A sliding mode control method for permanent magnet synchronous motors based on finite-time disturbance observers

Abstract

This invention belongs to the field of permanent magnet synchronous motor (PMSM) trajectory tracking technology, and relates to a sliding mode control method for PMSM based on a finite-time disturbance observer (FTDO). The method includes the following steps: establishing a mathematical model of the PMSM, converting it into a state equation form, and initializing the system state; proposing an improved non-singular terminal sliding mode finite-time disturbance observer (FTDO) control method, where FTDO is used to estimate unknown uncertainties and provide feedforward compensation; and proposing a novel fast sliding mode reaching law, which reduces the time required to reach the sliding surface when the control signal exhibits chattering; then, incorporating FTDO into the improved sliding manifold, proposing a finite-time non-singular terminal sliding mode (FTDO-MNTSMC) method. This invention can both compensate for unknown uncertainties and achieve finite-time convergence. Lyapunov stability theory is used to guarantee the finite-time stability of the closed system under the control strategy.

Description

Technical fields:

[0001] This invention belongs to the field of sliding mode control technology for permanent magnet synchronous motors, specifically relating to a sliding mode control method for permanent magnet synchronous motors based on a finite-time disturbance observer. Background technology:

[0002] In recent years, permanent magnet synchronous motors (PMSMs) have been widely used in industrial processes such as robotic arms, radar servo antennas, and electric vehicles due to their simplicity and efficiency. For the control of PMSMs, traditional PID control has the advantage of relatively simple structure; however, due to the nonlinearity in servo systems, PID control cannot achieve satisfactory control performance. Modern industrial production places higher demands on the control performance of PMSMs. Therefore, improving the control performance of PMSMs has become an urgent problem to be solved, leading to the emergence of various control methods, such as adaptive control, sliding mode control, and observer-based control. Furthermore, function approximation techniques such as neural networks and fuzzy logic systems have also attracted more attention in the control field. The above control schemes can improve tracking performance.

[0003] However, in practical industrial applications, permanent magnet synchronous motors also face unknown disturbances such as parameter uncertainties and external interference. SMC control technology, due to its robustness, has been widely used to address unknown disturbances. However, chattering is an inherent problem in SMCs due to the discontinuity of high-frequency switching terms. To overcome this problem, various improved sliding mode surfaces have been developed. For example, Chinese patent CN114389490A, based on this, designed a fixed-time SMC method for servo systems, achieving tracking control. For servo systems with unknown disturbances, for example, Chinese patent CN104201945B proposed a finite-time sliding mode controller, which allows the tracking error to converge to zero within a finite time. The system state can reach the sliding mode surface within a finite time, ensuring robustness. Based on this, continuous sliding mode reaching laws can be used to reduce system chattering. However, while continuous sliding mode reaching laws eliminate system chattering to a certain extent, they also reduce system performance.

[0004] Furthermore, these disturbances in permanent magnet synchronous motors (PMSMs) are difficult to measure or observe. Classical SMCs cannot suppress these unknown disturbances, potentially leading to a decline in control performance. To mitigate the impact of these disturbances, an effective method, such as the disturbance observer-based control technique employed in Chinese patent CN110492804A, is used. This involves estimating the unknown disturbance using a disturbance observer and compensating for it to reduce its impact. In recent years, some new disturbance observers, such as the extended state observer in Chinese patent CN104201941B, have also been developed for estimating unknown disturbances.

[0005] Existing technologies still have some problems, such as chattering and slow system convergence in sliding mode control of permanent magnet synchronous motors, and the need for the observer to satisfy the prior condition that the derivative of the disturbance is bounded when estimating the disturbance. Summary of the Invention:

[0006] To overcome the aforementioned shortcomings of existing technologies, an improved non-singular terminal sliding mode control method with finite-time disturbance compensation is proposed to address the speed tracking problem of permanent magnet synchronous motors (PMSMs) with parameter uncertainties and external disturbances. To reduce system chattering and the arrival time of error variables at the sliding surface, a new reaching law is proposed, replacing the sign function with a hyperbolic tangent function. Considering unknown disturbances, such as parameter uncertainties and external disturbances, a finite-time disturbance observer (FTDO) is constructed to estimate them. This FTDO does not require prior knowledge of whether the lumped total disturbance satisfies the given conditions. Combining the FTDO estimation and the proposed novel sliding surface, a non-singular terminal sliding mode control scheme based on FTDO is proposed. Therefore, under finite-time convergence, the tracking error is guaranteed, and the interference immunity of the PMSM is improved by incorporating the FTDO output into the controller for disturbance compensation.

