实时基本阻力，d(t)为附加阻力及外部扰动，为速度导数。Where m is the mass of the train, v(t) is the real-time speed of the train, x(t) is the real-time position of the train, f(t) is the traction/braking force of the train, w(t) is the real-time basic resistance, d(t) is the additional resistance and external disturbance, is the velocity derivative.
所述步骤三中通过卡尔曼滤波算法校准轮轴速度传感器误差的方法如下：The method for calibrating the wheel axle speed sensor error by using the Kalman filter algorithm in step 3 is as follows:
基于列车运行过程中存在的空转、打滑以及测量误差，建立如下误差公式：
v＝vk+dk#(3)Based on the idling, slipping and measurement errors during train operation, the following error formula is established:
v＝v k +d k #(3)
其中，dk为k周期列车运行时的补偿值；vk为k周期列车运行时包含测量误差的速度测量值，v为列车实际速度；
ac＝ak+εk#(4)Wherein, d k is the compensation value when the train is running for k cycles; v k is the speed measurement value including the measurement error when the train is running for k cycles, and v is the actual speed of the train;
a c = a k + ε k #(4)
其中，εk为k周期列车加速度测量误差补偿值；ak为加速度计的测量值，ac为列车实际加速度；Where, ε k is the k-cycle train acceleration measurement error compensation value; a k is the accelerometer measurement value, a c is the actual train acceleration;
建立如下噪声公式：
vk+1＝vk+akt+ωk#(5)The following noise formula is established:
v k+1 =v k +a k t+ω k #(5)
其中，ωk为加速度和速度的合成误差，akt为(无需解释)；vk为k周期列车运行时包含测量误差的速度测量值；vk+1为下一时刻速度值；Among them, ω k is the combined error of acceleration and speed, a k t is (no explanation required); v k is the speed measurement value containing measurement error during the k-cycle train operation; v k+1 is the speed value at the next moment;
建立如下观测方程：
X＝xk+Dk#(6)The following observation equation is established:
X＝x k +D k #(6)
其中，Dk为k周期内轮轴速度传感器本身精度误差造成的误差扰动，即观测噪声；xk为k周期内位移测量值；X为位移的实际量；Where Dk is the error disturbance caused by the accuracy error of the wheel axle speed sensor itself within k cycles, that is, the observation noise; xk is the displacement measurement value within k cycles; X is the actual amount of displacement;
将上述公式(5)用矩阵的形式进行表示：
The above formula (5) is expressed in matrix form:
其中，X(k+1)为k+1周期速度状态量；和B为系统参数；X(k)为k周期速度状态量；A(k)为k周期系统控制矩阵；ΓW(k)为高斯噪声；Among them, X(k+1) is the k+1 period speed state quantity; and B are system parameters; X(k) is the k-period velocity state quantity; A(k) is the k-period system control matrix; ΓW(k) is Gaussian noise;
即：
Right now:
将上述公式(6)用矩阵的形式进行表示：
Y(k)＝HX(k)+V(k)#(9)The above formula (6) is expressed in matrix form:
Y(k)＝HX(k)+V(k)#(9)
其中，Y(k)为位移观测量；H为测量系统的参数；V(k)为观测噪声；Among them, Y(k) is the displacement observation; H is the parameter of the measurement system; V(k) is the observation noise;
即：
Right now:
基于初始输入量预测下一个系统状态方程：
Predict the next system state equation based on the initial input:
其中，表示k时刻对k+1时刻的估计值；X(k+1)的最优线性预测估计值；φ和B为系统参数；A(k-1)为k-1周期时的系统控制矩阵；P(k)为k时刻协方差矩阵；in, represents the estimated value of k+1 at time k; the optimal linear prediction estimate of X(k+1); φ and B are system parameters; A(k-1) is the system control matrix at k-1 period; P(k) is the covariance matrix at time k;
此时的协方差为：
The covariance at this time is:
其中，P(k|k-1)为k-1时刻对k时刻的协方差预测；P(k-1|k-1)为 k-1时刻的最优协方差；Q(k-1)为k-1时刻系统过程的协方差；Among them, P(k|k-1) is the covariance prediction of time k-1 to time k; P(k-1|k-1) is The optimal covariance at time k-1; Q(k-1) is the covariance of the system process at time k-1;
滤波增益方程为：
K(k)＝P(k|k-1)HT[HP(k|k-1)HT+R(k)]-1#(13)The filter gain equation is:
K(k)＝P(k|k-1)H T [HP(k|k-1)H T +R(k)] -1 #(13)
其中，K(k)为滤波增益；P(k|k-1)为k-1时刻对k时刻的协方差预测；HT为H的转置矩阵；R(k)为k时刻高斯噪声；Where K(k) is the filter gain; P(k|k-1) is the covariance prediction of time k at time k-1; HT is the transposed matrix of H; R(k) is the Gaussian noise at time k;
根据上述公式(7)、(9)、(11)、(12)、(13)递推滤波估计方程：
According to the above formulas (7), (9), (11), (12), (13), the recursive filtering estimation equation is:
其中，为k时刻的速度最优估计值；X(k|k-1)为k-1时刻对k时刻的预测状态；K(k)为k时刻的滤波增益；V(k)为观测噪声；in, is the optimal estimated value of the speed at time k; X(k|k-1) is the predicted state at time k at time k-1; K(k) is the filter gain at time k; V(k) is the observation noise;
相应的协方差更新为：
P(k|k)＝[I-K(k)H]P(k|k-1)#(15)The corresponding covariance update is:
