A centering tracking control method and device based on FTESO and PNTSMC

Abstract

The application discloses a centering tracking control method and device based on FTESO and PNTSMC; the method comprises the following steps: a dynamic model of a centering platform is established, vertical displacement, pitch angle and roll angle of the centering platform are taken as generalized coordinates, and external disturbance and unmodeled dynamics are modeled as lumped disturbance; based on a finite time extended state observer, velocity states of the generalized coordinates and the lumped disturbance are estimated in real time; based on a pre-defined time nonsingular terminal sliding mode control strategy, a control law is designed; the control law controls driving force of a hydraulic cylinder based on disturbance estimation value provided by the finite time extended state observer, so that the centering platform can track an expected trajectory within a preset time. The application can realize fast, accurate and robust tracking of a pose of the centering platform, and allows a user to preset a convergence time, thereby significantly improving performance and reliability of an automatic centering process.

Description

Technical Field

[0001] This invention relates to the field of engine testing technology, and in particular to a centering and tracking control method and device based on FTESO and PNTSMC. Background Technology

[0002] During engine testing, the alignment accuracy of the test bench has a crucial impact on the accuracy of test data, the stability of equipment operation, and the lifespan of components. Traditional alignment methods often rely on manual operation using dial indicators, locating pins, etc., which is not only time-consuming but also prone to causing misalignment between the engine output shaft and the test bench drive shaft due to operational errors, leading to vibration, noise, abnormal bearing wear, or even equipment damage.

[0003] As engine testing evolves towards higher speeds, greater precision, and automation, particularly in new energy power systems, small high-speed engines, and unmanned systems, the tolerance for errors is further decreasing. Increased test frequency and the need for model changeover testing also place higher demands on rapid and efficient assembly. Existing automatic alignment systems mostly use laser sensors to detect deviations and combine them with PID or conventional sliding mode control for adjustment. However, when faced with complex disturbances such as unmodeled dynamics and external perturbations, they suffer from slow response speeds, insufficient disturbance rejection capabilities, and difficulty in predicting convergence times. Summary of the Invention

[0004] The purpose of this invention is to provide a centering and tracking control method and apparatus based on a Finite-Time Extended State Observer (FTESO) and Predefined Time Non-Singular Terminal Sliding Mode Control (PNTSMC). This invention enables fast, accurate, and robust tracking of the centering platform's pose and allows users to preset the convergence time, significantly improving the performance and reliability of the automatic centering process.

[0005] The technical solution of this invention: A centering and tracking control method based on FTESO and PNTSMC, applied to the centering platform of an engine test bench, wherein the centering platform includes at least three hydraulic cylinders for adjusting the vertical displacement, pitch angle, and roll angle of the platform; the method includes:

[0006] A dynamic model of the centering platform is established, and the vertical displacement, pitch angle, and roll angle of the centering platform are used as generalized coordinates. External disturbances and unmodeled dynamics are modeled as lumped disturbances.

[0007] Based on the finite-time extended state observer, the velocity state of the generalized coordinates and the lumped disturbance are estimated in real time.

[0008] Design a control law based on a predefined time-nonsingular terminal sliding mode control strategy;

[0009] The control law controls the driving force of the hydraulic cylinder based on the disturbance estimate provided by the finite-time extended state observer, so as to enable the centering platform to track the desired trajectory within a preset time.

[0010] The above-described centering tracking control method establishes the dynamic model of the centering platform as follows:

[0011] Establish a platform coordinate system with the center of mass of the platform as the origin. The axis is forward. The axis is perpendicular to the ground and pointing upwards;

[0012] The coordinates of the thrust points of the three hydraulic cylinders are as follows: The coordinates of the front cylinder are... The coordinates of the left rear cylinder are The coordinates of the right rear cylinder are ,in All are greater than 0;

[0013] When the centering platform is tilted, let the pitch angle be... The roll angle is The dynamic model of the platform is then expressed as:

[0014] ;

[0015] in, For generalized coordinates, This is the driving force vector of the hydraulic cylinder. These represent the driving forces of three hydraulic cylinders. The inertia matrix, Here is the damping matrix. The gravity vector For the force transfer matrix, For lumped disturbances; This is the transpose symbol.