[0007] To achieve the above objectives, the present invention provides a sliding mode control method for permanent magnet synchronous motors based on a finite-time disturbance observer, comprising the following steps:

[0008] S1. Establish the mathematical model of the permanent magnet synchronous motor, transform it into state equation form, and initialize the system state. The process is as follows:

[0009] The mathematical model of the S1.1 permanent magnet synchronous motor can be described in the following form:

[0010]

[0011] In the formula i d and i q These are the stator currents along the d-axis and q-axis, respectively; u d and u q d and q are the stator voltages, respectively; L is the stator inductance; R is the stator resistance; n p It is the number of magnetic poles; ψ f ω is the rotor flux linkage; ω is the angular velocity; B is the coefficient of viscous friction; J is the torque and moment of inertia; K t It is the torque constant; T L It is the load torque;

[0012] Generally, the d-axis current is i d =0,T e =K t i q and K t =1.5np ψ f Then we can obtain the following formula:

[0013]

[0014] S1.2 Selecting state variables to transform the mathematical model of the permanent magnet synchronous motor into state equation form:

[0015]

[0016] Selecting state variables Where a = -B / J, b = K t / J, d = -T L / J and u=i q Considering the uncertainty of the parameters, formula (3) can be rewritten as:

[0017]

[0018] Where a0, b0 and d0 are the nominal values ​​of a, b and d; Δa0, Δb0 and Δd0 are the uncertainties of the parameters, respectively;

[0019] This represents aggregate uncertainty;

[0020] S2. Design an improved sliding mode convergence rate and finite-time perturbation observer.

[0021] S2.1 Design Improvement Approach Law

[0022] Define the tracking error e1 and its derivative e2.

[0023]

[0024] Where x d For the desired trajectory, The derivative of the desired trajectory

[0025] The traditional non-singular terminal sliding mode function is defined as follows:

[0026]

[0027] Where λ1 is a positive constant, p and q are odd numbers, and 1

[0028]

[0029] Its convergence rate Where k1 and β1 are positive constants, for the traditional sliding mode approach rate, the tracking error converges to zero in a finite time; when ​When the time to reach the sliding surface increases, the problem is solved. To address this issue, this invention proposes a finite-time perturbation observer to estimate lumped uncertainty and a novel sliding surface reaching law to enable the state to reach the sliding surface more quickly.

[0030] For traditional non-singular terminal sliding mode functions, a new reaching law is designed as follows:

[0031]

[0032] in The hyperbolic tangent function, where e is the base of the natural logarithm; f(e1,s) denotes the tendency function, defined as:

[0033]

[0034] Where χ1>0, χ2>0, η>0, 0<μ<1, are all constants; As shown in (9), when |s| increases, the system trajectory will move away from the sliding surface, and the system trajectory reaches the sliding surface based on f(e1,s)tanh(s) and χ2s; conversely, if |s| decreases, the χ2s term gradually approaches 0; the variable term f(e1,s) converges to χ1|e1|, where the system trajectory e1 gradually decreases to zero under the sliding control law. Therefore, when the system state reaches the sliding surface, f(e1,s) gradually converges to a smaller value to suppress chattering; thus, compared with the conventional sliding surface, the proposed improved sliding surface can both suppress chattering and shorten the approximation time.