P(k|k)＝[IK(k)H]P(k|k-1)#(15)
其中，P(k|k)为k时刻的最优协方差，P(k|k-1)为k-1时刻对k时刻的协方差预测；I为单位矩阵；Where P(k|k) is the optimal covariance at time k, P(k|k-1) is the covariance prediction at time k-1 for time k; I is the identity matrix;
通过上面的递推步骤计算出卡尔曼滤波的估计值 The estimated value of the Kalman filter is calculated through the above recursive steps
所述步骤四中构建滑模控制器前，将速度位置误差状态方程定义为：
Before constructing the sliding mode controller in step 4, the speed position error state equation is defined as:
其中，e为列车位置误差；为列车速度误差；x为经过卡尔曼滤波器得到列车实际位置，xr为参考位置；v为经过卡尔曼滤波算法得到的真实速度；vr为参考速度；Where, e is the train position error; is the train speed error; x is the actual train position obtained by the Kalman filter, x r is the reference position; v is the real speed obtained by the Kalman filter algorithm; v r is the reference speed;
所述步骤四中引入分数阶微积分如下：
The fractional calculus is introduced in step 4 as follows:
其中，dm/dtm为传统意义上的微分，其中m为不小于分数阶a的最小整数，t为时间；τ为积分变量；当α<0时，为分数阶微分，当α>0时，其为分数阶积分；Γ(x)为伽马函数，m为分数阶限定整数； Among them, d m /dt m is the traditional differential, where m is the smallest integer not less than the fractional order a, t is time, τ is the integral variable, and when α<0, is a fractional differential, when α>0, it is a fractional integral; Γ(x) is a gamma function, m is a fractional order limiting integer;
所述步骤四中引入分数阶微积分的滑模面为：
The sliding surface introduced into the fractional calculus in step 4 is:
其中，λ为滑模面增益系数，λ>0；ei为列车位置误差，为列车速度误差，Dα-1为分数阶算子；Where λ is the sliding surface gain coefficient, λ>0; e i is the train position error, is the train speed error, D α-1 is a fractional order operator;
步骤四中建立的滑模控制器为：
The sliding mode controller established in step 4 is:
其中，为列车基本阻力的估计项；k2sgn(S)d为系统的非线性切换控制项，用于处理外部扰动以及不确定因素，k1、k2为控制增益，其中k1>0，k2>0；S为滑模切换函数。in, is the estimation term of the basic resistance of the train; k 2 sgn(S)d is the nonlinear switching control term of the system, which is used to deal with external disturbances and uncertain factors; k 1 and k 2 are control gains, where k 1 >0, k 2 >0; S is the sliding mode switching function.
通过该滑模控制器获取的跟踪误差并输出输入量至列车ATO系统，直至列车运行至终点。The tracking error is obtained through the sliding mode controller and the input is output to the train ATO system until the train reaches the destination.
与现有技术相比，本发明的有益效果是：Compared with the prior art, the present invention has the following beneficial effects:
为了提高城市轨道交通中列车速度控制的精度，本发明提出一种基于分数阶滑模控制的卡尔曼滤波算法。对于速度控制算法来说，由于卡尔曼滤波不仅可以消除前期系统噪声导致的测量误差，还可以降低滑模控制导致的抖振现象，考虑到滑模控制器的滑动模态与系统的参数及扰动无关，提出采用基于滑模控制的改进卡尔曼滤波控制算法，同时将分数阶微积分引入滑模切换函数以进一步抑制抖振现象；In order to improve the accuracy of train speed control in urban rail transit, the present invention proposes a Kalman filter algorithm based on fractional-order sliding mode control. For the speed control algorithm, since Kalman filtering can not only eliminate the measurement error caused by the previous system noise, but also reduce the chattering phenomenon caused by the sliding mode control, considering that the sliding mode of the sliding mode controller is independent of the parameters and disturbances of the system, it is proposed to adopt an improved Kalman filter control algorithm based on sliding mode control, and at the same time introduce fractional-order calculus into the sliding mode switching function to further suppress the chattering phenomenon;
本发明有效的抑制了列车速度控制算法中前期传感器数据测量误差，从而提高了实际控制精度，同时也保持了较快的响应速度和弱模型依赖效果。The present invention effectively suppresses the early sensor data measurement error in the train speed control algorithm, thereby improving the actual control accuracy, while also maintaining a faster response speed and weak model dependence effect.
附图说明BRIEF DESCRIPTION OF THE DRAWINGS
图1为本发明的流程图；Fig. 1 is a flow chart of the present invention;
图2为本发明的结构框图。FIG. 2 is a structural block diagram of the present invention.
具体实施方式 DETAILED DESCRIPTION
下面结合附图，对本发明的一个具体实施方式进行详细描述，但应当理解本发明的保护范围并不受具体实施方式的限制。A specific implementation of the present invention is described in detail below in conjunction with the accompanying drawings, but it should be understood that the protection scope of the present invention is not limited by the specific implementation.
