Artillery propellant coordination arm adaptive sliding mode control method based on high-gain observer

Abstract

The application discloses a kind of high-gain observer-based artillery propellant coordination arm adaptive sliding mode control method, first establish the mathematical control model of artillery propellant coordination arm electromechanical servo;Then high-gain observer is used to estimate the unknown state of artillery propellant coordination arm electromechanical servo system and effectively online tracking and compensation is carried out to it, sliding mode controller is designed to eliminate the error of observed state, so as to realize the fast high-precision control of artillery propellant coordination arm electromechanical servo system.For the high-frequency chattering phenomenon in sliding mode control process, an adaptive law is designed and combined with the sliding mode controller, so that the chattering of the control quantity is greatly weakened.Simulation experimental results show that, in the extreme condition that the propellant feeding machine is full of propellant, the control method has better dynamic tracking performance and robustness, and greatly improves the in-place speed and accuracy of the propellant coordination arm.

Description

Technical Field

[0001] This invention belongs to the field of electromechanical servo control, specifically an adaptive sliding mode control method for artillery propellant coordination arm based on a high-gain observer. Background Technology

[0002] As one of the core technologies of an automatic artillery loading system, the positioning accuracy of the propellant arm electromechanical servo system directly affects the rate of fire of the artillery. Therefore, improving the control performance of the propellant arm electromechanical system has significant practical application value.

[0003] However, due to the strong nonlinearity and uncertainty of the propellant coordination arm electromechanical servo system, it is difficult to achieve high-performance control. At present, the artillery propellant coordination system still adopts the PID control strategy.

[0004] In the paper "Integrated Modeling and Analysis of Dynamics and Control of a Certain Artillery Propellant Coordinator", a PID control strategy was adopted for the artillery propellant coordinator arm. The maximum angle error during the final measurement of the coordination process was 0.34°. Although the motion process was relatively stable, it was still difficult to control the angle error during the coordination process within the requirement of ±0.1°. At the same time, it also had the disadvantages of difficult tuning and weak ability to adapt to changes in system parameters. Therefore, a control method with higher accuracy and faster response is needed to meet the growing control performance requirements of the electromechanical servo system of the propellant coordinator arm. Summary of the Invention

[0005] The purpose of this invention is to provide an adaptive sliding mode control method for the artillery propellant coordination arm based on a high-gain observer, and to introduce an adaptive law to reduce the high-frequency chattering of the control quantity during the control process, thereby improving the control accuracy of the artillery propellant coordination arm electromechanical servo system.

[0006] The technical solution for achieving the present invention is: an adaptive sliding mode control method for artillery propellant coordination arm based on a high-gain observer, wherein the method is determined based on a high-gain observer and an adaptive sliding mode controller, and includes the following steps.

[0007] Step 1: Establish a dynamic model of the artillery propellant coordination arm electromechanical servo system.

[0008] Step 2: Design a high-gain observer based on the dynamic model of the artillery propellant coordination arm electromechanical servo system.

[0009] Step 3: Using the dynamic model of the artillery propellant coordination arm electromechanical servo system and a high-gain observer, and in conjunction with the sliding mode function, design the initial sliding mode controller u. SMC .

[0010] Step 4: Substitute the adaptive law into the initial sliding mode controller u SMC This yields the final sliding mode controller u.

[0011] Step 5: Adjust the parameters of the sliding mode controller u through simulation to achieve fast and high-precision control of the drug coordination arm electromechanical servo system.

[0012] Compared with the prior art, the present invention has the following significant advantages:

[0013] (1) A high-gain observer is used to realize the real-time online estimation of the unknown state of the drug coordination arm electromechanical servo system. The high gain is used to amplify the state estimation error, thereby improving the accuracy and robustness of the state estimation.

[0014] (2) The organic combination of high-gain observer and sliding mode controller overcomes observation error and ensures system stability.

[0015] (3) The adaptive law is combined with the sliding mode controller, thereby reducing the defect of high-frequency chattering in the sliding mode control process.

