Method and system for controlling preset performance under saturation of train actuator

Abstract

The invention provides a preset performance control method and system under saturation of a train actuator, and relates to the technical field of train control, and the method comprises the following steps: building a train longitudinal motion kinetic equation based on the Newton second law; defining actual control input under saturation constraint of a train actuator, and establishing a dynamic compensation function in combination with a train longitudinal motion kinetic equation; designing a tracking error in the train operation process, and defining a filtering error in combination with a power compensation function; designing a preset performance function based on the train longitudinal motion kinetic 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; and verifying the stability of the updated preset performance control law, and controlling the train operation by using the updated preset performance control law. Under the actual working condition of saturation constraint of the actuator, the tracking precision, the response speed and the overall stability of train operation control are remarkably improved.

Description

Technical Field

[0001] The present invention relates to the field of train control technology, and in particular to a method and system for controlling preset performance under saturation of a train actuator. Background Art

[0002] As rail transit systems rapidly develop towards higher speeds and greater intelligence, ensuring accurate and stable train operation control has become a core challenge for modern transportation systems. Against this backdrop, automatic train control technology, which dynamically adjusts train speed in real time, has become a key technology for improving railway transportation efficiency and safety.

[0003] High-speed train dynamic tracking control, as the core of automatic train control technology, has a direct impact on the operational efficiency and driving safety of rail transit systems. However, existing technologies for high-speed train dynamic tracking control suffer from the problem of actuator saturation. When outputting control commands, the actuator is unable to fully respond to the ideal commands calculated by the control system due to its own physical performance limitations. As a result, the actual output is rigidly constrained within the actuator's inherent physical performance limits. This in turn affects transient response (such as acceleration time and deceleration smoothness) and steady-state accuracy (such as arrival position deviation), making it difficult for the train to accurately track the preset speed and displacement trajectory. In addition, when the actuator is saturated, 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 cause imbalance in the dynamic characteristics of the control system and even cause oscillation, threatening the safety and stability of train operation.

[0004] How to solve the above technical problems is the subject faced by the present invention. Summary of the Invention

[0005] In order to address the deficiencies of the prior art, the present invention provides a method and system for preset performance control under actuator saturation of a train, which significantly improves the tracking accuracy, response speed and overall stability of train operation control under actual working conditions of actuator saturation constraints.

[0006] The technical solution adopted by the present invention to solve the technical problem is as follows: On the one hand, the present invention provides a method for controlling the preset performance of a train actuator under saturation, comprising the following steps: Based on Newton's second law, the longitudinal motion of the train is subjected to force analysis and the dynamic equation of the longitudinal motion of the train is established; Define the actual control input under the train actuator saturation constraint, and establish a power compensation function based on the train longitudinal motion dynamics equation and the actual control input under the train actuator saturation constraint; Design the tracking error during train operation and define the filtering error based on the power compensation function and the tracking error during train operation; Design a preset performance function based on the train longitudinal motion dynamics equation and filtering error, and define an error conversion mechanism based on the preset performance function; A preset performance control law is constructed based on the error conversion mechanism, and a parameter adaptive law is designed to update the preset performance control law to obtain an 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.

[0007] Preferably, the train longitudinal motion dynamics equation is expressed as follows:

[0008] Where, , is the running time of the train, 、 and are the displacement, velocity and acceleration of the train during operation, is the total weight of the train during operation, is the actual control input, is the basic operating resistance, For additional resistance.

[0009] It should be noted that the basic running resistance is related to the train speed. ,in, 、 and are the Davis equation coefficients respectively; additional resistance refers to the additional resistance encountered by the train when running on a fixed line, including curve resistance, slope resistance, tunnel resistance and other resistance caused by unmodeled factors.

[0010] Through precise dynamic modeling, a theoretical basis is provided for the subsequent control law design, ensuring that the control system can accurately reflect the controlled behavior of the actual train.

[0011] Preferably, the actual control input under the train actuator saturation constraint is:

[0012] Where, is the lower limit of the braking force, is the ideal control input, is the upper limit of traction; The saturation characteristics are explicitly modeled to ensure that the output of the control system does not exceed the capability of the actuator, providing a prerequisite for subsequent compensation.

[0013] The power compensation function is:

[0014] In the formula, is a compensation coefficient, which is a normal number selected according to experience value; is the difference between the actual control input and the ideal control input, , is an auxiliary signal.