如图1至图2所示，本发明实施例提供的一种基于分数阶滑模以及卡尔曼滤波的列车速度控制方法，包括如下步骤：As shown in FIG. 1 and FIG. 2 , a train speed control method based on fractional-order sliding mode and Kalman filtering provided by an embodiment of the present invention includes the following steps:
步骤一：建立列车动力学模型；Step 1: Establish a train dynamics model;
步骤二：基于列车动力学模型，建立列车运行状态空间方程；Step 2: Based on the train dynamics model, establish the train operation state space equation;
步骤三：通过卡尔曼滤波算法校准轮轴速度传感器误差；Step 3: Calibrate the wheel axle speed sensor error through the Kalman filter algorithm;
步骤四：建立滑模控制器，并引入分数阶微积分，实现对列车参考速度和参考位置的跟踪控制；Step 4: Establish a sliding mode controller and introduce fractional calculus to achieve tracking control of the train reference speed and reference position;
本发明的控制对象为单线高速列车，在整个运行过程中，对于控制器而言，其最大的控制难点在于对速度曲线的精确跟踪，其次，整个线路资源环境的复杂性决定了列车速度位置状态数据必然存在噪声和测量误差。所以若控制器本身具有较好的扰动抑制能力，则在运行过程中的跟踪精度将得以保证，并有利于实现列车的状态，在控制器的设计过程中需考虑系统模型参数的不确定性和传感器数据的误差，因此在开始设计了卡尔曼滤波模型消除噪声和数据测量误差，所设计的控制器应具备良好的鲁棒性，使其能克服系统外部未知干扰，并能克服测量数据的不确定性，从而实现快速稳定的在线控制，保证列车在追踪运行过程中实现高精度速度跟踪，以及平滑控制输入等要求；The control object of the present invention is a single-track high-speed train. During the entire operation process, the biggest control difficulty for the controller is the accurate tracking of the speed curve. Secondly, the complexity of the entire line resource environment determines that the train speed position state data must have noise and measurement errors. Therefore, if the controller itself has a good disturbance suppression ability, the tracking accuracy during the operation process will be guaranteed, and it will be beneficial to realize the state of the train. In the design process of the controller, the uncertainty of the system model parameters and the error of the sensor data need to be considered. Therefore, the Kalman filter model is designed at the beginning to eliminate noise and data measurement errors. The designed controller should have good robustness, so that it can overcome the unknown external interference of the system and the uncertainty of the measurement data, so as to achieve fast and stable online control, and ensure that the train can achieve high-precision speed tracking during the tracking operation, as well as smooth control input and other requirements;
步骤一中的列车动力车模型如下：
The train power car model in step 1 is as follows:
其中，式中:x为位移；t为运行时间；v为列车运行的实时速度；u为列车受到的牵引/制动力；w为列车所受基本阻力；a、b、c分别为列车滚动机械阻力系数、摩擦阻力系数、空气阻力系数；ac为列车实际加速度；为速度导数， 即加速度；ξ为列车加速度系数；γ为列车的车轮回转质量系数；Wherein: x is displacement; t is running time; v is the real-time speed of the train; u is the traction/braking force on the train; w is the basic resistance on the train; a, b, c are the rolling mechanical resistance coefficient, friction resistance coefficient, and air resistance coefficient of the train respectively; a c is the actual acceleration of the train; is the velocity derivative, That is, acceleration; ξ is the train acceleration coefficient; γ is the wheel rotation mass coefficient of the train;
实际运行中，列车的阻力包括附加阻力和基本阻力两部分，基本阻力会受列车速度、机械磨损的影响，但附加阻力只在线路固定部分出现，本文将附加阻力与不确定扰动部分合并处理；In actual operation, the resistance of the train consists of additional resistance and basic resistance. The basic resistance is affected by the train speed and mechanical wear, but the additional resistance only appears in the fixed part of the line. This paper combines the additional resistance with the uncertain disturbance part.
根据步骤一中的列车动力学模型建立如下列车运行状态空间方程：
According to the train dynamics model in step 1, the following train operation state space equation is established:
其中，m为列车的质量，v(t)为列车的实时速度，x(t)为列车的实时位置，f(t)为列车的牵引/制动力，w(t)为所受实时基本阻力，d(t)为附加阻力及外部扰动，为速度导数；Where m is the mass of the train, v(t) is the real-time speed of the train, x(t) is the real-time position of the train, f(t) is the traction/braking force of the train, w(t) is the real-time basic resistance, d(t) is the additional resistance and external disturbance, is the velocity derivative;
参照高速铁路技术规定，列车基本运行阻力受环境因素影响，如风速、轨面情况等，工程中通过多次试验拟合获得各项系数，因此，模型中使用的公式在列车实际运行过程中不可避免地存在外部环境因素引起的，基本运行阻力w的参数结构为w＝a+bv+cv2。According to the technical regulations of high-speed railways, the basic running resistance of trains is affected by environmental factors, such as wind speed and track surface conditions. Various coefficients are obtained through multiple test fittings in the project. Therefore, the formula used in the model is inevitably caused by external environmental factors during the actual operation of the train. The parameter structure of the basic running resistance w is w = a + bv + cv 2 .
