Tracking control method for preset performance of heavy haul train

Abstract

The invention discloses a heavy-load train preset performance tracking control method, and belongs to the technical field of multi-heavy-load train tracking control. The method comprises the following steps: analyzing dynamic characteristics of a multi-marshalling train in a longitudinal running process, and establishing a multi-mass-point dynamic model reflecting a train group stress relation; designing a finite time performance function for strictly constraining transient and steady-state performance of a system tracking error; a sliding mode controller based on preset performance is constructed, and rapid and accurate tracking of an expected operation curve is realized; based on the Lyapunov stability theory, it is proved that signals of a closed-loop system are bounded, and it is ensured that train distance errors converge within a boundary range specified by a preset performance function. According to the invention, through the designed preset performance control mechanism, the overshoot and convergence speed of the tracking error can be effectively limited, so that the operation safety and control precision of the heavy-load train under the complex working condition are remarkably improved.

Description

Technical Field

[0002] This invention relates to the field of multi-load train tracking control technology, and more specifically, to a method for controlling the preset performance of heavy-load trains based on a finite-time preset performance function. Background Technology

[0004] Heavy-haul trains, with their combined advantages of long-distance operation, large-capacity transport, low energy consumption, and high safety, have become a key carrier in the modern railway transportation system. However, heavy-haul trains typically consist of multiple locomotives and dozens or even hundreds of freight cars. The trains are long and heavy, and the cars are connected by couplers and buffer devices, resulting in complex longitudinal coupling dynamic characteristics during operation.

[0005] In actual operation, heavy-haul trains need to accurately track a preset cruise trajectory to ensure operational efficiency, safe distance, and energy optimization. However, due to the complex longitudinal forces on the train and the dynamic coupling between vehicles, traditional control methods struggle to simultaneously achieve the speed, accuracy, and stability of trajectory tracking.

[0006] To meet the high requirements of multiple locomotive units for traction and braking force, the train control strategy must ensure that its dynamic response performance, such as overshoot and convergence speed, is strictly limited within the allowable range; otherwise, it will directly affect the overall control quality and operational safety of the system. Summary of the Invention

[0008] To address the aforementioned problems, this invention proposes a preset performance tracking control method for heavy-haul trains. This method establishes a multi-mass model of the train, constructs a finite-time preset performance function, and combines it with an error transformation mechanism. By applying preset performance control, the transient and steady-state performance requirements of the system are directly transformed into strict mathematical constraints on the tracking error, effectively improving the system's dynamic response. This ensures that both the overshoot and convergence speed of the tracking error are limited to the range required by the preset performance function. This method not only significantly improves the controller's adaptability and reliability under complex operating conditions but also provides key technical support for achieving high-precision and robust operation control of heavy-haul trains.

[0009] The present invention provides a pre-set performance tracking control method for heavy-haul trains, comprising the following steps:

[0010] Step 1: Analyze the longitudinal forces acting on the heavy-haul train during operation, treating each locomotive and freight car as a point mass to establish a multi-mass dynamic model of the train:

[0011]

[0012] Where i represents the i-th car, and N represents the total number of locomotives and freight cars in the heavy-haul train. These are the mass, position, speed, and traction / braking control inputs for the i-th car, respectively. Locomotives can generate traction and braking forces, while freight cars lack traction and braking devices; therefore, for the i-th freight car, , ; These represent the coupling forces between the i-th vehicle and its two adjacent vehicles, respectively. This represents the basic resistance experienced by the vehicle in section i.

[0013] Step 2: Define the desired cruise trajectory and position error.

[0014] The desired cruising trajectory is:

[0015]

[0016] in, It is the desired position for train operation. It is the expected speed of the given train operation.

[0017] Define the position error of the i-th locomotive as:

[0018]

[0019] in, It is the first Positional error of the locomotive Indicates the first The expected distance between the locomotive and the reference trajectory.

[0020] Step 3: Design the finite-time performance function;

[0021]

[0022] in, This represents the initial performance boundary; This represents the steady-state performance boundary. and A constant that is greater than zero. The set convergence time.