[0016] The present invention will now be described in further detail with reference to the accompanying drawings. Attached Figure Description

[0017] Figure 1 This is a flowchart of the sliding mode control method for the artillery propellant coordination arm electromechanical servo system based on a high-gain observer, according to the present invention.

[0018] Figure 2 This is a block diagram of the sliding mode control method for the artillery propellant coordination arm electromechanical servo system based on a high-gain observer, according to the present invention.

[0019] Figure 3 This is a schematic diagram of the electromechanical servo system for the artillery propellant coordination arm of the present invention.

[0020] Figure 4 This is a simplified diagram of the motion mechanism of the artillery propellant coordination arm electromechanical servo system of the present invention.

[0021] Figure 5 This is a motion trajectory diagram of the electromechanical servo system for the artillery propellant coordination arm in this invention.

[0022] Figure 6 This is the control current curve of the electromechanical servo system for the artillery propellant coordination arm in this invention.

[0023] Figure 7 This is a position error diagram of the electromechanical servo system for the artillery propellant coordination arm in this invention. Detailed Implementation

[0024] Combination Figure 1 and Figure 2 A sliding mode control method for an electromechanical servo system of artillery propellant coordination arm based on a high-gain observer is described, with the following specific steps:

[0025] Step 1: Establish the dynamic model of the artillery propellant coordination arm electromechanical servo system. The specific steps are as follows:

[0026] Step 1.1: Set up the electromechanical servo system for the artillery propellant coordination arm:

[0027] Combination Figure 3 The artillery propellant coordination arm includes a propellant delivery machine 1, an electric cylinder 3, an attitude adjustment shaft 4, a coordination arm 5, a reducer 6, a servo motor 7, and several modular propellant 2. The servo motor 7 serves as the coordination motor, and the electric cylinder 3 serves as the attitude adjustment electric cylinder.

[0028] The first end of the coordinating arm 5 is connected to the attitude adjustment shaft 4 and the electric cylinder 3 respectively. The drug delivery machine 1 is connected to the attitude adjustment shaft 4 and the electric cylinder 3 respectively. The drug delivery machine 1 swings around the attitude adjustment shaft 4 on the coordinating arm 5 through the extension and retraction of the electric cylinder 3 to realize the attitude adjustment action of the drug delivery machine 1. The modular drug 2 is placed in the drug delivery machine 1, and six modular drugs 2 are loaded in the full load state. The second end of the coordinating arm 5 and the cradle fixing plate are connected through the reducer 6. The reducer 6 is then connected to the servo motor 7 fixed at the second end of the coordinating arm 5. The servo motor 7 drives the coordinating arm 5 to rotate. The coordinated action of the modular drug 2 is realized through the rotation of the coordinating arm 5 and the attitude adjustment of the drug delivery machine 1.

[0029] Step 1.2: Establish a simplified kinematic diagram of the electromechanical servo system for the artillery propellant coordination arm:

[0030] Combination Figure 4 Point O at the trunnion is used as the fixed fulcrum of the artillery propellant coordination arm electromechanical servo system, which is also the rotation center of the artillery propellant coordination arm electromechanical servo system; point A is the front fulcrum of electric cylinder 3, and point B is the rear fulcrum of electric cylinder 3. The front fulcrum A of electric cylinder 3 is hinged to the propellant conveyor 1, and the rear fulcrum B of electric cylinder 3 is hinged to the arm body of coordination arm 5; point C is the rotation center of propellant conveyor 1, and also the center of mass of propellant conveyor 1 and module propellant 2; point D is the center of mass of coordination arm 5.

[0031] Let the rotation angle of the coordinating arm 5 be θ, the rotation angle of the drug delivery machine 1 relative to the coordinating arm 5 be β, and the load-end torque be T. e The distance from electric cylinder 3 to the rotation center point O is d1, the distance from electric cylinder 3 to point C is d2, the distance from point D to point O is l1, the distance from point C to point O is l2, the mass of the coordinating arm 5 is m1, the mass of the drug delivery machine 1 is m2, the mass of the modular drug 2 is m3, F1 and F2 are both extension forces provided by the electric cylinder, and F1 and F2 are equal in magnitude and opposite in direction.