[0015] It should be noted that a first-order linear dynamic system is constructed, and the negative feedback term ensures its own stability (avoiding unbounded growth), and the input term responds to the saturation deviation in real time, dynamically quantifies and compensates for the difference between the actual input and the ideal command caused by saturation through the dynamic compensation function, reduces control distortion, and improves tracking accuracy.

[0016] Preferably, the tracking error during the train operation includes displacement tracking error and speed tracking error, and is specifically represented as follows:

[0017] In the formula, is the displacement tracking error, is the speed tracking error, and are the actual displacement tracking trajectory of the train and the actual speed tracking trajectory of the train, respectively, and are the expected displacement tracking trajectory of the train and the expected speed tracking trajectory of the train, respectively. The filtering error is specifically represented as follows:

[0018] In the formula, is a filtering coefficient, which is a normal number determined according to simulation experiments.

[0019] It should be noted that the displacement error, the speed error, and the anti-saturation compensation term are single variables , which simplifies the subsequent "multi-error constraint" to "single-error constraint" and reduces the complexity of control design.

[0020] Preferably, the preset performance function adopts an exponential preset performance function, and is specifically represented as follows:

[0021] In the formula, and are the initial preset performance boundary value and the steady-state preset performance boundary value of the preset performance function, respectively, satisfying the decay constraint ; is a decay rate, which is selected according to experience value.

[0022] It should be noted that the exponential decay boundary is used to explicitly constrain the transient convergence rate of the error ( The larger the value, the faster the convergence) and the maximum overshoot ( Define the initial allowable deviation) to achieve "predeterminable performance".

[0023] The error conversion mechanism is:

[0024] Where, is the error transfer function, is the performance boundary function, is the virtual tracking error; .

[0025] It should be noted that the error dynamic convergence speed and the maximum allowable range are constrained by presetting the performance boundary. The error conversion mechanism ensures that the error is strictly compressed within the performance boundary, thus realizing full-process error management.

[0026] Preferably, the preset performance control law is:

[0027] Where, is the controller parameter, is a positive constant determined by simulation experiments, 、 and are the estimated values ​​of the Davis equation coefficients, Unknown upper limit for additional resistance estimated value of; The parameter adaptation law is:

[0028] Where, 、 、 and These are all adaptive law parameters, and their values ​​are determined through simulation experiments.

[0029] It should be noted that the control law combines dynamic compensation and error filtering to achieve real-time error suppression. The adaptive law automatically estimates uncertain parameters, improving system adaptability and robustness and reducing reliance on prior knowledge of the system.

[0030] Preferably, the verifying the stability of the updated preset performance control law includes: The Lyapunov function is constructed for the updated preset performance control law as follows: ; Where, , , , ; The derivative of the Lyapunov function is obtained and sorted out, and the derivative is negative definite. According to the Lyapunov stability theory, the updated preset performance control law is asymptotically stable.

[0031] Based on Lyapunov stability theory, the system satisfies stability conditions. Specifically, under the preset performance control constraints imposed by actuator saturation, the displacement and velocity tracking errors of the train's closed-loop control system converge asymptotically to zero, achieving asymptotic tracking of the actual displacement and velocity to the desired trajectory.

[0032] In another aspect, the present invention provides a train actuator saturation preset performance control system, comprising: Dynamic modeling module, used to analyze the longitudinal motion of the train based on Newton's second law and establish the dynamic equation of the longitudinal motion of the train; Saturation compensation module, used to define the actual control input under the saturation constraint of the train actuator and establish the power compensation function; Error definition module, used to design and define tracking error and filtering error; Performance constraint module, used to design preset performance functions under train actuator saturation and define error conversion mechanism; A controller design module is used to construct a preset performance control law and design a 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.