[0016] The aforementioned centering tracking control method, wherein the real-time estimation based on a finite-time extended state observer includes:

[0017] The lumped disturbance Expanded into new state variables ;

[0018] Define the observation state vector , , Corresponding to generalized coordinates Speed ​​state and aggregated disturbance The estimated value;

[0019] The equations for designing a finite-time extended state observer are as follows:

[0020] ;

[0021] in, This corresponds to the observation error; and All are sign power functions. , ; , For the first Expected observation error of the state variable, This is the observer gain.

[0022] The aforementioned centering tracking control method, wherein the control law design based on a predefined time non-singular terminal sliding mode control strategy includes:

[0023] Define position tracking error Speed ​​tracking error , It is the expected trajectory; For actual speed, It is the expected speed;

[0024] Design a predefined time-nonsingular terminal sliding surface:

[0025] ;

[0026] In the formula, , , ; This is a preset time parameter;

[0027] Based on the output of the sliding surface and the finite-time extended state observer, the control law is designed as follows:

[0028] ;

[0029] in:

[0030] ;

[0031] In the formula: , , , To preset time gain, It is a saturation function. It is a constant greater than the upper bound of the observation error.

[0032] The aforementioned centering tracking control method further includes a centering process, comprising:

[0033] The actual coaxiality between the engine output shaft and the test bench drive shaft is obtained by a laser alignment instrument, and the coaxiality deviation is used as the basis for setting the desired trajectory.

[0034] The tilt angles of the engine in front-to-back and left-to-right directions are obtained by tilt sensors, and these tilt angles are used as the initial attitude error of the desired trajectory.

[0035] A centering platform device for implementing the aforementioned centering tracking control method includes:

[0036] Engine mounting platform, including a support frame for supporting and securing the engine;

[0037] The leveling mechanism, integrated on the support frame, includes at least three independently extendable hydraulic cylinders for driving the support frame to move in the vertical, pitch, and roll directions.

[0038] The sensing system includes a laser alignment instrument for measuring coaxiality and a tilt sensor for measuring the tilt angle of the platform.

[0039] The controller is communicatively connected to the hydraulic cylinder, laser alignment instrument, and tilt sensor, and is equipped with a control program.

[0040] The controller is configured to receive signals from the laser alignment instrument and the tilt sensor, calculate control commands based on the alignment tracking control method, and drive the hydraulic cylinder to perform actions until the engine output shaft and the transmission shaft reach a preset coaxial accuracy.

[0041] The aforementioned centering platform device includes a front support hydraulic cylinder arranged at the front end of the support frame and two rear support hydraulic cylinders symmetrically arranged at the rear of the support frame. The three hydraulic cylinders form a triangular support structure.

[0042] The aforementioned centering platform device further includes a moving propulsion mechanism. The moving propulsion mechanism includes a first slide groove disposed on both sides of the bottom of the support frame. A first slider is slidably disposed in front of and behind the first slide groove. A second slide groove is provided on the first slider. A second slider for supporting the hydraulic cylinder is slidably disposed in the second slide groove.

[0043] The aforementioned centering platform device further includes a brake for locking the position of the engine mounting platform relative to the base after centering is completed.

[0044] Compared with the prior art, the present invention has the following beneficial effects:

[0045] 1. The finite-time extended state observer used can quickly and accurately estimate and compensate for various lumped disturbances (such as unmodeled dynamics, friction, and external disturbances) that affect the system, so that the control system can still maintain stable control performance under complex operating conditions.

[0046] 2. The predefined time non-singular terminal sliding mode control strategy allows users to directly set the upper bound of the system's convergence time. This means that the completion time of the centering process can be predetermined and guaranteed, improving the predictability and planning of the process, while avoiding the singularity problem that may occur in traditional terminal sliding mode.

[0047] 3. By using a laser alignment instrument and tilt sensor to provide precise feedback signals, combined with advanced control algorithms, a fully automatic and high-precision alignment process is achieved, replacing inefficient and experience-dependent manual operation and significantly shortening test preparation time.