[0032] Step 1.3: When using servo motor 7 to perform position control on the electromechanical servo system of the artillery propellant coordination arm, the internal current loop characteristics of the motor are ignored, and a vector control method is adopted, with the output control current i... q The equation for the electromagnetic torque T of servo motor 7 is:

[0033]

[0034] In the formula: P n This refers to the number of 7 pole pairs of the servo motor; For rotor flux linkage; K t If the motor torque constant is given, then the equivalent torque T at the load end is... e for:

[0035] T e =T·ξ·i (2)

[0036] In the formula: i is the transmission ratio of the reducer; ξ is the transmission efficiency of the reducer.

[0037] Step 1.4: Taking the entire artillery propellant coordination arm electromechanical servo system as the object, with 2 degrees of freedom, and choosing θ and β as generalized coordinates, since the artillery propellant coordination arm electromechanical servo system is subject to unforced influences, the Lagrange equation is rewritten in its general form:

[0038]

[0039] In the formula: For generalized coordinates, Q j Let L be the non-potential generalized force in the system, L be the Lagrangian function, t represent time, and j represent the number of particles in the system.

[0040] in:

[0041] L=T′-V′ (4)

[0042] Here, T′ represents the kinetic energy of the system, and V′ represents the potential energy of the system. For the artillery propellant coordination arm electromechanical servo system, we have:

[0043]

[0044] In the formula, T1 is the kinetic energy of the coordinating arm 5, T2 is the kinetic energy of the drug delivery machine 1, and T′=T1+T2; J1 represents the moment of inertia of the coordinating arm 5 acting on point O, J2 is the moment of inertia of the drug delivery machine 1 acting on point D, and n is the number of module drugs 2. The first derivative of θ; It is the first derivative of β.

[0045] The Lagrange function here is then obtained as:

[0046]

[0047] The expressions for the parameters of the Lagrange equation in equation (6) are as follows:

[0048]

[0049] In the formula The second derivative of θ; It is the second derivative of β.

[0050] Let M1 be the control torque applied by the trunnion end to the coordinating arm 5, and M2 be the control torque applied by the attitude adjustment electric cylinder to the rotation center of the drug delivery machine 1, then:

[0051]

[0052] Where B′ is the equivalent damping coefficient of the coordinating arm 5.

[0053] The generalized force in the artillery propellant coordination arm electromechanical servo system satisfies:

[0054]

[0055] Where Q1 and Q2 are both non-potential generalized forces in the system; the generalized coordinate virtual displacement of the coordinating arm 5 is δq1, and the angular virtual displacement of the coordinating arm 5 is δθ; the generalized coordinate virtual displacement of the drug delivery machine 1 is δq2, and the angular virtual displacement of the drug delivery machine 1 is δβ; since δq1=δθ and δq2=δβ, then q1=M1 and q2=M2.

[0056] Substituting equations (6), (7), (8), and (9) into equation (3), we obtain the dynamic equation of the mechanical part of the artillery propellant coordination arm electromechanical servo system as follows:

[0057]

[0058] Substituting equation (2) into equation (10), we get:

[0059]

[0060] Further simplification yields the dynamic model of the artillery propellant coordination arm electromechanical servo system:

[0061]

[0062] In the above formula, system parameter A n System parameter B n The specific expression for the system parameter f is as follows:

[0063]

[0064] Proceed to step 2.

[0065] Step 2: Design a high-gain observer based on the dynamic model of the artillery propellant coordination arm electromechanical servo system. The specific steps are as follows:

[0066] Let the state variable matrix State variable x1 = θ, state variable Then the state-space equation of the system is obtained as follows:

[0067]

[0068] Where u is the sliding mode controller, and also the control variable, function To satisfy the Lipschitz condition, the observer is designed as follows:

[0069]

[0070] in and These represent the estimated values ​​of x1 and x2, respectively. for The first derivative, for The first derivative of y is the system output; h1 and h2 are the observer's adjustment parameters.

[0071] for The nominal model.

[0072] Take the observation error matrix of the high-gain observer in Let x1 be the observation error. The observation error is x2.

