A brushed DC motor control method based on data-driven second-order integral terminal sliding mode

Abstract

The present disclosure belongs to the technical field of motor control, and specifically relates to a DC brush motor control method based on data-driven second-order integral terminal sliding mode, comprising: obtaining a dynamic model of the DC brush motor; constructing a discrete time equation of the acquired dynamic model; calculating a disturbance estimation error of the discrete time equation; calculating a pseudo partial derivative parameter estimation error based on the disturbance estimation error; constructing a second-order discrete integral terminal sliding mode control function of the DC brush motor based on the obtained discrete time equation, the disturbance estimation error and the pseudo partial derivative parameter estimation error; and analyzing the stability of the control function to realize the control of the DC brush motor.

Description

Technical Field

[0001] The present invention belongs to the technical field of motor control, and in particular relates to a direct current brushed motor control method based on data-driven second-order integral terminal sliding mode. Background Art

[0002] The statements in this section merely provide background information related to the present disclosure and do not necessarily constitute prior art.

[0003] DC motors have been widely used in mobile robots, drones, 3D printers, and smart manufacturing. In many applications, the DC motor speed is regulated by a cascade controller consisting of a current (inner) and speed loop (outer). Each loop can be controlled using a simple proportional-integral controller and adjusted to obtain a good feedback gain through related techniques such as trial and error, loop shaping, Bode and Nyquist. Due to the similarity between the dynamics of DC motors and three-phase motors in the framework of rotating dq axes, the speed control performance of DC motors can be improved by applying various new technologies similar to those used for three-phase induction motors and permanent magnet synchronous motors, such as robust control, adaptive control, neural network control, feedback linearization control, sliding mode control, model predictive control, and active disturbance rejection control.

[0004] According to the inventors, in view of the practical problems of motor control, the speed control of DC motors is characterized by variable and unpredictable inputs, noise propagation along a series of unit processes, the presence of unknown parameters, and unknown dynamic changes of motors / loads; under these conditions, the traditional constant gain feedback controller cannot maintain the performance of the DC motor control system at a high level. Traditional DC motor drives are achieved by dynamically linearizing the DC motor control system and designing a linear feedback controller. However, in high-performance motor drives, this approach is rarely satisfactory because it leads to poor speed tracking when the load changes suddenly or the motor control system continues to accelerate or decelerate, and readjustment is required to ensure optimal performance. Therefore, in the past decade, there has been a significant increase in the development of adaptive control systems for motor drives. However, the state estimation and parameter identification methods adopted by most methods are based on and limited to linear models, and ignore the nonlinear characteristics of DC motors, which makes the motor control system impractical or even endangers its stability. Summary of the invention

[0005] In order to solve the above problems, the present invention proposes a DC brush motor control method based on data-driven second-order integral terminal sliding mode. For the speed control problem of the DC brush motor, the difficulty of establishing an accurate mathematical model in the existing methods and the shortcomings of the existing control technology are overcome, and a data-driven second-order integral terminal sliding mode control method is adopted to improve the stability of the DC motor control.

[0006] According to some embodiments, the solution of the present disclosure provides a DC brushed motor control method based on data-driven second-order integral terminal sliding mode, which adopts the following technical solutions:

[0007] A DC brushed motor control method based on data driven second-order integral terminal sliding mode, comprising:

[0008] Get the dynamic model of the brushed DC motor;

[0009] constructing discrete time equations of the acquired kinetic model;

[0010] calculating a perturbation estimate error of the discrete time equation;

[0011] Calculating a pseudo partial derivative parameter estimation error based on the disturbance estimation error;

[0012] According to the obtained discrete time equation, disturbance estimation error and pseudo partial derivative parameter estimation error, a second-order discrete integral terminal sliding mode control function of the brushed DC motor is constructed.

[0013] The stability of the control function is analyzed to realize the control of the brushed DC motor.

[0014] As a further technical limitation, the obtained dynamic model of the brushed DC motor includes the terminal voltage u(t) and armature current i of the brushed DC motor. a (t) and load torque T L (t); that is

[0015]

[0016]

[0017] T L (t) = λω 2 (t)sign(ω(t))

[0018] Where K represents the torque and back EMF constant, R is the armature resistance, L is the armature inductance, J is the rotor moment of inertia, A is the damping constant, λ is the switching gain constant, and ω(t) is the rotor angular velocity.

