Vienna rectifier control method and system based on double-layer adaptive super-helical sliding mode

Abstract

The present invention relates to a Vienna rectifier control method and system based on a double-layer adaptive super-spiral sliding mode. The method includes designing a double-layer adaptive super-spiral sliding mode controller based on a mathematical model of the Vienna rectifier and obtaining the system control rate of the double-layer adaptive super-spiral sliding mode controller; designing a PI controller based on the mathematical model of the Vienna rectifier; using the control rate obtained in the voltage outer loop based on the double-layer adaptive super-spiral sliding mode controller as the input of the current inner loop to obtain a voltage signal, and generating a PWM control signal based on the voltage signal to control the switching device of the Vienna rectifier, so that the DC output voltage of the Vienna rectifier tracks a given value. The present invention can not only solve the system chattering problem, but also ensure the robustness of the system and can quickly obtain a lower switching gain.

Description

Technical Field

[0001] The present invention relates to the field of electronic power conversion control, and more particularly to a Vienna rectifier control method and system based on a double-layer adaptive super-helical sliding mode. Background Art

[0002] Three-phase Vienna rectifiers are widely used in automotive charging modules due to their high efficiency and low harmonics. This enables them to achieve high conversion efficiency and power factor, thereby reducing energy loss and grid pollution. Furthermore, their compact design and excellent thermal management are suitable for space-constrained automotive applications. Their modular structure facilitates integration with other power electronics, meeting the high-performance charging system requirements of modern electric vehicles.

[0003] When designing a Vienna rectifier control system, not only must the DC bus voltage and AC side current be highly accurate and responsive, but the AC side current and DC bus voltage must also be robust to load disturbances, minimizing voltage and current amplitude variations and shortening the system's response time. Traditional control methods for Vienna rectifier systems employ PI controllers for both the voltage and current loops. This approach is simple and meets engineering requirements, leading to its widespread adoption. However, due to the strong coupling, nonlinearity, and multivariable nature of the Vienna rectifier, classical control theory can effectively control system performance under well-matched parameters. However, when system parameters change, the system's dynamic response and interference immunity deteriorate, resulting in large overshoots in the DC output voltage during dynamic operation and even system loss of control.

[0004] Because the real-time and robustness of PI controllers cannot meet current demands for high-quality AC power, some existing technologies employ nonlinear control strategies to improve rectifier system performance. Sliding-mode variable structure control is widely used due to its advantages, such as simple physical implementation and indifference to parameter variations. However, the switching terms in sliding-mode control systems can cause chattering, especially when operating at finite frequencies. This chattering can increase DC voltage overshoot at the rectifier output, increase regulation time, introduce static errors in the DC output voltage, and reduce energy transfer efficiency. Summary of the Invention

[0005] The technical problem to be solved by the present invention is that, in response to the above-mentioned defects of the prior art, a Vienna rectifier control method and system based on a double-layer adaptive super-spiral sliding mode is provided. The double-layer adaptive super-spiral sliding mode design can not only solve the system chattering problem, but also ensure the robustness of the system and quickly obtain a lower switching gain.

[0006] The technical solution adopted by the present invention to solve the technical problem is to construct a Vienna rectifier control method based on a double-layer adaptive super-helical sliding mode, comprising:

[0007] Step S1, designing a double-layer adaptive super-spiral sliding mode controller based on a mathematical model of a Vienna rectifier and obtaining a system control rate of the double-layer adaptive super-spiral sliding mode controller;

[0008] Step S2: designing a PI controller based on the mathematical model of the Vienna rectifier;

[0009] Step S3: Using the control rate obtained in the voltage outer loop based on the double-layer adaptive super-spiral sliding mode controller as the input of the current inner loop to obtain a voltage signal, and generating a PWM control signal based on the voltage signal to control the switching device of the Vienna rectifier, so that the DC output voltage of the Vienna rectifier tracks a given value.

