Train actuator saturation under preset performance control method and system

Abstract

The application provides a train actuator saturation-based preset performance control method and system, and relates to the technical field of train control, including the following steps: establishing a train longitudinal motion dynamics equation based on Newton's second law; defining actual control input under train actuator saturation constraint, combining the train longitudinal motion dynamics equation to establish a power compensation function; designing a tracking error in the train running process, combining the power compensation function to define a filtering error; designing a preset performance function based on the train longitudinal motion dynamics equation and the filtering error, and defining an error conversion mechanism; constructing a preset performance control law based on the error conversion mechanism, and designing a parameter adaptive law to update the preset performance control law; verifying the stability of the updated preset performance control law, and using the updated preset performance control law to control the train running. The application significantly improves the tracking accuracy, response speed and overall stability of train running control under the actual working condition of actuator saturation constraint.

Description

Technical Field

[0001] This invention relates to the field of train control technology, and in particular to a method and system for preset performance control of train actuators under saturation. Background Technology

[0002] With the rapid development of rail transit systems towards higher speeds and greater intelligence, the precision and stability of train operation control have become core challenges for modern transportation systems. Against this backdrop, automatic train control technology, through real-time dynamic speed adjustment, has become a key technology for improving railway transportation efficiency and safety.

[0003] As the core of automatic train control technology, dynamic tracking control of high-speed trains directly affects the operational efficiency and safety of rail transit systems. However, existing technologies in dynamic tracking control of high-speed trains suffer from actuator saturation. When outputting control commands, actuators, limited by their own physical properties, cannot fully respond to the ideal commands calculated by the control system. This results in the actual output being rigidly constrained within the inherent physical performance limits of the actuators, which in turn affects transient responses (such as acceleration time and deceleration smoothness) and steady-state accuracy (such as deviation from the station stopping position), making it difficult for the train to accurately track the preset speed and displacement trajectory. In addition, under actuator saturation, the traction and braking systems may deviate from their rated operating range, reducing energy conversion efficiency and increasing energy consumption. Finally, long-term or frequent actuator saturation may lead to imbalances in the dynamic characteristics of the control system, or even cause oscillations, threatening the safety and stability of train operation.

[0004] How to solve the above-mentioned technical problems is the challenge facing this invention. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a method and system for pre-setting performance control under actuator saturation, which significantly improves the tracking accuracy, response speed, and overall stability of train operation control under actual operating conditions of actuator saturation constraints.

[0006] The technical solution adopted by this invention to solve its technical problem is as follows: On the one hand, this invention provides a method for preset performance control of train actuators under saturation, comprising the following steps:

[0007] Based on Newton's second law, the force analysis of the train's longitudinal motion is carried out, and the dynamic equation of the train's longitudinal motion is established.

[0008] Define the actual control input under saturation constraints of the train actuator, and establish a dynamic compensation function based on the train longitudinal motion dynamics equation and the actual control input under saturation constraints of the train actuator.

[0009] The tracking error during train operation is designed, and the filtering error is defined based on the dynamic compensation function and the tracking error during train operation.

[0010] Based on the train's longitudinal motion dynamics equations and filtering errors, a preset performance function is designed, and an error conversion mechanism is defined based on the preset performance function;

[0011] Based on the error transformation mechanism, a preset performance control law is constructed, and a parameter adaptive law is designed to update the preset performance control law, thus obtaining the updated preset performance control law.

[0012] Verify the stability of the updated preset performance control law, and control the train operation based on the updated preset performance control law;

[0013] The preset performance control law is:

[0014]

[0015] In the formula, For controller parameters, and The coefficients of the Davis equation are respectively , , The estimated value, The upper limit of additional resistance is unknown. The estimated value;

[0016] The adaptive law for the parameters is:

[0017]

[0018] In the formula, , , and All values ​​are positive numbers, and their values ​​were determined through simulation experiments. This is the error transformation function.

