A design method of electric rudder based on adaptive smith compensation

Abstract

The application provides a method for constructing a Smith compensator by measuring a rudder deflection angle and a rudder deflection angle velocity and realizing fast response control of a rudder by using an adaptive method. Firstly, the rudder deflection angle error is obtained by comparing the rudder deflection angle with a rudder deflection angle command, and then the compensation error is obtained by comparing the rudder deflection angle error with the output of the Smith compensator; the error sliding mode is constructed according to the compensation error, the rudder deflection angle velocity and the integral of the compensation error, on one hand, the Smith compensator is constructed by using a lag operation according to the control signal of the rudder system, and an adaptive algorithm is used to adaptively estimate the lag time parameter in the Smith compensation; on the other hand, the constant disturbance compensation term and the angular velocity disturbance compensation term in the sliding mode control are designed by using the adaptive algorithm, and the nonlinear change of the sliding mode signal and the differential filtering signal are superposed, so that the fast control of the rudder system is realized. The method has the advantage of good rudder response rapidity.

Description

Technical Field

[0001] This invention relates to the field of rapid control of industrial electric servo motors, and more specifically, to a design method for electric servo motors based on adaptive Schmisch compensation. Background Technology

[0002] Servo motors, as the core actuators of control systems, are widely used in many large-scale military and civilian systems. For high-speed aircraft, due to technological advancements, flight speeds are increasing, demanding ever-faster response times from the entire flight control system; otherwise, safety hazards in obstacle avoidance and other aspects will arise. The faster the response speed of the flight control system, the higher the requirements for the response speed of the core actuator, the servo motor; some even require a servo motor response speed of less than 10 milliseconds. Therefore, speed is the most critical indicator for such servo motors, but inertial lag is an unavoidable and difficult-to-eliminate problem affecting speed. While Smith compensators have some successful applications in industrial temperature control, servo systems are faster and more complex than stable control systems. Based on this background, this invention proposes a method combining adaptive and Smith compensation. The main reason is that if the relevant servo motor parameters of the Smith compensator are not properly handled, the compensation effect will be greatly reduced. Therefore, we use an adaptive method to estimate the relevant parameters of the Smith compensator, thereby achieving high-speed control of the servo motor and giving this invention high engineering application value.

[0003] It should be noted that the information in the background section above is only used to enhance the understanding of the background of the present invention, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0004] The purpose of this invention is to provide a design method for an electric servo motor based on adaptive Schmisch compensation, thereby overcoming the problem of insufficient servo motor speed capability caused by defects in related technologies.

[0005] According to one aspect of the present invention, a design method for an electric servo motor based on adaptive Schmisch compensation is provided, comprising the following four steps:

[0006] Step S10: Use an angle sensor to measure the rudder deflection angle of the electric servo motor, denoted as δ; use a speed sensor to measure the rudder deflection angular velocity of the electric servo motor, denoted as ω.

[0007] Step S20: Compare the rudder deflection angle signal of the electric servo motor with the input command signal of the electric servo motor to obtain the rudder deflection angle error signal; compare the rudder deflection angle error signal with the output signal of the Schmis compensator to obtain the Schmis compensation error signal, wherein the initial value of the output signal of the Schmis compensator is set to 0; then, obtain the compensation error sliding mode signal by superimposing its integral signal and the rudder deflection angular velocity signal on the Schmis compensation error signal; then, perform a terminal nonlinear transformation on the compensation error sliding mode signal to obtain the compensation error sliding mode terminal transformation signal; finally, design an adaptive estimation law for the lag time parameter of the Schmis compensator based on the compensation error sliding mode signal and the compensation error sliding mode terminal transformation signal.

[0008] Step S30: Based on the adaptive estimation law of the lag time parameter of the Schmis compensator, the estimated value of the lag time parameter of the Schmis compensator is obtained by nonlinear integral solution. Then, the growth rate signal of the total control inertial lag is obtained by fractional-order approximate differentiation based on the total control servo control signal and the total control inertial lag signal. Then, the total control inertial lag signal is obtained by nonlinear integral solution based on the growth rate signal of the total control inertial lag, wherein the initial value of the total control inertial lag signal and the total control servo control signal is selected as 0. Finally, the output signal of the Schmis compensator is obtained by subtracting the total control inertial lag signal from its previous data.