[0010] In the Vienna rectifier control method based on double-layer adaptive super-helical sliding mode of the present invention, step S1 further includes:

[0011] Step S11, obtaining a mathematical model of the Vienna rectifier in a two-phase rotating coordinate system;

[0012] Step S12: defining a sliding mode surface based on the DC bus voltage error, and designing a sliding mode controller based on the mathematical model and the sliding mode surface;

[0013] S13. Design a super helical sliding mode controller based on the super helical algorithm and the sliding mode controller, introduce system uncertainty into the super helical sliding mode controller to design the double-layer adaptive super helical sliding mode controller and obtain the system control rate of the double-layer adaptive super helical sliding mode controller.

[0014] In the Vienna rectifier control method based on double-layer adaptive super-helical sliding mode of the present invention, step S11 further includes:

[0015] Step S111: The switching sequence of the switching devices of the Vienna rectifier is set to the switching function S j To express:

[0016]

[0017] Among them S j is the potential state of phases a, b, and c of the Vienna rectifier; i j is the current of phases a, b, and c, where j = a, b, c;

[0018] Step S112: Convert the mathematical model of the Vienna rectifier in the three-phase stationary coordinate system into the two-phase rotating coordinate system to obtain the mathematical model of the Vienna rectifier in the two-phase rotating coordinate system.

[0019]

[0020] in, V dc Indicates the DC bus voltage, S d and S q Represent the components of the potential state on the dq axis respectively; e d and e q They represent the components of the grid-side voltage on the dq axis, L represents the system input inductance, C represents the system capacitance, r represents the equivalent resistance, ω represents the grid angular frequency, and i d and i q Represents the component of the grid-side current on the dq axis, i dc Indicates the load current.

[0021] In the Vienna rectifier control method based on double-layer adaptive super-helical sliding mode of the present invention, step S12 further includes:

[0022] Step S121: define the DC bus voltage error as z=V dc -V dcref , where V dcref Indicates the reference value of DC bus voltage, V dc Indicates the DC bus voltage;

[0023] Step S122: define the sliding surface as Where k>0 is the integral gain;

[0024] Step S123: Derivative the sliding surface and select the Lyapunov candidate function And derive the Lyapunov candidate function V1 and substitute the derivative of the sliding surface to obtain:

[0025]

[0026] Indicates V dcref The derivative of represents the derivative of the Lyapunov candidate function V1, i d and i q Represents the component of the grid-side current on the dq axis, i dc represents the load current, and C represents the system capacitance;

[0027] Step S124: Perform voltage outer loop control of the Vienna rectifier based on the sliding mode controller to calculate the system control rate of the sliding mode controller:

[0028]

[0029] In the Vienna rectifier control method based on double-layer adaptive super-helical sliding mode of the present invention, step S13 further includes:

[0030] Step S131: Select the supercoil algorithm as:

[0031]

[0032] Where λ and η are switching term gains, and η>|d p |, sign(·) is the sign function, d p represents the lumped uncertainty of the system and d p (t)≤ρ, ρ is a positive constant, represents the derivative of the sliding surface s, represents the derivative of the supercoil factor μ;

[0033] Step S132: Design a switching control rate based on the superhelical algorithm:

[0034]

[0035] Step S133: Obtain the system control rate of the super-helical sliding mode controller based on the system control rate of the sliding mode controller and the switching control rate:

[0036]

[0037] Step S134: Introducing system uncertainty To reconstruct the supercoil algorithm:

[0038]

[0039] Where λ(t) and η(t) are the changes of switching term gain over time; s(t) represents the change of sliding surface over time; represents the uncertainty term in the super-helical sliding mode control law; L s (t) represents the time-varying gain and satisfies L s (t)>l s0 > 0, satisfying the bounded and differentiable constraints, Indicates L s The derivative of (t);

[0040] Step S135. Obtain the reconstructed system control law of the hyperbolic sliding mode controller based on the reconstructed hyperbolic algorithm:

[0041]

[0042] Step S136. Design the system control law of the double - layer adaptive hyperbolic sliding mode controller as:

[0043]

[0044] where and are the estimated values of the switching - term gains λ and η, is the estimated value of the time - varying gain L s (t).

