A High-Order All-Drive Motor Modeling and Control Method Based on Rigorous Feedback Structure
By adopting a high-order modeling and control method for all-drive motors with a rigorous feedback structure, the problem of insufficient description of the high-order coupling relationship between electromagnetic thrust, electrical dynamics and mechanical motion in the LSRM system is solved, achieving high-precision and robust motion control and improving the system's stability and dynamic response speed.
Patent Information
- Application Number
- CN202610422478.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-04-01
- Publication Date
- 2026-05-26
AI Technical Summary
Existing LSRM modeling and control methods are insufficient to fully describe the high-order coupling relationship between electromagnetic thrust, electrical dynamics and mechanical motion. The models lack accuracy, the physical meaning of the control parameters is unclear, and there is a lack of a unified control framework, making it difficult to achieve high-precision and robust motion control.
A high-order all-drive motor modeling method based on a strict feedback structure is adopted. By coupling the fundamental equations, Taylor expansion, state transformation and Lyapunov stability analysis, an integrated feedforward and feedback trajectory tracking control law is constructed to improve the system's stability and dynamic response speed.
It improves model accuracy and applicable operating conditions, enhances system robustness and dynamic response speed, ensures asymptotic stability of closed-loop system and convergence speed of tracking error, and has good engineering practicality and promotion value.
Smart Images
Figure CN122092744A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the technical field of motor control, specifically relating to a high-order all-drive motor modeling and control method based on a strict feedback structure. Background Technology
[0002] To meet the demands of the rapid development of intelligent manufacturing, high-end equipment, and emerging industrial clusters, linear switched reluctance motors (LSRMs) have been widely researched and applied in precision motion control, industrial automation, and intelligent transportation due to their advantages such as simple structure, high reliability, no need for mechanical transmission, direct drive capability, and high-precision positioning. Compared to traditional rotary motors and "rotation-linear" transmission structures, LSRMs effectively reduce system mechanical complexity and maintenance costs by eliminating intermediate mechanical components such as reducers and lead screws, and exhibit higher dynamic performance and operating efficiency in applications such as CNC machining, high-speed transportation, and rail transit.
[0003] With the continuous development of control theory and computational capabilities, dynamic modeling and control methods for LSRM systems are also constantly evolving. Among them, high-order system modeling and control methods have gradually attracted attention. Existing research has proposed combining multiple low-order physical subsystems in LSRM for modeling and further constructing high-order system representations to more accurately describe electromagnetic coupling effects, nonlinear magnetic properties, and electromechanical interactions within the system. Building on this, some studies have introduced the concept of High-Order Fully Actuated (HOFA) system modeling, transforming underactuated or structurally complex systems into equivalent fully actuated system models, thereby providing greater freedom for controller design.
[0004] However, existing LSRM modeling and control methods still have certain shortcomings. First, traditional state-space modeling methods often require linearization or order reduction of the system in practical applications, making it difficult to fully characterize the nonlinear characteristics and parameter coupling relationships of LSRM over a wide operating range. Model accuracy decreases significantly under high-speed, high-load, or strong disturbance conditions. Second, while some higher-order modeling methods improve system description capabilities, they lack a unified control-oriented modeling framework between model structure and controller design. This leads to unclear physical meanings of control parameters, reliance on experience in the design process, and difficulty in balancing performance and stability. Third, existing HOFA-related methods mostly focus on theoretical modeling and pole placement analysis, lacking targeted design for the systematic allocation of closed-loop eigenvalues and their engineering implementation in practical motor control, limiting their promotion in high-precision trajectory tracking and industrial applications.
[0005] In summary, how to construct a HOFA modeling and control method with a clear structure, adjustable parameters, and easy control design while preserving the complete physical characteristics of the LSRM system, so as to achieve high-precision and high-robust motion control, remains an urgent problem to be solved in the existing technology. Summary of the Invention
[0006] The purpose of this invention is to address the aforementioned shortcomings of the prior art by providing a high-order all-drive motor modeling and control method based on a strict feedback structure, in order to solve the following problems: Existing LSRM control methods are mostly based on low-order or simplified state-space models, which are difficult to fully describe the high-order coupling relationship between electromagnetic thrust, electrical dynamics and mechanical motion. This results in insufficient model accuracy under complex working conditions, thus limiting the accuracy and stability of position and trajectory tracking control. While existing high-order modeling methods can improve the ability to describe systems, they usually do not use a strict-feedback structure for systematic modeling. The model structure and controller design lack inherent consistency, making it difficult to directly support stability analysis and control law construction. Existing HOFA-related methods mostly remain at the level of theoretical modeling or pole placement, lacking a unified control framework for engineering implementation. The physical meaning of control parameters is unclear, the parameter configuration process is complex, and it is difficult to simultaneously take into account dynamic response speed, steady-state accuracy and system stability. In existing control methods, stability analysis of nonlinear and high-order LSRM systems often relies on empirical design or local linearization, making it difficult to provide rigorous global or semi-global asymptotic stability proofs, which restricts their application in high-reliability industrial scenarios.