采用轮轴速度传感器能够减少数据处理和降低通信产生的负担，但在列车运行过程中，存在空转、打滑的误差以及测量误差；The use of axle speed sensors can reduce the burden of data processing and communication, but there are errors such as idling, slipping, and measurement errors during train operation;
所述步骤三中通过卡尔曼滤波算法校准轮轴速度传感器误差的方法如下：The method for calibrating the wheel axle speed sensor error by using the Kalman filter algorithm in step 3 is as follows:
基于列车运行过程中存在的空转、打滑以及测量误差，建立如下误差公式：
v＝vk+dk#(3)Based on the idling, slipping and measurement errors during train operation, the following error formula is established:
v＝v k +d k #(3)
其中，dk为k周期列车运行时的补偿值；vk为k周期列车运行时不含测量误差的速度真实值，v为列车实际速度；
ac＝ak+εk#(4)Where d k is the compensation value when the train is running for k cycles; v k is the true value of the speed without measurement error when the train is running for k cycles, and v is the actual speed of the train;
a c = a k + ε k #(4)
其中，εk为k周期列车加速度测量误差补偿值；ak为加速度计的测量值，ac为列车实际加速度；Where, ε k is the k-cycle train acceleration measurement error compensation value; a k is the accelerometer measurement value, a c is the actual train acceleration;
首先离散化列车的运行过程，设采样时间为T，采样间隔足够小且为t。因为采样间隔足够小，可以将两个采样点之间看成匀加速运动，因此根据运动学公式可以得到如下噪声公式：
vk+1＝vk+akt+ωk#(5)First, discretize the running process of the train, set the sampling time to T, and the sampling interval to be small enough to be t. Because the sampling interval is small enough, the motion between two sampling points can be regarded as uniform acceleration, so the following noise formula can be obtained according to the kinematic formula:
v k+1 =v k +a k t+ω k #(5)
其中，ωk为加速度和速度的合成误差，akt为(无需解释)；vk为k周期列车运行时包含测量误差的速度测量值；vk+1为下一时刻速度值；Among them, ω k is the combined error of acceleration and speed, a k t is (no explanation required); v k is the speed measurement value containing measurement error during the k-cycle train operation; v k+1 is the speed value at the next moment;
对于列车位置来说，用轮轴速度传感器的位置计算值作为观测量能够简化程序。因此，这里将轮轴速度传感器的位移方程作为观测方程，如下：
X＝xk+Dk#(6)For the train position, using the position calculation value of the axle speed sensor as the observation value can simplify the program. Therefore, the displacement equation of the axle speed sensor is used as the observation equation, as follows:
X＝x k +D k #(6)
其中，Dk为k周期内轮轴速度传感器本身精度误差造成的误差扰动，即观测噪声；xk为k周期的测量位移；X为位移的实际量；Where Dk is the error disturbance caused by the accuracy error of the wheel axle speed sensor itself within k cycles, that is, the observation noise; xk is the measured displacement of k cycles; X is the actual amount of displacement;
将上述公式(5)用矩阵的形式进行表示：
The above formula (5) is expressed in matrix form:
其中，X(k+1)为k+1周期速度状态量；和B为系统参数；X(k)为K周期速度状态量；A(k)为k周期系统控制矩阵；ΓW(k)为高斯噪声；Among them, X(k+1) is the k+1 period speed state quantity; and B are system parameters; X(k) is the K-period velocity state quantity; A(k) is the k-period system control matrix; ΓW(k) is Gaussian noise;
即：
Right now:
将上述公式(6)用矩阵的形式进行表示：
Y(k)＝HX(k)+V(k)#(9)The above formula (6) is expressed in matrix form:
Y(k)＝HX(k)+V(k)#(9)
其中，Y(k)为位移观测量；H为测量系统的参数；V(k)为观测噪声；Among them, Y(k) is the displacement observation; H is the parameter of the measurement system; V(k) is the observation noise;
即：
Right now:
基于初始输入量预测下一个系统状态方程：
Predict the next system state equation based on the initial input:
其中，表示k时刻对k+1时刻的估计值；X(k+1)的最优线性预测估计值；φ和B为系统参数；A(k-1)为k-1周期时的系统控制矩阵；P(k)为k时刻协方差矩阵；in, represents the estimated value of k+1 at time k; the optimal linear prediction estimate of X(k+1); φ and B are system parameters; A(k-1) is the system control matrix at k-1 period; P(k) is the covariance matrix at time k;
此时的协方差为：
The covariance at this time is:
其中，P(k|k-1)为k-1时刻对k时刻的协方差预测；P(k-1|k-1)为k-1时刻的最优协方差；Q(k-1)为k-1时刻系统过程的协方差；Among them, P(k|k-1) is the covariance prediction of time k at time k; P(k-1|k-1) is the optimal covariance at time k-1; Q(k-1) is the covariance of the system process at time k-1;
滤波增益方程为：
K(k)＝P(k|k-1)HT[HP(k|k-1)HT+R(k)]-1#(13)The filter gain equation is:
K(k)＝P(k|k-1)H T [HP(k|k-1)H T +R(k)] -1 #(13)
其中，K(k)为滤波增益；P(k|k-1)为k-1时刻对k时刻的协方差预测；HT为H的转置矩阵；R(k)为k时刻高斯噪声；Where K(k) is the filter gain; P(k|k-1) is the covariance prediction of time k at time k-1; HT is the transposed matrix of H; R(k) is the Gaussian noise at time k;
根据上述公式(7)、(9)、(11)、(12)、(13)递推滤波估计方程：
According to the above formulas (7), (9), (11), (12), (13), the recursive filtering estimation equation is:
其中，为k时刻的速度最优估计值；X(k|k-1)为k-1时刻对k时刻的预测状态；K(k)为k时刻的滤波增益；V(k)为观测噪声；in, is the optimal estimated value of the speed at time k; X(k|k-1) is the predicted state at time k at time k-1; K(k) is the filter gain at time k; V(k) is the observation noise;
相应的协方差更新为：
P(k|k)＝[I-K(k)H]P(k|k-1)#(15)The corresponding covariance update is:
P(k|k)＝[IK(k)H]P(k|k-1)#(15)
其中，P(k|k)为k时刻的最优协方差，P(k|k-1)为k-1时刻对k时刻的协方差预测；I为单位矩阵；Where P(k|k) is the optimal covariance at time k, P(k|k-1) is the covariance prediction at time k-1 for time k; I is the identity matrix;
通过上面的递推步骤计算出卡尔曼滤波的估计值 The estimated value of the Kalman filter is calculated through the above recursive steps
通过上面的递推步骤可以算出卡尔曼滤波的估计值上面步骤中I表示单位矩阵。协方差矩阵Q由ΓW(k)决定，协方差矩阵R由V(k)决定。V(k)表示观测噪声；The estimated value of the Kalman filter can be calculated through the above recursive steps In the above steps, I represents the identity matrix. The covariance matrix Q is determined by ΓW(k), and the covariance matrix R is determined by V(k). V(k) represents the observation noise;
滑模控制具备很强的鲁棒性，可使系统状态在有限的时间内收敛到期望的运行轨迹。其还具备较强的参数自适应处理功能，保证系统在具备参数不确定性时，不会出现不连续切换，避免对系统造成不利影响；Sliding mode control has strong robustness, which can make the system state converge to the desired running trajectory within a limited time. It also has strong parameter adaptive processing function, ensuring that the system will not have discontinuous switching when there is parameter uncertainty, avoiding adverse effects on the system;
步骤四中构建滑模控制器前，将速度位置误差状态方程定义为：
Before constructing the sliding mode controller in step 4, the speed position error state equation is defined as:
其中，e为列车位置误差；为列车速度误差；x为经过卡尔曼滤波器得到列车实际位置，xr为参考位置；v为经过卡尔曼滤波算法得到的真实速度；vr为 参考速度；Where, e is the train position error; is the train speed error; x is the actual position of the train obtained by the Kalman filter, x r is the reference position; v is the real speed obtained by the Kalman filter algorithm; v r is Reference speed;
因滑模控制不可避免的存在开关现象，为抑制其产生的抖振，引入分数阶微积分来改善这一问题，基于分数阶微积分在柔化不连续切换问题上的优势，本发明采用的Caputo形式的分数阶微积分定义如下：Since the switching phenomenon is inevitable in sliding mode control, in order to suppress the chattering caused by it, fractional-order calculus is introduced to improve this problem. Based on the advantages of fractional-order calculus in softening the discontinuous switching problem, the Caputo form of fractional-order calculus used in the present invention is defined as follows:
步骤四中引入分数阶微积分如下：
In step 4, fractional calculus is introduced as follows:
其中，dm/dtm为传统意义上的微分，其中m为不小于分数阶a的最小整数，t为时间；τ为积分变量；当α<0时，为分数阶微分，当α>0时，其为分数阶积分；Γ(x)为伽马函数，m为分数阶限定整数；Among them, d m /dt m is the traditional differential, where m is the smallest integer not less than the fractional order a, t is time, τ is the integral variable, and when α<0, is a fractional differential, when α>0, it is a fractional integral; Γ(x) is a gamma function, m is a fractional order limiting integer;
基于分数阶的滑模控制可使误差系统收敛更快、控制精度提高，且使控制过程更加平滑。不同分数阶下调节过程性能有异，根据现场实际运行状态，选取恰当的分数阶微积分算子，使系统满足不同的动态和静态性能。因整数阶微分是特例，相较于整数阶，分数阶微积分参数适应对象选择范围更大、更灵活，有较好的动态处理效果；Fractional-order sliding mode control can make the error system converge faster, improve control accuracy, and make the control process smoother. The performance of the regulation process is different under different fractional orders. According to the actual operating status on site, the appropriate fractional-order calculus operator is selected to make the system meet different dynamic and static performances. Because integer-order differentials are special cases, compared with integer orders, fractional-order calculus parameters have a wider range of adaptability and more flexibility in object selection, and have better dynamic processing effects;
列车追踪运行过程中，需对参考位置和参考速度曲线二者同时实现精确的跟踪，因此设计的滑动超平面需要引入列车位置误差ei和列车速度误差以保证误差的快速同步收敛；步骤四中引入分数阶微积分的滑模面为：
During the train tracking operation, it is necessary to accurately track both the reference position and the reference speed curve at the same time. Therefore, the designed sliding hyperplane needs to introduce the train position error e i and the train speed error To ensure the rapid synchronous convergence of the error; the sliding surface of the fractional calculus introduced in step 4 is:
其中，λ为滑模面增益系数，λ>0；ei为列车位置误差，为列车速度误差，Dα-1为分数阶算子；Where λ is the sliding surface gain coefficient, λ>0; e i is the train position error, is the train speed error, D α-1 is a fractional order operator;
为实现对列车参考速度和参考位置的在线跟踪，步骤四中建立的滑模控制器为：
In order to achieve online tracking of the train reference speed and reference position, the sliding mode controller established in step 4 is:
其中，为列车基本阻力的估计项；k2sgn(S)d为系统的非线性切换控制 项，用于处理外部扰动以及不确定因素，k1、k2为控制增益，其中k1>0，k2>0；S为滑模切换函数。in, is the estimated term of the basic resistance of the train; k 2 sgn(S)d is the nonlinear switching control of the system The term is used to deal with external disturbances and uncertain factors. k 1 and k 2 are control gains, where k 1 >0 and k 2 >0. S is the sliding mode switching function.