[0009] Step S40: Perform a second-order differential filtering transformation on the compensation error sliding mode terminal transformation signal to obtain the compensation error sliding mode second-order filtered signal; then, based on the compensation error sliding mode terminal transformation signal and the compensation error sliding mode signal, use a nonlinear adaptive method to design the growth rate signal of the sliding mode constant interference parameter and the growth rate signal of the sliding mode angular velocity interference parameter; then, perform nonlinear integration to obtain the sliding mode constant interference parameter and the sliding mode angular velocity interference parameter respectively; and finally, superimpose the compensation error sliding mode terminal transformation signal, the compensation error sliding mode signal, and the compensation error sliding mode second-order filtered signal to obtain the final servo motor overall control signal, which is then sent to the DC motor to realize the servo motor's rapid tracking of the input command.

[0010] In one exemplary embodiment of the present invention, the rudder deflection angle signal of the electric servo motor is compared with the input command signal of the electric servo motor to obtain the rudder deflection angle error signal; the rudder deflection angle error signal is compared with the output signal of the Schmis compensator to obtain the Schmis compensation error signal; then, the Schmis compensation error sliding mode signal is obtained by superimposing its integral signal and the rudder deflection angular velocity signal; then, a terminal nonlinear transformation is performed on the compensation error sliding mode signal to obtain the compensation error sliding mode terminal transformation signal; finally, the adaptive estimation law of the hysteresis time parameter of the Schmis compensator is designed based on the compensation error sliding mode signal and the compensation error sliding mode terminal transformation signal, including:

[0011] e1=δ-δ d ;

[0012] e = e1 - u s

[0013] s1=k1e+k2ω+k3∫edt;

[0014]

[0015]

[0016] Where δ d The input command signal for the servo motor, u s The Schmidt compensator output signal is used in the first calculation, with the initial value set to 0. Subsequent calculations will follow in the next step. e1 is the servo deflection angle error signal; e is the Schmidt compensation error signal; s1 is the compensation error sliding mode signal; k1, k2, and k3 are constant parameters; s a To compensate for error in the sliding mode terminal conversion signal, T 2d The adaptive estimation law for the lag time parameter of the Schmisch compensator; k a3 This is a constant parameter used to adjust the adaptive convergence speed of the Schmis compensator's hysteresis time parameter.

[0017] In one exemplary embodiment of the present invention, based on the adaptive estimation law of the lag time parameter of the Schmis compensator, a nonlinear integral solution is used to obtain the estimated value of the lag time parameter of the Schmis compensator. Then, fractional-order approximate differentiation is performed on the total control signal of the servo motor and the total control inertial lag signal to obtain the growth rate signal of the total control inertial lag. Then, nonlinear integral solution is performed on the growth rate signal of the total control inertial lag to obtain the total control inertial lag signal. Finally, the difference between the total control inertial lag signal and its previous data is calculated to obtain the output signal of the Schmis compensator, including:

[0018]

[0019]

[0020]

[0021]

[0022]

[0023] in Here, u represents the estimated lag time parameter, and u is the total control signal of the servo motor. In the first step of the calculation, the initial value is selected as 0; subsequent calculations will be discussed in the next step. sadThe growth rate signal of the total control inertial lag; u sa The total control inertial lag signal is represented by T1, where T1 is the constant time constant of the Schmisch compensator; T is the constant integral time parameter; and τ is the lag time parameter. sa (n-τ / T) is u sa The value at time nT-τ. s This is the output signal of the Schmis compensator, which is used to solve the output signal of the Schmis compensator in the previous step.

[0024] In one exemplary embodiment of the present invention, a second-order differential filtering transformation is performed on the compensated error sliding mode termination transformation signal to obtain a compensated error sliding mode second-order filtered signal; then, based on the compensated error sliding mode termination transformation signal and the compensated error sliding mode signal, a nonlinear adaptive method is used to design the growth rate signal of the sliding mode constant disturbance parameter and the growth rate signal of the sliding mode angular velocity disturbance parameter; then, nonlinear integration is performed respectively to obtain the sliding mode constant disturbance parameter and the sliding mode angular velocity disturbance parameter; and finally, the compensated error sliding mode termination transformation signal, the compensated error sliding mode signal, and the compensated error sliding mode second-order filtered signal are superimposed to obtain the final servo motor overall control signal, including:

[0025]

[0026]

[0027]

[0028]

[0029]

[0030]

[0031] Where s b To compensate for errors, a second-order sliding mode filtered signal; 1d The growth rate signal of the sliding mode constant disturbance parameter; a 2d This is the growth rate signal of the sliding mode angular velocity disturbance parameter; These are constant disturbance parameters for sliding mode. For sliding mode angular velocity disturbance parameters; k a1 For constant parameters, the adaptive convergence speed of sliding mode constant disturbance parameters, k a2 These are constant parameters used to adjust the adaptive convergence speed of the sliding mode angular velocity disturbance parameters. k4, k5, and k6 are constant control parameters, and u is the servo motor's overall control signal.