[0073] Then, from equations (14) and (15), we get:

[0074]

[0075] in, for The first derivative, for The first derivative of , where v is the measurement noise.

[0076] Due to modeling uncertainty The first derivative matrix of observation error Equation (16) can be rewritten as:

[0077]

[0078] Wherein, constant matrix

[0079] When δ and v are not considered, if the eigenvalues ​​of A are taken to be negative, then Asymptotic convergence; therefore, the values ​​of h1 and h2 need to satisfy Hurwitz.

[0080] Pick Where, coefficients α1 and α2 are positive real numbers, and ε is the observer bandwidth parameter that satisfies ε << 1;

[0081] The expression for the high-gain observer is:

[0082]

[0083] Proceed to step 3.

[0084] Step 3: Using the dynamic model of the artillery propellant coordination arm electromechanical servo system and a high-gain observer, and in conjunction with the sliding mode function, design the initial sliding mode controller u. SMC The specific steps are as follows:

[0085] Let the desired angular displacement trajectory be θ d Then the angular displacement error of the system is e = θ d -θ, and thus the sliding mode function s is:

[0086]

[0087] in, Let e ​​be the first derivative of e, c be the sliding mode coefficient, and c satisfy the Routh-Hurwitz stability criterion. The system is asymptotically stable when c > 0.

[0088] From equations (14) and (19), we obtain:

[0089]

[0090] in, Let be the first derivative of s. For θ d The second derivative;

[0091] when Then, combining equations (14) and (20), the equivalent control term u of the artillery propellant coordination arm electromechanical servo system is obtained. eq The expression is as follows:

[0092]

[0093] in Let θ be the observed value. for The first derivative; For the observed value of e, for The first derivative.

[0094] To ensure the eventual stability of the system, an initial sliding mode controller u is designed. SMC for:

[0095]

[0096] In the above formula, u eq The equivalent control term for the sliding mode control law of the artillery propellant coordination arm electromechanical servo system is the control law of the system under ideal conditions; u f The exponent term of the sliding mode control law for the artillery propellant coordination arm electromechanical servo system determines the velocity at which the system's motion tends towards the sliding surface; u r The switching term in sliding mode control is responsible for reducing chattering in the control quantity; the exponential reaching law parameter q > 0, and the larger the q value, the faster the system approaches the sliding surface; η is the switching term gain, and sgn(s) is the sign function, the specific expression of which is as follows:

[0097]

[0098] Proceed to step 4.

[0099] Step 4: Substitute the adaptive law into the initial sliding mode controller u SMC The final sliding mode controller u is obtained as follows:

[0100] It is difficult to accurately estimate the value of the switching term gain η. If η is too large, it can easily lead to system chattering; if η is too small, it will make the system unstable. Neither of these situations is conducive to the smooth operation of the drug coordination device for replenishing and administering drugs. Therefore, an adaptive algorithm is used for optimized control. The adaptive law of η is designed as follows:

[0101]

[0102] In the formula, For the gain estimate of the switching term The derivative, μ is the adaptive coefficient; Substituting into equation (22), the final sliding mode controller u is obtained as:

[0103]

[0104] Where q > 0, The estimated value of the sliding mode function is

[0105] Taking sliding mode control, the Lyapunov function V is:

[0106]

[0107] get:

[0108]

[0109] in Let θ be the observation error. for The observation error; Let e ​​be the observation error. for The observation error; Let s be the observation error.

[0110] and

[0111] but

[0112]

[0113] in It is the first derivative of V.

[0114] Since q > 0, then we conclude That is, the sliding mode controller u is stable and reliable in the Lyapunov sense.