[0048] 4. Precise alignment effectively avoids equipment vibration, wear and damage caused by misalignment of the shaft, protects expensive testing equipment, extends its service life, and ensures the reliability and repeatability of test data. Attached Figure Description

[0049] Figure 1 This is a schematic diagram of the structure of the device of the present invention;

[0050] Figure 2 This is an overview diagram of the simulation model;

[0051] Figure 3 This is a diagram of the FTESO module setup;

[0052] Figure 4 This is a diagram of the PNTSMC module setup;

[0053] Figure 5 It is a graph of vertical displacement tracking error under external force disturbance;

[0054] Figure 6 This is a curve showing the roll angle tracking error under external force disturbance;

[0055] Figure 7 It is the pitch angle tracking error curve under external force disturbance;

[0056] Figure 8 This is a graph showing the real-time observations of the lumped disturbance corresponding to the vertical displacement by FTESO over time.

[0057] Figure 9 This is a graph showing the real-time observations of the lumped disturbance corresponding to the roll angle by FTESO.

[0058] Figure 10 This is a graph showing the real-time observations of the lumped disturbance corresponding to the pitch angle by FTESO.

[0059] Figure 11 This is a graph showing the input thrust of the front cylinder, left rear cylinder, and right rear cylinder over time under the FTESO+PNTSMC algorithm.

[0060] Figure 12 This is a graph of the sensor noise signal.

[0061] Figure 13 These are the vertical displacement tracking error curves for the four algorithms;

[0062] Figure 14 These are the roll angle tracking error curves for the four algorithms;

[0063] Figure 15 These are the pitch tracking error curves for the four algorithms.

[0064] Figure Labels

[0065] 1. Engine mounting platform; 2. Leveling mechanism; 3. Laser alignment instrument; 4. Tilt sensor; 5. Moving propulsion mechanism; 6. First slide rail; 7. First slider; 8. Second slide rail; 9. Second slider. Detailed Implementation

[0066] The present invention will be further described below with reference to the accompanying drawings and embodiments, but this should not be construed as limiting the present invention.

[0067] Example: A centering and tracking control method and device based on Finite-Time Extended State Observer (FTESO) and Predefined Time Non-Singular Terminal Sliding Mode Control (PNTSMC) is applied to the centering platform control of an engine test bench. It achieves fast, accurate, and robust trajectory tracking of the platform's vertical displacement, pitch angle, and roll angle, solving problems such as weak disturbance rejection, uncontrollable convergence time, and low tracking accuracy in traditional control methods. This embodiment will describe in detail the specific execution steps of the method, the structural composition of the device, and the collaborative working mode of each module.

[0068] I. Overall Structure of the Centering Platform Device

[0069] The centering platform device of this invention is a dedicated centering platform for engine test benches. Its core consists of an engine mounting platform, a leveling mechanism, a sensing system, a controller, a moving propulsion mechanism, and a brake. These components work together to achieve engine position adjustment and precise centering. The structure and function of each part of the device are as follows:

[0070] Engine mounting platform 1: The main body is a rigid support frame, which is used to support and fix different models of engines. The structural stiffness of the frame is adapted to the load requirements of engine testing. Its center of mass is the origin of the coordinate system of the entire centering platform and is the reference point for position and posture adjustment.

[0071] Leveling Mechanism 2: This is the actuator for adjusting the platform's posture. Integrated at the bottom of the support frame, it adopts a triangular support structure with a single front cylinder and two rear cylinders. It includes one front support hydraulic cylinder and two symmetrically arranged rear support hydraulic cylinders. All three hydraulic cylinders can extend and retract independently, and their initial installation direction is perpendicular to the ground. By adjusting the extension and retraction of the three hydraulic cylinders, the support frame can be precisely driven to move up and down in the vertical direction, rotate around the horizontal axis in the pitch direction, and rotate around the longitudinal axis in the roll direction, achieving independent control of the platform's three-dimensional posture.

[0072] Sensing system: Provides accurate status detection signals for control, including laser alignment instrument 3 and tilt sensor 4: The laser alignment instrument is used to measure the actual coaxiality between the engine output shaft and the test bench drive shaft in real time and outputs coaxiality deviation data; The tilt sensor is installed at the center of gravity of the engine mounting platform and is used to collect the platform's pitch angle and roll angle in real time and output the platform's actual tilt angle data as the basis for determining the initial attitude error.