[0045] In the control method of the Vienna rectifier based on the double - layer adaptive hyperbolic sliding mode of the present invention, step S136 further includes:

[0046] Step S1361. Define the equivalent value of the uncertainty term f(t) in the hyperbolic sliding mode control law:

[0047]

[0048] sign(s)| eq represents the average value of the switching term that maintains the control system state in the sliding mode;

[0049] Step S1362. Design the adaptive law of the switching gain in the reconstructed system control law of the hyperbolic sliding mode controller as:

[0050]

[0051] where λ0 and η0 are positive adjustable parameters, and is the estimated value of λ(t), is the estimated value of η(t), is the estimated value of the time - varying gain L s (t);

[0052] Step S1363. Define the adjustment variable δ(t), and increase or decrease the switching gain based on the sign direction of the adjustment variable δ(t), and adjust the change speed of the switching positive pole according to the magnitude of the adjustment variable δ(t):

[0053]

[0054] where a is a positive adjustable parameter, and 0 < aη0 < 1, ε is the approaching error, taking a positive value.

[0055] In the Vienna rectifier control method based on double-layer adaptive super-helical sliding mode of the present invention, step S1363 further includes:

[0056] Step S13631: For the time-varying gain L s (t) Design adaptive law:

[0057]

[0058]

[0059]

[0060]

[0061] where l s0 , r0 and γ are all positive adjustable parameters. When δ(t)=0 Ensure that the switching item gain is greater than the boundary value of the uncertain item, that is,

[0062] Step S13632: When the sign of the adjustment variable δ(t) is positive, Reduce the time-varying gain L s (t), and when the sign of the adjustment variable δ(t) is negative, according to Increase the time-varying gain L s (t);

[0063] Step S13633: When the absolute value of the adjustment variable δ(t) is large, Increase the time-varying gain L s (t), when the absolute value of the adjustment variable δ(t) is small, according to Reduce the time-varying gain L s The rate of change of (t).

[0064] In the Vienna rectifier control method based on a double-layer adaptive super-helical sliding mode according to the present invention, step S2 further includes designing a PI controller based on a mathematical model of the Vienna rectifier:

[0065]

[0066] k p 、k i Respectively represent the proportional and integral parameters of the PI controller, u d and u q Represent the components of the voltage vector on the dq axis, i dref1 and i qref1Respectively represent the reference value of current on the dq axis, e d and e q They represent the components of the grid-side voltage on the dq axis, ω represents the grid angular frequency, i d and i q represents the component of the grid-side current on the dq axis, L represents the system input inductance, and s represents the sliding mode surface.

[0067] Another technical solution adopted by the present invention to solve the technical problem is to construct a Vienna rectifier control system based on a double-layer adaptive super-helical sliding mode, comprising:

[0068] A voltage outer loop double-layer adaptive super-spiral sliding mode control module is used to design a double-layer adaptive super-spiral sliding mode controller based on a mathematical model of a Vienna rectifier and obtain a system control rate of the double-layer adaptive super-spiral sliding mode controller;

[0069] a current inner loop PI feedforward decoupling control module, configured to use the control rate obtained in the voltage outer loop of the PI controller based on the double-layer adaptive super-helical sliding mode controller as an input to the current inner loop of the PI controller to obtain a voltage signal, and generate a PWM control signal based on the voltage signal;

[0070] A PWM control module controls the switching device of the Vienna rectifier based on the PWM control signal so that the DC output voltage of the Vienna rectifier tracks a given value.