通过该滑模控制器获取的跟踪误差并输出输入量至列车ATO系统，直至列车运行至终点；The tracking error obtained by the sliding mode controller is output as input to the train ATO system until the train reaches the destination;
本发明采用了卡尔曼滤波算法从前端消除了各种突变数据和观测噪声及测量误差，从而给控制器输入了一个优化的控制数据；The present invention adopts the Kalman filter algorithm to eliminate various mutation data, observation noise and measurement errors from the front end, thereby inputting an optimized control data into the controller;
将分数阶微积分引入到滑模切换函数，进一步提高了调节精度，同时也抑制了抖振出现的频率和幅度；Introducing fractional calculus into the sliding mode switching function further improves the regulation accuracy and also suppresses the frequency and amplitude of chattering.
经过验证可知基于分数阶滑模的卡尔曼滤波速度控制算法可以有效克服滑模控制产生的抖振现象，实现了较高精度的速度控制要求。It has been verified that the Kalman filter speed control algorithm based on fractional-order sliding mode can effectively overcome the chattering phenomenon caused by sliding mode control and achieve higher-precision speed control requirements.
对于本领域技术人员而言，显然本发明不限于上述示范性实施例的细节，而且在不背离本发明的精神和基本特征的情况下，能够以其他的具体形式实现本发明。因此，无论从哪一点来看，均应将实施例看作是示范性的，而且是非限制性的，本发明的范围由所附权利要求而不是上述说明限定，因此旨在将落在权利要求的等同要件的含义和范围内的所有变化囊括在本发明内。不应将权利要求中的任何附图标记视为限制所涉及的权利要求。It will be apparent to those skilled in the art that the invention is not limited to the details of the exemplary embodiments described above and that the invention can be implemented in other specific forms without departing from the spirit and essential features of the invention. Therefore, the embodiments should be considered exemplary and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description, and it is intended that all variations within the meaning and scope of the equivalent elements of the claims be included in the invention. Any reference numeral in a claim should not be considered as limiting the claim to which it relates.
此外，应当理解，虽然本说明书按照实施方式加以描述，但并非每个实施方式仅包含一个独立的技术方案，说明书的这种叙述方式仅仅为清楚起见，本领域技术人员应当将说明书作为一个整体，各实施例中的技术方案也可以经适当组合，形成本领域技术人员可以理解的其他实施方式。 In addition, it should be understood that although the present specification is described according to implementation modes, not every implementation mode contains only one independent technical solution. This description of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment may also be appropriately combined to form other implementation modes that can be understood by those skilled in the art.

Claims (7)

  1. 一种基于分数阶滑模以及卡尔曼滤波的列车速度控制方法，其特征在于，包括如下步骤：A train speed control method based on fractional order sliding mode and Kalman filtering, characterized in that it comprises the following steps:
    步骤一：建立列车动力学模型；Step 1: Establish a train dynamics model;
    步骤二：基于列车动力学模型，建立列车运行状态空间方程；Step 2: Based on the train dynamics model, establish the train operation state space equation;
    步骤三：通过卡尔曼滤波算法校准轮轴速度传感器误差；Step 3: Calibrate the wheel axle speed sensor error through the Kalman filter algorithm;
    步骤四：建立滑模控制器，并引入分数阶微积分，实现对列车参考速度和参考位置的跟踪控制。Step 4: Establish a sliding mode controller and introduce fractional-order calculus to achieve tracking control of the train reference speed and reference position.
  2. 如权利要求1所述的一种基于分数阶滑模以及卡尔曼滤波的列车速度控制方法，其特征在于，所述步骤一中的列车动力车模型如下：
    The train speed control method based on fractional-order sliding mode and Kalman filtering according to claim 1 is characterized in that the train power car model in step 1 is as follows:
    其中，式中:x为位移；t为运行时间；v为列车运行的实时速度；u为列车受到的牵引/制动力；w为列车所受基本阻力；a、b、c分别为列车滚动机械阻力系数、摩擦阻力系数、空气阻力系数；ac为列车实际加速度；为速度导数，即加速度；ξ为列车加速度系数；γ为列车的车轮回转质量系数。Wherein: x is displacement; t is running time; v is the real-time speed of the train; u is the traction/braking force on the train; w is the basic resistance on the train; a, b, c are the rolling mechanical resistance coefficient, friction resistance coefficient, and air resistance coefficient of the train respectively; a c is the actual acceleration of the train; is the velocity derivative, i.e. acceleration; ξ is the train acceleration coefficient; γ is the wheel rotation mass coefficient of the train.