[0019] Furthermore, the terminal voltage u(t) and armature current i of the DC brushed motor are obtained. a (t) Merge,

[0020]

[0021] Take the sampling time as T, approximate the first-order derivative and the second-order derivative with the first-order difference and the second-order difference respectively, and construct the discrete time difference equation of the DC brushed motor, that is, ω(k+1)=α1ω(k)+α2ω(k-1)+α3sign(ω(k))ω 2 (k)+α4sign(ω(k-1))ω 2 (k-1)+α5u(k)

[0022] in,

[0023] As a further technical limitation, the discrete time equation of the brushed DC motor is: ω(k+1)=f(ω(k),ω(k-1),ω(kn y ),u(k),u(k-1),L,u(kn u ))+d(k), where ω(k+1) represents the angular velocity of the brushed DC motor at time k+1, u(k) represents the input voltage of the brushed DC motor at time k; d(k) represents the disturbance or unmodeled dynamics, n y and n u Both represent the unknown order of the system, and f(·) represents the unknown nonlinear function.

[0024] Furthermore, the angular velocity of the DC motor at time k+1 without considering system disturbances or modeling dynamics is:

[0025] ω m (k+1)=ω(k+1)-d(k)=f(ω(k),ω(k-1),ω(kn y ),u(k),u(k-1),…,u(kn u )) That is, ω(k+1)=ω m (k+1)+d(k).

[0026] Furthermore, when Δu(k)=u(k)-u(k-1) and |Δu(k)|≠0, there exists a pseudo partial derivative φ(k) such that Δω m (k+1)=φ(k)Δu(k), |φ(k)|≤b, b represents a positive constant, Δω m (k+1)=ω m (k+1)-ω m (k), then we get ω m (k+1)=ω m (k)+φ(k)Δu(k), Δω(k+1)=Δω m (k+1)+Δd(k), Δd(k)=d(k)-d(k-1), ω(k+1)=ω(k)+φ(k)Δu(k)+Δd(k).

[0027] Furthermore, the delay estimation error is obtained according to ω(k+1)=ω(k)+φ(k)Δu(k)+Δd(k): for

[0028] The disturbance estimation error of the discrete time equation is obtained based on the obtained delay estimation error for That is

[0029]

[0030] As a further technical qualification, consider the quadratic index function In the best conditions Next, get

[0031] when Or |Δu(k-1)|≤ε, Among them, u>0; η∈(0,1]; ε represents a positive constant, for The initial value of Available where δ(k) represents the pseudo-partial derivative parameter estimation error, and

[0032] As a further technical limitation, the output angular velocity tracking error e(k) of the DC brushed motor is: e(k)=ω(k)-ω r (k), where ω(k) is the system output angular velocity, ω r (k) is the expected output angular velocity; the discrete integral terminal sliding mode function s(k) is: s(k) = e(k) + λE(k-1), where λ>0, and the integral error term is expressed as: Wherein, α represents the ratio of two odd integers, 0<α<1; the second-order discrete integral terminal sliding mode control function ρ(k) of the brushed DC motor is: ρ(k)=s(k)+βs(k-1), where 0≤β≤1, when β=0, ρ(k) represents the traditional first-order discrete integral terminal sliding mode function; using the discrete reaching law ρ(k+1)=0, we get s(k+1)=-βs(k), ω(k+1)-ω r (k+1)+λE(k)=-βs(k),

[0033] Furthermore, assuming that the disturbance estimation error That is, equivalent control Δu eq (k) Consider Δu eq (k) Robustness of the switching controller Δu sw (k) is: Δusw (k) = Δu sw (k-1)-λ s sign(ρ(k)); where λ s >0 indicates the switching control gain, sign(·) indicates the sign function; that is, the overall control law Δu(k) is: Δu(k)=Δu eq (k)+Δu sw (k), i.e.

[0034]

[0035] Compared with the prior art, the present invention has the following beneficial effects:

[0036] The present invention discloses an online estimation method for estimating unknown disturbances of the system through a disturbance estimation algorithm in the presence of external disturbances; by adjusting controller parameters, the given speed of a brushed DC motor can be tracked quickly and stably; the method is only related to the online measurement data of the control system and does not require an accurate mathematical model of the brushed DC motor. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] The accompanying drawings constituting a part of the present disclosure are used to provide a further understanding of the present disclosure. The illustrative embodiments of the present disclosure and their descriptions are used to explain the present disclosure and do not constitute an improper limitation on the present disclosure.