[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A high-order all-drive motor modeling and control method based on a strict feedback structure includes the following steps: S1. Obtain the electrical and mechanical dynamic parameters of the linear switched reluctance motor, and establish the fundamental equations for the coupling of electrical, mechanical, and force. S2. Perform Taylor expansion on the fundamental coupled equations and combine them with instantaneous electric power to construct coupled dynamic equations; S3. Transform the coupled dynamic equations into a high-order rigorous feedback nonlinear system model; S4. Based on the state transformation mechanism, the high-order strict feedback nonlinear system model is transformed into a high-order full-drive model that satisfies the feedback form. S5. Construct a trajectory tracking control law that integrates feedforward and feedback; S6. Substitute the trajectory tracking control law into the high-order all-drive model to obtain the all-drive closed-loop LSRM system, and use the parameterized configuration method based on feature structure allocation to solve the feedback gain vector. S7. Perform Lyapunov stability analysis on the all-drive closed-loop LSRM system, and realize the closed-loop stability of the system and the tracking of the reference trajectory based on the analysis results.
[0008] Furthermore, in S1, the fundamental equations for the coupling of electrical-mechanical-force include the voltage balance equation, the second-order mechanical motion equation, and the electromagnetic thrust equation for the linear switched reluctance motor.
[0009] Furthermore, S2 specifically includes: A Taylor series expansion of the electromagnetic thrust equation is performed, retaining the second-order terms to obtain an analytical thrust expression. Differentiation of the Taylor expansion terms reveals the relationship between the time derivative of the electromagnetic thrust and the derivatives of the current and displacement. Combined with the instantaneous electric power equation, the coupled dynamic equation of the linear switched reluctance motor is obtained, expressed as: In the formula, The acceleration of the mover. The damping coefficient is... For the quality of the sports platform, The velocity of the mover, For total electromagnetic thrust, For external load force, Total electromagnetic thrust The first derivative, This is the second-order partial derivative of the phase inductance with respect to displacement. This is the first-order partial derivative of the phase inductance with respect to displacement. For the first The resistance of the phase winding, For the first Phase inductance, The force-flow conversion coefficient, This refers to instantaneous electrical power.
[0010] Furthermore, in S3, the coupled dynamic equations are transformed into a high-order rigorous feedback nonlinear system model, which is expressed as: in: In the formula, State variables The second time derivative, For the second state variable The first derivative; This is the first part of the nonlinear dynamic function. State variables The set of the 0th and 1st derivatives, For time; This refers to the gain coefficient for the first part; This refers to the gain coefficient in the second part; This is the second part, the nonlinear dynamic function. State variables The set of 0th, 1st, and 2nd derivatives, For the second state variable, This is the actual control input.
[0011] Furthermore, in S4, by transforming This transforms the high-order rigorous feedback nonlinear system model into a HOFA model that satisfies the feedback form. in: In the formula, The variables after the state transition. Let be the third time derivative of the variable after the state transformation; It is the inverse of the first part of the gain coefficient. The second-order time derivative of the variable after the state transformation. This is the first part of the nonlinear dynamic function after the state transformation. Let be the set of the 0th and 1st derivatives of the variables after the state transformation. This is the nonlinear term in the HOFA model. Let be the set of the 0th, 1st, and 2nd derivatives of the variable after the state transformation. This is the gain term of the HOFA model. Let be the first-order time derivative of the variable after the state transformation.
[0012] Furthermore, in S5, a trajectory tracking control law integrating feedforward and feedback is constructed, which is expressed as: In the formula, This is the inverse of the gain term in the HOFA model. It is a nonlinear dynamic compensation term. For feedforward tracking term, For the feedback gain vector, For the desired reference trajectory The set of 0th, 1st, and 2nd derivatives, For the desired reference trajectory The third time derivative.
