Global backstepping adaptive sliding mode controller for gun servo system, design method, electronic device and readable storage medium

Abstract

The global backstepping adaptive sliding mode controller, design method, electronic equipment and readable storage medium of the gun servo system belong to the field of automatic control, in order to solve the problem of weakening the transmission torque, the chattering of the load speed at the time of reversing, and compensating for the measurement error when there are uncertain parameters in the system, the key points are that the gun servo system with a double inertia model is decomposed into three first-order subsystems through backstepping control; according to the first-order subsystem, the adaptive law of the equivalent stiffness of the uncertain parameter transmission output shaft of the controller and the friction coefficient of the uncertain parameter transmission output shaft of the controller is determined by using sliding mode control, which can weaken the transmission torque and the chattering of the load speed at the time of reversing.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of automatic control, and relates to a global backstepping adaptive sliding mode controller of a gun servo system and a design method of the controller. BACKGROUND

[0002] In the gun servo system, the backlash is the main nonlinear link of the mechanical transmission device and the largest nonlinear factor affecting the system performance. The backlash has the nonlinear properties of dynamics, non-differentiability and non-smoothness, and can cause the chattering of the transmission torque and the load speed during commutation, and reduce the position tracking accuracy and stability of the system. Therefore, it is of important theoretical significance and engineering practical value to study the nonlinear backlash compensation method in the gun servo system. The technical approach of backlash compensation mainly includes mechanical technology and control technology. The former usually adopts the multi-motor synchronous linkage method, which can eliminate the uncontrollability of the transmission torque and the load speed during the backlash period, but the new driving device not only has high requirements for the mechanical structure, but also makes the system more complex. The latter mainly uses control methods to compensate for the nonlinear backlash. In recent years, modern control methods such as backstepping control, adaptive control, sliding mode control and fuzzy control have made rapid development in backlash compensation. Among them, the backstepping control divides the complex high-order system into low-order subsystems, and realizes the rapid convergence of tracking error through recursive construction of Lyapunov function, which is a powerful tool for dealing with high-order nonlinear servo systems. Compared with general systems, the gun servo system has the characteristics of large load inertia and easy torsional deformation of the transmission shaft, which aggravates the influence of backlash. Combined with the sliding mode control, the chattering of the transmission torque and the load speed during commutation can be weakened. When the system is running, the equivalent stiffness and friction coefficient of the transmission output shaft can be regarded as constant parameters in a short time. Due to the influence of temperature, stress, material performance and other factors, it is not easy to accurately measure these parameters. The existing technology usually calculates these parameters as constants, which leads to large measurement error of the system and affects the performance of the system, thereby reducing the backlash compensation effect. SUMMARY

[0003] In order to solve the problem of weakening the chattering of the transmission torque and the load speed during commutation, and compensating for the measurement error when there are uncertain parameters in the system, the application combines the adaptive control to approximate the uncertain parameters which can be regarded as constant parameters in a short time due to the influence of temperature, stress, material performance and other factors, so as to compensate for the influence of measurement error on the performance of the system, and further improve the backlash compensation effect.

[0004] In the first aspect, the global backstepping adaptive sliding mode controller of the gun servo system according to some embodiments of the application, the control quantity of the controller is represented as:

[0005]

[0006] Adaptive law of the equivalent stiffness K of the uncertain parameter transmission output shaft of the controller

[0007]

[0008] Adaptive law of the friction coefficient C of the uncertain parameter transmission output shaft of the controller

[0009]

[0010] wherein

[0011]

[0012] wherein: N represents the transmission ratio of the reduction gear, represents the estimated value of the friction coefficient C of the uncertain parameter transmission output shaft, wherein J L represents the moment of inertia of the driven wheel, K v represents the proportional coefficient of the speed regulator, K pwm represents, K t represents the motor torque coefficient, J M represents the moment of inertia of the driving wheel, R represents the armature circuit resistance, r represents the approximation degree of the approximation of the model function of the approximate nonlinear gear gap, j represents half of the gear gap, z = θ M / N - θ L , θ M represents the driving wheel rotation angle, θ L represents the driven wheel rotation angle;

[0013] e1 = x1d - x1, e2 = x2d - x2, x i d represents the expected value of the virtual control quantity x i of the system, s = c1e1 + c2e2 + e3, wherein e3 = x3d - a1x3; c i > 0, i = 1, 2 represent the design parameters of the controller, x1 = θ L , f i > 0, i = 1, 2, 3, 4 represent the design parameters of the controller, M r represents the equivalent external nonlinear disturbance at the motor end at the time of shooting in the current sea state;