[0032] Beneficial effects

[0033] This invention provides a design method for an electric servo motor based on adaptive Schmisch compensation. Its main innovations are as follows: First, it cleverly applies the Schmisch compensator to servo motor control, solving the bottleneck problem affecting the rapid ascent of the servo motor system from a fundamental perspective. Second, it combines adaptive control with the Schmisch compensator, using a nonlinear adaptive algorithm to estimate the key parameter of the Schmisch compensator, namely the lag time constant. This enables the entire Schmisch compensation scheme to achieve good control performance when applied to servo motor control.

[0034] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and are not intended to limit the invention. Attached Figure Description

[0035] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the invention and, together with the description, serve to explain the principles of the invention. It is obvious that the drawings described below are merely some embodiments of the invention, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort.

[0036] Figure 1 This is a flowchart of an electric servo design method based on adaptive Schmisch compensation provided by the present invention.

[0037] Figure 2 This is the rudder deflection angle signal curve (unit: degrees) of the electric servo motor provided by the embodiment of the present invention;

[0038] Figure 3 This is the rudder deflection angular velocity signal curve (unit: radians per second) of the electric servo motor provided by the embodiment of the present invention;

[0039] Figure 4 This is the compensation error sliding mode signal curve (unitless) of the electric servo motor provided by the embodiment of the present invention;

[0040] Figure 5 This is the servo motor total control signal curve (unitless) of the method provided in the embodiments of the present invention. Detailed Implementation

[0041] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided to make the invention more comprehensive and complete, and to fully convey the concept of the exemplary embodiments to those skilled in the art. The described features, structures, or characteristics can be combined in any suitable manner in one or more embodiments. In the following description, numerous specific details are provided to give a full understanding of embodiments of the invention. However, those skilled in the art will recognize that the technical solutions of the invention may be practiced with one or more of these specific details omitted, or other methods, components, apparatus, steps, etc., may be employed. In other instances, well-known technical solutions are not shown or described in detail to avoid obscuring various aspects of the invention.

[0042] This invention provides a method for constructing a Schmisch compensator by measuring the servo deflection angle and angular velocity, and then using an adaptive method to achieve fast servo response control. First, the servo deflection angle is compared with the servo deflection angle command to obtain the servo deflection angle error, which is then compared with the output of the Schmisch compensator to obtain the compensation error. Based on the compensation error, the integral of the servo deflection angular velocity, and the compensation error, an error sliding mode is constructed. On one hand, based on the control signal of the servo system, a Schmisch compensator is constructed through hysteresis calculation, and an adaptive algorithm is used to adaptively estimate the hysteresis time parameter in the Schmisch compensation. On the other hand, a constant disturbance compensation term and an angular velocity disturbance compensation term are designed in the sliding mode control using an adaptive algorithm, and the nonlinear change of the sliding mode signal and the differential filter signal are superimposed to achieve fast control of the servo system. This method has the advantage of good servo response speed.

[0043] The following will, with reference to the accompanying drawings, further explain and illustrate the design method of an electric servo motor based on adaptive Schmisch compensation according to the present invention. (Reference) Figure 1 As shown, this electric servo design method based on adaptive Schmisch compensation includes the following steps:

[0044] Step S10: Use an angle sensor to measure the rudder deflection angle of the electric servo motor, denoted as δ; use a speed sensor to measure the rudder deflection angular velocity of the electric servo motor, denoted as ω.

[0045] Step S20: Compare the rudder deflection angle signal of the electric servo motor with the input command signal of the electric servo motor to obtain the rudder deflection angle error signal; compare the rudder deflection angle error signal with the output signal of the Schmis compensator to obtain the Schmis compensation error signal, wherein the initial value of the output signal of the Schmis compensator is set to 0; then, obtain the compensation error sliding mode signal by superimposing its integral signal and the rudder deflection angular velocity signal on the Schmis compensation error signal; then, perform a terminal nonlinear transformation on the compensation error sliding mode signal to obtain the compensation error sliding mode terminal transformation signal; finally, design an adaptive estimation law for the lag time parameter of the Schmis compensator based on the compensation error sliding mode signal and the compensation error sliding mode terminal transformation signal.