[0035] To demonstrate the convergence of the designed reaching law, three reaching laws were compared: the traditional sliding mode SMC rate, the traditional non-singular terminal sliding mode NTSMC rate, and the improved non-singular terminal sliding mode MNTSMC rate of this invention; reference signal x d = sin(t); When k1 = 5, the SMC reaching law NTSMC Approach Law k1 = 5, β1 = 2.4; MNTSMC reaching law Where χ1=5, χ2=30, μ=2.4, η=0.01; simulation results are as follows: Figure 2 This indicates that the improved approach law achieves faster tracking performance and reduces system chattering compared to the traditional sliding mode SMC rate and the traditional non-singular terminal sliding mode NTSMC.

[0036] S2.2 Design a Finite-Time Perturbation Observer (FTDO). The specific steps are as follows:

[0037] A novel finite-time perturbation observer is proposed to estimate lumped uncertainty; by defining z1 = e1, z2 = e2, Error dynamics can be written as

[0038]

[0039] In order to estimate the unknown lumped uncertainty Design a finite-time perturbation observer for

[0040]

[0041] Where ω i i = 1, 2, 3, κ i,j ,i=1,2,3,j=1,2,3ω i and κ i,j All are positive numbers;

[0042] Error formula ε i i = 1, 2, 3 are defined as

[0043]

[0044] According to the finite-time lemma, the estimation error ε i The expression i = 1, 2, 3 converges in finite time (FT).

[0045] Compared to traditional high-order sliding mode observers, the finite-time perturbation observer proposed in this invention does not require knowledge of z. i The upper bound of the Lipschitz constant of the input signal derivative; furthermore, the proposed perturbation observer. It can accurately estimate the unknown state z in a finite time interval, even in the presence of bounded noise. i ;

[0046] S3. Design an FTDO-MNTSMC controller based on FTDO, and analyze its stability using Lyapunov functions; the specific design steps are as follows:

[0047] S3.1 Design of an Improved Non-Singular Terminal Sliding Mode Based on FTDO

[0048] Based on FTDO, an improved sliding surface was designed:

[0049]

[0050] Its derivative is:

[0051]

[0052] Therefore, the control law u is designed as follows:

[0053]

[0054] Substituting formula (15) into (14), we have

[0055]

[0056] S3.2 Choose the Lyapunov function and prove the system stability.

[0057] Choose a Lyapunov function as follows:

[0058]

[0059] The time derivative with respect to V2 is:

[0060]

[0061] in From equation (18), we can obtain Λ1>0 and Λ2>0. There exist constants γ1 and γ2, where γ1>Λ1 and γ2>Λ2. Therefore, the following inequality holds:

[0062]

[0063] Therefore, based on the finite-time stability theory, the finite time for the control error e1 to arrive is...

[0064] The control method described in this invention follows this process: First, a mathematical model of the permanent magnet synchronous motor (PMSM) is established and transformed into a state equation form to initialize the system state. Then, for PMSMs with unknown uncertainties such as system uncertainties and disturbances, an improved non-singular terminal sliding mode finite-time disturbance observer (FTDO) control method is proposed. In the control design, FTDO is used to estimate unknown uncertainties and provide feedforward compensation. A novel fast sliding mode reaching law is also proposed, reducing the time required to reach the sliding surface when chattering occurs in the control signal. Finally, FTDO is added to the improved sliding manifold to propose a finite-time non-singular terminal sliding mode (FTDO-MNTSMC) method. This invention can both compensate for unknown uncertainties and achieve finite-time convergence. Lyapunov stability theory is used to guarantee the finite-time stability of the closed system under the control strategy.

[0065] Compared with existing technologies, this invention proposes a novel fast anti-disturbance sliding mode control method combining a reaching law and FTDO for permanent magnet synchronous motors with unknown disturbances. An improved sliding surface based on a hyperbolic tangent function is introduced into the reaching law, effectively suppressing chattering and shortening the convergence time. For the MNTSMC-based speed controller, a feedback-compensated FTDO is designed, effectively suppressing unknown disturbances and improving control performance. Comparative results show that the proposed improved non-singular terminal sliding mode control FTDO-MNTSMC based on a finite-time disturbance observer exhibits better transient response and steady-state performance than PI control, the traditional non-singular terminal sliding mode control NTMSC, and MNTSMC using only the improved non-singular terminal sliding mode control. Attached image description:

[0066] Figure 1 This is a schematic diagram illustrating the technological principle of the sliding mode control method for permanent magnet synchronous motors based on a finite-time disturbance observer, which is involved in this invention.