[0014] C min represents the minimum friction coefficient of the uncertain parameter transmission output shaft, C max represents the maximum friction coefficient of the uncertain parameter transmission output shaft, K min represents the minimum equivalent stiffness of the uncertain parameter transmission output shaft, K maxrepresents the maximum equivalent stiffness of the uncertain parameter transmission output shaft, ΔK represents the difference between the expected value and the actual value of the equivalent stiffness K of the uncertain parameter transmission output shaft, ΔC represents the difference between the expected value and the actual value of the friction coefficient C of the uncertain parameter transmission output shaft, γ i > 0, i = 1, 2 are design parameters of the controller;

[0015]

[0016] wherein B L represents the friction coefficient of the driven wheel, K represents the equivalent stiffness of the uncertain parameter transmission output shaft, represents the estimated value of the equivalent stiffness of the uncertain parameter transmission output shaft, C represents the friction coefficient of the uncertain parameter transmission output shaft, wherein K vf represents the speed loop feedback coefficient, K e is the back electromotive force coefficient of the motor.

[0017] In a second aspect, the design method of the global backstepping adaptive sliding mode controller of the gun servo system according to some embodiments of the present application comprises the following steps:

[0018] The gun servo system with a double-inertia model containing a gear gap is decomposed into three first-order subsystems through backstepping control;

[0019] According to the first-order subsystem, the adaptive law of the equivalent stiffness K of the uncertain parameter transmission output shaft of the controller and the friction coefficient C of the uncertain parameter transmission output shaft of the controller are determined using sliding mode control.

[0020] The design method of the global backstepping adaptive sliding mode controller of the gun servo system according to some embodiments of the present application comprises the following steps:

[0021]

[0022] wherein: θ L represents the rotation angle of the driven wheel, represents the angular velocity of the driven wheel, z = θ M / N - θ L , θ M represents the rotation angle of the driving wheel, r represents the approximation degree of the model function of the approximate nonlinear gear gap, j represents half of the gear gap;

[0023] The state equation of the system is constructed as

[0024]

[0025] wherein: B L denotes the friction coefficient of the driven wheel, J L denotes the moment of inertia of the driven wheel, J M denotes the moment of inertia of the driving wheel, B M denotes the friction coefficient of the driving wheel, K vf denotes the speed loop feedback coefficient, K v denotes the speed regulator proportional coefficient, K pwm denotes, K t denotes the motor torque coefficient, K e is the motor back EMF coefficient, R denotes the armature circuit resistance, T = Kx3 + Cx4, K denotes the equivalent stiffness of the controller's uncertain parameter transmission output shaft, and C denotes the friction coefficient of the controller's uncertain parameter transmission output shaft;

[0026] According to the design method of the global backstepping adaptive sliding mode controller of the gun servo system according to some embodiments of the application, the method for determining the adaptive law of the equivalent stiffness K of the controller's uncertain parameter transmission output shaft and the friction coefficient C of the controller's uncertain parameter transmission output shaft using sliding mode control according to the first-order subsystem comprises

[0027] Define the system position error variable

[0028] e1 = x1d - x1 (5)

[0029] where x i d, i = 1, 2, 3 is the expected value of the system virtual control variable x i ;

[0030] Differentiate the system position error variable represented by equation (5) to obtain

[0031]

[0032] Construct a Lyapunov function for equation (6) to obtain the first subsystem

[0033]

[0034] Differentiate the first subsystem represented by equation (7) to obtain

[0035]

[0036] The expected value of the virtual control variable is represented as

[0037]

[0038] Define system speed error variable

[0039] e2 = x2d - x2 (10)

[0040] Substitute the expected value of the virtual control variable represented by equation (9) into equation (8) to obtain

[0041]

[0042] Wherein, f i > 0, i = 1, 2, 3, 4 represents the design parameters of the controller;

[0043] Substitute the expected value of the virtual control variable represented by equation (9) into equation (10) to obtain

[0044]

[0045] Derive the system speed error variable represented by equation (12) to obtain

[0046]

[0047] Because the equivalent stiffness K of the uncertain parameter transmission output shaft of the controller and the friction coefficient C of the uncertain parameter transmission output shaft of the controller are uncertain, let represent the estimated value of the equivalent stiffness K of the uncertain parameter transmission output shaft, represent the estimated value of the friction coefficient C of the uncertain parameter transmission output shaft, define the variable β and its estimated value β = e2 - e1

[0048]

[0049] Substitute the variable β represented by equation (14) and its estimated value into equation (13) to obtain

[0050]

[0051] Construct a Lyapunov function for equation (15) to obtain the second subsystem

[0052]

[0053] Wherein, γ i > 0, i = 1, 2 are the design parameters of the controller, ΔK represents the difference between the expected value and the actual value of the equivalent stiffness K of the uncertain parameter transmission output shaft, and ΔC represents the difference between the expected value and the actual value of the friction coefficient C of the uncertain parameter transmission output shaft.