[0013] Furthermore, in S6, the trajectory tracking control law is substituted into the HOFA model to obtain the all-drive closed-loop LSRM system, which is expressed as: .
[0014] Furthermore, in step S6, the feedback gain vector is solved using a parameterized configuration method, which is expressed as: Define matrix and : Using similarity transformation Based on this, the feedback gain vector is obtained. ; In the formula, , For parameterized configuration of intermediate matrices, Configure matrices for the poles. Configure matrices for poles of Power of 1 Configure matrices for poles of Power of 1 The state matrix of the all-drive closed-loop LSRM system. for The feedback gain vector corresponding to the order system, It is a non-singular transformation matrix. It is the inverse of the non-singular transformation matrix. It is a parameter matrix.
[0015] Furthermore, in S7, a Lyapunov stability analysis was performed on the all-drive closed-loop LSRM system, including: The error system of the all-drive closed-loop LSRM system is expressed as follows: In the formula, For tracking error The third time derivative, For tracking error The set of 0th, 1st, and 2nd derivatives; Based on this error system, the positive definite Lyapunov function is constructed as follows: In the formula, It is a positive definite Lyapunov function. It is a positive definite matrix; The derivative is: In the formula, positive definite Lyapunov function The first time derivative, for Time derivative, It is a positive number; when Then: This ensures the asymptotic stability of the all-drive closed-loop LSRM system; among which, for The positive definite Lyapunov function at time t. Let be the positive definite Lyapunov function at the initial time.
[0016] The high-order all-drive motor modeling and control method based on a strict feedback structure provided by this invention has the following beneficial effects: This invention provides a unified modeling of the high-order nonlinear coupling relationships between the electrical dynamics, mechanical motion, and electromagnetic thrust of a linear switched reluctance motor. This avoids traditional small-signal linearization and order reduction modeling methods while preserving the main physical coupling characteristics between the system's electrical dynamics, mechanical motion, and electromagnetic thrust, thus improving model accuracy and expanding the system's applicable operating conditions. Based on this, a trajectory tracking control method based on the HOFA model is constructed, allowing the control input to directly act on the equivalent all-drive system. This avoids the error accumulation and dynamic lag problems caused by multiple control loops in traditional cascaded control structures. Furthermore, through nonlinear compensation and integrated feedforward-feedback design, the system's dynamic response speed and steady-state tracking accuracy are improved. Simultaneously, a parameterized control gain design mechanism allows for flexible adjustment of the closed-loop system's stability and dynamic performance according to actual needs, thereby enhancing system robustness while ensuring rapid response. Based on Lyapunov stability analysis, this invention theoretically guarantees the asymptotic stability of the closed-loop system. In practical applications, it exhibits fast convergence speed of tracking error, smooth changes in control input, and stable and reliable system operation. The overall technical effect is significantly better than existing linear switched reluctance motor control methods, and it has good engineering practicality and promotion value. Attached Figure Description
[0017] Figure 1 This is a flowchart of the high-order all-drive motor modeling and control method based on a strict feedback structure in the embodiment.
[0018] Figure 2 The diagram shows the structural block diagram of the high-order all-drive motor modeling and control method based on a strict feedback structure in the embodiment.
[0019] Figure 3 The image shows the tracking diagram under the action of the HOFA tracking control law in the embodiment.
[0020] Figure 4 The error diagram shown in the example is the result of the HOFA tracking control law.
[0021] Figure 5 The diagram shows the control input under the action of the HOFA tracking control law in the example. Detailed Implementation
[0022] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.
[0023] This embodiment provides a high-order all-drive motor modeling and control method based on a strict feedback structure, which includes the following steps: S1. Obtain the electrical and mechanical dynamic parameters of the linear switched reluctance motor, and establish the fundamental equations for the coupling of electrical, mechanical, and force. The fundamental equations for the electromechanical-force coupling in this embodiment include the voltage balance equation, the second-order mechanical motion equation, and the electromagnetic thrust equation for the linear switched reluctance motor, as detailed below: Considering the electrical characteristics of each phase of a linear switched reluctance motor, the following voltage balance equation is established by applying Kirchhoff's voltage law (KVL) to the windings of each phase: (1) In a three-phase linear switched reluctance motor (LSRM) system, for each phase , For specific three-phase applications, the electrical parameters are defined as follows: Indicates instantaneous phase current. Indicates phase voltage. It is the first Resistance of phase winding; displacement Indicates the mover relative to the first The displacement of the phase stator; It is the phase inductance, which depends on the phase current. relative displacement of the mover ; For time; By neglecting leakage flux and mutual inductance, the second-order mechanical equations of motion are derived: (2) In the formula, Indicates the quality of the motion platform. Indicates external load force; For the displacement of the mover; Let be the total electromagnetic thrust, and be the damping coefficient; The expression for is: (3) In the formula, For the first The electromagnetic thrust of the phase.