[0046] Specifically, it can be broken down into the following five steps. Step 1: Compare the rudder deflection angle signal of the electric servo motor with the input command signal of the electric servo motor to obtain the rudder deflection angle error signal of the electric servo motor as follows:

[0047] e1=δ-δ d ;

[0048] Where δ d e1 is the input command signal for the servo motor, and e1 is the servo motor's deflection angle error signal.

[0049] The second step involves comparing the rudder deflection angle error signal with the output signal of the Schmidt compensator to obtain the Schmidt compensation error signal as follows:

[0050] e = e1 - u s ;

[0051] Where u s The output signal of the Schmis compensator is used in the first calculation, which uses the initial value set to 0. Subsequent calculations are described below.

[0052] The third step is to obtain the compensation error sliding mode signal by superimposing the Schmis compensation error signal with its integral signal and the rudder deflection angular velocity signal, as follows:

[0053] s1=k1e+k2ω+k3∫edt;

[0054] Where s1 is the sliding mode signal for compensating for errors, and k1, k2, and k3 are constant parameters.

[0055] The fourth step is to perform a terminal nonlinear transformation based on the compensation error sliding mode signal, resulting in the following compensation error sliding mode terminal transformation signal:

[0056]

[0057] Where s a To compensate for errors, the sliding mode terminal transforms the signal, and ε1 is a constant parameter of the terminal nonlinear transformation.

[0058] The fifth step involves designing the adaptive estimation rules for the lag time parameters of the Schmis compensator based on the sliding mode signal and the sliding mode terminal transformation signal of the compensation error. The rules are as follows:

[0059]

[0060] Where T 2d The adaptive estimation law for the lag time parameter of the Schmisch compensator; k a3 This is a constant parameter used to adjust the adaptive convergence speed of the Schmis compensator's hysteresis time parameter.

[0061] Step S30: Based on the adaptive estimation law of the lag time parameter of the Schmis compensator, the estimated value of the lag time parameter of the Schmis compensator is obtained by nonlinear integral solution. Then, the growth rate signal of the total control inertial lag is obtained by fractional-order approximate differentiation based on the total control servo control signal and the total control inertial lag signal. Then, the total control inertial lag signal is obtained by nonlinear integral solution based on the growth rate signal of the total control inertial lag, wherein the initial value of the total control inertial lag signal and the total control servo control signal is selected as 0. Finally, the output signal of the Schmis compensator is obtained by subtracting the total control inertial lag signal from its previous data.

[0062] Specifically, it can be broken down into the following five steps. The first step, based on the adaptive estimation law of the lag time parameter of the Schmis compensator, uses nonlinear integral calculation to obtain the estimated values ​​of the lag time parameter of the Schmis compensator as follows:

[0063]

[0064] in is the estimated value of the lag time parameter; T is the constant integral time parameter.

[0065] The second step is to calculate the lag time parameters based on the estimated values ​​of the lag time parameters, as follows:

[0066]

[0067] Where T1 is the constant time constant of the Schmis compensator; τ is the lag time parameter.

[0068] The third step involves performing fractional-order approximate differential calculations on the servo motor's total control signal and the total control inertial hysteresis signal to obtain the growth rate signal of the total control inertial hysteresis as follows:

[0069]

[0070] Where u is the servo motor's total control signal, and its initial value is selected as 0 in the first step of the calculation. Subsequent calculations are shown in step S40; u sadThe growth rate signal of the total control inertial lag; u sa This is the overall control inertial lag signal.

[0071] The fourth step involves performing nonlinear integral calculations based on the growth rate signal of the total control inertial lag to obtain the total control inertial lag signal as follows:

[0072]

[0073] Where u sa The initial values ​​of the total control inertial hysteresis signal and the servo motor total control signal are both selected as 0.

[0074] Fifth, by subtracting the total control inertial lag signal from its previous data, the output signal of the Schmis compensator is obtained as follows:

[0075]

[0076] Where u sa (n-τ / T) is u sa The value at time nT-τ; u s This is the output signal of the Schmis compensator, which is used to solve the Schmis compensator output signal in step S20.