[0054] Define the subsystem error variable

[0055] ​e3 = x3d - a1x3 (17)

[0056] Differentiating the subsystem error variable represented by equation (16) gives

[0057]

[0058] Taking the expected value of the virtual control variable

[0059]

[0060] Substituting the expected value of the virtual control variable represented by equation (19) into equation (18) gives

[0061]

[0062] When the estimated value of the equivalent stiffness K of the uncertain parameter transmission output shaft The estimated value of the friction coefficient C of the uncertain parameter transmission output shaft converges to the equivalent stiffness K of the uncertain parameter transmission output shaft, the friction coefficient C of the uncertain parameter transmission output shaft, and a1x3 is equal to the expected value x3d of a1x3, then ΔK = 0, ΔC = 0, e3 = 0, which guarantees Negative, so that e1 and e2 can gradually stabilize to zero;

[0063] Differentiating equation (17) by substituting the expected value of the virtual control variable represented by equation (19) gives

[0064]

[0065] In equation (21), each parameter takes the value

[0066]

[0067] The sliding manifold of the sliding mode control is defined as

[0068] s = c1e1 + c2e2 + e3 (23)

[0069] Differentiating the sliding manifold of the sliding mode control represented by equation (23) gives

[0070]

[0071] Wherein, c i > 0, i = 1, 2 represents the design parameter of the controller

[0072] When the state variable slides on the sliding surface s = 0, then Holds, so that equation (24) is a constant of Hurwitz;

[0073] Construct a system Lyapunov function to obtain the third subsystem

[0074]

[0075] Differentiate the third subsystem represented by formula (25), and substitute formula (20), (21), (24) into it to obtain

[0076]

[0077] According to the formula (26), the output of the controller is

[0078]

[0079] Substitute the output of the controller represented by formula (27) into formula (26) to obtain

[0080]

[0081] The adaptive law of the uncertain parameters of the controller, the equivalent stiffness K of the transmission output shaft, and the friction coefficient C of the transmission output shaft of the controller is

[0082]

[0083] Consider the estimated value of the equivalent stiffness K of the uncertain parameter transmission output shaft The estimated value of the friction coefficient C of the uncertain parameter transmission output shaft There are upper and lower bounds, and the adaptive law is adjusted.

[0084]

[0085]

[0086] By simultaneously solving formula (28)-(31), we obtain

[0087]

[0088] In formula (32):

[0089]

[0090] The embodiment of the application further provides an electronic device, the electronic device comprising: one or more processors, a memory, and one or more programs; wherein the one or more programs are stored in the memory, and the one or more programs comprise instructions, when the instructions are executed by the electronic device, the electronic device executes the technical solutions of the second aspect and any possible design of the second aspect of the embodiment of the application.

[0091] The embodiment of the application further provides a computer readable storage medium, which comprises a computer program, and when the computer program runs on an electronic device, the electronic device executes the technical solutions of the second aspect of the embodiment of the application and any possible design of the second aspect.

[0092] The application has the following beneficial effects: in one aspect, the application can weaken the buffeting of the transmission torque and the load speed when reversing by applying the sliding mode control to the gun servo system which has the characteristics of large load inertia and easy torsional deformation of the transmission shaft, thereby aggravating the influence of the backlash; in another aspect, the application can compensate the influence of the measurement error on the system performance and improve the backlash compensation effect by applying the short-time constant parameters in the adaptive control approximation system to the uncertain parameters which are not easy to measure accurately due to the influence of temperature, stress, material performance and other factors; in a third aspect, the controller of the application can make the servo system track the large-angle turning expected position signal faster and more accurately, and the system has good position tracking performance and robustness; and in a fourth aspect, the controller of the application can converge the position error of the servo system to a small range in a short time, so that the system can track the sinusoidal expected position signal quickly and accurately, and has good dynamic quality and robustness.

[0093] The above effects are shown in the simulation experiment analysis part of the specific embodiment of the application. The technical effects that can be achieved by each aspect are described above in the description of the technical effects that can be achieved by the first aspect, and will not be repeated here. Additional aspects and advantages of the application will be partially given in the following description, partially become obvious from the following description, or be understood through the practice of the application. BRIEF DESCRIPTION OF DRAWINGS

[0094] Figure 1 is a double-inertia model with backlash.

[0095] Figure 2 is a system structure diagram.

[0096] Figure 3 is the system response curve of the global backstepping adaptive sliding mode controller and the PID controller under the large-angle turning working condition, wherein (a) is the position tracking, (b) is the load speed, (c) is the transmission torque, and (d) is the sliding surface.