[0067] Figure 2 This is a schematic diagram showing the comparative simulation results of the reaching laws of different sliding surfaces involved in this invention.

[0068] Figure 3 This is a schematic diagram comparing the speed response simulation results of the four controllers involved in this invention under a desired trajectory of ω = 200 r / min under normal load disturbance.

[0069] Figure 4 This is a schematic diagram comparing the speed response simulation results of the four controllers involved in this invention under a desired trajectory of ω = 500 r / min under normal load.

[0070] Figure 5 This is a schematic diagram comparing the simulation results of the speed response of the four controllers involved in this invention under a desired trajectory of ω = 800 r / min under normal load disturbance.

[0071] Figure 6 This is a schematic diagram comparing the simulation results of the speed response of the four controllers involved in this invention under the desired trajectory of ω = 200 r / min under varying load disturbance.

[0072] Figure 7 This is a schematic diagram comparing the speed response simulation results of the four controllers involved in this invention under a desired trajectory of ω = 500 r / min during variable load disturbance.

[0073] Figure 8 This is a schematic diagram showing the comparison of the speed response simulation effects of the four controllers involved in this invention under the desired trajectory of ω = 800 r / min during variable load disturbance.

[0074] Figure 9This is a schematic diagram illustrating the simulation effect of the finite-time perturbation observer involved in this invention.

[0075] Figure 10 This is a diagram of the experimental apparatus for the servo mechanism involved in this invention.

[0076] Figure 11 This is a schematic diagram showing the experimental comparison of the speed response of the four controllers involved in this invention under a desired trajectory of ω = 200 r / min under normal load disturbance.

[0077] Figure 12 This is a schematic diagram showing the experimental comparison of the speed response of the four controllers involved in this invention under a desired trajectory of ω = 500 r / min under normal load disturbance.

[0078] Figure 13 This is a schematic diagram showing the experimental comparison of the speed response of the four controllers involved in this invention under a desired trajectory of ω = 800 r / min under normal load disturbance.

[0079] Figure 14 This is a schematic diagram showing the experimental comparison of the velocity response of the four controllers involved in this invention under the desired trajectory of ω = 200 r / min under varying load disturbance.

[0080] Figure 15 This is a schematic diagram showing the experimental comparison of the velocity response of the four controllers involved in this invention under a desired trajectory of ω = 500 r / min under varying load disturbance.

[0081] Figure 16 This is a schematic diagram showing the experimental comparison of the velocity response of the four controllers involved in this invention under a desired trajectory of ω = 800 r / min under varying load disturbance.

[0082] Figure 17 This is a schematic diagram illustrating the experimental results of the finite-time perturbation observer involved in this invention. Detailed implementation method:

[0083] The present invention will be further described below with reference to specific embodiments and accompanying drawings.

[0084] Example 1:

[0085] S1. Establish the mathematical model of the permanent magnet synchronous motor, transform it into state equation form, and initialize the system state. The process is as follows:

[0086] The mathematical model of the S1.1 permanent magnet synchronous motor can be described in the following form:

[0087]

[0088] In the formula i d and i qThese are the stator currents along the d-axis and q-axis, respectively; u d and u q d and q are the stator voltages, respectively; L is the stator inductance; R is the stator resistance; n p It is the number of magnetic poles; ψ f ω is the rotor flux linkage; ω is the angular velocity; B is the coefficient of viscous friction; J is the torque and moment of inertia; K t It is the torque constant; T L It is the load torque.