[0033] The beneficial effects of the present invention are as follows: under the actual working conditions of actuator saturation constraints, the present invention significantly improves the tracking accuracy, response speed and overall stability of train operation control. A dynamic compensation function is introduced to dynamically compensate for the control output deviation caused by actuator saturation, effectively reducing the error between the actual output and the ideal control instruction, thereby optimizing the transient response characteristics and improving the smoothness of the train during acceleration and deceleration. A filtering error based on the tracking error and an exponential preset performance function are designed, and combined with an error conversion mechanism, dynamic constraints on the displacement and speed tracking errors during train operation are achieved, ensuring that the tracking error is always compressed within the set performance boundaries throughout the entire operation process, greatly improving the steady-state accuracy and trajectory tracking capability. The use of a preset performance control law based on a parameter adaptive law can estimate the uncertain parameters of the system (such as the Davis equation coefficient, the upper limit of the additional resistance, etc.) online, significantly enhancing the control system's ability to adapt to environmental changes and model uncertainties. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 A diagram showing the steps of the method of the present invention.

[0035] Figure 2 It is a system module diagram of the present invention.

[0036] Figure 3 This is a curve diagram of the expected displacement and actual displacement of the train in Example 3 of the present invention.

[0037] Figure 4 This is a curve diagram of the expected speed and actual speed of the train in embodiment 3 of the present invention.

[0038] Figure 5 This is a graph showing actual control input for train operation according to Embodiment 3 of the present invention.

[0039] Figure 6 Schematic diagram of the filtering error curve and the preset performance function boundary of Example 3 of the present invention. DETAILED DESCRIPTION

[0040] In order to clearly illustrate the technical features of this solution, the solution is described below through specific implementation methods.

[0041] Example 1: See also Figure 1 As shown, this embodiment is a method for controlling preset performance under saturation of a train actuator, comprising the following steps: S1. Analyze the longitudinal motion of the train based on Newton's second law and establish the dynamic equation of the longitudinal motion of the train; The train longitudinal motion dynamics equation is expressed as follows:

[0042] Where, , is the running time of the train, 、 and are the displacement, velocity and acceleration of the train during operation, is the total weight of the train during operation, is the actual control input, is the basic operating resistance, For additional resistance.

[0043] It should be noted that the basic running resistance is related to the train speed. ,in, 、 and are the Davis equation coefficients respectively; additional resistance refers to the additional resistance encountered by a train running on a fixed line, including curve resistance, slope resistance, tunnel resistance and other resistances caused by unmodeled factors.

[0044] Through precise dynamic modeling, a theoretical basis is provided for the subsequent control law design, ensuring that the control system can accurately reflect the controlled behavior of the actual train.

[0045] S2. Define the actual control input under the train actuator saturation constraint, and establish a power compensation function based on the train longitudinal motion dynamics equation and the actual control input under the train actuator saturation constraint; 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:

[0046] Where, is the lower limit of the braking force, is the ideal control input, is the upper limit of traction; The saturation characteristics are explicitly modeled to ensure that the output of the control system does not exceed the capability of the actuator, providing a prerequisite for subsequent compensation.

[0047] A power compensation function is designed to compensate for actuator saturation during train operation. The power compensation function formula is as follows:

[0048] Where, is the compensation coefficient, which is a positive constant selected based on experience; is the difference between the actual control input and the ideal control input, For auxiliary signal.

[0049] It should be noted that when constructing a first-order linear dynamic system, the negative feedback term ensure Self-stable (avoid unbounded growth), input Respond to saturation deviation in real time, dynamically quantify and compensate the difference between actual input and ideal command caused by saturation through the power compensation function, reduce control distortion and improve tracking accuracy.

[0050] S3. Designing a tracking error during train operation, and defining a filtering error based on a power compensation function and the tracking error during train operation; The tracking error during train operation includes displacement tracking error and speed tracking error, which are specifically expressed as follows:

[0051] Where, is the displacement tracking error, is the velocity tracking error, and They are the actual displacement tracking trajectory of the train and the actual speed tracking trajectory of the train, and They are the expected displacement tracking trajectory of the train and the expected speed tracking trajectory of the train respectively; The filtering error is specifically expressed as follows:

[0052] Where, is the filter coefficient, which is a positive constant selected based on simulation experiments.

[0053] It should be noted that the integrated displacement error, velocity error, and anti-saturation compensation term are single variables. , simplifying the subsequent “multiple error constraints” to “single error constraints” and reducing the complexity of control design.