[0071] In the Vienna rectifier control system based on a double-layer adaptive super-spiral sliding mode described in the present invention, the voltage outer loop double-layer adaptive super-spiral sliding mode control module is further used to obtain a mathematical model of the Vienna rectifier in a two-phase rotating coordinate system; define a sliding mode surface based on a DC bus voltage error, and design a sliding mode controller based on the mathematical model and the sliding mode surface; design a super-spiral sliding mode controller based on a super-spiral algorithm and the sliding mode controller, and introduce system uncertainty into the super-spiral sliding mode controller to design the double-layer adaptive super-spiral sliding mode controller and obtain the system control rate of the double-layer adaptive super-spiral sliding mode controller.

[0072] The Vienna rectifier control method and system based on a dual-layer adaptive super-helical sliding mode employs the present invention. By incorporating a dual-layer adaptive law into the super-helical sliding mode, equivalent control is reconstructed to estimate the equivalent value of the uncertain terms in real time and obtain the controller output. This ensures temporal continuity of control, mitigates chattering, and enhances the outer loop's speed and robustness. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] The present invention will be further described below with reference to the accompanying drawings and embodiments, in which:

[0074] Figure 1 This is the circuit topology diagram of the Vienna rectifier;

[0075] Figure 2 This is the equivalent circuit diagram of the Vienna rectifier;

[0076] Figure 3 is a flow chart of the Vienna rectifier control method based on double-layer adaptive super-helical sliding mode of the present invention;

[0077] Figure 4 1 is a phase trajectory diagram of the super-helical algorithm used in the Vienna rectifier control method based on the double-layer adaptive super-helical sliding mode of the present invention;

[0078] Figure 5 This is a control flow chart of a double-layer adaptive law adopted by the Vienna rectifier control method based on a double-layer adaptive super-helical sliding mode of the present invention;

[0079] Figure 6 It is a control block diagram of the Vienna rectifier control method based on double-layer adaptive super-helical sliding mode of the present invention. DETAILED DESCRIPTION

[0080] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0081] Figure 1 This is the circuit topology diagram of the Vienna rectifier. Figure 2 This is the equivalent circuit diagram of the Vienna rectifier. Figure 1 As shown, each phase arm of the Vienna rectifier consists of two fast recovery diodes D x1 , D x1 (x=a,b,c) and a bidirectional power flow unit S x1 , S x2 Each bidirectional power flow unit is composed of two switching tubes with anti-parallel diodes connected in series in reverse order, and the two switching tubes share a driving signal. On the AC side, e a 、e b 、e c It is a three-phase AC power supply. The grid is connected to the midpoint of the diode of each bridge arm through the filter inductor L and its parasitic resistance r. On the DC side, two filter capacitors C1 and C2 are connected in series to the positive and negative busbars on the DC side. The DC side load resistor R L The upper voltage is the bus voltage V dcThe midpoints of the two filter capacitors are connected to the three-phase bidirectional power flow unit. According to the working principle of the Vienna rectifier, each phase of this topology has three output states, so each phase can be simplified as follows: Figure 2 Single-pole three-switch model shown.

[0082] The Vienna rectifier control method based on double-layer adaptive super spiral sliding mode of the present invention is suitable for Figure 1-2 The Vienna rectifier shown in the figure has a flow chart as follows Figure 3 As shown. Figure 3 As shown, in step S1, a double-layer adaptive super-spiral sliding mode controller is designed based on the mathematical model of the Vienna rectifier and the system control rate of the double-layer adaptive super-spiral sliding mode controller is obtained.

[0083] In a preferred embodiment of the present invention, step S1 further includes obtaining a mathematical model of the Vienna rectifier in a two-phase rotating coordinate system; defining a sliding mode surface based on a DC bus voltage error, and designing a sliding mode controller based on the mathematical model and the sliding mode surface; designing a super spiral sliding mode controller based on a super spiral algorithm and the sliding mode controller, and introducing system uncertainty into the super spiral sliding mode controller to design the double-layer adaptive super spiral sliding mode controller and obtain the system control rate of the double-layer adaptive super spiral sliding mode controller.