[0115] Example:

[0116] The trajectory planning of the coordinating arm 5 adopts the S-curve speed curve planning method. This method effectively reduces the impact on the servo motor 7 during startup and shutdown, extends motor life, and improves system stability. The trajectory planning designed in this paper aims to complete the downward swing motion of the coordinating arm 5 within 0.7 seconds. Figure 5 Considering the extreme working condition of the delivery machine 1 carrying six modular explosives 2, a mathematical model of the electromechanical servo system of the artillery explosive coordination arm was built in Simulink, and then a simulation experiment was conducted. The movement angle of the coordination arm 5 was 47.9°, i.e., a firing angle of 30°, with a peak angular velocity of 125° / s and a peak angular acceleration of 638° / s. 2 Within 0 to 0.7 seconds, the coordinated arm 5 swings down 47.9° from the horizontal position (i.e., the medicine receiving position). After 0.7 seconds, the motor brake locks in place, and the coordinated action ends.

[0117] A comparative simulation experiment was conducted between the adaptive sliding mode controller based on the high-gain observer and the PID controller.

[0118] Simulation parameters:

[0119] Adaptive sliding mode controller based on high-gain observer: Observer bandwidth parameter ε = 0.01, coefficient α1 = 1, coefficient α2 = 1, adaptive coefficient μ = 0.1; equivalent damping coefficient of coordinating arm 5 B′ = 0.15, motor torque constant K... t = 0.99 N·m / A; System parameter A n =5.634e-3, system parameter A n =6.76e-4; sliding mode coefficient c = 45, reaching law coefficient q = 50.

[0120] PID controller: PID parameters are tuned to: proportional coefficient Kp =11.5, integral coefficient K i =4, differential coefficient K d =45.

[0121] Figure 6 This is the control current curve of the electromechanical servo system for the artillery propellant coordination arm in this invention, which is... Figure 6 It can be seen that the maximum current of the coordinating arm 5 when it swings under full load is 35.2A. At this time, the maximum current in the coordinating motor does not exceed 50A, which meets the requirements.

[0122] Figure 7 The diagram shows the position error of the electromechanical servo system for the propellant coordinating arm in this invention. Under full load conditions, the adaptive sliding mode controller based on a high-gain observer can converge the tracking error to a small fluctuation range in about 0.084s. When the coordinating arm 5 swings down to the propellant delivery position in 0.7s, the angle error is 0.0032°. The maximum dynamic angle error of the coordinating arm under the control group PID control is about 0.63°, and it fluctuates greatly throughout the process. There is still an angle error of 0.42° when the propellant coordinating arm is in position.

[0123] The research results show that the designed control method has a smaller dynamic angle error and better tracking effect compared with PID control. It significantly improves the positioning speed and accuracy of the coordinating arm 5, and greatly reduces the chattering of the control quantity, thus ensuring the fast and high-precision control of the artillery propellant coordinating arm electromechanical servo system.

Claims

1. An adaptive sliding mode control method for artillery propellant coordination arm based on a high-gain observer, characterized in that, The steps are as follows: Step 1: Establish the dynamic model of the artillery propellant coordination arm electromechanical servo system, then proceed to Step 2; Step 2: Design a high-gain observer based on the dynamic model of the artillery propellant coordination arm electromechanical servo system, as follows: Let the state variable matrix State variables State variables Then the state-space equation of the system is obtained as follows: (14)， in, For sliding mode controllers, and also for control variables. For system parameters, For system parameters, For system parameters, To coordinate the rotation angle of the arm (5); function To satisfy the Lipschitz condition, the observer is designed as follows: (15)， in and They correspond to each other. and Estimated value for The first derivative, for The first derivative, For system output; and These are all adjustment parameters for the observer; for The nominal model; Take the observation error matrix of the high-gain observer ,in for The observation error, for The observation error; Then, from equations (14) and (15), we get: (16)， in, for The first derivative, for The first derivative, For measuring noise; Due to modeling uncertainty The first derivative matrix of the observation error Equation (16) can be rewritten as: (17)， Wherein, constant matrix ; When not considering When and v, if we take If the eigenvalue is negative, then , Gradual convergence; therefore and The value of needs to be made Satisfying Hurwitz; Pick , , where the coefficient Sum of coefficients It is a positive real number. The observer bandwidth parameter and ; The expression for the high-gain observer is: (18)， Proceed to step 3; Step 3: Using the dynamic model of the artillery propellant coordination arm electromechanical servo system and a high-gain observer, combined with the sliding mode function, design the initial sliding mode controller. Proceed to step 4; Step 4: Substitute the adaptive law into the initial sliding mode controller. The final sliding mode controller u is obtained, and the process proceeds to step 5. Step 5: Adjust the parameters of the sliding mode controller u through simulation to achieve fast and high-precision control of the drug coordination arm electromechanical servo system.