[0073] The controller is the core of the entire system, employing an embedded controller or industrial PLC. It establishes wired / wireless communication connections with the hydraulic cylinders of the leveling mechanism, the laser alignment instrument, and the tilt sensor of the sensing system. The controller is pre-configured with the FTESO and PNTSMC control programs of this invention. It receives detection signals from the sensing system, processes them using the control algorithm, generates control commands, drives the hydraulic cylinders to complete the extension and retraction movements, and provides real-time feedback on the adjustment results, forming a closed-loop control.

[0074] The mobile propulsion mechanism 5 includes first slide grooves 6 located on both sides of the bottom of the support frame. First sliders 7 are slidably mounted on the front and rear of the first slide grooves 6, respectively. A second slide groove 8 is formed on the first slider 7, and a second slider 9 for supporting the hydraulic cylinder is slidably mounted in the second slide groove 8. The mobile propulsion mechanism 5 enables coarse adjustment of the engine mounting platform 1 in the horizontal plane, and, in conjunction with the leveling mechanism, fine adjustment of its spatial orientation, completes full-dimensional alignment of the engine output shaft and the transmission shaft.

[0075] The brake adopts an electromagnetic braking or mechanical locking structure and is connected to the engine mounting platform and base. When the platform is aligned and reaches the preset coaxial accuracy, the brake is activated and locks the position of the platform relative to the base to prevent platform displacement or attitude deviation caused by vibration and load changes during engine testing, thus ensuring test stability.

[0076] Based on the above centering device, the specific implementation steps of the centering tracking control method of the present invention are as follows:

[0077] Step 1: Establish the dynamic model of the centering platform, taking the vertical displacement, pitch angle, and roll angle of the centering platform as generalized coordinates, and modeling external disturbances and unmodeled dynamics as lumped disturbances;

[0078] In this step, a platform coordinate system is established with the center of mass of the engine mounting platform as the origin, and the coordinate system is defined. The axis is forward of the platform. The axis is perpendicular to the ground and pointing upwards. shaft and , The axes form a right-handed coordinate system; the coordinates of the thrust points of the three hydraulic cylinders are as follows: front cylinder 1 Left rear cylinder 2 Right rear cylinder 3 ,and All are greater than 0.

[0079] 1.1 Determine the thrust vector of the hydraulic cylinder;

[0080] The hydraulic cylinder is initially installed perpendicular to the ground. When the platform tilts, the direction of the hydraulic cylinder's thrust changes in the platform coordinate system, and the tilt angle is defined. These are the roll angle (positive when tilting to the right) and the pitch angle (positive when tilting forward). In the platform coordinate system, the thrust vector of the hydraulic cylinder (initially along the z-axis of the ground) changes with the tilt of the platform. Let the rotation matrix from the ground coordinate system to the platform coordinate system be (approximate for small angles, ignoring second-order minor quantities):

[0081] ;

[0082] The thrust of each hydraulic cylinder is vertically upward, a unit vector pointing vertically upward in the ground coordinate system. In the platform coordinate system Therefore, the thrust vectors of each hydraulic cylinder in the platform coordinate system are as follows: , The driving force of the hydraulic cylinder

[0083] 1.2 Establish the core dynamic equations;

[0084] Let the vertical displacement of the platform be... Based on the translational and rotational equations, we can obtain:

[0085] ;

[0086] The following dynamic model can be established for the control of the central platform:

[0087]

[0088] in, These are generalized coordinates, corresponding to the platform's vertical displacement, pitch angle, and roll angle; This is the driving force vector of the hydraulic cylinder. The inertia matrix, For the damping matrix ( ), This is the force transmission matrix, used to establish the mapping relationship between the hydraulic cylinder thrust and the platform's generalized coordinates. This is the gravity vector, determined by the total gravity of the platform and engine, as well as the platform's attitude. This refers to the lumped disturbance (including all unknown disturbances such as unmodeled dynamics, friction, external interference, and sensor noise during the platform's motion). It is the transpose symbol. These represent the driving force of three hydraulic cylinders.

