Electric steering engine fine anti-interference control method under rudder deflection angle constraint

Abstract

The invention relates to an electric steering engine fine anti-interference control method under the constraint of a rudder deflection angle, and belongs to the technical field of electric steering engine control. Firstly, an electric steering engine mathematical model considering unknown frequency multi-source interference is established; secondly, aiming at multi-source interference generated by cogging torque, magnetic flux harmonic waves, PWM dead zone torque and the like, constructing an unknown frequency interference observer to estimate interference; and finally, designing a backstepping controller based on a obstacle Lyapunov function, and completing the design of the fine anti-interference control method of the electric steering engine under the constraint of the rudder deflection angle by combining the interference and the estimated value of the first derivative of the interference. The method realizes fine anti-interference control of the electric steering engine, has the characteristics of high control precision and good reliability, and is suitable for the control problem of the electric steering engine under multi-source interference and constraint.

Description

Technical Field

[0001] The present invention belongs to the technical field of electric steering gear control, and specifically relates to a fine anti-interference control method for an electric steering gear under rudder angle constraints. The method solves the problems of existing anti-interference control methods inaccurately estimating multi-unknown frequency sinusoidal interference and having difficulty coping with rudder angle constraints. The method is applicable to the rudder angle tracking control problem of an electric steering gear under the influence of multi-unknown frequency sinusoidal interference and constraints. Background Art

[0002] With the widespread application of automation technology in various fields, steering servo systems are playing an increasingly important role as the "muscle system" (i.e., actuator) of various mechanical devices. Electric steering gears are widely used in various mechanical devices due to their high reliability, high efficiency, lightweight design, and ease of maintenance. However, due to harsh operating environments and various interference and constraints, the rudder angle output by electric steering gears struggles to accurately track command signals. For example, friction and backlash increase lag in the steering gear system, reduce bandwidth, and increase position tracking error, severely impacting performance. Rudder angles are also limited by physical constraints. Exceeding these constraints can cause the electric steering gear to jam, leading to controller failure and severely impacting mechanical device performance. Consequently, electric steering control issues have garnered extensive attention and research.

[0003] The primary task of an electric servo control system is to control the output rudder angle to the desired command angle, thereby assisting mechanical equipment in achieving various functions. Traditional robust control, PID control, and variable structure control methods primarily rely on interference suppression to address various interference effects. These methods offer relatively conservative control effects, limited adaptability, and lack proactive estimation and compensation. Chinese patent CN104698835B utilizes a variable structure controller, a differential controller, a proportional controller, and a proportional-integral controller to control a DC motor, effectively addressing the overshoot problem of integral control and the inherent jitter problem of variable structure control.

[0004] To fully utilize known information about disturbances and reduce the conservatism of control effects, extensive research has been conducted on disturbance cancellation control methods based on the principle of disturbance invariance, such as active disturbance rejection control (ADRC) and control based on disturbance observers. Chinese patent CN114815595A describes an ADRC controller that reduces the impact of external disturbances on the electric servo system, improving rudder angle tracking and system robustness.

[0005] However, current research results have insufficiently considered the constraints faced by electric servos, and the accuracy of multi-source interference estimation needs to be improved. Therefore, it is urgent to explore rudder angle tracking control methods that are applicable to the influence of multi-frequency sinusoidal interference and constraints. Summary of the Invention

[0006] Aiming at the problem of rudder angle tracking under the influence of multi-unknown frequency sinusoidal interference and constraints in an electric servo servo system, and to overcome the shortcomings of the existing technology, the present invention provides a fine anti-interference control method for an electric servo under rudder angle constraints. By establishing a mathematical model of an electric servo considering multi-source interference of unknown frequencies, the foundation for the design of a control scheme is laid. Then, an unknown frequency interference observer is constructed to estimate the interference. Finally, a backstepping controller based on the barrier Lyapunov function is designed. Combined with the interference and its first-order derivative estimate, the fine anti-interference control method for the electric servo under rudder angle constraints is designed, thereby improving the control accuracy and reliability of the electric servo servo system.

[0007] In order to achieve the above object, the present invention adopts the following technical solutions:

[0008] A method for fine anti-interference control of an electric servo under rudder angle constraint, comprising the following steps:

[0009] The first step is to establish a mathematical model of the electric servo considering multi-source interference of unknown frequencies;

[0010] In the second step, the interference description form conversion, auxiliary observer design, interference and frequency information decoupling, unknown frequency information estimation, and interference estimation are carried out in sequence. Through the above steps, an unknown frequency interference observer is constructed to estimate multi-unknown frequency sinusoidal interference;

[0011] The third step is to design a backstepping controller based on the obstacle Lyapunov function, and combine the disturbance and its first-order derivative estimation to complete the design of the electric servo's fine anti-disturbance control method under the rudder angle constraint.