[0024] S2. Perform a Taylor expansion of the fundamental coupled equations and combine them with instantaneous electric power to construct the coupled dynamic equations, which specifically include the following: No. electromagnetic thrust of phase exist Approximating this point using Taylor expansion, we obtain: (4) In the formula, Let this be the reference point for the current in the Taylor expansion. For the first The first time derivative of the electromagnetic thrust of the phase, For the first The second time derivative of the electromagnetic thrust of the phase; . For specific representation: (5) in, It is a higher-order term in a Taylor expansion, for sufficiently small Negligible, therefore there is .
[0025] Next, we define ,as well as ; electromagnetic thrust Taking the derivative with respect to time, we get: (6) In the formula, This is the first-order partial derivative of the phase inductance with respect to displacement. This is the second-order partial derivative of the phase inductance with respect to displacement. The velocity of the mover, This is the first-order time derivative of the instantaneous phase current; Combining equations (3) and (6), we can... Expressed as: (7) Multiply the voltage balance equation (1) by The instantaneous electric power is obtained as follows: (8) In the formula, Instantaneous electrical power; Substituting equation (7) and the force expression (3) into equation (8), we get: (9) Finally, by combining the second-order mechanical motion equation (2) with the electric power balance equation (9), the total electromagnetic thrust is... and Associated through the force flow conversion module, it is represented as The dynamic equations of the coupling are: (10) In the formula, It is the force-fluid conversion coefficient. The acceleration of the mover. Total electromagnetic thrust The first derivative.
[0026] S3. Transform the coupled dynamic equations into a high-order rigorous feedback nonlinear system model, which specifically includes the following: The high-order rigorous feedback nonlinear system model is described as follows: (11) In the formula, State variables The second time derivative, For the second state variable The first derivative; This is the first part of the nonlinear dynamic function. State variables The set of the 0th and 1st derivatives, This is the second part, the nonlinear dynamic function. State variables The set of 0th, 1st, and 2nd derivatives, For the second state variable, For actual control input; This refers to the gain coefficient for the first part; This refers to the gain coefficient in the second part; Among them, if And for and , for In a real vector space of dimension 1, we have: (12) Then in In this case, the high-order strictly feedback nonlinear system model (HOSFS) can be transformed into the following HOFA model: (13) In the formula, Let be the third time derivative of the variable after the state transformation; Let be the set of the 0th, 1st, and 2nd derivatives of the variable after the state transformation. This is the nonlinear term in the HOFA model. This is the gain term of the HOFA model. For actual control input; in: (14) and: (15) In the formula, It is an identity matrix, whose dimensions match the dimensions of the state variables; This is the first-order time derivative of the first part of the nonlinear dynamic function after the state transformation; This is the second part of the nonlinear dynamic function after the state transformation; and Its derivative is given and determined by the following formula: (16) In the formula, Let be the second time derivative of the variable after the state transformation; set up and set , The final form of the high-order rigorous feedback nonlinear system model is: (17) In the formula, , ,in: and As shown below: (18) (19) S4. Based on the state reconstruction mechanism, the high-order strictly feedback nonlinear system model is transformed into a HOFA model that satisfies the feedback form. This specifically includes the following: Considering the HOSFS given by equation (17), if and If all feasible states are nonsingular, then the system can be reconstructed as a third-order HOFA model, specifically: Through transformation, we can obtain: (20) Based on this, we obtain the derivative: (twenty one) Then, the variables after the state transformation The third derivative can be expressed as: (twenty two) Therefore, we obtain the following expression: (twenty three) and: (twenty four) Finally, the HOFA model is expressed as: (25) in: (26) and: (27) Therefore, the proof of the entire construction of the HOFA model is complete.