[0089] Generally, the d-axis current is i d =0,T e =K t i q and K t =1.5n p ψ f Then we can obtain the following formula:

[0090]

[0091] S1.2 Selecting state variables to transform the mathematical model of the permanent magnet synchronous motor into state equation form:

[0092]

[0093] Selecting state variables Where a = -B / J, b = K t / J, d = -T L / J and u=i q Considering the uncertainty of the parameters, formula (3) can be rewritten as:

[0094]

[0095] Where a0, b0 and d0 are the nominal values ​​of a, b and d; Δa0, Δb0 and Δd0 are the uncertainties of the parameters, respectively;

[0096] This represents aggregate uncertainty;

[0097] S2. Design an improved sliding mode convergence rate and finite-time perturbation observer.

[0098] S2.1 Design Improvement Approach Law

[0099] Define the tracking error e1 and its derivative e2.

[0100]

[0101] Where x d For the desired trajectory, The derivative of the desired trajectory

[0102] The traditional non-singular terminal sliding mode function is defined as follows:

[0103]

[0104] Where λ1 is a positive constant, p and q are odd numbers, and 1

[0105]

[0106] Its convergence rate Where k1 and β1 are positive constants, for the traditional sliding mode approach rate, the tracking error converges to zero in a finite time; when When the time to reach the sliding surface increases, in order to solve the above problem, this invention proposes a finite-time perturbation observer to estimate the lumped uncertainty and proposes a new sliding surface reaching law to enable the state to reach the sliding surface faster.

[0107] The new convergence law is designed as follows:

[0108]

[0109] in The hyperbolic tangent function, where e is the base of the natural logarithm; f(e1,s) denotes the tendency function, defined as:

[0110]

[0111] Where χ1>0, χ2>0, η>0, and 0<μ<1 are all constants. As shown in (9), when |s| increases, the system trajectory will move away from the sliding surface, and the system trajectory reaches the sliding surface based on f(e1,s)tanh(s) and χ2s; conversely, if |s| decreases, the χ2s term gradually approaches 0; the variable term f(e1,s) converges to χ1|e1|, where the system trajectory e1 gradually decreases to zero under the sliding control law. Therefore, when the system state reaches the sliding surface, f(e1,s) gradually converges to a smaller value to suppress chattering; thus, compared with the conventional sliding surface, the proposed improved sliding surface can both suppress chattering and shorten the approximation time.

[0112] To demonstrate the convergence of the designed reaching law, three reaching laws were compared: the traditional sliding mode SMC rate, the traditional non-singular terminal sliding mode NTSMC rate, and the improved non-singular terminal sliding mode MNTSMC rate of this invention; reference signal x d = sin(t); When k1 = 5, the SMC reaching law NTSMC Approach Law k1 = 5, β1 = 2.4; MNTSMC reaching law ​Where χ1=5, χ2=30, μ=2.4, η=0.01; simulation results are as follows: Figure 2 This indicates that the improved approach law achieves faster tracking performance and reduces system chattering compared to the traditional sliding mode SMC rate and the traditional non-singular terminal sliding mode NTSMC.

[0113] S2.2 Design a Finite-Time Perturbation Observer (FTDO). The specific steps are as follows:

[0114] A novel finite-time perturbation observer is proposed to estimate lumped uncertainty; by defining z1 = e1, z2 = e2, Error dynamics can be written as

[0115]

[0116] In order to estimate the unknown lumped uncertainty Design a finite-time perturbation observer for

[0117]

[0118] Where ω i i = 1, 2, 3, κ i,j ,i=1,2,3,j=1,2,3ω i and κ i,j All are positive numbers;

[0119] Error formula ε i i = 1, 2, 3 are defined as

[0120]

[0121] According to the finite-time lemma, the estimation error ε i The expression i = 1, 2, 3 converges in finite time (FT).

[0122] Compared to traditional high-order sliding mode observers, the finite-time perturbation observer proposed in this invention does not require knowledge of z. i The upper bound of the Lipschitz constant of the input signal derivative; furthermore, the proposed perturbation observer. Accurate estimation of the unknown state z in a finite time interval, even in the presence of bounded noise. i .