[0019] It should be noted that the control law, combined with dynamic compensation and error filtering, achieves real-time suppression of errors. The adaptive law automatically estimates uncertain parameters, improving the system's adaptability and robustness, and reducing reliance on prior knowledge of the system.

[0020] Preferably, the equation of motion for the train's longitudinal motion is expressed as follows:

[0021]

[0022] In the formula, , For train travel time, , and These are displacement, velocity, and acceleration during train operation. The total weight of the train during its operation. For actual control input, As the basic operating resistance, This adds resistance.

[0023] It should be noted that the basic operating resistance is related to the train speed. ,in, , and These are the coefficients of the Davis equation; additional resistance refers to the extra resistance experienced by a train running on a fixed track, including curve resistance, slope resistance, tunnel resistance, and other resistances caused by unmodeled factors.

[0024] Precise dynamic modeling provides a theoretical basis for subsequent control law design, ensuring that the control system can accurately reflect the controlled behavior of the actual train.

[0025] Preferably, the actual control input under the saturation constraint of the train actuator is:

[0026]

[0027] In the formula, This is the lower limit of braking force. For ideal control input, This is the upper limit of traction force;

[0028] By explicitly modeling the saturation characteristics, we can ensure that the output of the control system does not exceed the capability of the actuator, thus providing a basis for subsequent compensation.

[0029] The dynamic compensation function is:

[0030]

[0031] In the formula, The compensation coefficient is a normal value selected based on experience. This is the difference between the actual control input and the ideal control input. , This is an auxiliary signal.

[0032] It should be noted that in constructing a first-order linear dynamic system, the negative feedback term... ensure Self-stable (avoiding unbounded growth), input items Real-time response to saturation deviation: The difference between the actual input and the ideal command caused by saturation is dynamically quantified and compensated by the dynamic compensation function, thereby reducing control distortion and improving tracking accuracy.

[0033] Preferably, the tracking error during train operation includes displacement tracking error and speed tracking error, specifically as follows:

[0034]

[0035] In the formula, For displacement tracking error, For speed tracking error, and These are the actual train displacement tracking trajectory and the actual train speed tracking trajectory, respectively. and These are the train's expected displacement tracking trajectory and the train's expected speed tracking trajectory, respectively.

[0036] The filtering error is specifically represented as follows:

[0037]

[0038] In the formula, These are the filter coefficients, which are constants determined based on simulation experiments.

[0039] It should be noted that the integrated displacement error, velocity error, and anti-saturation compensation term are all single variables. This simplifies the subsequent "multiple error constraints" into "single error constraints," reducing the complexity of control design.

[0040] Preferably, the preset performance function is an exponential preset performance function, specifically expressed as follows:

[0041]

[0042] In the formula, and These are the initial preset performance boundary values ​​and the steady-state preset performance boundary values ​​of the preset performance function, respectively, satisfying the decay constraint. ; The decay rate is selected based on empirical values.

[0043] It should be noted that, using exponentially decaying boundary conditions, the transient convergence rate of the explicit constraint error ( The larger the value, the faster the convergence) and the maximum overshoot ( Define the initial allowable deviation) to achieve "performance can be preset".

[0044] The error conversion mechanism is as follows:

[0045]

[0046] In the formula, For error transformation function, For performance boundary functions, This is for virtual tracking error;

[0047] .

[0048] It should be noted that by setting performance boundaries to constrain the dynamic convergence speed and maximum allowable range of errors, the error transformation mechanism ensures that errors are strictly compressed within the performance boundaries, thus achieving full-process error management.

[0049] Preferably, the verification of the stability of the updated preset performance control law includes:

[0050] The Lyapunov function is constructed for the updated preset performance control law as follows:

[0051]

[0052] In the formula, , , , ;

[0053] By differentiating and rearranging the Lyapunov function, we obtain a negative definite derivative. According to Lyapunov stability theory, the updated preset performance control law is asymptotically stable.