[0038] Figure 1 is a flow chart of a DC brushed motor control method based on data-driven second-order integral terminal sliding mode in an embodiment of the present disclosure;

[0039] Figure 2 is a schematic diagram of tracking performance when the angular velocity is a curve in an embodiment of the present disclosure;

[0040] Figure 3 is a schematic diagram of control input when the angular velocity is a curve in an embodiment of the present disclosure;

[0041] Figure 4 is a schematic diagram of a pseudo partial derivative update process when the angular velocity is a curve in an embodiment of the present disclosure;

[0042] Figure 5 is a schematic diagram of tracking performance when the angular velocity is a step signal in an embodiment of the present disclosure;

[0043] Figure 6 is a schematic diagram of control input when the angular velocity is a step signal in an embodiment of the present disclosure;

[0044] Figure 7 It is a schematic diagram of the pseudo partial derivative update process when the angular velocity is a step signal in an embodiment of the present disclosure. DETAILED DESCRIPTION

[0045] The present disclosure is further described below in conjunction with the accompanying drawings and embodiments.

[0046] It should be noted that the following detailed descriptions are all illustrative and are intended to provide further explanation of the present disclosure. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present disclosure belongs.

[0047] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present disclosure. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0048] In the present disclosure, terms such as "upper", "lower", "left", "right", "front", "back", "vertical", "horizontal", "side", "bottom" and the like indicating directions or positional relationships are based on the directions or positional relationships shown in the accompanying drawings. They are relational words determined only for the convenience of describing the structural relationships of the various parts or elements of the present disclosure, and do not specifically refer to any part or element in the present disclosure and should not be understood as limitations on the present disclosure.

[0049] In the present disclosure, terms such as "fixed connection", "connected", "connection", etc. should be understood in a broad sense, indicating that it can be fixedly connected, integrally connected or detachably connected; it can be directly connected or indirectly connected through an intermediate medium. For relevant scientific research or technical personnel in this field, the specific meanings of the above terms in the present disclosure can be determined according to specific circumstances, and they cannot be understood as limitations on the present disclosure.

[0050] Example

[0051] The disclosed embodiment introduces a DC brushed motor control method based on data-driven second-order integral terminal sliding mode.

[0052] like Figure 1 A DC brushed motor control method based on data-driven second-order integral terminal sliding mode is shown, comprising:

[0053] Get the dynamic model of the brushed DC motor;

[0054] constructing discrete time equations of the acquired kinetic model;

[0055] calculating a perturbation estimate error of the discrete time equation;

[0056] Calculating the pseudo partial derivative parameter estimation error according to the disturbance estimation error;

[0057] According to the obtained discrete time equation, disturbance estimation error and pseudo partial derivative parameter estimation error, a second-order discrete integral terminal sliding mode control function of the brushed DC motor is constructed.

[0058] The stability of the control function is analyzed to realize the control of the brushed DC motor.

[0059] As one or more implementations, the dynamic model of the brushed DC motor is:

[0060]

[0061]

[0062] T L (t) = λω 2 (t)sign(ω(t)) (3)

[0063] Where K represents the torque and back EMF constant, R is the armature resistance, L is the armature inductance, J is the rotor moment of inertia, A is the damping constant, λ is the switching gain constant, ω(t) is the rotor angular velocity, i a (t) is the armature current, u(t) is the motor terminal voltage and T L (t) is the load torque.

[0064] Combining formula (1) and formula (2) into

[0065]

[0066] Taking the sampling time as T, the first-order and second-order derivatives in formula (4) are approximated by first-order and second-order differences respectively, and the discrete time difference equation of the DC brushed motor can be obtained as follows:

[0067] ω(k+1)=α1ω(k)+α2ω(k-1)+α3sign(ω(k))ω 2 (k)+α4sign(ω(k-1))ω 2 (k-1)+α5u(k) (5)

[0068] in,

[0069] The mathematical model of a brushed DC motor can be expressed as the following general discrete-time system:

[0070] ω(k+1)=f(ω(k),ω(k-1),ω(kn y ),u(k),u(k-1),L,u(kn u ))+d(k) (6)

[0071] Where, ω(k+1) and u(k) are the angular velocity of the DC motor of the control system at time k+1 and the input voltage of the DC motor at time k, respectively; d(k) represents the system disturbance or unmodeled dynamics, which is defined as a generalized disturbance here, and |d(k)|≤D, D>0 is a positive constant; n y and n u is the unknown order of the system; f(·) is the unknown nonlinear function.