[0123] S3. Design an FTDO-MNTSMC controller based on FTDO, and analyze its stability using Lyapunov functions; the specific design steps are as follows:

[0124] S3.1 Design of an Improved Non-Singular Terminal Sliding Mode Based on FTDO

[0125] Based on FTDO, an improved sliding surface was designed:

[0126]

[0127] Its derivative is:

[0128]

[0129] Therefore, the control law u is designed as follows:

[0130]

[0131] Substituting formula (15) into (14), we have

[0132]

[0133] S3.2 Choose the Lyapunov function and prove the system stability.

[0134] Choose a Lyapunov function as follows:

[0135]

[0136] The time derivative with respect to V2 is:

[0137]

[0138] in From equation (18), we can obtain Λ1>0 and Λ2>0. There exist constants γ1 and γ2, where γ1>Λ1 and γ2>Λ2. Therefore, the following inequality holds:

[0139]

[0140] Therefore, based on the finite-time stability theory, the finite time for the control error e1 to arrive is...

[0141] The finite-time lemma and finite-time stability theory involved in this example are both existing technologies, namely:

[0142] Finite-time lemma: Consider the following nonlinear system

[0143]

[0144] in Given a continuous, differentiable input signal; m1, m2, and n are positive constants, and θ is a variable; then, the following inequalities hold true in finite time.

[0145]

[0146] Where δ is a positive constant; the proof of the finite-time lemma is in Appendix A;

[0147] Appendix A: For nonlinear systems

[0148]

[0149] Choose a Lyapunov function as

[0150]

[0151] The following equation can be obtained:

[0152]

[0153] Where log is a logarithmic function; take the derivative of V3:

[0154]

[0155] The system is stable in finite time. Note that |dtanh(θ) / dθ|=1-tanh 2 (θ), then we get

[0156]

[0157] In addition, it can be obtained

[0158] in

[0159] Finite-time stability theory:

[0160] For a given sliding surface s, the following inequalities hold:

[0161] s tanh(s)=|stanh(s)|=|s||tanh(s)|≥0 (28)

[0162] Consider the system, design a controller and a finite-time observer, and ensure that the control error e1 converges to a small region within a finite time.

[0163] Compared with existing technologies, this invention proposes a novel fast anti-disturbance sliding mode control method combining a reaching law and FTDO for permanent magnet synchronous motors with unknown disturbances. An improved sliding surface based on a hyperbolic tangent function is introduced into the reaching law, effectively suppressing chattering and shortening the convergence time. For the MNTSMC-based speed controller, a feedback-compensated FTDO is designed, effectively suppressing unknown disturbances and improving control performance. Comparative results show that the proposed improved non-singular terminal sliding mode control FTDO-MNTSMC based on a finite-time disturbance observer exhibits better transient response and steady-state performance than PI control, the traditional non-singular terminal sliding mode control NTMSC, and MNTSMC using only the improved non-singular terminal sliding mode control.

[0164] Example 2:

[0165] To verify the effectiveness of the control method proposed in Example 1, this embodiment uses a permanent magnet synchronous motor module in MATLAB for simulation. The parameters of the permanent magnet synchronous motor are shown in Table 1.

[0166] Table 1. Parameter data of permanent magnet synchronous motor

[0167]

[0168]

[0169] This paper compares the traditional non-singular terminal sliding mode (NTSMC), the improved non-singular terminal sliding mode (MNTSMC), and the widely used PI control method with the improved non-singular terminal sliding mode control (FTDO-MNTSMC) based on a finite-time perturbation observer. The PI control gain is selected as kp = 15, ki = 900. The parameters of the traditional non-singular terminal sliding mode (NTSMC) are defined as λ1 = 0.0004, k1 = 55, β1 = 20; the parameters of the improved non-singular terminal sliding mode control (FTDO-MNTSMC) based on a finite-time perturbation observer are λ1 = 0.0004, χ1 = 21, q = 5, p = 3, μ = 0.45, η = 0.5. The parameters of the finite-time perturbation observer (FTDO) are selected as ω1 = 0.018, ω2 = 0.015, ω3 = 0.015, κ... 11 =20,κ 12 =20,κ 21 =25,κ 22 =26,κ 31 =14κ 32 =2.5.