[0027] This embodiment unifies the modeling of the electrical subsystem, mechanical motion subsystem, and electromagnetic thrust relationship of a linear switched reluctance motor, and introduces intermediate state variables and a state reconstruction mechanism. This systematically transforms the originally complex and strongly coupled high-order nonlinear system into a HOFA model that satisfies a strict feedback form. This modeling method, without linearization or order reduction approximation, fully preserves the physical characteristics of the system, providing a unified and standardized model foundation for subsequent control law design and stability analysis. This is the fundamental technical feature that distinguishes this invention from existing technologies.
[0028] S5. Construct a trajectory tracking control law that integrates feedforward and feedback, which specifically includes the following: The control objective is to achieve control over the reference trajectory. The tracking is performed while considering the following assumptions: Assumption 1: Under the working condition under study, in addition to the external load force Apart from its function, the impact of other external disturbances, parameter perturbations, and unmodeled dynamics during system operation is relatively small and can be ignored.
[0029] Assumption 2: Assume that the actuator operates without introducing delays, dead inputs, faults or other problems.
[0030] Assumption 3: All system states are bounded over the entire operation time.
[0031] Assumption 4: Reference Trajectory It is smooth and bounded, and its derivatives are continuous up to the required order.
[0032] For the LSRM system based on the HOFA model in this embodiment, a HOFA tracking control law is proposed: (28) In the formula, This is the inverse of the gain term in the higher-order all-wheel drive model. This is a nonlinear dynamic compensation term, responsible for compensating for nonlinear dynamics and ensuring the stability of the closed-loop system. As a feedforward tracking term, used for feedforward tracking, it is designed to improve the accuracy of the desired reference trajectory. Tracking accuracy; The feedback gain vector can be parameterized to meet the desired stability and performance requirements; For the desired reference trajectory The set of 0th, 1st, and 2nd derivatives, For the desired reference trajectory The third time derivative.
[0033] S6. Substitute the trajectory tracking control law into the HOFA model to obtain the all-drive closed-loop LSRM system, and use the parameterized configuration method to solve for the feedback gain vector, which specifically includes the following: Substituting the trajectory tracking control law into the HOFA model, we obtain the all-drive closed-loop LSRM system: (29) The LSRM system can achieve tracking control and remain stable when the following conditions are met: (1) The system has bounded input and bounded output stability: when ,have ; (2) Asymptotic convergence of the system state: ; In summary, for the LSRM system, under assumptions 1-4, a HOFA control law was designed. The control law is required to simultaneously guarantee the stability of the closed-loop system and the trajectory tracking performance, and to satisfy the above conditions (1) and (2).
[0034] This embodiment introduces a parameter matrix and a non-singular transformation matrix to represent the control gain in an adjustable parameterized form, enabling the dynamic characteristics and stability of the closed-loop system to be systematically configured through parameter selection. This method avoids the reliance on experience or iterative trial-and-error parameter tuning, giving the controller design process clear physical meaning and engineering feasibility, and significantly improving the method's adaptability to different operating conditions and application scenarios.
[0035] Specifically, this embodiment provides a system-wide parameterized method for solving the problem based on the HOFA parameter configuration framework. : Define matrix and : (30) (31) in, It is an arbitrary parameter matrix; , An intermediate matrix for parameterized configuration; Configure matrices for the poles. Configure matrices for poles of Power of 1 Configure matrices for poles of Power of; but and Provides the general solution to the matrix equation; for any chosen... and arbitrary non-singular transformation matrix satisfy: (32) All gains The parameters are given by the following formula: (33) Specifically, when When, it becomes: (34) In the formula, The state matrix of the all-drive closed-loop LSRM system. for The feedback gain vector corresponding to the order system, It is the inverse of the non-singular transformation matrix; in: ,choose Make: (35) as well as: (36) in, These are the tuning parameters that are crucial for convergence; if Then calculate Otherwise, the matrix must be chosen again. and .
[0036] S7. Perform Lyapunov stability analysis on the all-drive closed-loop LSRM system, and implement reference trajectory tracking based on the analysis results. This includes the following: Design a HOFA tracking controller to ensure system stability, tracking performance, and full-drive characteristics.