[0077] Step S40: Perform a second-order differential filtering transformation on the compensation error sliding mode terminal transformation signal to obtain the compensation error sliding mode second-order filtered signal; then, based on the compensation error sliding mode terminal transformation signal and the compensation error sliding mode signal, use a nonlinear adaptive method to design the growth rate signal of the sliding mode constant interference parameter and the growth rate signal of the sliding mode angular velocity interference parameter; then, perform nonlinear integration to obtain the sliding mode constant interference parameter and the sliding mode angular velocity interference parameter respectively; and finally, superimpose the compensation error sliding mode terminal transformation signal, the compensation error sliding mode signal, and the compensation error sliding mode second-order filtered signal to obtain the final servo motor overall control signal, which is then sent to the DC motor to realize the servo motor's rapid tracking of input commands.

[0078] Specifically, it can be broken down into the following four steps. The first step is to perform a second-order differential filtering transformation on the compensation error sliding mode terminal transformation signal to obtain the compensation error sliding mode second-order filtered signal as follows:

[0079]

[0080] Where s b The signal is a sliding mode second-order filtered signal to compensate for errors; c1, c2, c3, and c4 are constant parameters of the second-order filter, and s is the differential operator of the transfer function of the second-order filter.

[0081] The second step involves designing the growth rate signals of the sliding mode constant disturbance parameter and the sliding mode angular velocity disturbance parameter using a nonlinear adaptive method based on the aforementioned compensation error sliding mode terminal transformation signal and compensation error sliding mode signal, as follows:

[0082]

[0083]

[0084] Where a 1d The growth rate signal of the sliding mode constant disturbance parameter; a 2d The growth rate signal of the sliding mode angular velocity disturbance parameter; k a1 For constant parameters, the adaptive convergence speed of sliding mode constant disturbance parameters, k a2 This is a constant parameter used to adjust the adaptive convergence speed of the sliding mode angular velocity disturbance parameter.

[0085] The third step involves performing nonlinear integration on the growth rate signals of the sliding mode constant disturbance parameter and the sliding mode angular velocity disturbance parameter, respectively, to obtain the following sliding mode constant disturbance parameter and sliding mode angular velocity disturbance parameter:

[0086]

[0087]

[0088] in These are constant disturbance parameters for sliding mode. These are the parameters for the sliding mode angular velocity disturbance.

[0089] The fourth step involves superimposing the sliding mode constant interference parameters and sliding mode angular velocity interference parameters to compensate for the error sliding mode terminal transformation signal, the compensation error sliding mode signal, and the compensation error sliding mode second-order filtered signal, resulting in the final servo motor overall control signal as follows:

[0090]

[0091] Where k4, k5, and k6 are constant control parameters, and u is the servo motor's overall control signal.

[0092] The main control signal of the servo motor is sent to the DC motor inside the servo system, which can drive the servo deflection angle to track the input command signal.

[0093] Case Implementation and Computer Simulation Results Analysis

[0094] In step S10, an angle sensor is used to measure the deflection angle of the electric servo motor, such as... Figure 2 As shown; a speed sensor is used to measure the rudder deflection angular velocity of the electric servo motor, such as... Figure 3 As shown.

[0095] In step S20, the input command signal δ of the servo motor is selected. d =9 degrees, select k1=25, k2=3, k3=1.5, and obtain the compensation error sliding mode signal as follows: Figure 4 As shown.

[0096] In step S30, τ = 0.002 and T = 0.0005 are selected. In step S40, c1 = 0.01, c2 = 0.03, c3 = 0.5, c4 = 0.3, and k are selected. a1 =0.002, k a2 =0.002, and the final servo motor control signal is as follows: Figure 5 As shown.

[0097] Depend on Figure 2 It can be seen that the servo can complete the main tracking of a given command of 9 degrees within 5 milliseconds, without overshoot, and complete all adjustments within 15 milliseconds. Figure 3 It can be seen that the rudder deflection rate fluctuates significantly, mainly due to the requirement of no overshoot, which causes the rudder deflection angle to increase and decrease rapidly. Figure 4 It can be seen that the compensation error sliding mode signal converges stably to 0 after oscillation; Figure 5 It can be seen that the control quantity touches saturation multiple times in the initial stage. The main reason is that the servo motor has high speed, which is about milliseconds. This shows that the electric servo motor design method based on adaptive Schmis compensation provided by this invention is stable, convergent and effective, and has very good speed, thus having good engineering application value.