[0072] Let ω m (k+1)=f(ω(k),ω(k-1),ω(kn y ),u(k),u(k-1),L,u(kn u )) (7)

[0073] Among them, ω m (k+1) represents the angular velocity of the DC motor at time k+1 without considering system disturbance or modeling dynamics. From formula (6), we can know

[0074] ω(k+1)=ω m (k+1)+d(k) (8)

[0075] Assumption 1: The input and output of system (6) are observable and controllable, that is, the expected output signal ω r When (k+1) is bounded and contains the generalized disturbance d(k), there exists a bounded control input signal so that the output of the system under the action of this signal is equal to the expected output of the system.

[0076] Assumption 2: The partial derivatives of f(·) with respect to u(k) are continuous.

[0077] Assumption 3: Formula (6) satisfies the generalized Lipschitz, that is, for any k and |Δu(k)|≠0,

[0078] |Δω(k+1)|≤b|Δu(k)| (9)

[0079] Where Δω(k+1)=ω(k+1)-ω(k), Δu(k)=u(k)-u(k-1), and b is a normal number.

[0080] As shown in formula (7), the nonlinear system satisfies assumptions 1, 2 and 3. When |Δu(k)|≠0, there exists a pseudo partial derivative φ(k) such that

[0081] Δω m (k+1)=φ(k)Δu(k) (10)

[0082] Moreover, |φ(k)|≤b, where b is a positive constant, Δω m (k+1)=ωm (k+1)-ω m (k), Δu(k)=u(k)-u(k-1).

[0083] Rewrite formula (10) to get

[0084] ω m (k+1)=ω m (k)+φ(k)Δu(k) (11)

[0085] From formula (8), we can deduce

[0086] Δω(k+1)=Δω m (k+1)+Δd(k) (12)

[0087] Among them, Δω m (k+1)=ω m (k+1)-ω m (k), Δω(k+1)=ω(k+1)-ω(k), Δd(k)=d(k)-d(k-1).

[0088] Substituting formula (10) into formula (12), we can get

[0089] ω(k+1)=ω(k)+φ(k)Δu(k)+Δd(k) (13)

[0090] Usually, in actual control systems, the disturbance term Δd(k) in formula (13) is unknown and can be estimated using its one-step delay as follows:

[0091]

[0092] Then formula (14) becomes

[0093]

[0094] in, represents the disturbance estimation error, and is bounded.

[0095] Consider the following quadratic index function

[0096]

[0097] By optimal conditions have to

[0098]

[0099] when Or |Δu(k-1)|≤ε,

[0100] Among them, u>0; η∈(0,1]; ε is a sufficiently small positive number, for The initial value of

[0101] Formula (15) can be rewritten as

[0102]

[0103] in represents the pseudopartial derivative parameter estimation error.

[0104] The output angular velocity tracking error is defined as follows:

[0105] e(k)=ω(k)-ω r (k) (20)

[0106] Where ω(k) is the system output angular velocity, ω r (k) is the desired output angular velocity.

[0107] The discrete integral terminal sliding mode function is defined as follows:

[0108] s(k)=e(k)+λE(k-1) (21)

[0109] Where λ>0, the integral error term is expressed as:

[0110]

[0111] Where 0<α<1, represents the ratio of two odd integers.

[0112] Design the second-order discrete integral terminal sliding mode function as:

[0113] ρ(k)=s(k)+βs(k-1) (23)

[0114] Where 0≤β≤1. If β=0, it represents the traditional first-order discrete integral terminal sliding mode function.

[0115] The following discrete reaching law is used

[0116] ρ(k+1)=0 (24)

[0117] Substituting formula (23) into formula (24), we can get

[0118] s(k+1)=-βs(k) (25)

[0119] ω(k+1)-ω r (k+1)+λE(k)=-βs(k) (26)

[0120] Substituting formula (19) into formula (26), we can obtain

[0121]

[0122] Ignore the interference estimation error The equivalent control Δu can be obtained eq (k)

[0123]

[0124] It is worth noting that formula (28) assumes But in fact Therefore, to ensure Δu eq (k) The robustness of the switching controller is designed as follows:

[0125] Δu sw (k) = Δu sw (k-1)-λ s sign(ρ(k)) (29)

[0126] where λ s >0 is the switching control gain, and sign(·) represents the sign function.