[0097] Figure 4 is the system response curve of the global backstepping adaptive sliding mode controller and the PID controller under the sinusoidal tracking working condition, wherein (a) is the position tracking, (b) is the load speed, (c) is the transmission torque, and (d) is the sliding surface. DETAILED DESCRIPTION

[0098] Embodiments of the present application are described below in detail with reference to the accompanying drawings, examples of which are shown in the drawings. The present application provides a global backstepping adaptive sliding mode controller of a gun servo system, a design method of the controller, an electronic device, and a computer readable storage medium, to solve the problems of weakening the transmission torque, the chattering of the load speed at the time of commutation, and compensating for measurement errors when there are uncertain parameters in the system. The controller, the design method, the device, and the computer readable storage medium are based on the same technical concept, and the principles of solving the problems are similar. Therefore, the implementation of each subject can be referred to each other, and the repeated parts will not be described again.

[0099] The present application takes a double-inertia servo system of a certain type of gun as the research object, introduces an approximate dead zone model into the system, and establishes a system state space equation. For unknown parameters such as the equivalent stiffness and friction coefficient of the transmission output shaft, the existing technology often does not consider the elastic change of the transmission shaft, but considers it as rigid. For example, if one end of the transmission output shaft is rotated by 1 degree, the other end is also rotated by 1 degree, that is, the driving wheel and the driven wheel are both rotated by 1 degree. However, the inventors found that due to factors such as temperature, stress, and material properties, the transmission output shaft is not rigid, but has elastic changes. Especially under heavy load, the elastic change should be considered. For example, under such load, one end of the transmission output shaft is rotated by 1 degree, while the other end is only rotated by 0.95 degrees. However, the controller designed without considering the elastic change of the shaft will cause corresponding errors in transmission control. The present application considers the elastic change of the transmission output shaft, and the system model can be close to the actual situation, which also leads to a more complex system model. However, in the practice of the present application, the inventors found that the equivalent stiffness and friction coefficient of the transmission output shaft are very difficult to measure in practice. The present application approximates the uncertain parameters in the system through feedback or signal transmission of the control system, especially through sliding mode control and adaptive control. The obtained controller can make the transmission system inside the transmission shaft reach a stable transmission control state, compensate for the influence of measurement errors on system performance, and further improve the effect of gear gap compensation.

[0100] From the above, the present application uses adaptive control to deal with the nonlinear gear gap and the chattering of the transmission torque and load speed in the system, combines backstepping sliding mode control, and further designs a global backstepping adaptive sliding mode controller. The global stability of the closed-loop system is proved by Barbalat theorem. Simulation results show that this method can effectively compensate the gear gap and weaken the chattering of the transmission torque and load speed at the time of commutation, so that the system has higher position tracking accuracy and robustness.

[0101] 1. System modeling

[0102] 1.1 Double-inertia model with gear gap

[0103] Figure 1 is a typical double-inertia model with backlash in gun servo system. The motor drives the large inertia load to rotate to the desired position through the reduction gear with the transmission ratio N. The torsional deformation of the mechanical transmission device is concentrated in the system output shaft (load end). The friction torque of the motor and load end is proportional to the transmission rate. Let θ M 、 J M 、B M 、θ L 、 J L 、B L be the rotation angle, angular velocity, angular acceleration, moment of inertia, and friction coefficient of the master and slave wheels, respectively. It is assumed that θ M 、 θ L 、 can be measured. K t is the motor torque coefficient, K t i is the system input torque, T K is the transmission torque equivalent to the output shaft, M r is the external nonlinear disturbance equivalent to the motor end in five-level sea state shooting.

[0104] The system dynamics equation is

[0105]

[0106] Let z = θ M / N - θ L , and T be

[0107] T = Kf(z) + Cf'(z) (2)

[0108] In equation (2), K and C are the equivalent stiffness and friction coefficient of the transmission output shaft, respectively. f(z) is a model function describing the nonlinear backlash. Since the "dead zone" function is not differentiable, it is not convenient for control design. Therefore, a smooth, continuous, and differentiable "approximate dead zone" function such as equation (3) is introduced. The parameters reflect the approximation degree of the two, and the approximation degree gradually deteriorates as r decreases.

[0109]

[0110] 1.2 Gun servo system model

[0111] In a certain type of gun "three closed loop" servo system, the double-inertia model with backlash is introduced, and the system structure diagram is shown in Figure 2 K e is the motor back electromotive force coefficient. K vf is the speed loop feedback coefficient. The speed regulator is a proportional coefficient K vR, L are armature circuit resistance, inductance, where L≈0, which can be ignored in modeling. PWM is approximately proportional link. u is the output signal of the designed global backstepping adaptive sliding mode controller. θ * (x1d) is the desired position signal, assuming its first three derivatives exist and are known.