[0054] Based on Lyapunov stability theory, it is shown that the system satisfies the stability condition. That is, under the preset performance control action with actuator saturation constraints, the displacement and speed tracking errors of the train closed-loop control system asymptotically converge to zero, realizing the asymptotic tracking of the actual displacement and speed to the desired trajectory.

[0055] On the other hand, the present invention provides a preset performance control system for train actuators under saturation, comprising:

[0056] The dynamics modeling module is used to perform force analysis on the longitudinal motion of the train according to Newton's second law and establish the dynamic equations of the train's longitudinal motion.

[0057] The saturation compensation module is used to define the actual control input under the saturation constraints of the train actuator and to establish the dynamic compensation function.

[0058] The error definition module is used to design and define tracking error and filtering error;

[0059] The performance constraint module is used to design the preset performance function under train actuator saturation and define the error conversion mechanism;

[0060] The controller design module is used to construct the preset performance control law and design the parameter adaptive law to update the preset performance control law;

[0061] The stability analysis module is used to select a suitable Lyapunov function, verify the stability of the updated preset performance control law, and control the train operation based on the updated preset performance control law.

[0062] The beneficial effects of this invention are as follows: Under actual operating conditions with actuator saturation constraints, this invention significantly improves the tracking accuracy, response speed, and overall stability of train operation control. By introducing a dynamic compensation function, the control output deviation caused by actuator saturation is dynamically compensated, effectively reducing the error between the actual output and the ideal control command, thereby optimizing transient response characteristics and improving the smoothness of train acceleration and deceleration. A filtering error based on tracking error and an exponential preset performance function are designed, combined with an error transformation mechanism, to achieve dynamic constraints on displacement and speed tracking errors during train operation. This ensures that the tracking error is always compressed within the set performance boundaries throughout the entire operation, significantly improving steady-state accuracy and trajectory tracking capability. The use of a preset performance control law based on parameter adaptive law enables online estimation of uncertain system parameters (such as Davis equation coefficients, upper limits of additional resistance, etc.), significantly enhancing the control system's adaptability to environmental changes and model uncertainties. Attached Figure Description

[0063] Figure 1 This is a diagram illustrating the method steps of the present invention.

[0064] Figure 2 This is a system module diagram of the present invention.

[0065] Figure 3 This is a graph showing the expected displacement and actual displacement of the train in Embodiment 3 of the present invention.

[0066] Figure 4 This is a graph showing the expected speed versus actual speed of the train in Embodiment 3 of the present invention.

[0067] Figure 5 This is a graph showing the actual control input curves for train operation in Embodiment 3 of the present invention.

[0068] Figure 6 This is a schematic diagram of the filtering error curve and the boundary of the preset performance function in Embodiment 3 of the present invention. Detailed Implementation

[0069] To clearly illustrate the technical features of this solution, the following detailed implementation method will be used to explain the solution.

[0070] Example 1:

[0071] See Figure 1 As shown, this embodiment is a method for preset performance control of train actuators under saturation, including the following steps:

[0072] S1. Based on Newton's second law, perform force analysis on the longitudinal motion of the train and establish the dynamic equation of the longitudinal motion of the train.

[0073] The equation of motion for the train's longitudinal motion is expressed as follows:

[0074]

[0075] In the formula, , For train travel time, , and These are displacement, velocity, and acceleration during train operation. The total weight of the train during its operation. For actual control input, As the basic operating resistance, This adds resistance.

[0076] It should be noted that the basic operating resistance is related to the train speed. ,in, , and These are the coefficients of the Davis equation; additional resistance refers to the extra resistance a train experiences while running on a fixed track, including curve resistance, slope resistance, tunnel resistance, and other resistances caused by unmodeled factors.

[0077] Precise dynamic modeling provides a theoretical basis for subsequent control law design, ensuring that the control system can accurately reflect the controlled behavior of the actual train.