[0037] Assumption , Let the space be an r×r dimensional real matrix, satisfying: (37) in, For positive integers, Then there exists a matrix Make: (38) The error system is represented as: (39) In the formula, For tracking error The third time derivative, For tracking error The set of 0th, 1st, and 2nd derivatives; Where, expression This represents the tracking error, and it can be further expressed as: (40) In the formula, for The first time derivative; because Therefore, there exists a positive definite matrix that satisfies condition (37) and condition (38). ; Proof: To verify system (39), the positive definite Lyapunov function is constructed as follows: (41) In the formula, It is a positive definite Lyapunov function. It is a positive definite matrix; Given n=3, the expression simplifies to: (42) definition ,but The derivative is: (43) In the formula, positive definite Lyapunov function The first time derivative, for The time derivative; when At that time, this means: (44) In the formula, for The positive definite Lyapunov function at time t. Let be the positive definite Lyapunov function at the initial time.
[0038] Therefore, the HOFA tracking control law (28) proposed in this embodiment guarantees the asymptotic stability of the all-drive closed-loop LSRM system (29).
[0039] This implementation constructs a Lyapunov function that matches the HOFA error system and conducts a rigorous stability analysis on the closed-loop system under the proposed control method, proving that the system state has asymptotic convergence under given assumptions. This stability proof provides theoretical support and verifiable evidence for the promotion of the control method of this invention in high-reliability, high-precision industrial applications.
[0040] In some embodiments, the method of the present invention is analyzed based on experimental results, which specifically includes the following: The main parameters of the LSRM design are shown in Table 1, including the inductance function. It can be represented in the following form: (45) To reduce computational complexity, a standard cubic polynomial is used for the position-current correlation function. Approximately expressed as Based on this expression, we can obtain: (46) Table 1. Key Parameters of LSRM Configure the closed-loop characteristic poles of the system as follows: , , Let the matrix ,matrix Through simulation calculations, the HOFA control gain is obtained as follows: (47) In the experimental verification section, this experiment uses a reference trajectory composed of four sinusoidal components with different frequencies and initial phases: The fundamental frequency of this trajectory is 0.159Hz. (See attached image.) Figure 3 and Figure 4 As shown, under the action of the HOFA tracking control law, the HOFA-LSRM system described by the HOFA model (25) can rapidly converge its tracking error to a stable range of 1% within 6 seconds, achieving the expected tracking control performance requirements and verifying the effectiveness of the control strategy under real-time implementation conditions. Appendix Figure 5 Experimental data on the control input of the HOFA model (25) under the HOFA tracking control law (28) are presented. The results show that the control input converges asymptotically, causing the system to stabilize rapidly. This dynamic response characteristic is highly consistent with the asymptotic convergence conclusion of the control law obtained from theoretical analysis. The experimental data show that the HOFA motor position tracking control system based on strict feedback system modeling has significant advantages in key performance indicators such as dynamic response speed and steady-state accuracy, fully demonstrating its superior comprehensive control performance.
[0041] Although specific embodiments of the invention have been described in detail with reference to the accompanying drawings, this should not be construed as limiting the scope of protection of this patent. Various modifications and variations that can be made by a person skilled in the art without inventive effort within the scope described in the claims still fall within the scope of protection of this patent.
Claims
1. A high-order all-drive motor modeling and control method based on a strict feedback structure, characterized in that, Includes the following steps: S1. Obtain the electrical and mechanical dynamic parameters of the linear switched reluctance motor, and establish the fundamental equations for the coupling of electrical, mechanical, and force. S2. Perform Taylor expansion on the fundamental coupled equations and combine them with instantaneous electric power to construct coupled dynamic equations; S3. Transform the coupled dynamic equations into a high-order rigorous feedback nonlinear system model; S4. Based on the state transformation mechanism, the high-order strict feedback nonlinear system model is transformed into a high-order full-drive model that satisfies the feedback form. S5. Construct a trajectory tracking control law that integrates feedforward and feedback; S6. Substitute the trajectory tracking control law into the high-order all-drive model to obtain the all-drive closed-loop LSRM system, and use the parameterized configuration method based on feature structure allocation to solve the feedback gain vector. S7. Perform Lyapunov stability analysis on the all-drive closed-loop LSRM system, and realize the closed-loop stability of the system and the tracking of the reference trajectory based on the analysis results.
2. The high-order all-drive motor modeling and control method based on a strict feedback structure according to claim 1, characterized in that: In S1, the fundamental equations for the coupling of electrical-mechanical-force include the voltage balance equation, the second-order mechanical motion equation, and the electromagnetic thrust equation for the linear switched reluctance motor.