[0112] Define the state variable of the system as x1=θ L ,

[0113] The state equation of the system is constructed as

[0114]

[0115] In equation (4), the values of each parameter are

[0116] 2. Controller design

[0117] From equation (4), the master and slave of the system are in series, so backstepping control is used to decompose the complex high-order gun servo system into three first-order subsystems, recursively construct Lyapunov functions, and make the subsystems have asymptotic stability. A series of virtual control quantities are obtained through recursion to get the final controller output signal of the system. The application of sliding mode control in backstepping control can weaken the chattering of transmission torque and load speed when reversing, and the adaptive law of uncertain parameters K, C is designed combined with adaptive control, and then the global backstepping adaptive sliding mode controller is designed, which ensures the global stability of the closed-loop system and makes the system track the desired position with high precision.

[0118] 2.1 Design of global backstepping adaptive sliding mode controller

[0119] In the following derivation process, f i > 0 (i = 1, 2, 3, 4), c i > 0 (i = 1, 2), γ i > 0 (i = 1, 2) are the design parameters of the controller, x i > 0 (i = 1, 2, 3, 4) are the state variables of the system, x i d (i = 1, 2, 3) are the expected values of the virtual control quantities of the system.

[0120] Step 1 Define the system position error variable

[0121] e1 = x1d - x1 (5)

[0122] Taking the derivative of equation (5) gives

[0123]

[0124] For the first subsystem, take Lyapunov function

[0125]

[0126] Differentiate equation (7) to get

[0127]

[0128] Take the expected value of the virtual control variable

[0129]

[0130] Step 2 defines the system speed error variable

[0131] e2 = x2d - x2 (10)

[0132] Substitute equation (9) into equation (8) to get

[0133]

[0134] Substitute equation (10) into equation (9) to get

[0135]

[0136] Differentiate equation (12) to get

[0137]

[0138] Since the parameters K, C are uncertain, let Their estimates are respectively, for convenience of description, define the variable β and its estimate

[0139]

[0140] Substitute equation (14) into equation (13) to get

[0141]

[0142] For the second subsystem, take Lyapunov function

[0143]

[0144] Step 3 in equation (16) defines the subsystem error variable

[0145] e3 = x3d - a1x3 (17)

[0146] Differentiate equation (16) to get

[0147] ​

[0148] Taking the expected value of the virtual control variable

[0149]

[0150] Substitute equation (19) into equation (18) to get

[0151]

[0152] When Converge to K, C, and a1x3 is equal to its expected value x3d, then ΔK = 0, ΔC = 0, e3 = 0, which can guarantee Negative, so that e1, e2 can gradually stabilize to zero.

[0153] Substitute equation (19) into equation (17), and take the derivative to get

[0154]

[0155] In equation (21), the values of each parameter are

[0156]

[0157] Combined with the sliding mode control, define its sliding manifold as

[0158] s = c1e1 + c2e2 + e3 (23)

[0159] Take the derivative of equation (23) to get

[0160]

[0161] Where, in order for equation (24) to be a constant of Hurwitz, when the state variable slides on the sliding surface s = 0, then The system Lyapunov function is constructed

[0162]

[0163] Take the derivative of equation (25), and substitute equations (20), (21), (24) into it to get

[0164]

[0165] The output of the designed controller is

[0166]

[0167] Substitute equation (27) into equation (26) to get

[0168]

[0169] The adaptive law of the uncertain parameter, is taken as

[0170]

[0171] Considering that and exist upper and lower bounds, the adaptive law thereof needs to be adjusted.

[0172]

[0173]

[0174] The simultaneous equations (28)-(31) are obtained

[0175]

[0176] In equation (32), the following is obtained:

[0177]

[0178] Based on the above, the present application proposes a compensation method based on global backstepping adaptive sliding mode control for the nonlinear gear gap existing in the gun servo system. First, an approximate dead zone model is introduced in the double-inertia system, the nonlinear disturbance in five-level sea state shooting is considered, a system state space model is established, and the model is divided into three subsystems. Then, based on the backstepping control theory, a Lyapunov function is recursively constructed step by step, the adaptive law of the uncertain parameter of the system is given in combination with the sliding mode control in the third step, a global backstepping adaptive sliding mode controller is designed, and the global stability of the closed-loop system is proved by using the Barbalat theorem. The simulation results show that, under the same working conditions, the method can more effectively compensate the gear gap and weaken the transmission torque and the load speed chattering at the time of commutation, so that the system has higher position tracking accuracy and robustness.

[0179] 2.2 Proof of system stability:

[0180] For the gun double-inertia servo system (4), the controller is designed to take equation (27), the adaptive law of the uncertain parameter is taken as equations (30) and (31), and the controller parameters are selected to satisfy equation (34), so that the first to third order principal minors of the matrix Q are all greater than zero, and therefore Q is a positive definite matrix.