  3. 如权利要求2所述的一种基于分数阶滑模以及卡尔曼滤波的列车速度控制方法，其特征在于，根据步骤一中的列车动力学模型建立如下列车运行状态空间方程：
    The train speed control method based on fractional-order sliding mode and Kalman filtering as claimed in claim 2 is characterized in that the following train operation state space equation is established according to the train dynamics model in step 1:
    其中，m为列车的质量，v(t)为列车的实时速度，x(t)为列车的实时位置，f(t)为列车的牵引/制动力，w(t)为所受实时基本阻力，d(t)为附加阻力及外部扰动，为速度导数。 Where m is the mass of the train, v(t) is the real-time speed of the train, x(t) is the real-time position of the train, f(t) is the traction/braking force of the train, w(t) is the real-time basic resistance, d(t) is the additional resistance and external disturbance, is the velocity derivative.
  4. 如权利要求2所述的一种基于分数阶滑模以及卡尔曼滤波的列车速度控制方法，其特征在于，所述步骤三中通过卡尔曼滤波算法校准轮轴速度传感器误差的方法如下：The train speed control method based on fractional-order sliding mode and Kalman filtering according to claim 2 is characterized in that the method of calibrating the wheel axle speed sensor error by using the Kalman filtering algorithm in step 3 is as follows:
    基于列车运行过程中存在的空转、打滑以及测量误差，建立如下误差公式：
    v＝vk+dk#(3)    Based on the idling, slipping and measurement errors during train operation, the following error formula is established:
    v＝v k +d k #(3)
    其中，dk为k周期列车运行时的补偿值；vk为k周期列车运行时包含测量误差的速度测量值，v为列车实际速度；
    ac＝ak+εk#(4)    Wherein, d k is the compensation value when the train is running for k cycles; v k is the speed measurement value including the measurement error when the train is running for k cycles, and v is the actual speed of the train;
    a c = a k + ε k #(4)
    其中，εk为k周期列车加速度测量误差补偿值；ak为k周期列车加速度；且ak为加速度计的测量值，ac为列车实际加速度；Wherein, ε k is the k-cycle train acceleration measurement error compensation value; a k is the k-cycle train acceleration; and a k is the measured value of the accelerometer, and a c is the actual train acceleration;
    建立如下噪声公式：
    vk+1＝vk+akt+ωk#(5)    The following noise formula is established:
    v k+1 =v k +a k t+ω k #(5)
    其中，ωk为加速度和速度的合成误差，akt为(无需解释)；vk为k周期列车运行时包含测量误差的速度测量值；vk+1为下一时刻速度值；Among them, ω k is the combined error of acceleration and speed, a k t is (no explanation required); v k is the speed measurement value containing measurement error during the k-cycle train operation; v k+1 is the speed value at the next moment;
    建立如下观测方程：
    X＝xk+Dk#(6)    The following observation equation is established:
    X＝x k +D k #(6)
    其中，Dk为k周期内轮轴速度传感器本身精度误差造成的误差扰动，即观测噪声；xk为k周期内的测量位移；X为位移的实际量；Where Dk is the error disturbance caused by the accuracy error of the wheel axle speed sensor itself within k cycles, that is, the observation noise; xk is the measured displacement within k cycles; X is the actual amount of displacement;
    将上述公式(5)用矩阵的形式进行表示：
    The above formula (5) is expressed in matrix form:
    其中，X(k+1)为k+1周期速度状态量；和B为系统参数；X(k)为K周期速度状态量；A(k)为k周期系统控制矩阵；ΓW(k)为高斯噪声；Among them, X(k+1) is the k+1 period speed state quantity; and B are system parameters; X(k) is the K-period velocity state quantity; A(k) is the k-period system control matrix; ΓW(k) is Gaussian noise;
    即：
    Right now:
    将上述公式(6)用矩阵的形式进行表示：
    Y(k)＝HX(k)+V(k)#(9)     The above formula (6) is expressed in matrix form:
    Y(k)＝HX(k)+V(k)#(9)
    其中，Y(k)为位移观测量；H为测量系统的参数；V(k)为观测噪声；Among them, Y(k) is the displacement observation; H is the parameter of the measurement system; V(k) is the observation noise;
    即：
    Right now:
    基于初始输入量预测下一个系统状态方程：
    Predict the next system state equation based on the initial input:
    其中，表示k时刻对k+1时刻的估计值；X(k+1)的最优线性预测估计值；φ和B为系统参数；A(k-1)为k-1周期时的系统控制矩阵；P(k)为k时刻协方差矩阵；in, represents the estimated value of k+1 at time k; the optimal linear prediction estimate of X(k+1); φ and B are system parameters; A(k-1) is the system control matrix at k-1 period; P(k) is the covariance matrix at time k;
    此时的协方差为：
    The covariance at this time is:
    其中，P(k|k-1)为k-1时刻对k时刻的协方差预测；P(k-1|k-1)为k-1时刻的最优协方差；Q(k-1)为k-1时刻系统过程的协方差；Among them, P(k|k-1) is the covariance prediction of time k at time k; P(k-1|k-1) is the optimal covariance at time k-1; Q(k-1) is the covariance of the system process at time k-1;
    滤波增益方程为：
    K(k)＝P(k|k-1)HT[HP(k|k-1)HT+R(k)]-1#(13)    The filter gain equation is:
    K(k)＝P(k|k-1)H T [HP(k|k-1)H T +R(k)] -1 #(13)
    其中，K(k)为滤波增益；P(k|k-1)为k-1时刻对k时刻的协方差预测；HT为H的转置矩阵；R(k)为k时刻高斯噪声；Where K(k) is the filter gain; P(k|k-1) is the covariance prediction of time k at time k-1; HT is the transposed matrix of H; R(k) is the Gaussian noise at time k;
    根据上述公式(7)、(9)、(11)、(12)、(13)递推滤波估计方程：
    According to the above formulas (7), (9), (11), (12), (13), the recursive filtering estimation equation is:
    其中，为k时刻的速度最优估计值；X(k|k-1)为k-1时刻对k时刻的预测状态；K(k)为k时刻的滤波增益；V(k)为观测噪声；in, is the optimal estimated value of the speed at time k; X(k|k-1) is the predicted state at time k at time k-1; K(k) is the filter gain at time k; V(k) is the observation noise;
    相应的协方差更新为：
    P(k|k)＝[I-K(k)H]P(k|k-1)#(15)    The corresponding covariance update is:
    P(k|k)＝[IK(k)H]P(k|k-1)#(15)
    其中，P(k|k)为k时刻的最优协方差，P(k|k-1)为k-1时刻对k时刻的协方差预测；I为单位矩阵；Where P(k|k) is the optimal covariance at time k, P(k|k-1) is the covariance prediction at time k-1 for time k; I is the identity matrix;
    通过上面的递推步骤计算出卡尔曼滤波的估计值 The estimated value of the Kalman filter is calculated through the above recursive steps
  5. 如权利要求1所述的一种基于分数阶滑模以及卡尔曼滤波的列车速度 控制方法，所述步骤四中构建滑模控制器前，将速度位置误差状态方程定义为：
    A train speed detector based on fractional order sliding mode and Kalman filtering as claimed in claim 1 Control method, before constructing the sliding mode controller in step 4, the speed position error state equation is defined as:
    其中，e为列车位置误差；为列车速度误差；x为经过卡尔曼滤波器得到列车实际位置，xr为参考位置；v为经过卡尔曼滤波算法得到的真实速度；vr为参考速度。Where, e is the train position error; is the train speed error; x is the actual position of the train obtained by the Kalman filter, x r is the reference position; v is the real speed obtained by the Kalman filter algorithm; v r is the reference speed.
  6. 如权利要求1所述的一种基于分数阶滑模以及卡尔曼滤波的列车速度控制方法，所述步骤四中引入分数阶微积分如下：
    In the train speed control method based on fractional-order sliding mode and Kalman filtering as claimed in claim 1, the fractional-order calculus is introduced in step 4 as follows:
    其中，dm/dtm为传统意义上的微分，其中m为不小于分数阶a的最小整数，t为时间；τ为积分变量；当α<0时，为分数阶微分，当α>0时，其为分数阶积分；Γ(x)为伽马函数，m为分数阶限定整数。Among them, d m /dt m is the traditional differential, where m is the smallest integer not less than the fractional order a, t is time, τ is the integral variable, and when α<0, is a fractional differential, when α>0, it is a fractional integral; Γ(x) is a gamma function, m is a fractional order limiting integer.
  7. 如权利要求6所述的一种基于分数阶滑模以及卡尔曼滤波的列车速度控制方法，所述步骤四中引入分数阶微积分的滑模面为：
    In the train speed control method based on fractional-order sliding mode and Kalman filtering according to claim 6, the sliding mode surface introduced into the fractional-order calculus in step 4 is:
    其中，λ为滑模面增益系数，λ>0；ei为列车位置误差，为列车速度误差，Dα-1为分数阶算子；Where λ is the sliding surface gain coefficient, λ>0; e i is the train position error, is the train speed error, D α-1 is a fractional order operator;
    步骤四中建立的滑模控制器为：
    The sliding mode controller established in step 4 is:
    其中，为列车基本阻力的估计项；k2sgn(S)d为系统的非线性切换控制项，用于处理外部扰动以及不确定因素，k1、k2为控制增益，其中k1>0，k2>0；S为滑模切换函数。in, is the estimation term of the basic resistance of the train; k 2 sgn(S)d is the nonlinear switching control term of the system, which is used to deal with external disturbances and uncertain factors; k 1 and k 2 are control gains, where k 1 >0, k 2 >0; S is the sliding mode switching function.
    通过该滑模控制器获取的跟踪误差并输出输入量至列车ATO系统，直至列车运行至终点。 The tracking error is obtained through the sliding mode controller and the input is output to the train ATO system until the train reaches the destination.
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