[0127] Therefore, the overall control law is:

[0128] Δu(k)=Δu eq (k)+Δu sw (k) (30)

[0129] Right now

[0130]

[0131] Since φ(k) is unknown, the pseudo partial derivative parameter estimation error δ(k) is unknown. Assume that δ(k) is bounded, for example, |δ(k)|≤M. To facilitate controller parameter tuning, δ(k) is taken as a constant δ not greater than M.

[0132] Prove the stability of the designed control system. In order to facilitate stability analysis, assumption 4 is introduced.

[0133] Assumption 4: Switching control gain λ s Satisfies the following inequality

[0134]

[0135] in,

[0136] Theorem 1: The discrete-time nonlinear system formula (19) that satisfies assumptions 1-4, and By using equation (14) and equation (17) for online updating respectively and adopting the control law equation (31), the control system will converge within a finite number of steps.

[0137] From formula (21), we can see that the sliding mode function can be expressed as

[0138] s(k+1)=e(k+1)+λE(k) (33)

[0139] From formula (33), we can deduce

[0140]

[0141] From formula (23) and formula (34), we can know that

[0142] ρ(k+1)=s(k+1)+βs(k)=Δd(k)-Δd(k-1)+Δu sw (k) (35)

[0143] From formula (35), we can deduce

[0144] ρ(k)=Δd(k-1)-Δd(k-2)+Δu sw (k-1) (36)

[0145] Subtracting formula (36) from both sides of formula (35) yields

[0146] ρ(k+1)-ρ(k)=(Δd(k)-2Δd(k-1)+Δd(k-2))+(Δu sw (k)-Δu sw (k-1)) (37)

[0147] According to formula (29) and formula (37), we can get

[0148] ρ(k+1)-ρ(k)=(Δd(k)-2Δd(k-1)+Δd(k-2))-λ s sign(ρ(k)) (38)

[0149] Considering Assumption 4 and Formula (38), we can get

[0150]

[0151] 1): Prove the convergence of ρ(k): If ρ(k)>0, from formula (39) we can get

[0152]

[0153] If ρ(k)<0, then

[0154]

[0155] Therefore, from formula (40) and formula (41), we can know that

[0156] |ρ(k+1)|<|ρ(k)| (42)

[0157] From formula (42), we can see that ρ(k) is convergent.

[0158] 2): Prove that ρ(k) will enter the quasi-sliding mode domain after M steps

[0159] The quasi-sliding mode domain is defined as

[0160]

[0161] Assume that the initial value ρ(0) of the second-order sliding mode function does not exist in the bandwidth, that is, Then, from formula (38) we can deduce

[0162]

[0163] Assume that ρ(k) never enters the quasi-sliding mode region Θ and When k→∞, it can be deduced from formula (44)

[0164]

[0165] From formula (45), we can see that is convergent. According to the Cauchy array convergence criterion, when k→∞, λ s -(Δd(i)-2Δd(i-1)+Δd(i-2)) converges to zero, that is

[0166]

[0167] Equation (46) conflicts with equation (32). Therefore, the assumption that ρ(k) never enters the quasi-sliding mode region Θ is incorrect.

[0168] When the initial value is , similar conclusions can be obtained.

[0169] Therefore, the second-order sliding mode function ρ(k) enters the quasi-sliding mode domain within a finite number of steps (M) and can be calculated as follows:

[0170]

[0171] where the operator [·] gives an integer less than or equal to ρ(0).

[0172] 3) Prove that ρ(k) remains in the quasi-sliding mode domain after M steps

[0173] When ρ(M) is positive in the quasi-sliding region, that is,

[0174]

[0175] Knowable

[0176]

[0177] From formula (38) and formula (49), we can deduce

[0178] ρ(M+1)-ρ(M)=(Δd(M)-2Δd(M-1)+Δd(M-2))-λ s (50)

[0179] Considering formula (32) as well as formulas (49) and (50), the following relationship is obtained:

[0180]

[0181] Formula (51) shows that ρ(M+1)∈Θ.