[0089] 1.3. Convert to state-space expression;

[0090] Define state variables Then the state-space expression of the system is:

[0091] ;

[0092] However, the platform experiences unknown disturbances during its motion, including unmodeled dynamics, friction, and external disturbances. Therefore, the system is rewritten as follows:

[0093] ;

[0094] in, For lumped disturbances, satisfy ,in It is a constant, and it is assumed that... Bounded, meaning there exists a constant. Make .

[0095] Step 2: Based on the finite-time extended state observer, estimate the velocity state of the generalized coordinates and the lumped disturbance in real time;

[0096] This step addresses lumped disturbances. To address the unknown nature of the disturbances, a state extension method is employed to incorporate them into the state variables. FTESO is designed to achieve finite-time real-time estimation of the velocity state and lumped disturbances in the generalized coordinate system, providing a basis for disturbance compensation in the control law. The specific design and implementation are as follows:

[0097] 2.1 State expansion;

[0098] Extend the disturbance into a new state variable:

[0099] , ;

[0100] Combining the state-space expression from step 1, we obtain the extended system:

[0101] ;

[0102] 2.2 Design of FTESO Core Equations

[0103] Define the observation state vector , , Corresponding to generalized coordinates Speed ​​state and aggregated disturbance The estimated value;

[0104] The equations for designing a finite-time extended state observer are as follows:

[0105] ;

[0106] in, This corresponds to the observation error; and All are sign power functions, defined as follows: , , ; , For the first Expected observation error of the state variable, The observer gain is determined by those skilled in the art based on the platform's dynamic characteristics and must meet the positive definite condition.

[0107] Then the dynamic equation of the observation error is obtained:

[0108]

[0109] In the formula, the definition is... , , It is the upper bound of the unknown error.

[0110] 2.3 Observer Stability Analysis

[0111] Define the transformed state vector:

[0112] ;

[0113] Choose the Lyapunov function:

[0114] ;

[0115] in It is a positive definite symmetric matrix.

[0116] calculate :

[0117] ;

[0118] Substitute into the error dynamics equation and calculate term by term:

[0119] ;Will Written in matrix form:

[0120] ;

[0121] in,

[0122] , ,

[0123] , ;

[0124] right Differentiation yields:

[0125] ;

[0126] choose Make: , ,in ,but:

[0127] ;

[0128] in, Considering and We can obtain:

[0129] ;

[0130] Based on the dynamic equation of observation error and inequalities have to:

[0131] ;

[0132] in:

[0133] ;

[0134] ;

[0135] ;

[0136] By the finite-time convergence lemma, we obtain:

[0137] Theorem: The observation error converges to the region in a finite time:

[0138]

[0139] Upper bound of convergence time:

[0140] in, .

[0141] Step 3: Based on the finite-time extended state observer, estimate the velocity state of the generalized coordinates and the lumped disturbance in real time.

[0142] In this step, based on the FTESO observation results from step 2, and with the goal of tracking the desired trajectory within a preset time, a PNTSMC control law is designed. By defining the tracking error, designing a non-singular sliding surface, and introducing a saturation function to avoid singularities, the control command for the hydraulic cylinder driving force is finally generated, achieving compensation for lumped disturbances and accurate tracking of the desired trajectory. The specific design and implementation are as follows:

[0143] Define tracking error:

[0144] ;in, It is the expected trajectory; For actual speed, It is the expected speed;

[0145] Design a predefined time-nonsingular terminal sliding surface:

[0146]

[0147] in:

[0148] , , , This is a preset time parameter; To preset the convergence time, .

[0149] Design control law:

[0150] ;

[0151] in, , ;

[0152] , ;

[0153] because There is To avoid singularity, a saturation function is introduced:

[0154] ;

[0155] The final modified control law is obtained:

[0156] .

[0157] In this step, the stability is proven as follows:

[0158] 1. Arrival stage;

[0159] Differentiating with respect to the sliding surface, we get:

[0160] ;

[0161] Substitution Simplifying, we get (assuming during convergence) (Saturation not triggered, simplified proof)

[0162] ;

[0163] Based on the finite-time convergence property of the observer, when When, there exists a sufficiently small constant. , making ,Pick Consider the following Lyapunov function:

[0164] ;

[0165] Differentiating, we get:

[0166] ;

[0167] Substitution and have to

[0168] ;

[0169] Based on the Lyapunov-type lemma proposed according to the predefined time-stability characteristics, the convergence time to the sliding surface is... .