[0078] S2. Define the actual control input under the saturation constraint of the train actuator, and establish a dynamic compensation function based on the train longitudinal motion dynamics equation and the actual control input under the saturation constraint of the train actuator.

[0079] Due to the saturation constraint caused by the limited output capacity of the actuator during train operation, the actual control input of the train actuator is restricted to the following form:

[0080]

[0081] In the formula, This is the lower limit of braking force. For ideal control input, This is the upper limit of traction force;

[0082] By explicitly modeling the saturation characteristics, we can ensure that the output of the control system does not exceed the capability of the actuator, thus providing a basis for subsequent compensation.

[0083] A dynamic compensation function is designed to compensate for actuator saturation during train operation. The formula for the dynamic compensation function is as follows:

[0084]

[0085] In the formula, The compensation coefficient is a normal value selected based on experience. This is the difference between the actual control input and the ideal control input. , This is an auxiliary signal.

[0086] It should be noted that in constructing a first-order linear dynamic system, the negative feedback term... ensure Self-stable (avoiding unbounded growth), input items Real-time response to saturation deviation: The difference between the actual input and the ideal command caused by saturation is dynamically quantified and compensated by the dynamic compensation function, thereby reducing control distortion and improving tracking accuracy.

[0087] S3. Design the tracking error during train operation, and define the filtering error based on the dynamic compensation function and the tracking error during train operation;

[0088] The tracking error during train operation includes displacement tracking error and speed tracking error, which are specifically represented as follows:

[0089]

[0090] In the formula, For displacement tracking error, For speed tracking error, and These are the actual train displacement tracking trajectory and the actual train speed tracking trajectory, respectively. and These are the train's expected displacement tracking trajectory and the train's expected speed tracking trajectory, respectively.

[0091] The filtering error is specifically represented as follows:

[0092]

[0093] In the formula, These are the filter coefficients, which are constants determined based on simulation experiments.

[0094] It should be noted that the integrated displacement error, velocity error, and anti-saturation compensation term are all single variables. This simplifies the subsequent "multiple error constraints" into "single error constraints," reducing the complexity of control design.

[0095] S4. Design a preset performance function based on the train's longitudinal motion dynamics equation and filtering error, and define an error conversion mechanism based on the preset performance function;

[0096] Convergence time and overshoot constraints are applied to the filtering error during train operation to ensure that the transient response of the control system converges to the desired state quickly and smoothly. The preset performance function adopts an exponential preset performance function, which is specifically expressed as follows:

[0097]

[0098] In the formula, and These are the initial preset performance boundary values ​​and the steady-state preset performance boundary values ​​of the preset performance function, respectively, satisfying the decay constraint. ; The decay rate is selected based on empirical values.

[0099] It should be noted that, using exponentially decaying boundary conditions, the transient convergence rate of the explicit constraint error ( The larger the value, the faster the convergence) and the maximum overshoot ( Define the initial allowable deviation) to achieve "performance can be preset".

[0100] Based on preset performance boundaries, the error transformation mechanism is established as follows:

[0101]

[0102] In the formula, For error transformation function, For performance boundary functions, This is for virtual tracking error;

[0103] .

[0104] It should be noted that by setting performance boundaries to constrain the dynamic convergence speed and maximum allowable range of errors, the error transformation mechanism ensures that errors are strictly compressed within the performance boundaries, thus achieving full-process error management.

[0105] S5. Construct a preset performance control law based on the error conversion mechanism, and design a parameter adaptive law to update the preset performance control law, so as to obtain the updated preset performance control law.

[0106] Let the performance control law be:

[0107]

[0108] In the formula, For controller parameters, and The coefficients of the Davis equation are respectively , , The estimated value, The upper limit of additional resistance is unknown. The estimated value;

[0109] The adaptive law for parameters is:

[0110]

[0111] In the formula, , , and All values ​​are positive numbers, and their values ​​were determined through simulation experiments. This is the error transformation function.