[0182] When ρ(M) is a negative value in the quasi-sliding domain, that is,

[0183] The same conclusion as formula (51) can be obtained. Therefore, it can be seen that for any positive integer N, there exists ρ(M+1)∈Θ.

[0184] The effectiveness of the proposed control scheme is verified through simulation experiments. The brushless DC motor uses a separately excited DC motor with a rated value of 0.735KW, 220V and 550r / min. The DC brush motor discrete difference model shown in formula (5) is used in the simulation experiment, and the physical parameters are J = 0.068Kg·m 2 , K=3.475N·m·A -1 , R=7.56Ω, L=0.055H, A=0.03475N·m·s, λ=0.0039MΩ·m·s 2 .

[0185] It should be noted here that the mathematical model parameters given are only used to generate input and output data in the simulation and have nothing to do with the controller design process. Considering the existence of external disturbances, the disturbance d(k) = 0.1ω(k) is added to formula (5).

[0186] The desired angular velocity of the brushless DC motor is set as two types: curve and step signal.

[0187] 1) The desired angular velocity is set as a curve

[0188]

[0189] The sampling time T is taken as 0.01s.

[0190] The initial values ​​of input and output in the simulation are set to u(1)=u(2)=0, ω(1)=ω(2)=0, The adjustable parameters of the pseudo partial derivative estimation algorithm are set to η = μ = 1. The parameters of the proposed control method are set to λ = 0.01, β = 0.7, α = 1 / 9, λ s =0.002, δ=3.

[0191] 2) The expected angular velocity is set as a step signal

[0192]

[0193] During the simulation, the initial value settings, the adjustable parameters of the pseudo partial derivative estimation algorithm, and the controller parameters are the same as those when the expected angular velocity is a curve.

[0194] from Figure 2 It can be clearly seen that when the angular velocity desired signal is a curve, the proposed method can quickly track the given angular velocity and obtain better control performance. The control input and pseudo partial derivative parameter update process corresponding to the proposed control method are shown in Figure 3 and Figure 4 As shown. Figure 5 It can be seen that when the expected signal is a step signal, the proposed method can track the changing angular velocity step signal well, and when the amplitude of the step signal changes, the output response has almost no overshoot. Figure 6 and Figure 7 The control input and pseudo partial derivative updating processes are given respectively when the expected signal is a step signal.

[0195] The whole design process focuses on the simplicity, stability and fast and accurate angular velocity tracking of the DC brush motor controller design. For the problem under consideration, the discrete differential mathematical model of the DC brush motor is first determined; the data-driven model of the DC brush motor is given; the disturbance estimation method is given in particular; the estimation method of the pseudo-partial derivative in the data model is given; a second-order discrete integral terminal sliding mode controller based on the data-driven model is designed; the stability of the designed controller is analyzed; simulation experiments and parameter adjustments are given. After the above steps, the design is completed and the control of the DC brush motor is completed.

[0196] In the presence of external disturbances, this embodiment estimates the unknown disturbance of the system online through a disturbance estimation algorithm; by adjusting the controller parameters, it can quickly and stably track the given speed of the DC brush motor; it is only related to the online measurement data of the control system and does not require an accurate mathematical model of the DC brush motor.

[0197] The above description is only a preferred embodiment of the present disclosure and is not intended to limit the present disclosure. For those skilled in the art, the present disclosure may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present disclosure shall be included in the protection scope of the present disclosure.