[0012] The beneficial effects of the present invention compared with the prior art are:

[0013] The fine anti-interference control algorithm involved in the present invention aims to address the shortcomings of traditional methods, such as relatively conservative control effects, insufficient utilization of known interference information, insufficient consideration of the constraints faced by electric steering gears, and insufficient estimation accuracy of multi-source interference. An anti-interference control method based on an unknown frequency interference observer and a backstepping controller is designed to achieve online estimation and compensation of multi-source interference, so that the steering gear servo system can be controlled according to the rudder deflection angle output constraint requirements, and complete the design of anti-interference control laws for controlled objects such as electric steering gears with complex interference characteristics and constraints. The algorithm has the characteristics of high control accuracy and good reliability, and is suitable for electric steering gear servo systems facing multi-source interference and with stringent control performance requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 The flowchart of the electric servo fine anti-interference control method under rudder deflection angle constraint of the present invention is shown.

[0015] Figure 2The figure is a principle block diagram of a method for fine anti-interference control of an electric servo under rudder deflection angle constraint according to the present invention. DETAILED DESCRIPTION

[0016] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are only intended to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other. The present invention is described in detail below with reference to the accompanying drawings and examples.

[0017] like Figure 1 As shown, the present invention discloses a fine anti-interference control method for an electric servo under rudder deflection angle constraint, comprising the following steps:

[0018] The first step is to establish a mathematical model of the electric servo considering multi-source interference of unknown frequencies, which provides a basis for the design of the observer and controller in the next two steps.

[0019] The second step is to construct an unknown frequency disturbance observer to estimate the disturbance so as to utilize the estimation results of the disturbance and its first-order derivative in the controller design;

[0020] The third step is to design a backstepping controller based on the obstacle Lyapunov function to complete the design of the electric servo's fine anti-interference control method.

[0021] The present invention can meet the anti-interference control requirements under multi-unknown frequency sinusoidal interference and rudder angle constraints, improve the anti-interference and rudder angle tracking capabilities of the control system, and has the characteristics of high control accuracy and good reliability. It is suitable for electric steering gear servo systems facing complex interference environments and specific output constraints. The electric steering gear is driven by a servo motor through a reduction gear to drive the ball screw to rotate. After passing through the rudder shaft, the rotation of the ball screw drives the rudder surface to produce an angular deflection. In addition, to prevent the structure from getting stuck, the rudder surface deflection angle will be within the rudder angle constraint.

[0022] Specifically, if Figure 2 As shown, in the first step, the mathematical model of the electric servo considering the unknown frequency multi-source interference is established as follows:

[0023] ;

[0024] Among them, the superscript represents the first-order derivative, is the rudder deflection angle (rad); is the motor angular velocity, that is, the rotor mechanical angular velocity (rad / s); is the total transmission ratio of the reduction gear and the ball screw (dimensionless); is the moment of inertia of the motor rotor and motor gear (kg·m 2 ); is the torque coefficient (Nm / A); is the input voltage (V); is the motor armature current (A); is the armature resistance (Ω); is the motor back EMF coefficient (V / (rad / s)); is the motor inductance (H); It is a multi-frequency sinusoidal interference signal, representing the multi-source interference generated by cogging torque, flux harmonics, PWM dead zone torque, etc. are unknown parameters, representing amplitude, frequency, and phase respectively. Indicates the An interference, is the number of interferences, For time; For system output, you can set .

[0025] Choose the state vector to be , Represents the three state variables of the system, with superscript Represents the transpose of the matrix, then the mathematical model of the electric servo can be written as:

[0026] ;

[0027] Let the intermediate matrix ;

[0028] The state equation of the electric servo can be obtained as:

[0029] ;

[0030] Specifically, in the second step, Figure 2 As shown in the figure, an unknown frequency interference observer is designed to estimate complex non-matching interference with multiple unknown frequency characteristics. The unknown frequency interference observer consists of an auxiliary observer, unknown frequency information estimation, and interference reconstruction.

[0031] First, to facilitate observer design, the disturbance is written as follows:

[0032] ;

[0033] Among them, the status , are intermediate matrices that describe interference. The eigenvalues ​​of are located on the imaginary axis, specifically:

[0034] ;

[0035] in, Respectively represent The intermediate matrix corresponding to the interference is Indicates the The square of the frequency corresponding to the interference, generally speaking, Multiple sinusoidal signals with unknown amplitude, phase, and frequency can be expressed using the above formula.