[0023] Step 4: Combine positional error Establish a conversion error function based on the designed performance function.

[0024] The conversion error function is as follows:

[0025]

[0026] in, Pre-set a performance function for a finite time. This represents the positional error.

[0027] Step 5: Based on the conversion error function Based on the multi-mass dynamics model of a heavy-haul train, and under the constraints of a pre-defined performance function within a limited time, a finite-time sliding mode controller is designed as follows:

[0028]

[0029] In the formula, For the traction / braking control input of the i-th vehicle; ,

[0030] ; , These are design constants that are greater than zero.

[0031] For sliding surfaces:

[0032]

[0033] In the formula, and The design constant is greater than 0; ultimately, the conversion error is... It converges to a bounded region near zero within a finite time, thus ensuring the position error. Meets the preset performance requirements for a limited time.

[0034] The advantages of this invention are:

[0035] 1. The present invention provides a preset performance tracking control method for heavy-haul trains, which directly transforms the transient and steady-state performance of train tracking error into strict mathematical constraints. Through the parameterized design of the performance function, the error control boundary is precisely set, so that the dynamic response of the system is completely within the predictable and controllable range. This effectively avoids problems such as excessive overshoot and response lag in traditional control methods, and ensures that the overshoot and convergence speed of the tracking error strictly meet the requirements of the preset performance function.

[0036] 2. The pre-set performance tracking control method for heavy-haul trains of the present invention designs a finite-time pre-set performance function. By reasonably configuring the initial performance boundary, steady-state performance boundary and convergence time parameters, it can ensure that the performance function stably converges to the steady-state performance boundary within a pre-set finite time T, and continues to remain within this boundary thereafter, significantly improving the response speed of train operation and the timeliness of trajectory tracking.

[0037] 3. The heavy-haul train preset performance tracking control method of this invention, through the coordinated design of error conversion mechanism and performance function, ensures that the train tracking error is always limited within the envelope of the preset performance function, fundamentally avoiding the risk of error divergence or exceeding the safety threshold. This strict error constraint characteristic not only significantly improves the dynamic response speed of the control system, but also achieves high-precision trajectory tracking. Attached Figure Description

[0039] Figure 1 This is a flowchart of the pre-set performance tracking control method for heavy-haul trains according to the present invention;

[0040] Figure 2 This is a schematic diagram of the position trajectory of some vehicles in the heavy-haul train of the present invention;

[0041] Figure 3 This is a schematic diagram illustrating the positional errors of each locomotive in the heavy-haul train of this invention. Detailed Implementation

[0043] The present invention will now be described in further detail with reference to the accompanying drawings.

[0044] The present invention provides a pre-set performance tracking control method for heavy-haul trains, such as... Figure 1 As shown, the specific steps are as follows:

[0045] Step 1: Multi-mass dynamics modeling of heavy-haul trains.

[0046] To analyze the longitudinal forces acting on a heavy-haul train during operation, a multi-mass dynamic model of the train is established by treating each locomotive and freight car as a point mass. The specific form of the model is as follows:

[0047]

[0048] Where i represents the i-th car, and N represents the total number of locomotives and freight cars in the heavy-haul train. These are the mass, position, speed, and traction / braking control inputs for the i-th car, respectively. Locomotives can generate traction and braking forces, while freight cars lack traction and braking devices; therefore, for the i-th freight car, , ; These represent the coupling forces between the i-th vehicle and its two adjacent vehicles, respectively. This represents the basic resistance experienced by the vehicle in section i.

[0049] The forces exerted by the front and rear couplers on the aforementioned train are modeled using a spring model as follows:

[0050]

[0051]

[0052] in, and These represent the stiffness coefficient and damping coefficient of the buffer device connecting the i-th and i+1-th vehicle sections, respectively. This represents the static balance length of the buffer device connecting the i-th and i+1-th vehicles.