[0112] It should be noted that the control law, combined with dynamic compensation and error filtering, achieves real-time suppression of errors. The adaptive law automatically estimates uncertain parameters, improving the system's adaptability and robustness, and reducing reliance on prior knowledge of the system.

[0113] S6. Verify the stability of the updated preset performance control law, and control the train operation based on the updated preset performance control law.

[0114] The Lyapunov function is constructed for the updated preset performance control law as follows:

[0115]

[0116] In the formula, , , , ;

[0117] By differentiating and rearranging the Lyapunov function, we obtain a negative definite derivative. According to Lyapunov stability theory, the updated preset performance control law is asymptotically stable.

[0118] Based on Lyapunov stability theory, it is shown that the system satisfies the stability condition. That is, under the preset performance control action with actuator saturation constraints, the displacement and speed tracking errors of the train closed-loop control system asymptotically converge to zero, realizing the asymptotic tracking of the actual displacement and speed to the desired trajectory.

[0119] Example 2:

[0120] See Figure 2 As shown, this embodiment is a preset performance control system for train actuators under saturation, including:

[0121] The dynamics modeling module is used to perform force analysis on the longitudinal motion of the train according to Newton's second law and establish the dynamic equations of the train's longitudinal motion.

[0122] The saturation compensation module is used to define the actual control input under the saturation constraints of the train actuator and to establish the dynamic compensation function.

[0123] The error definition module is used to design and define tracking error and filtering error;

[0124] The performance constraint module is used to design the preset performance function under train actuator saturation and define the error conversion mechanism;

[0125] The controller design module is used to construct the preset performance control law and design the parameter adaptive law to update the preset performance control law;

[0126] The stability analysis module is used to select a suitable Lyapunov function, verify the stability of the updated preset performance control law, and control the train operation based on the updated preset performance control law.

[0127] Example 3:

[0128] To verify the feasibility and effectiveness of the preset performance control method for train actuators under saturation constraints provided by this invention, this experimental example uses MATLAB for simulation experiments and provides a detailed explanation.

[0129] The single-mass model of the train in this embodiment considers the impact of actuator saturation on position and speed tracking during train operation. Through longitudinal motion force analysis, a power assist system is introduced to compensate for the saturation effect, and a preset performance strategy constraint is used to constrain the convergence performance of the filtering error, effectively improving control accuracy and system stability.

[0130] In the simulation experiment, the train's running time was 2000s, its total mass was 500t, the upper limit of the train's actuator saturation was 60kN, and the lower limit was -12kN. The basic resistance-related parameters were as follows: .

[0131] Based on the above simulation conditions, simulation experiments were conducted using MATLAB. The desired displacement versus actual displacement curves and the desired speed versus actual speed curves of the train under the proposed actuator saturation preset performance control method were obtained, as shown below. Figure 3 and Figure 4 As shown.

[0132] See Figure 5 As shown, during train operation, a large traction force is required to propel the train forward during the start-up phase. However, due to the actuator saturation constraint of the high-speed train, the controller input is truncated at the upper limit of the saturation constraint. Furthermore, during train operation, when the train is in a deceleration scenario, a large braking force is required to reduce the train's speed. Similarly, due to the actuator saturation constraint, the controller input is truncated at the lower limit of the saturation constraint.

[0133] See Figure 6 As shown, during train operation, under the preset performance control method with actuator saturation, the train can achieve good tracking performance, and the filtering error is constrained within the preset performance function range, achieving the expected effect and proving the effectiveness of the control method adopted in this embodiment.

[0134] The technical features of this invention not described can be implemented by or using existing technology, and will not be repeated here. Of course, the above description is not a limitation of this invention, and this invention is not limited to the examples above. Any changes, modifications, additions or substitutions made by those skilled in the art within the scope of this invention should also be within the protection scope of this invention.