[0036] The core goal of the auxiliary observer is to decouple the interference from its unknown frequency information, which is as follows:

[0037] ;

[0038] in, is the decomposed interference signal, is an intermediate vector of the auxiliary observer and has compatible dimensions, and is defined as , among which The term can be expanded to , each entry in this vector contains the Partial interference information of interference. Pseudo-inverse Make , the value is . Auxiliary observer coefficient matrix and matrix satisfy:

[0039] ;

[0040] in, is a Hurwitz matrix, and It is controllable. The convergence rate depends on , and there are:

[0041] ;

[0042] in, For the The auxiliary observer gain is increased, and the larger its value is, The faster the convergence rate, the greater the overshoot may be. .

[0043] Next, we use the observer to estimate the interference Unknown frequency information, construct the unknown frequency information observer:

[0044] ;

[0045] in, is the estimated value of the unknown frequency information vector, each item in this vector contains the Part of the unknown frequency information of the interference; is the gain value of the unknown frequency information observer, which can be tuned The fast convergence characteristic of the estimation error is ; , , are all intermediate matrices of unknown frequency information observer, where, They are The odd and even terms of ; For the The odd-numbered terms in the auxiliary observer gain.

[0046] Finally, define , the odd-numbered items are the estimated values ​​of the unknown frequency information vector, and the even-numbered items are the The even-numbered terms of the auxiliary observer gain, the complex non-matching interference with multiple unknown frequency characteristics and its first-order derivative can be expressed as:

[0047] ;

[0048] Therefore, the unknown frequency disturbance observer provides an estimate of the disturbance and its first-order derivative.

[0049] Specifically, in the third step, Figure 2 As shown in the figure, after obtaining the estimated values ​​of the disturbance and its first-order derivative in the second step, a backstepping controller based on the barrier Lyapunov function is further proposed.

[0050] The controller is designed with two main goals: 1) to limit the rudder angle of the electric servo to a preset range; and 2) to track the rudder angle to the desired angle under multiple unknown frequency interferences.

[0051] The following three steps are used to derive the controller based on the mathematical model of the electric servo:

[0052] Step 3.1: Consider the following obstacle Lyapunov function :

[0053] ;

[0054] in, is the tracking error of the rudder angle, is the rudder angle command signal, and its value is rad, is a constant value, which is 0.51. Taking the first-order derivative we get:

[0055] ;

[0056] Designing the first stabilization function for:

[0057] ;

[0058] in, is the control gain, which is .

[0059] definition is the state quantity and the stabilization function The difference between them is:

[0060] ;

[0061] therefore It can be written as:

[0062] ;

[0063] Step 3.2: Choose the quasi-Lyapunov function :

[0064] ;

[0065] for Taking the first-order derivative we get:

[0066] ;

[0067] Design a second stabilization function for:

[0068] ;

[0069] in, is the control gain, which is , is the interference suppression gain, which is , is the disturbance estimate of the disturbance observer. Definition is the state quantity and the stabilization function The difference between them is:

[0070] ;

[0071] definition For the disturbance estimation error of the disturbance observer, Young’s inequality is introduced:

[0072] ;

[0073] therefore It can be written as:

[0074] ;

[0075] Step 3.3: Choose the quasi-Lyapunov function :

[0076] ;

[0077] for Taking the first-order derivative we get:

[0078] ;

[0079] To simplify the subsequent design process, the following definitions are made:

[0080] ;

[0081] Among them, the superscript represents the second-order derivative, the superscript represents the third-order derivative, It represents the first-order derivative estimate of the disturbance of the unknown frequency disturbance observer.

[0082] Therefore, the control law can be designed for:

[0083] ;

[0084] in, is the control gain, which is , is the interference suppression gain, which is .

[0085] Introducing Young's inequality:

[0086] ;

[0087] therefore It can be written as:

[0088] ;

[0089] make , ,in, is a positive constant, then:

[0090] ;

[0091] From the above formula, we can get:

[0092] ;

[0093] in, Quasi-Lyapunov function The initial value of . Bounded, thus Bounded, and .

[0094] From the above derivation, it can be seen that is the rudder angle tracking error correction term, and its value can be adjusted to reduce the impact of the interference estimation error.

[0095] The method of the present invention is used to perform fine anti-interference control of electric servos. The interference and unknown frequency information can be decoupled through an auxiliary observer, and the frequency information can be estimated separately, which greatly improves the interference estimation accuracy of the system. Combined with the obstacle Lyapunov function, it solves the problems of existing anti-interference control methods such as inaccurate estimation of multi-unknown frequency sinusoidal interference and difficulty in coping with rudder angle constraints, thereby achieving the requirements of high control accuracy and good reliability.

[0096] The contents not described in detail in the specification of the present invention belong to the prior art known to those skilled in the art.