3. The high-order all-drive motor modeling and control method based on a strict feedback structure according to claim 1, characterized in that, S2 specifically includes: A Taylor series expansion of the electromagnetic thrust equation is performed, retaining the second-order terms to obtain an analytical thrust expression. Differentiation of the Taylor expansion terms reveals the relationship between the time derivative of the electromagnetic thrust and the derivatives of the current and displacement. Combined with the instantaneous electric power equation, the coupled dynamic equation of the linear switched reluctance motor is obtained, expressed as: In the formula, The acceleration of the mover. The damping coefficient is... For the quality of the sports platform, The velocity of the mover, For total electromagnetic thrust, For external load force, Total electromagnetic thrust The first derivative, Let be the second-order partial derivative of the phase inductance with respect to displacement. . represents the first-order partial derivative of the phase inductance with respect to displacement. For the first The resistance of the phase winding, For the first Phase inductance, The force-flow conversion coefficient, This refers to instantaneous electrical power.
4. The high-order all-drive motor modeling and control method based on a strict feedback structure according to claim 3, characterized in that, In S3, the coupled dynamic equations are transformed into a high-order rigorous feedback nonlinear system model, which is expressed as: in: In the formula, State variables The second time derivative, For the second state variable The first derivative; This is the first part of the nonlinear dynamic function. State variables The set of the 0th and 1st derivatives, For time; This refers to the gain coefficient for the first part; This refers to the gain coefficient in the second part; This is the second part, the nonlinear dynamic function. State variables The set of 0th, 1st, and 2nd derivatives, For the second state variable, This is the actual control input.
5. The high-order all-drive motor modeling and control method based on a strict feedback structure according to claim 4, characterized in that, In S4, by transformation The high-order strict feedback nonlinear system model is transformed into a high-order all-drive model that satisfies the feedback form. in: In the formula, The variables after the state transition. Let be the third time derivative of the variable after the state transformation; It is the inverse of the first part of the gain coefficient. The second-order time derivative of the variable after the state transformation. This is the first part of the nonlinear dynamic function after the state transformation. Let be the set of the 0th and 1st derivatives of the variables after the state transformation. For the nonlinear terms of the high-order all-wheel drive model, Let be the set of the 0th, 1st, and 2nd derivatives of the variable after the state transformation. This is the gain term for the high-order all-wheel drive model. Let be the first-order time derivative of the variable after the state transformation.
6. The high-order all-drive motor modeling and control method based on a strict feedback structure according to claim 5, characterized in that, In S5, a trajectory tracking control law integrating feedforward and feedback is constructed, which is expressed as: In the formula, This is the inverse of the gain term in the higher-order all-wheel drive model. It is a nonlinear dynamic compensation term. For feedforward tracking term, For the feedback gain vector, For the desired reference trajectory The set of 0th, 1st, and 2nd derivatives, For the desired reference trajectory The third time derivative.
7. The high-order all-drive motor modeling and control method based on a strict feedback structure according to claim 6, characterized in that, In S6, substituting the trajectory tracking control law into the high-order all-wheel drive model yields the all-wheel drive closed-loop LSRM system, which is expressed as: 。 8. The high-order all-drive motor modeling and control method based on a strict feedback structure according to claim 6, characterized in that, In step S6, the feedback gain vector is solved using a parameterized configuration method, which is expressed as follows: Define matrix and : Using similarity transformation Based on this, the feedback gain vector is obtained. ; In the formula, , For parameterized configuration of intermediate matrices, Configure matrices for the poles. Configure matrices for poles of Power of 1 Configure matrices for poles of Power of 1 The state matrix of the all-drive closed-loop LSRM system. for The feedback gain vector corresponding to the order system, It is a non-singular transformation matrix. It is the inverse of the non-singular transformation matrix. It is a parameter matrix.
9. The high-order all-drive motor modeling and control method based on a strict feedback structure according to claim 7, characterized in that, In S7, Lyapunov stability analysis was performed on the all-drive closed-loop LSRM system, including: The error system of the all-drive closed-loop LSRM system is expressed as follows: In the formula, For tracking error The third time derivative, For tracking error The set of 0th, 1st, and 2nd derivatives; Based on this error system, the positive definite Lyapunov function is constructed as follows: In the formula, It is a positive definite Lyapunov function. It is a positive definite matrix; The derivative is: In the formula, positive definite Lyapunov function The first time derivative, for Time derivative, It is a positive number; when Then: This ensures the asymptotic stability of the all-drive closed-loop LSRM system; among which, Let be a positive definite Lyapunov function at time t. Let be the positive definite Lyapunov function at the initial time.