[0181]

[0182] The system stability condition can be obtained by analyzing the Lyapunov function V3, and P=E T QE, and from equation (32) Therefore,

[0183]

[0184] It is easy to know that e iIf all of (i = 1, 2, 3) are bounded, then V3 is bounded, and according to Barbalat theorem, we can get

[0185]

[0186] Then the whole system is asymptotically stable, the position error of the system converges, and the state variables of the system tend to the sliding surface s = 0 in finite time and move along the desired state trajectory, which completes the proof.

[0187] 3 Simulation analysis

[0188] According to the actual working conditions of a certain type of gun double-inertia servo system, the main parameters of the system are given (Table 1):

[0189] Table 1 Main parameters of the system

[0190]

[0191] To verify the effectiveness of the proposed method, a certain type of gun double-inertia servo system with backlash is taken as the controlled object, and a simulation model is built in Simulink. Under the conditions of large-angle turning and sinusoidal tracking, the control and backlash compensation effects of the designed controller and PID controller are simulated, and the initial values of the system state variables are all zero. The form of the PID controller used in the simulation is

[0192]

[0193] In equation (37), K P = 7000, K I = 10, and K D = 2.

[0194] The parameters of the designed controller are f1 = 80, f2 = 5, f3 = 80, f4 = 10, c1 = 5, c2 = 2, γ1 = 2, and γ2 = 2.

[0195] The simulation results under the large-angle turning condition are shown in Figure 3 , and the desired position signal is

[0196] As shown in (a) of Figure 3 , compared with the PID controller, the designed controller can make the servo system respond faster and track the large-angle turning desired position signal with higher precision. As shown in (b) of Figure 3 , (c) of Figure 3 , during the large-angle turning of the gun, the PID controller has no obvious control effect on the chattering of the transmission torque and the load speed during the reversal, while the designed controller can make the system pass through the backlash stage smoothly and continuously, to a certain extent, avoiding the strong repeated collision and impact during the reversal. Figure 3As shown in (d), the designed controller enables the system state to quickly approach the sliding surface and run along the desired trajectory. Simulation results show that, under large-angle rotation and with uncertain parameters K and C in the system, the global backstepping adaptive sliding mode controller outperforms the PID controller in terms of backlash compensation and reduction of chattering in transmission torque and load speed, while also giving the system good position tracking performance and robustness.

[0197] Simulation results under sinusoidal tracking conditions are as follows: Figure 4 As shown, the desired position signal is

[0198] Depend on Figure 4 As shown in (a), compared to the PID controller, the designed controller can converge the position error of the servo system to a small range in a short time, enabling the system to track the sinusoidal desired position signal quickly and with high precision. Depend on Figure 4 (b) Figure 4 From (c), it can be seen that during the sinusoidal tracking period of the artillery, the transmission torque and load speed under PID control exhibit significant chattering. However, the designed controller enables the system to smoothly and continuously navigate the backlash phase, ensuring system stability during reversal. From Figure 4 As shown in (d), the designed controller can rapidly bring the system state close to the sliding surface and run along the desired trajectory. Simulation results show that, under sinusoidal tracking and with uncertain parameters K and C in the system, the global backstepping adaptive sliding mode controller outperforms the PID controller in terms of backlash compensation and reducing chattering of transmission torque and load speed, giving the system good dynamic quality and robustness.

[0199] This invention proposes a global backstepping adaptive sliding mode control method to compensate for the nonlinear backlash in a dual-inertia servo system of a certain type of artillery. By progressively constructing a Lyapunov function through backstepping control, the global asymptotic stability of the closed-loop system is guaranteed. Adaptive control is combined to approximate the uncertain parameters K and C of the system, compensating for the impact of measurement errors on system performance. Applying sliding mode control to backstepping control reduces chattering of the transmission torque and load speed during commutation. Simulation results show that compared with PID control, this method not only compensates for backlash more effectively but also reduces chattering of the transmission torque and load speed during commutation, while simultaneously giving the system higher position tracking accuracy and robustness.

[0200] Based on the above embodiments, this application also provides an electronic device, the electronic device including: one or more processors, a memory, and one or more programs; wherein, the one or more programs are stored in the memory, and the one or more programs include instructions, which, when executed by the electronic device, cause the electronic device to perform the method provided in the above embodiments.

[0201] Based on the above embodiments, the embodiments of the present application further provide a computer storage medium, wherein the computer storage medium stores a computer program, and the computer program is executed by a computer to enable the computer to perform the method provided by the above embodiments.

[0202] The storage medium can be any available medium that can be accessed by a computer. Examples of computer-readable media include a RAM, a ROM, an EEPROM, a CD-ROM or other optical disk storage, magnetic disk storage media or other magnetic storage devices, or any other medium that can be used to carry or store desired program code in the form of instructions or data structures and that can be accessed by a computer.