Claims

1. A DC brushed motor control method based on data-driven second-order integral terminal sliding mode, characterized in that: include: Get the dynamic model of the brushed DC motor; constructing discrete time equations of the acquired kinetic model; calculating a perturbation estimate error of the discrete time equation; Calculating a pseudo partial derivative parameter estimation error based on the disturbance estimation error; According to the obtained discrete time equation, disturbance estimation error and pseudo partial derivative parameter estimation error, a second-order discrete integral terminal sliding mode control function of the brushed DC motor is constructed. Analyze the stability of the control function to achieve control of the brushed DC motor; The discrete time equation of the brushed DC motor is: ω(k+1)=f(ω(k),ω(k-1),ω(kn y ),u(k),u(k-1),…,u(kn u ))+d(k), where ω(k+1) represents the angular velocity of the brushed DC motor at time k+1, u(k) represents the input voltage of the brushed DC motor at time k; d(k) represents the disturbance or unmodeled dynamics, n y and n u All represent the unknown order of the system, and f(·) represents the unknown nonlinear function; The angular velocity of the DC motor at time k+1 without considering system disturbances or modeling dynamics is: oh m (k+1)=ω(k+1)-d(k)=f(ω(k),ω(k-1),ω(kn y ),u(k),u(k-1),…,u(kn u )) and ω(k+1)=ω m (k+1)+d(k); The output angular velocity tracking error e(k) of the DC brushed motor is: e(k)=ω(k)-ω r (k), where ω(k) is the system output angular velocity, ω r (k) is the expected output angular velocity; the discrete integral terminal sliding mode function s(k) is: s(k) = e(k) + λE(k-1), where λ>0, and the integral error term is expressed as: Wherein, α represents the ratio of two odd integers, 0<α<1; the second-order discrete integral terminal sliding mode control function ρ(k) of the brushed DC motor is: ρ(k)=s(k)+βs(k-1), where 0≤β≤1, when β=0, ρ(k) represents the traditional first-order discrete integral terminal sliding mode function; using the discrete reaching law ρ(k+1)=0, we get s(k+1)=-βs(k), ω(k+1)-ω r (k+1)+λE(k)=-βs(k) 2. A DC brushed motor control method based on data driven second-order integral terminal sliding mode as described in claim 1, characterized in that: The obtained dynamic model of the brushed DC motor includes the terminal voltage u(t) and armature current i a (t) and load torque T L (t); that is T L (t)=λω 2 (t)sign(ω(t)) Where K represents the torque and back EMF constant, R is the armature resistance, L is the armature inductance, J is the rotor moment of inertia, A is the damping constant, λ is the switching gain constant, and ω(t) is the rotor angular velocity.

3. A DC brushed motor control method based on data driven second-order integral terminal sliding mode as described in claim 2, characterized in that: The terminal voltage u(t) and armature current i of the brushed DC motor are obtained. a (t) Merge, Take the sampling time as T, approximate the first-order derivative and the second-order derivative with the first-order difference and the second-order difference respectively, and construct the discrete time difference equation of the DC brushed motor, that is, ω(k+1)=α1ω(k)+α2ω(k-1)+α3sign(ω(k))ω 2 (k)+α4sign(ω(k-1))ω 2 (k-1)+α5u(k) in, 4. A DC brushed motor control method based on data driven second-order integral terminal sliding mode as claimed in claim 1, characterized in that: Δu(k) = u(k) - u(k - 1). When |Δu(k)| ≠ 0, there exists a pseudo partial derivative φ(k) such that Δω m (k + 1) = φ(k)Δu(k), where |φ(k)| ≤ b, and b represents a positive constant. Δω m (k + 1) = ω m (k + 1) - ω m (k), thus obtaining ω m (k + 1) = ω m (k) + φ(k)Δu(k), Δω(k + 1) = Δω m (k + 1) + Δd(k), Δd(k) = d(k) - d(k - 1), ω(k + 1) = ω(k) + φ(k)Δu(k) + Δd(k).

5. A DC brushed motor control method based on data driven second-order integral terminal sliding mode as claimed in claim 4, characterized in that: The delay estimation error is obtained according to ω(k+1)=ω(k)+φ(k)Δu(k)+Δd(k) for The disturbance estimation error of the discrete time equation is obtained based on the obtained delay estimation error for That is 6. A DC brushed motor control method based on data driven second order integral terminal sliding mode as claimed in claim 1, characterized in that: Consider the quadratic index function In the best conditions Next, get Or |Δu(k-1)|≤ε, Among them, u>0; η∈(0,1]; ε represents a positive constant, for The initial value of Available where δ(k) represents the pseudo-partial derivative parameter estimation error, and 7. A DC brushed motor control method based on data driven second order integral terminal sliding mode as claimed in claim 1, characterized in that: Assume the disturbance estimation error That is, equivalent control Δu eq (k) Consider Δu eq (k) Robustness of the switching controller Δu sw (k) is: Δu sw (k) = Δu sw (k-1)-λ s sign(ρ(k)); where λ s >0 indicates the switching control gain, sign(·) indicates the sign function; that is, the overall control law Δu(k) is: Δu(k)=Δu eq (k)+Δu sw (k), i.e.

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