[0170] Figure 3-5Simulation results are presented for the speed tracking performance, tracking error, and control input of different controllers at startup speeds of 200 r / min, 500 r / min, and 800 r / min, with a load torque TL = 3 N·m. These results demonstrate that the developed FTDO-MNTSMC control method achieves faster response and better control input. In other words, the proposed FTDO-MNTSMC control method can compensate for unknown disturbances by using FTDO, thereby achieving satisfactory tracking performance.

[0171] To further verify the control performance of the proposed method, four controllers were compared under varying load conditions. Figure 6-8 The description describes the applied torque T at rotational speeds of 200 r / min, 500 r / min, and 800 r / min, with a time interval of t=3s. L =3 N·m to T L The response to a loading torque of 9 N·m. From Figure 6-8 It can be seen that the proposed FTDO-MNTSMC method also exhibits good control performance, indicating that the FTDO-MNTSMC method has better anti-interference performance than the PI, NTSMC, and MNTSMC methods. Among these controllers, the tracking error of the PI controller is larger than that of the other three controllers. Therefore, the PI control method has the worst anti-interference capability. Figure 9 It is evident that FTDO can accurately estimate unknown disturbances.

[0172] Example 3:

[0173] This embodiment verifies the control performance of the FTDO-MNTSMC controller designed in Embodiment 1 using an experimental setup, with a permanent magnet synchronous motor drive system as the test bench (e.g., ...). Figure 10 (As shown). This experimental setup consists of a 130MB150A non-salient pole permanent magnet synchronous motor connected to a load motor and an IGBT-based power converter. The control algorithm is implemented in LINKS-RT, with a sampling frequency of 10kHz. The phase current is measured by a Hall effect device and converted into a digital signal, and the rotor position is measured using an encoder. In the experiment, the moment of inertia of the load can be adjusted by increasing the load component.

[0174] To evaluate the tracking accuracy of the proposed method, experiments were conducted on a permanent magnet synchronous motor under normal load (TL = 2 N·m). The accuracy was compared with that of the designed controller FTDO-MNTSMC using PI, NTSMC, and MNTSMC. The control parameters were the same as in Example 2. Figure 11-13 The speed response curves, tracking error, and control law u are shown for speeds of 200 r / min, 500 r / min, and 800 r / min, respectively. Figure 11-13As can be seen, compared with the other three control methods, the FTDO-MNTSMC control method of the present invention provides satisfactory tracking accuracy and control input. Figure 14-16 Comparative experimental results for load abrupt changes at speeds of 200 r / min, 500 r / min, and 800 r / min are presented, including the output speed, tracking error, and control input of different controllers. Figure 14-16 As can be seen from this, when the load torque changes from T... L =0 N·m increased to T L At a torque of 3 N·m, speed tracking and control input exhibit fluctuations. However, the proposed FTDO-MNTSMC scheme demonstrates superior control performance compared to the PI, NTSMC, and MNTSMC methods. The controller designed in this invention produces smaller waveforms of speed and control signals compared to the other three control methods when the load torque changes. A comparison of NTSMC and MNTSMC shows that MNTSMC's control performance is superior to NTSMC because an improved approaching rate is incorporated into the controller design, reducing chattering. A comparison of MNTSMC and the FTDO-MNTSMC method shows that the proposed FTDO-MNTSMC control performance is superior to MNTSMC at different speeds. Therefore, the developed FTDO-MNTSMC scheme outperforms the PI, NTSMC, and MNTSMC methods in terms of load torque variation. Figure 17 The FTDO designed in this paper estimates unknown disturbances. It is evident that FTDO can accurately estimate unknown disturbances.

[0175] According to the control method proposed in this invention, the observed values ​​are incorporated into the control law u. The experimental results show that, compared with PI, NTSMC, and MNTSMC, the control method designed in this invention achieves better control performance in both velocity tracking and disturbance compensation. Furthermore, the FTDO-MNTSMC method developed in this invention has certain advantages over the other three control methods in terms of transient response and robustness to unknown disturbances.