[0170] 2. Sliding phase:

[0171] when hour, ;

[0172] Take the Lyapunov function:

[0173] ;

[0174] ;

[0175] Substitution , Gain and simplification yield:

[0176] ;

[0177] Finally, the convergence time of the tracking error can be obtained as follows: .

[0178] Furthermore, the optimized control law is multiplied by the inverse of the force transfer matrix on both sides to calculate the driving force command for the three hydraulic cylinders. The controller then converts the driving force command into a control signal for the extension and retraction of the hydraulic cylinders, thereby driving the three hydraulic cylinders of the leveling mechanism to move independently.

[0179] Step 4: Closed-loop control and alignment completion determination;

[0180] The controller sends the hydraulic cylinder control signal generated in step 3 to the leveling mechanism, driving the hydraulic cylinder to extend and retract as instructed, thereby adjusting the platform's posture. Simultaneously, the sensing system collects the platform's actual generalized coordinates and the actual coaxiality between the engine output shaft and the transmission shaft in real time, and uses the coaxiality deviation as the basis for setting the desired trajectory. The tilt sensor obtains the engine's front-to-back and left-to-right tilt, and uses this tilt as the initial posture error of the desired trajectory. The detection data is fed back to the controller to form a closed-loop control.

[0181] The controller calculates the tracking error in real time. When the absolute value of the tracking error is less than the preset accuracy threshold and the coaxiality of the engine output shaft and the transmission shaft reaches the preset alignment accuracy, the alignment is determined to be complete. At this time, the controller stops outputting hydraulic cylinder control signals, the brake is activated and the platform position is locked, and the entire alignment process is completed.

[0182] The working principle of this invention is briefly described as follows:

[0183] After the operator installs the engine onto the platform and performs coarse adjustments, the automatic alignment program is initiated. The laser alignment instrument and tilt sensor continuously collect data and send it to the controller. The FTESO within the controller estimates the platform's precise motion state and the disturbances it experiences in real time. The PNTSMC controller then calculates the precise thrust required by the three hydraulic cylinders based on these estimates, sensor feedback errors, and the user-preset convergence time. The hydraulic cylinders operate according to instructions, first performing horizontal leveling, then axial alignment, ultimately ensuring precise alignment between the engine output shaft and the test bench drive shaft. Once alignment is complete, the brakes lock the platform.

[0184] Furthermore, in this embodiment, during the solution of the control law, the finite-time extended state observer and the predefined-time non-singular terminal sliding mode controller are simulated using the Simulink simulation environment to verify their robustness and preset-time convergence performance under conditions of external disturbances and sensor noise.

[0185] Figure 2 An overview diagram of the simulation model is shown. It illustrates the overall signal flow and module composition of the simulation system, including the core signals and modules:

[0186] Input signals: reference signal (the desired trajectory of the centering platform, corresponding to the target values ​​of vertical displacement, pitch angle, and roll angle), disturbance signal (simulating unmodeled dynamics and lumped disturbances such as external force interference in the motion of the platform), and noise signal (simulating the measurement noise when the sensor collects data, which is close to the actual engineering scenario).

[0187] Control algorithm module: Four control algorithm modules—PID, ADRC (Active Disturbance Rejection Control), ADRSMC (Active Disturbance Rejection Sliding Mode Control), and FTESO+PNTSMC (this invention)—were built in parallel to achieve comparative simulations under the same operating conditions; among them, Figure 3 The diagram shows the FTESO module setup. Figure 4 The diagram shows the setup of the PNTSMC module.

[0188] Output signal: The tracking error of each algorithm (the difference between the actual trajectory and the reference signal qd), which provides core data for subsequent comparison of control effects;

[0189] Overall logic: Input signals are passed to each control algorithm module, and after algorithm calculation, hydraulic cylinder control commands are output to drive the platform model to move. Finally, the tracking errors of each algorithm are collected and output to realize the comparison of multiple algorithms.