[0054] S4. Designing a preset performance function based on the train longitudinal motion dynamics equation and the filter error, and defining an error conversion mechanism based on the preset performance function; Convergence time and overshoot constraints are imposed on the filter error during train operation to ensure that the transient response of the control system converges quickly and smoothly to the desired state. The preset performance function adopts an exponential preset performance function, which is specifically expressed as follows:

[0055] Where, and They are the initial preset performance boundary value and the steady-state preset performance boundary value of the preset performance function, respectively, satisfying the attenuation constraint ; is the decay rate, determined based on empirical values; It should be noted that the exponential decay boundary is used to explicitly constrain the transient convergence rate of the error ( The larger the value, the faster the convergence) and the maximum overshoot ( Define the initial allowable deviation) to achieve "predeterminable performance".

[0056] Based on the preset performance boundary, the error conversion mechanism is established as follows:

[0057] Where, is the error transfer function, is the performance boundary function, is the virtual tracking error; .

[0058] It should be noted that the error dynamic convergence speed and the maximum allowable range are constrained by presetting the performance boundary. The error conversion mechanism ensures that the error is strictly compressed within the performance boundary, thus realizing full-process error management.

[0059] S5. 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, thereby obtaining an updated preset performance control law; Assume the performance control law is:

[0060] Where, is the controller parameter, is a positive constant determined by simulation experiments, 、 and are the estimated values ​​of the Davis equation coefficients, Unknown upper limit for additional resistance estimated value of; The parameter adaptation law is:

[0061] Where, 、 、 and These are all adaptive law parameters, and their values ​​are determined through simulation experiments.

[0062] It should be noted that the control law combines dynamic compensation and error filtering to achieve real-time error suppression. The adaptive law automatically estimates uncertain parameters, improving system adaptability and robustness and reducing reliance on prior knowledge of the system.

[0063] S6. Verify the stability of the updated preset performance control law, and control the train operation based on the updated preset performance control law.

[0064] The Lyapunov function is constructed for the updated preset performance control law as follows: ; Where, , , , ; The derivative of the Lyapunov function is obtained and sorted out, and the derivative is negative definite. According to the Lyapunov stability theory, the updated preset performance control law is asymptotically stable.

[0065] Based on Lyapunov stability theory, the system satisfies stability conditions. Specifically, under the preset performance control constraints imposed by actuator saturation, the displacement and velocity tracking errors of the train's closed-loop control system converge asymptotically to zero, achieving asymptotic tracking of the actual displacement and velocity to the desired trajectory.

[0066] Example 2: See also Figure 2 As shown, this embodiment is a preset performance control system under train actuator saturation, including: Dynamic modeling module, used to analyze the longitudinal motion of the train based on Newton's second law and establish the dynamic equation of the longitudinal motion of the train; Saturation compensation module, used to define the actual control input under the saturation constraint of the train actuator and establish the power compensation function; Error definition module, used to design and define tracking error and filtering error; Performance constraint module, used to design preset performance functions under train actuator saturation and define error conversion mechanism; A controller design module is used to construct a preset performance control law and design a 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.

[0067] Example 3: In order to verify the feasibility and effectiveness of the preset performance control method under the train actuator saturation constraint provided by the present invention, this experimental example uses MATLAB to conduct simulation experiments and provides detailed explanations.

[0068] The single-point train model in this embodiment considers the impact of actuator saturation on position and velocity tracking during train operation. Through longitudinal motion force analysis, a power-assisted system is introduced to compensate for saturation effects. Preset performance strategy constraints are used to constrain the convergence of filtering errors, effectively improving control accuracy and system stability.

[0069] In the simulation experiment, the train running time is 2000s, the total mass is 500t, the upper limit of the actuator saturation is 60kN, the lower limit is -12kN, and the basic resistance related parameters are .

[0070] Based on the above simulation conditions, MATLAB is used to conduct simulation experiments, and the curves of train expected displacement and actual displacement and train expected speed and actual speed under the preset performance control method under actuator saturation are obtained, as shown in the following figure. Figure 3 and Figure 4 shown.

[0071] See also Figure 5 As shown in the figure, during the train operation, a large traction force is required to propel the train body forward during the startup phase. However, due to the actuator saturation constraint of high-speed trains, the controller input is truncated at the upper limit of the saturation constraint. In addition, during the train operation, when the train is in a deceleration scenario, a large braking force is required to reduce the train speed. Similarly, due to the actuator saturation constraint, the controller input is truncated at the lower limit of the saturation constraint.