Claims

1. A fine anti-interference control method for an electric servo under rudder angle constraint, characterized in that: The following steps are involved: The first step is to establish a mathematical model of the electric servo considering multi-source interference of unknown frequencies; In the second step, the interference description form conversion, auxiliary observer design, interference and frequency information decoupling, unknown frequency information estimation, and interference estimation are carried out in sequence. Through the above steps, an unknown frequency interference observer is constructed to estimate multi-unknown frequency sinusoidal interference; The third step is to design a backstepping controller based on the obstacle Lyapunov function, and combine the disturbance and its first-order derivative estimation to complete the design of the electric servo's fine anti-disturbance control method under the rudder angle constraint.

2. The method for fine anti-interference control of an electric servo under rudder angle constraint according to claim 1, characterized in that: In the first step, a mathematical model of the electric servo considering multi-source interference of unknown frequencies is established as follows: ； Among them, the superscript represents the first-order derivative, is the rudder deflection angle, in rad; is the motor angular velocity, that is, the rotor mechanical angular velocity, in rad / s; is the total transmission ratio of the reduction gear and the ball screw, dimensionless; is the moment of inertia of the motor rotor and motor gear, in kg·m 2 ; is the torque coefficient, the unit is Nm / A; is the input voltage, in V; is the motor armature current, in A; is the armature resistance, in Ω; is the motor back electromotive force coefficient, in V / (rad / s); is the motor inductance, in H; It is a multi-frequency sinusoidal interference signal, representing the multi-source interference generated by cogging torque, flux harmonics, PWM dead zone torque, etc. are unknown parameters, representing amplitude, frequency, and phase respectively. Indicates the An interference, is the number of interferences, For time; Output of the system.

3. The method for fine anti-interference control of an electric servo under rudder angle constraint according to claim 2, characterized in that: In the second step, first, to facilitate observer design, the interference is written as follows: ； Among them, the status , Both are intermediate matrices describing interference; matrix The eigenvalues ​​of are on the imaginary axis, and we have: ； in, Respectively represent The intermediate matrix corresponding to the interference is Indicates the The square of the frequency corresponding to the interference, With impressive standard type, ; Multiple sinusoidal signals with unknown amplitude, phase and frequency are expressed by the above formula.

4. The method for fine anti-interference control of an electric steering gear under rudder angle constraint according to claim 3, characterized in that: The core goal of the auxiliary observer is to decouple the interference from its unknown frequency information, which is as follows: ； in, is the decomposed interference signal, is an intermediate vector of the auxiliary observer and has compatible dimensions, and is defined as , among which The term expands to , each entry in this vector contains the Partial interference information of an interference.

5. The method for fine anti-interference control of an electric servo under rudder angle constraint according to claim 4, characterized in that: exist Pseudo-inverse Make ; Auxiliary observer coefficient matrix and matrix satisfy: ； in, is a Hurwitz matrix, and It is controllable; The convergence rate depends on , and there are: ； in, For the The auxiliary observer gain.

6. The method for fine anti-interference control of an electric steering gear under rudder angle constraint according to claim 5, characterized in that: Using observers to estimate interference Unknown frequency information, construct the unknown frequency information observer: ； in, is an estimate of the unknown frequency information vector, each of which contains the Partial unknown frequency information of interference; is the gain value of the unknown frequency information observer; , , are all intermediate matrices of unknown frequency information observer, where, They are The odd and even terms of ; For the The odd-numbered terms in the auxiliary observer gain.

7. The method for fine anti-interference control of an electric servo under rudder angle constraint according to claim 6, characterized in that: definition , the odd-numbered items are the estimated values ​​of the unknown frequency information vector, and the even-numbered items are the The even-numbered terms of the auxiliary observer gain are then expressed as: ； Therefore, the unknown frequency disturbance observer provides an estimate of the disturbance and its first-order derivative.

8. The method for fine anti-interference control of an electric servo under rudder angle constraint according to claim 7, characterized in that: In the third step, the first stabilization function is designed for: ； in, To control the gain, is the tracking error of the rudder angle, It is the rudder angle command signal.

9. The method for fine anti-interference control of an electric servo under rudder angle constraint according to claim 8, characterized in that: Design a second stabilization function for: ； in, To control the gain, is the state quantity and the stabilization function The difference between is the interference estimate, is the interference rejection gain, Is a constant value.

10. The method for fine anti-interference control of an electric servo under rudder angle constraint according to claim 9, characterized in that: Design control law for: ； in, To control the gain, is the state quantity and the stabilization function The difference between is the interference suppression gain, parameter With variables They are defined as: ； Among them, the superscript represents the second-order derivative, the superscript represents the third-order derivative, It represents the first-order derivative estimate of the disturbance of the unknown frequency disturbance observer.

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