[0190] Figure 5 The vertical displacement tracking error curve under external force disturbance is shown. It can be seen that the error curve of FTESO+PNTSMC of the present invention is closest to the 0 axis, with an error amplitude of <0.02, which is much smaller than that of PID (error ≈ ±0.1) and ADRC / ADRSMC (error ≈ ±0.06), and has the best disturbance rejection performance.

[0191] Figure 6 The roll angle tracking error curve under external force disturbance is shown. It can be seen that the roll angle error of the FTESO+PNTSMC algorithm of this invention is almost zero, the PID error amplitude is the largest (≈±5.0), and the ADRC / ADRSMC error is between the two. The algorithm of this invention has a much higher angle tracking accuracy than traditional algorithms.

[0192] Figure 7 The pitch angle tracking error curves under external force disturbances are shown. It can be seen that the pitch angle error of the FTESO+PNTSMC algorithm of this invention approaches 0, while the PID / ADRC algorithm exhibits significant fluctuations (error ≈ ±0.5), and the ADRSMC error fluctuates slightly. The algorithm of this invention demonstrates the best pitch angle tracking stability.

[0193] Figure 8The curves showing the real-time observations of the lumped disturbance corresponding to vertical displacement using FTESO are presented. It is evident that the observed signal curves are smooth and exhibit no significant chattering, demonstrating that FTESO can quickly and accurately estimate displacement-related disturbances, providing a reliable basis for control law compensation.

[0194] Figure 9 The real-time observation curves of FTESO for the lumped disturbance corresponding to the roll angle are shown. It can be seen that the observed signal changes smoothly within 0-2 seconds, with an amplitude between -5 and 20, without abrupt changes, demonstrating FTESO's effective observation capability for angular disturbances.

[0195] Figure 10 The real-time observation curves of the lumped disturbance corresponding to the pitch angle by FTESO are shown. It can be seen that the amplitude of the observed signal fluctuates smoothly between 0 and 15, matching the actual disturbance trend, thus verifying the disturbance observation accuracy of FTESO.

[0196] Figure 11 The curves showing the input thrust of the front cylinder, left rear cylinder, and right rear cylinder over time under the FTESO+PNTSMC algorithm are presented. It can be seen that the thrust curves are smooth, with amplitudes between -15 and 20 N, and no obvious chattering, proving that the algorithm effectively avoids the chattering problem of sliding mode control, resulting in stable actuator output.

[0197] Figure 12 The sensor noise signal curve is shown. The noise signal is a small-amplitude random fluctuation with an amplitude of <±0.015, which simulates the common noise characteristics of sensors in actual engineering.

[0198] Figure 13 The vertical displacement tracking error curves of the four algorithms are shown. It can be seen that after adding noise, the PID error further increases (≈±0.12), the ADRC / ADRSMC error fluctuates significantly, while the FTESO+PNTSMC error of the present invention remains close to the 0 axis (<0.02), showing the best noise suppression capability.

[0199] Figure 14 The roll angle tracking error curves of four algorithms are shown. It can be seen that the TESO+PNTSMC algorithm of this invention has an almost zero roll angle error, the PID error amplitude is the largest (≈±2), and the ADRC / ADRSMC error fluctuates significantly due to noise. The algorithm of this invention exhibits the best robustness to angle variations.

[0200] Figure 15 The pitch tracking error curves of four algorithms are shown. It can be seen that the pitch error of the FTESO+PNTSMC algorithm of this invention is still close to 0, while the PID / ADRC algorithm is more susceptible to noise fluctuations. This proves that the algorithm of this invention maintains extremely high tracking accuracy even under sensor noise interference.

[0201] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the invention without departing from the spirit and scope of the present invention.

Claims

1. A centering and tracking control method based on FTESO and PNTSMC, applied to the centering platform of an engine test bench, wherein the centering platform includes at least three hydraulic cylinders for adjusting the vertical displacement, pitch angle, and roll angle of the platform; characterized in that, The method includes: A dynamic model of the centering platform is established, and the vertical displacement, pitch angle, and roll angle of the centering platform are used as generalized coordinates. External disturbances and unmodeled dynamics are modeled as lumped disturbances. Based on the finite-time extended state observer, the velocity state of the generalized coordinates and the lumped disturbance are estimated in real time. Design a control law based on a predefined time-nonsingular terminal sliding mode control strategy; The control law controls the driving force of the hydraulic cylinder based on the disturbance estimate provided by the finite-time extended state observer, so as to enable the centering platform to track the desired trajectory within a preset time.