[0072] See also Figure 6 As shown, it can be seen that during the operation of the train, the train can obtain good tracking performance when the preset performance control method is used under actuator saturation, and the filtering error is constrained within the preset performance function range, achieving the expected effect, which proves the effectiveness of the control method adopted in this embodiment.

[0073] Technical features not described in the present invention can be achieved through or by adopting existing technologies and will not be described in detail here. Of course, the above description is not a limitation of the present invention, and the present invention is not limited to the above examples. Changes, modifications, additions or substitutions made by ordinary technicians in this technical field within the essential scope of the present invention should also fall within the scope of protection of the present invention.

Claims

1. A method for controlling the preset performance of a train actuator under saturation, characterized in that: The following steps are involved: Based on Newton's second law, the longitudinal motion of the train is subjected to force analysis and the dynamic equation of the longitudinal motion of the train is established; Define the actual control input under the train actuator saturation constraint, and establish a power compensation function based on the train longitudinal motion dynamics equation and the actual control input under the train actuator saturation constraint; Design the tracking error during train operation and define the filtering error based on the power compensation function and the tracking error during train operation; Design a preset performance function based on the train longitudinal motion dynamics equation and filtering error, and define an error conversion mechanism based on the preset performance function; A preset performance control law is constructed based on the error conversion mechanism, and a parameter adaptive law is designed to update the preset performance control law to obtain an 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.

2. The method for controlling the preset performance of a train actuator under saturation according to claim 1, characterized in that: The train longitudinal motion dynamics equation is expressed as follows: ； Where, , is the running time of the train, 、 and are the displacement, velocity and acceleration of the train during operation, is the total weight of the train during operation, is the actual control input, is the basic operating resistance, For additional resistance.

3. The method for controlling the preset performance of a train actuator under saturation according to claim 2, characterized in that: The actual control input under the train actuator saturation constraint is: Where, is the lower limit of the braking force, is the ideal control input, is the upper limit of traction; The power compensation function is: ； Where, is the compensation coefficient, is the difference between the actual control input and the ideal control input, is the auxiliary signal.

4. The method for controlling the preset performance of a train actuator under saturation according to claim 3, characterized in that: The tracking error during train operation includes displacement tracking error and speed tracking error, which are specifically expressed as follows: ； Where, is the displacement tracking error, is the velocity tracking error, and They are the actual displacement tracking trajectory of the train and the actual speed tracking trajectory of the train, and They are the expected displacement tracking trajectory of the train and the expected speed tracking trajectory of the train respectively; The filtering error is specifically expressed as follows: ； Where, is the filter coefficient.

5. The method for controlling the preset performance of a train actuator under saturation according to claim 4, characterized in that: The preset performance function adopts an exponential preset performance function, which is specifically expressed as follows: ； Where, and They are the initial preset performance boundary value and the steady-state preset performance boundary value of the preset performance function, respectively, satisfying the attenuation constraint ; is the decay rate; The error conversion mechanism is: ； Where, is the error transfer function, is the performance boundary function, is the virtual tracking error; 。 6. The method for controlling the preset performance of a train actuator under saturation according to claim 5, characterized in that: The preset performance control law is: ； Where, is the controller parameter, 、 and are the Davis equation coefficients 、 、 The estimated value of Unknown upper limit for additional resistance estimated value of; The parameter adaptation law is: ； Where, 、 、 and All are normal numbers.

7. The method for controlling the preset performance of a train actuator under saturation according to claim 6, characterized in that: Verifying the stability of the updated preset performance control law includes: The Lyapunov function is constructed for the updated preset performance control law as follows: ； Where, , , , ; The derivative of the Lyapunov function is obtained and sorted out, and the derivative is negative definite. According to the Lyapunov stability theory, the updated preset performance control law is asymptotically stable.

8. A train actuator saturation preset performance control system, characterized in that: The method for controlling the preset performance of a train actuator under saturation according to any one of claims 1 to 7 comprises: Dynamic modeling module, used to analyze the longitudinal motion of the train based on Newton's second law and establish the dynamic equation of the longitudinal motion of the train; Saturation compensation module, used to define the actual control input under the saturation constraint of the train actuator and establish the power compensation function; Error definition module, used to design and define tracking error and filtering error; Performance constraint module, used to design preset performance functions under train actuator saturation and define error conversion mechanism; A controller design module is used to construct a preset performance control law and design a 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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