[0203] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system, or a computer program product. Therefore, the present application can take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can take the form of a computer program product implemented on one or more computer-usable storage media (including, but not limited to, a disk memory, a CD-ROM, an optical memory, etc.) containing computer-usable program code.

[0204] The present application is described with reference to flowcharts and / or block diagrams of the method, device (system), and computer program product according to the present application. It should be understood that each flow and / or block in the flowcharts and / or block diagrams, as well as a combination of flows and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing apparatus to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing apparatus generate a means for implementing the functions specified in the flowcharts and / or block diagrams. Figure 1 The functions specified in a flow or multiple flows and / or blocks Figure 1 The functions specified in a flow or multiple flows and / or blocks

[0205] These computer program instructions can also be stored in a computer-readable memory that can direct the computer or other programmable data processing apparatus to work in a specific manner, so that the instructions stored in the computer-readable memory produce a manufactured product including instruction means, which implements the functions specified in the flowcharts and / or block diagrams. Figure 1 The functions specified in a flow or multiple flows and / or blocks Figure 1 The functions specified in a flow or multiple flows and / or blocks

[0206] These computer program instructions can also be loaded into a computer or other programmable data processing devices, so that a series of operational steps are performed on the computer or other programmable data processing devices to generate computer-implemented processes, thus the instructions executed on the computer or other programmable data processing devices provide processes for implementing the functions specified in the flowchart Figure 1 one or more flows and / or blocks Figure 1 one or more blocks or steps of the functions specified in the flowchart

[0207] Obviously, those skilled in the art can make various modifications and variations to the present application without departing from the spirit and scope of the present application. Thus, if these modifications and variations of the present application belong to the scope of the claims of the present application and their equivalent technologies, the present application also intends to include these modifications and variations.

Claims

1. A global backstepping adaptive sliding mode controller for an artillery servo system, characterized in that, The control quantity of the controller is expressed as follows: （27） The controller's uncertain parameter, the equivalent stiffness of the transmission output shaft. Adaptive law (30) The uncertain parameter of the controller is the coefficient of friction of the transmission output shaft. Adaptive law (31) in (29) in: This indicates the transmission ratio of the reduction gear. , , , The coefficient of friction of the output shaft of an uncertain parameter transmission. The estimated value, of which This represents the moment of inertia of the driven wheel. This indicates that the speed regulator is a proportional coefficient. Indicates the motor torque coefficient. This represents the moment of inertia of the driving wheel. Indicates the armature circuit resistance. The approximation function represents the degree of approximation of the model function for the approximately nonlinear tooth backlash. It represents half of the tooth gap. , Indicates the active rotation angle. Indicates the rotation angle of the driven wheel; , , , , , Represents the virtual control quantity of the system Expected value ,in ; Indicates the design parameters of the controller. , Indicates the design parameters of the controller. , This represents the external nonlinear disturbance equivalent to that at the motor end during firing in the current sea state; C min C represents the minimum coefficient of friction of the output shaft of an uncertain parameter transmission. max K represents the maximum coefficient of friction of the output shaft of an uncertain parameter transmission. min K represents the minimum equivalent stiffness of the output shaft of an uncertain parameter transmission. max This represents the maximum equivalent stiffness of the output shaft of the uncertain parameter transmission. Represents the equivalent stiffness of the output shaft of an uncertain parameter transmission. The difference between the expected value and the actual value, The coefficient of friction of the output shaft of an uncertain parameter transmission. The difference between the expected value and the actual value, These are the design parameters for the controller; in , This represents the coefficient of friction of the driven wheel. , This represents the equivalent stiffness of the output shaft of a transmission with uncertain parameters. This represents an estimate of the equivalent stiffness of the output shaft of a transmission with uncertain parameters. The coefficient of friction of the output shaft of the uncertain parameter transmission is represented by, where Indicates the speed loop feedback coefficient. This is the back EMF coefficient of the motor. This represents the friction coefficient of the driving wheel.

2. A design method for a global backstepping adaptive sliding mode controller for the artillery servo system as described in claim 1, characterized in that, Includes the following steps: The artillery servo system with a backlash dual inertia model is decomposed into three first-order subsystems by backstepping control. Based on the first-order subsystem, sliding mode control is used to determine the uncertain parameters of the controller, specifically the equivalent stiffness of the transmission output shaft. The uncertain parameter of the controller is the coefficient of friction of the transmission output shaft. The adaptive law.