Claims

1. A design method for an electric servo motor based on adaptive Schmisch compensation, characterized in that, Includes the following steps: Step S10: Use an angle sensor to measure the deflection angle of the electric servo motor, denoted as δ; A speed sensor is used to measure the rudder deflection angular velocity of the electric servo motor, denoted as ω; Step S20: Compare the rudder deflection angle signal of the electric servo motor with the input command signal of the electric servo motor to obtain the rudder deflection angle error signal; compare the rudder deflection angle error signal with the output signal of the Schmis compensator to obtain the Schmis compensation error signal, wherein the initial value of the Schmis compensator output signal is set to 0; then, obtain the compensation error sliding mode signal by superimposing its integral signal and the rudder deflection angular velocity signal on the Schmis compensation error signal; then, perform a terminal nonlinear transformation on the compensation error sliding mode signal to obtain the compensation error sliding mode terminal transformation signal; finally, design the adaptive estimation law of the lag time parameter of the Schmis compensator based on the compensation error sliding mode signal and the compensation error sliding mode terminal transformation signal as follows: e1=δ-δ d ; e=e1-u s s1=k1e+k2ω+k3∫edt; Where δ d The input command signal for the servo motor, u s The output signal of the Schmis compensator is used in the first calculation, with the initial value set to 0. Subsequent calculations will follow in the next step. e1 is the servo deflection angle error signal; e is the Schmis compensation error signal; s1 is the compensation error sliding mode signal; k1, k2, and k3 are constant parameters; ε1 is the constant parameter of the terminal nonlinear transformation, s a To compensate for error in the sliding mode terminal conversion signal, T 2d The adaptive estimation law for the lag time parameter of the Schmisch compensator; k a3 This is a constant parameter used to adjust the adaptive convergence speed of the Schmisc compensator's hysteresis parameter. Step S30: Based on the adaptive estimation law of the lag time parameter of the Schmis compensator, the estimated value of the lag time parameter of the Schmis compensator is obtained by nonlinear integral solution. Then, fractional-order approximate differentiation is performed on the total control signal of the servo motor and the total control inertial lag signal to obtain the growth rate signal of the total control inertial lag. Then, nonlinear integral solution is performed on the growth rate signal of the total control inertial lag to obtain the total control inertial lag signal, wherein the initial values ​​of the total control inertial lag signal and the total control signal of the servo motor are selected as 0. Finally, the difference between the total control inertial lag signal and its previous data is calculated to obtain the output signal of the Schmis compensator as follows: in Here, u represents the estimated lag time parameter, and u is the total control signal of the servo motor. In the first step of the calculation, the initial value is selected as 0; subsequent calculations will be discussed in the next step. sad The growth rate signal of the total control inertial lag; u sa The total control inertial lag signal is given by T1, where T1 is the constant time constant of the Schmisch compensator; T is the constant integral time parameter; τ is the lag time parameter; and u is the constant time constant of the Schmisch compensator. sa (n-τ / T) is u sa The value at time nT-τ; u s This is the output signal of the Schmis compensator, which is used to solve the output signal of the Schmis compensator in the previous step; Step S40: Perform a second-order differential filtering transformation on the compensated error sliding mode termination signal to obtain a compensated error sliding mode second-order filtered signal; then, based on the compensated error sliding mode termination signal and the compensated error sliding mode signal, use a nonlinear adaptive method to design the growth rate signals of the sliding mode constant interference parameter and the sliding mode angular velocity interference parameter; then, perform nonlinear integration to obtain the sliding mode constant interference parameter and the sliding mode angular velocity interference parameter respectively; finally, superimpose the compensated error sliding mode termination signal, the compensated error sliding mode signal, and the compensated error sliding mode second-order filtered signal to obtain the final servo motor overall control signal, which is then sent to the DC motor to achieve rapid tracking of input commands by the servo motor as follows: Where c1, c2, c3, and c4 are constant parameters of the second-order filter, and s is the differential operator of the second-order filter transfer function. b To compensate for errors, a second-order sliding mode filtered signal; 1d The growth rate signal of the sliding mode constant disturbance parameter; a 2d This is the growth rate signal of the sliding mode angular velocity disturbance parameter; These are the constant disturbance parameters for sliding mode; For sliding mode angular velocity disturbance parameters; k a1 k is a constant parameter used to adjust the adaptive convergence speed of the sliding mode constant disturbance parameter. a2 These are constant parameters used to adjust the adaptive convergence speed of the sliding mode angular velocity disturbance parameters. k4, k5, and k6 are constant control parameters, and u is the servo motor's overall control signal.

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