[0053] The basic resistance experienced by the vehicle during operation as described in Section i above for:

[0054]

[0055] in, , , These are the basic drag coefficients, obtained through wind tunnel testing.

[0056] Step 2: Define the desired cruise trajectory and position error.

[0057] The desired cruising trajectory is:

[0058]

[0059] in, It is the desired position for train operation. It is the expected speed of the given train operation.

[0060] Define the position error of the i-th locomotive as:

[0061]

[0062] in, It is the first Positional error of the locomotive Indicates the first The expected distance between the locomotive and the reference trajectory.

[0063] Step 3: Design a finite-time performance function to constrain the position error.

[0064] The finite-time preset performance function is:

[0065]

[0066] in, This represents the initial performance boundary; This represents the steady-state performance boundary. and A constant that is greater than zero. The set convergence time.

[0067] It can be seen that the finite-time performance function remains constant after time T. This can effectively constrain the tracking error and ensure that the error converges to the steady-state boundary within a finite time.

[0068] Step 4: Combine positional error Establish a conversion error function based on the designed performance function.

[0069] The conversion error function is as follows:

[0070]

[0071] in, Pre-set a performance function for a finite time. For position error, when position error initial value satisfy When, if the conversion error function If bounded, then the position error Always can be enclosed in a finite-time preset performance function Within the envelope. If there exists a certain moment... ,because and The continuity of the transformation error function will lead to the transformation error function Unbounded. Therefore, by ensuring the transformation error function... The boundedness of the property can achieve the preset performance constraint of the error.

[0072] Step 5: Design of finite-time sliding mode controller for heavy-haul trains.

[0073] According to the conversion error function Based on the multi-mass dynamics model of a heavy-haul train, and under the constraint of a pre-set performance function within a limited time, a finite-time sliding mode controller is designed to minimize the conversion error. It converges to a bounded region near zero within a finite time, thus ensuring the position error. Meets the preset performance requirements for a limited time.

[0074] Finite-time tracking sliding mode controller;

[0075] Sliding surface Designed as:

[0076]

[0077] In the formula, , Both are design constants greater than 0, and their values ​​will affect the control performance requirements such as the dynamic response speed of the system.

[0078] Combining the multi-mass dynamics model of heavy-haul trains with the designed sliding surface, the sliding mode controller is designed as follows:

[0079]

[0080] In the formula, For the traction / braking control input of the i-th vehicle; ,

[0081] ; , Both are design constants that are greater than zero, and their magnitudes will affect the system's convergence speed.

[0082] Step 5: Prove the system stability and ensure that the tracking error of the train is safely bounded under the preset performance control.

[0083] The effectiveness of the proposed control method is demonstrated by constructing the following Lyapunov function.

[0084]

[0085] Differentiation yields:

[0086]

[0087] because

[0088] Furthermore

[0089]

[0090] because

[0091] According to the controller designed in step 4), Substituting can yield

[0092]

[0093] when At that time, one can obtain

[0094]

[0095] when When can be obtained Bounded, therefore Bounded, further having Bounded, thus satisfying This enables preset performance control for heavy-haul trains.

[0096] Therefore, when the controller parameters satisfy , , , At that time, it will reach the sliding surface, and then It will converge, thereby achieving preset performance control.

[0097] To verify the aforementioned pre-set performance tracking control method for heavy-haul trains, simulation verification was performed using MATLAB software, detailed as follows:

[0098] The heavy-haul trains are configured in a 1-2-1 formation (1 HXD1 locomotive + 100 C80 freight cars + 2 HXD1 locomotives + 100 C80 freight cars + 1 HXD1 locomotive). The locomotive mass is... kg, the truck's mass is kg, the spring stiffness coefficient is The damping coefficient is The static balance length of the buffer device is 1m, and the basic drag coefficient is:

[0099]

[0100]

[0101] .

[0102] The finite-time performance function is:

[0103]

[0104] The convergence time of the performance function is 600s, and the final value is 1.