2. The adaptive sliding mode control method for the propellant coordination arm based on a high-gain observer according to claim 1, characterized in that, In step 1, a dynamic model of the artillery propellant coordination arm electromechanical servo system is established, as follows: Step 1.1: Set up the electromechanical servo system for the artillery propellant coordination arm: The artillery propellant coordination arm includes a propellant delivery machine (1), an electric cylinder (3), an attitude adjustment shaft (4), a coordination arm (5), a reducer (6), a servo motor (7), and several modular propellants (2). The servo motor (7) serves as the coordination motor, and the electric cylinder (3) serves as the attitude adjustment electric cylinder. The first end of the coordinating arm (5) is connected to the attitude adjustment shaft (4) and the electric cylinder (3) respectively. The drug delivery machine (1) is connected to the attitude adjustment shaft (4) and the electric cylinder (3) respectively. The drug delivery machine (1) swings around the attitude adjustment shaft (4) on the coordinating arm (5) through the extension and retraction of the electric cylinder (3) to realize the attitude adjustment action of the drug delivery machine (1). The modular drug (2) is placed in the drug delivery machine (1), and 6 modular drugs (2) are loaded in the full load state. The second end of the coordinating arm (5) and the cradle fixing plate are connected through the reducer (6). The reducer (6) is then connected to the servo motor (7) fixed at the second end of the coordinating arm (5). The servo motor (7) drives the coordinating arm (5) to rotate. The coordinated action of the modular drug (2) is realized through the rotation of the coordinating arm (5) and the attitude adjustment of the drug delivery machine (1). Step 1.2: Establish a simplified kinematic diagram of the electromechanical servo system for the artillery propellant coordination arm: Point at the trunnion As the fixed fulcrum of the artillery propellant coordination arm electromechanical servo system, it is also the rotation center of the artillery propellant coordination arm electromechanical servo system; point The front fulcrum of the electric cylinder (3) is the point. The rear pivot point of the electric cylinder (3), where the front pivot point of the electric cylinder (3) is... Hinged onto the drug delivery machine (1), the rear fulcrum of the electric cylinder (3) Hinged to the body of the coordinating arm (5); point The point is the center of rotation of the drug delivery machine (1), and also the center of mass of both the drug delivery machine (1) and the modular drug (2); The center of mass of the coordinating arm (5); Let the rotation angle of the coordinating arm (5) be... The rotation angle of the drug delivery machine (1) relative to the coordinating arm (5) is: The load-side torque is The electric cylinder (3) moves to the center of rotation. The distance is Electric cylinder (3) reaches the point The distance is ,point Time The distance is ,point Time The distance is The mass of the coordinating arm (5) is The mass of the drug delivery machine (1) is The mass of module drug (2) is , , The extension and retraction force is provided by the electric cylinder. and Equal in size but opposite in direction; Step 1.3: When using the servo motor (7) to perform position control on the electromechanical servo system of the artillery propellant arm, the internal current loop characteristics of the motor are ignored, and the vector control method is adopted to output the control current. The electromagnetic torque of the servo motor (7) The equation is: (1)， In the formula: The number of pole pairs of the servo motor (7); For rotor flux linkage; Let be the motor torque constant; then the equivalent torque at the load end is... for: (2)， In the formula: The gear ratio of the reducer; The transmission efficiency of the reducer; Step 1.4: Taking the entire artillery propellant coordination arm electromechanical servo system as the object, with 2 degrees of freedom, select... and For generalized coordinates, since the artillery propellant coordination arm electromechanical servo system is subject to non-forces, the Lagrange equations are rewritten in general form: (3)， In the formula: For generalized coordinates, For generalized acceleration; express right The partial derivatives, express right The partial derivatives; For non-potential generalized forces in the system, Let be the Lagrangian function, t represent time, and j represent the number of particles in the system; where: (4)， Here This represents the kinetic energy of the system. Representing the potential energy of the system, for the artillery propellant coordinating arm electromechanical servo system, we have: (5)， In the formula, To coordinate the kinetic energy of arm (5), For the kinetic energy of the drug delivery machine (1), This indicates that the coordinating arm (5) acts at the point. Moment of inertia of the axis, The drug delivery machine (1) acts on The moment of inertia at point n, where n is the number of modules (2); for The first derivative; for The first derivative of ; g represents gravitational acceleration; The Lagrange function obtained here is: (6)， The expressions for the parameters of the Lagrange equation in equation (6) are as follows: (7)， In the formula for The second derivative; for The second derivative; Let the control torque applied by the trunnion end to the coordinating arm (5) be... The control torque of the posture adjustment electric cylinder on the rotation center of the drug delivery machine (1) is ,but: (8)， in, The equivalent damping coefficient of the coordinating arm (5); The generalized force in the artillery propellant coordination arm electromechanical servo system satisfies: (9)， in, and All are non-potential generalized forces in the system; the virtual displacement of the generalized coordinate of the coordinating arm (5) is The virtual displacement of the coordinating arm (5) angle is The generalized coordinate virtual displacement of the drug delivery machine (1) is: The angular displacement of the drug delivery machine (1) is ; Substituting equations (6), (7), (8), and (9) into equation (3), we obtain the dynamic equation of the mechanical part of the artillery propellant coordination arm electromechanical servo system as follows: (10)， Substituting equation (2) into equation (10), we get: (11)， Further simplification yields the dynamic model of the artillery propellant coordination arm electromechanical servo system: (12)， In the above formula, system parameters System parameters System parameters The specific expression is as follows: (13)。 3. The adaptive sliding mode control method for the propellant coordination arm based on a high-gain observer according to claim 2, characterized in that, In step 1, The value is 0.