2. The centering tracking control method according to claim 1, characterized in that, Establishing the dynamic model of the centering platform includes: Establish a platform coordinate system with the center of mass of the platform as the origin. The axis is forward. The axis is perpendicular to the ground and pointing upwards; The coordinates of the thrust points of the three hydraulic cylinders are as follows: The coordinates of the front cylinder are... The coordinates of the left rear cylinder are The coordinates of the right rear cylinder are ,in All are greater than 0; When the centering platform is tilted, let the pitch angle be... The roll angle is The dynamic model of the platform is then expressed as: ； in, For generalized coordinates, This is the driving force vector of the hydraulic cylinder. These represent the driving forces of three hydraulic cylinders. The inertia matrix, Here is the damping matrix. The gravity vector For the force transfer matrix, For lumped disturbances; This is the transpose symbol.

3. The centering tracking control method according to claim 2, characterized in that, The real-time estimation based on the finite-time extended state observer includes: The lumped disturbance Expanded into new state variables ; Define the observation state vector , , Corresponding to generalized coordinates Speed ​​state and aggregated disturbance The estimated value; The equations for designing a finite-time extended state observer are as follows: ； in, This corresponds to the observation error; and All are sign power functions. , ; , For the first Expected observation error of the state variable, This is the observer gain.

4. The centering tracking control method according to claim 3, characterized in that, The control law design based on the predefined time non-singular terminal sliding mode control strategy includes: Define position tracking error Speed ​​tracking error , It is the expected trajectory; For actual speed, It is the expected speed; Design a predefined time-nonsingular terminal sliding surface: ； In the formula, , , ; This is a preset time parameter; Based on the output of the sliding surface and the finite-time extended state observer, the control law is designed as follows: ； in: ； In the formula: , , , To preset time gain, It is a saturation function. It is a constant greater than the upper bound of the observation error.

5. The centering tracking control method according to claim 4, characterized in that, The method also includes a centering process, comprising: The actual coaxiality between the engine output shaft and the test bench drive shaft is obtained by a laser alignment instrument, and the coaxiality deviation is used as the basis for setting the desired trajectory. The tilt angles of the engine in front-to-back and left-to-right directions are obtained by tilt sensors, and these tilt angles are used as the initial attitude error of the desired trajectory.

6. A centering platform device for implementing the centering tracking control method as described in any one of claims 1-5, characterized in that, include: An engine mounting platform (1) includes a support frame for supporting and securing the engine; The leveling mechanism (2), integrated on the support frame (1), includes at least three independently telescopic hydraulic cylinders for driving the engine to move in the vertical, pitch and roll directions; The sensing system includes a laser alignment instrument (3) for measuring coaxiality and a tilt sensor (4) for measuring the tilt angle of the platform. The controller is connected in communication with the hydraulic cylinder, the laser alignment instrument (3), and the tilt sensor (4), and is equipped with a control program. The controller is configured to receive signals from the laser alignment instrument and the tilt sensor, calculate control commands based on the alignment tracking control method, and drive the hydraulic cylinder to perform actions until the engine output shaft and the transmission shaft reach a preset coaxial accuracy.

7. The centering platform device according to claim 6, characterized in that, The hydraulic cylinder (2) includes a front support hydraulic cylinder arranged at the front end of the support frame and two rear support hydraulic cylinders symmetrically arranged at the rear of the support frame. The three hydraulic cylinders form a triangular support structure.

8. The centering platform device according to claim 6, characterized in that, The device also includes a moving propulsion mechanism (5), which includes a first slide groove (6) provided on both sides of the bottom of the support frame. A first slider (7) is slidably provided in front of and behind the first slide groove (6). A second slide groove (8) is provided on the first slider (7). A second slider (9) for supporting the hydraulic cylinder is slidably provided in the second slide groove (8).

9. The centering platform device according to claim 6, characterized in that, The device also includes a brake for locking the engine mounting platform after alignment is completed.

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