[0105] Simulation results are as follows Figure 2 , Figure 3 As shown. Among them, Figure 2 The position curves of each car in the heavy-haul train show that the entire convoy effectively tracked the reference trajectory and maintained the preset safe distance. The train as a whole experienced acceleration, constant speed, and deceleration phases, with the total displacement continuously increasing and the cars maintaining a stable interval throughout, which confirms the overall stability of the train convoy during operation.

[0106] Figure 3 The locomotive's tracking error curve shows that the performance function converges to 1 after 600 seconds. Throughout the tracking process, the locomotive's tracking error remains within the envelope of the performance function.

[0107] Therefore, the pre-set performance tracking control method for heavy-haul trains proposed in this invention can ensure that the tracking error of each locomotive is strictly constrained within the envelope of the finite-time performance function, thereby improving the dynamic response speed and control accuracy of the control system.

Claims

1. A method for tracking and controlling the preset performance of heavy-haul trains, characterized in that: Step 1: Analyze the longitudinal forces acting on the heavy-haul train during operation, treating each locomotive and freight car as a point mass to establish a multi-mass dynamic model of the train: Where i represents the i-th car, and N represents the total number of locomotives and freight cars in the heavy-haul train. These are the mass, position, speed, and traction / braking control inputs for the i-th car, respectively. Locomotives can generate traction and braking forces, while freight cars lack traction and braking devices; therefore, for the i-th freight car, , ; These represent the coupling forces between the i-th vehicle and its two adjacent vehicles, respectively. This represents the basic resistance experienced by the vehicle in section i. Step 2: Define the desired cruise trajectory and position error; The desired cruising trajectory is: in, It is the desired position for train operation. It is the desired speed of the given train. Define the position error of the i-th locomotive as: in, It is the first Positional error of the locomotive Indicates the first The expected distance between the locomotive and the reference trajectory; Step 3: Design the finite-time performance function; in, This represents the initial performance boundary; This represents the steady-state performance boundary. and A constant that is greater than zero. The set convergence time; Step 4: Combine position error Establish a conversion error function based on the designed performance function; The conversion error function is as follows: in, Pre-set a performance function for a finite time. This refers to the positional error; Step 5: Based on the conversion error function Based on the multi-mass dynamics model of a heavy-haul train, and under the constraints of a pre-defined performance function within a limited time, a finite-time sliding mode controller is designed as follows: In the formula, For the traction / braking control input of the i-th vehicle; , ; , These are the constants to be designed; For sliding surfaces: In the formula, , These are the constants to be designed; Ultimately, this leads to conversion error. It converges to a bounded region near zero within a finite time, thus ensuring the position error. Meets the preset performance requirements for a limited time.

2. The method for tracking and controlling the preset performance of heavy-haul trains as described in claim 1, characterized in that: In the multi-mass dynamics model of heavy-haul trains: in, and These represent the stiffness coefficient and damping coefficient of the buffer device connecting the i-th and i+1-th vehicle sections, respectively. This represents the static balance length of the buffer device connecting the i-th and i+1-th vehicles.

3. The method for tracking and controlling the preset performance of heavy-haul trains as described in claim 1, characterized in that: In the multi-mass dynamics model of heavy-haul trains: in, , , These are the basic drag coefficients, obtained through wind tunnel testing; It can be seen that the finite-time performance function remains constant after time T. This can effectively constrain the tracking error and ensure that the error converges to the steady-state boundary within a finite time.

4. The method for preset performance tracking control of heavy-haul trains as described in claim 1, characterized in that: In the transformation error function, when the position error initial value satisfy When, if the conversion error function If bounded, then the position error Always enclosed in a finite-time preset performance function Within the envelope; if at a certain moment... This will lead to a transformation error function Unbounded; and further, by ensuring the transformation error function The boundedness of the implementation error is subject to preset performance constraints.

5. The method for preset performance tracking control of heavy-haul trains as described in claim 1, characterized in that: Finite-time sliding mode controller parameters satisfy , , , At that time, it will reach the sliding surface, and then It will subside.

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