99.

4. The adaptive sliding mode control method for the propellant coordination arm based on a high-gain observer according to claim 2, characterized in that, In step 3, an initial sliding mode controller is designed using the dynamic model of the artillery propellant coordination arm electromechanical servo system and a high-gain observer, combined with a sliding mode function. The details are as follows: Let the desired angular displacement trajectory be The angular displacement error of the system Take the sliding mode function for: (19)， in, for The first derivative, Let be the sliding mode coefficient, and Satisfying the Routh-Hurwitz stability criterion, The system gradually stabilizes. From equations (14) and (19), we obtain: (20)， in, for The first derivative, for The second derivative; when Then, combining equations (14) and (20), the equivalent control term of the artillery propellant coordination arm electromechanical servo system is obtained. The expression is as follows: (21)， in for The estimated value, for The first derivative; for The estimated value, for The first derivative; To ensure the eventual stability of the system, an initial sliding mode controller is designed. for: (22)， In the above formula, The equivalent control term for the sliding mode control rate of the artillery propellant coordination arm electromechanical servo system; For the sliding mode control law of the artillery propellant coordination arm electromechanical servo system; For the switching term of sliding mode control; where the exponential reaching law parameter is... >0, the larger the q value, the faster the system tends to the sliding surface; For the gain of the switching item, This is a symbolic function, and its specific expression is as follows: (23)。 5. The adaptive sliding mode control method for the propellant coordination arm based on a high-gain observer according to claim 4, characterized in that, In step 4, the adaptive law is substituted into the initial sliding mode controller. The final sliding mode controller u is obtained as follows: design The adaptive law is as follows: (24)， In the formula, For the gain estimate of the switching term The derivative of For adaptive parameters; Substituting into equation (22), the final sliding mode controller u is obtained as: (25)， in, , Sliding mode function estimate for ; Taking sliding mode control, the Lyapunov function V is: (26)， get: ， in for The observation error, for The observation error; for The observation error, for The observation error; for The observation error; and , , , , ; but (27)， in for The first derivative; because Then we get That is, the sliding mode controller u is stable and reliable in the Lyapunov sense.

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