Claims

1. A sliding mode control method for a permanent magnet synchronous motor based on a finite-time disturbance observer, characterized in that, Includes the following steps: S1. Establish the mathematical model of the permanent magnet synchronous motor, transform it into state equation form, and initialize the system state. The process is as follows: The mathematical model of the S1.1 permanent magnet synchronous motor can be described in the following form: In the formula i d and i q These are the stator currents along the d-axis and q-axis, respectively; u d and u q d and q are the stator voltages, respectively; L is the stator inductance; R is the stator resistance; n p It refers to the number of magnetic poles; ψ f ω is the rotor flux linkage; ω is the angular velocity; B is the coefficient of viscous friction; J is the moment of inertia; K t It is the torque constant; T L It is the load torque; Generally, the d-axis current is i d =0,T e =K t i q and K t =1.5n p ψ f Then we can obtain the following formula: S1.2 Selecting state variables to transform the mathematical model of the permanent magnet synchronous motor into state equation form: Selecting state variables Where a = -B / J, b = K t / J, d = -T L / J and u=i q Considering the uncertainty of the parameters, formula (3) is rewritten as: Where a0, b0, and d0 are the nominal values ​​of a, b, and d; Δa0, Δb0, and Δd0 are the uncertainties of the parameters, respectively. This represents aggregate uncertainty; S2. Design an improved sliding mode convergence rate and finite-time perturbation observer. S2.1 Design Improvement Approach Law Define the tracking error e1 and its derivative e2. Where x d For the desired trajectory, The derivative of the desired trajectory; The traditional non-singular terminal sliding mode function is defined as follows: Where λ1 is a positive constant, p and q are odd numbers, and 1 is a positive constant. For traditional non-singular terminal sliding mode functions, a new reaching law is designed as follows: Its convergence rate Where k1 and β1 are positive constants, for the traditional sliding mode approach rate, the tracking error converges to zero in a finite time; when When the time to reach the sliding surface increases, in order to solve the above problem, this invention proposes a finite-time perturbation observer to estimate the lumped uncertainty and proposes a new sliding surface reaching law to enable the state to reach the sliding surface faster. S2.2 Design a finite-time perturbation observer (FTDO). The specific steps are as follows: in The hyperbolic tangent function, where e is the base of the natural logarithm; f(e1,s) denotes the tendency function, defined as: Where χ1>0, χ2>0, η>0, and 0<μ<1 are all constants. S3. Design an FTDO-MNTSMC controller based on FTDO and analyze its stability using Lyapunov functions; A novel finite-time perturbation observer is proposed to estimate lumped uncertainty; by defining z1 = e1, z2 = e2, Error dynamics can be written as In order to estimate the unknown lumped uncertainty Design a finite-time perturbation observer for Where ω i i = 1, 2, 3, κ i,j ,i=1,2,3,j=1,2,3ω i and κ i,j All are positive numbers; Error formula ε i i = 1, 2, 3 are defined as According to the finite-time lemma, the estimation error ε i The expression i = 1, 2, 3 converges in finite time. Compared to traditional high-order sliding mode observers, the finite-time perturbation observer proposed in this invention does not require knowledge of z. i The upper bound of the Lipschitz constant of the derivative of the input signal; Furthermore, the proposed perturbation observer It can accurately estimate the unknown state z in a finite time interval, even in the presence of bounded noise. i ; The specific design steps are as follows: S3.1 Design of an Improved Non-Singular Terminal Sliding Mode Based on FTDO Based on FTDO, an improved sliding surface was designed: Its derivative is: Therefore, the control law u is designed as follows: Substituting formula (15) into (14), we have S3.2 Choose the Lyapunov function and prove the system stability. Choose a Lyapunov function as follows: The time derivative with respect to V2 is: ​ in From equation (18), we can obtain Λ1>0 and Λ2>0; there exist constants γ1 and γ2, where γ1>Λ1 and γ2>Λ2; therefore, we have the following inequality: Therefore, based on the finite-time stability theory, the finite time for the control error e1 to arrive is...

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