3. The design method of the global backstepping adaptive sliding mode controller for the artillery servo system according to claim 2, characterized in that, The state variables of the gun servo system with a backlash dual inertia model are: , , , in: Indicates the rotation angle of the driven wheel. Indicates the angular velocity of the driven wheel. , Indicates the active rotation angle. The approximation function represents the degree of approximation of the model function for the approximately nonlinear tooth backlash. Indicates half of the tooth gap; The state equation of the system is constructed as follows (4) in: , This represents the coefficient of friction of the driven wheel. This represents the moment of inertia of the driven wheel. , , This represents the moment of inertia of the driving wheel. Indicates the coefficient of friction of the driving wheel. Indicates the speed loop feedback coefficient. This indicates that the speed regulator is a proportional coefficient. Indicates the motor torque coefficient. This is the back EMF coefficient of the motor. Indicates the armature circuit resistance. , , , The uncertain parameters of the controller include the equivalent stiffness of the transmission output shaft. The coefficient of friction of the transmission output shaft represents an uncertain parameter of the controller. , .

4. The design method of the global backstepping adaptive sliding mode controller for the artillery servo system according to claim 3, characterized in that, The step described above uses sliding mode control to determine the equivalent stiffness of the transmission output shaft, an uncertain parameter of the controller, based on the first-order subsystem. The uncertain parameter of the controller is the coefficient of friction of the transmission output shaft. Methods of adaptive laws, including Define system position error variables (5) in, For system virtual control quantity Expected value; Taking the derivative of the system position error variable represented by equation (5), we get (6) Constructing the Lyapunov function for equation (6) yields the first subsystem. (7) Differentiating the first subsystem represented by equation (7) yields (8) The expected value of the virtual control quantity is expressed as (9) Define system speed error variable (10) Substituting the expected value of the virtual control quantity expressed in equation (9) into equation (8) yields... (11) in, Indicates the controller's design parameters; Substituting the expected value of the virtual control quantity expressed in equation (9) into equation (10) yields... (12) Differentiating the system velocity error variable represented by equation (12) yields (13) Due to the uncertain parameters of the controller, the equivalent stiffness of the transmission output shaft The uncertain parameter of the controller is the coefficient of friction of the transmission output shaft. Uncertainty, Represents the equivalent stiffness of the output shaft of an uncertain parameter transmission. The estimated value The coefficient of friction of the output shaft of an uncertain parameter transmission. The estimated value, defining variables and its estimated value for (14) The variable represented by equation (14) and its estimated value Substituting into equation (13) yields (15) Constructing a Lyapunov function from equation (15) yields the second subsystem. (16) in, For the controller's design parameters, Represents the equivalent stiffness of the output shaft of an uncertain parameter transmission. The difference between the expected value and the actual value, The coefficient of friction of the output shaft of an uncertain parameter transmission. The difference between the expected value and the actual value; Define subsystem error variables (17) Differentiating the subsystem error variable represented by equation (16) yields (18) Take the expected value of the virtual control quantity (19) Substituting the expected value of the virtual control quantity expressed in equation (19) into equation (18) yields... (20) When the equivalent stiffness of the transmission output shaft is uncertain The estimated value Uncertain parameter: coefficient of friction of the transmission output shaft The estimated values ​​converge to the equivalent stiffness of the uncertain parameter transmission output shaft. Uncertain parameter: coefficient of friction of the transmission output shaft ,and equal Expected value At that time, there is , , ,ensure Negative definite, make , It can gradually and stably approach zero; Substituting the expected value of the virtual control quantity represented by equation (19) into equation (17) and differentiating, we get... (21) In equation (21), the values ​​of each parameter are... (22) Define the sliding manifold for sliding mode control as follows: (23) Differentiating the sliding manifold of sliding mode control expressed by equation (23) yields (24) in, Indicates the design parameters of the controller When the state variable slides on the sliding mode ,but This holds true, making equation (24) a constant of Hurwitz; Construct Lyapunov functions to obtain the third subsystem. (25) Differentiating the third subsystem represented by equation (25) and substituting equations (20), (21), and (24) into the equation, we get... (26) According to equation (26), the output of the controller is: （27） Substituting the output of the controller represented by equation (27) into equation (26) yields (28) The controller's uncertain parameter, the equivalent stiffness of the transmission output shaft. The uncertain parameter of the controller is the coefficient of friction of the transmission output shaft. The adaptive law is (29) Considering the equivalent stiffness of the transmission output shaft with uncertain parameters The estimated value Uncertain parameter: coefficient of friction of the transmission output shaft The estimated value There are upper and lower bounds; adjust the adaptive law accordingly. (30) (31) Solving equations (28) to (31) gives us... (32) In equation (32): (33)。 5. An electronic device, the electronic device comprising: One or more processors, a memory, and one or more programs; wherein the one or more programs are stored in the memory, and the one or more programs include instructions that, when executed by the electronic device, cause the electronic device to perform the method of any one of claims 2-4.

6. A computer-readable storage medium comprising a computer program that, when executed on an electronic device, causes the electronic device to perform the method of any one of claims 2-4.

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