Claims

1. A method for preset performance control of train actuators under saturation, characterized in that, Includes the following steps: Based on Newton's second law, the force analysis of the train's longitudinal motion is carried out, and the dynamic equation of the train's longitudinal motion is established. Define the actual control input under saturation constraints of the train actuator, and establish a dynamic compensation function based on the train longitudinal motion dynamics equation and the actual control input under saturation constraints of the train actuator. The tracking error during train operation is designed, and the filtering error is defined based on the dynamic compensation function and the tracking error during train operation. Based on the train's longitudinal motion dynamics equations and filtering errors, a preset performance function is designed, and an error conversion mechanism is defined based on the preset performance function; Based on the error transformation mechanism, a preset performance control law is constructed, and a parameter adaptive law is designed to update the preset performance control law, thus obtaining the updated preset performance control law. Verify the stability of the updated preset performance control law, and control the train operation based on the updated preset performance control law; The preset performance control law is: In the formula, For controller parameters, and The coefficients of the Davis equation are respectively , , The estimated value, The upper limit of additional resistance is unknown. The estimated value; The adaptive law for the parameters is: In the formula, , , and All are positive numbers. This is the error transformation function.

2. The method for preset performance control of train actuators under saturation according to claim 1, characterized in that, The equation of motion for the train's longitudinal movement is expressed as follows: In the formula, , For train travel time, , and These are displacement, velocity, and acceleration during train operation. The total weight of the train during its operation. For actual control input, As the basic operating resistance, This adds resistance.

3. The method for preset performance control of train actuators under saturation according to claim 2, characterized in that, The actual control input under the saturation constraint of the train actuator is: In the formula, This is the lower limit of braking force. For ideal control input, This is the upper limit of traction force; The dynamic compensation function is: In the formula, For compensation coefficient, This is the difference between the actual control input and the ideal control input. This is an auxiliary signal.

4. The method for preset performance control of train actuators under saturation according to claim 3, characterized in that, The tracking errors during train operation include displacement tracking error and speed tracking error, specifically as follows: In the formula, For displacement tracking error, For speed tracking error, and These are the actual train displacement tracking trajectory and the actual train speed tracking trajectory, respectively. and These are the train's expected displacement tracking trajectory and the train's expected speed tracking trajectory, respectively. The filtering error is specifically represented as follows: In the formula, These are the filter coefficients.

5. The method for preset performance control of train actuators under saturation according to claim 4, characterized in that, The preset performance function adopts an exponential preset performance function, specifically expressed as follows: In the formula, and These are the initial preset performance boundary values ​​and the steady-state preset performance boundary values ​​of the preset performance function, respectively, satisfying the decay constraint. ; The decay rate; The error conversion mechanism is as follows: In the formula, For error transformation function, For performance boundary functions, This is for virtual tracking error; 。 6. The method for preset performance control of train actuators under saturation according to claim 5, characterized in that, The stability of the updated preset performance control law is verified as follows: The Lyapunov function is constructed for the updated preset performance control law as follows: In the formula, , , , ; By differentiating and rearranging the Lyapunov function, we obtain a negative definite derivative. According to Lyapunov stability theory, the updated preset performance control law is asymptotically stable.

7. A preset performance control system for train actuators under saturation, characterized in that, The method for implementing the train actuator saturation preset performance control method according to any one of claims 1-6 includes: The dynamics modeling module is used to perform force analysis on the longitudinal motion of the train according to Newton's second law and establish the dynamic equations of the train's longitudinal motion. The saturation compensation module is used to define the actual control input under the saturation constraints of the train actuator and to establish the dynamic compensation function. The error definition module is used to design and define tracking error and filtering error; The performance constraint module is used to design the preset performance function under train actuator saturation and define the error conversion mechanism; The controller design module is used to construct the preset performance control law and design the parameter adaptive law to update the preset performance control law; The stability analysis module is used to select a suitable Lyapunov function, verify the stability of the updated preset performance control law, and control the train operation based on the updated preset performance control law.

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