[0084] It should be noted that, in other preferred embodiments of the present invention, Vienna rectifiers with other known structures and other known mathematical model construction methods can be used to construct the mathematical model of the Vienna rectifier, all of which fall within the scope of protection of the present invention.

[0085] In step S2, a PI controller is designed based on the mathematical model of the Vienna rectifier. In a preferred embodiment of the present invention, a feedforward decoupling control method is used based on Figure 1-2 The mathematical model of the Vienna rectifier shown is used to design a PI controller. In other preferred embodiments of the present invention, any suitable PI controller known in the art can be used.

[0086] Step S3: Using the control rate obtained in the voltage outer loop based on the double-layer adaptive super-spiral sliding mode controller as the input of the current inner loop to obtain a voltage signal, and generating a PWM control signal based on the voltage signal to control the switching device of the Vienna rectifier, so that the DC output voltage of the Vienna rectifier tracks a given value.

[0087] In other preferred embodiments of the present invention, a space vector pulse width modulation (SVPWM) strategy can be used to control the switching devices of the Vienna rectifier. Any known SVPWM method can be used, and this application will not further elaborate on it. Of course, in other preferred embodiments of the present invention, any other suitable PWM control method can also be used, and all of these fall within the scope of protection of the present invention.

[0088] The Vienna rectifier control method based on a dual-layer adaptive super-helical sliding mode of the present invention introduces a super-helical algorithm on the basis of sliding mode control, making the control continuous in time and thus improving the chattering phenomenon. A dual-layer adaptive law is added to the super-helical algorithm. By reconstructing equivalent control, the equivalent value of the uncertain term is estimated in real time, the controller output is obtained, and the speed and robustness of the outer loop are improved. Furthermore, the inner current loop uses PI feedforward decoupling control to eliminate the mutual influence between the active current and the reactive current. Finally, SVPWM is used to control the signal of the Vienna rectifier switch, which can further improve the chattering phenomenon and provide stronger robustness and adaptability to parameter changes and load disturbances in the system.

[0089] The following combination Figure 1-2 The Vienna rectifier shown and Figure 6 The control block diagram shown further illustrates a preferred embodiment of the Vienna rectifier control method based on a double-layer adaptive super-spiral sliding mode according to the present invention as follows.

[0090] 1. Obtaining the mathematical model of the Vienna rectifier in a two-phase rotating coordinate system

[0091] The switching sequence of the switching devices of the Vienna rectifier is adjusted using the switching function S j To express:

[0092]

[0093] Among them S j is the potential state of phases a, b, and c of the Vienna rectifier; i j are the a, b, and c phase currents, where j = a, b, c.

[0094] The mathematical model of the Vienna rectifier in the three-phase stationary coordinate system is:

[0095]

[0096] where i a,b,c Respectively expressed as Figure 2 The a, b, c phase currents shown, ea,b,c Respectively expressed as Figure 2 The a, b, and c phase voltages are shown, L represents the system input inductance, C represents the system capacitance, r is the equivalent capacitance, V c1，c2 Represents the voltage across capacitors C1 and C2, S ap，an，bn，bp，cn，cp Respectively Figure 2 The switching function shown is 1 when on and 0 when off.

[0097] The mathematical model of the Vienna rectifier in the three-phase stationary coordinate system is converted into the two-phase rotating coordinate system to obtain the mathematical model of the Vienna rectifier in the two-phase rotating coordinate system:

[0098]

[0099] in, V dc Indicates the DC bus voltage, S d and S q Represent the components of the potential state on the dq axis respectively; e d and e q They represent the components of the grid-side voltage on the dq axis, L represents the system input inductance, C represents the system capacitance, r represents the equivalent resistance, ω represents the grid angular frequency, and i d and i q Represents the component of the grid-side current on the dq axis, i dc Indicates the load current.

[0100] 2. Design of Sliding Mode Controller

[0101] The DC bus voltage error is defined as z=V dc -V dcref (4)

[0102] Where V dcref Indicates the reference value of DC bus voltage, V dc Indicates the DC bus voltage.

[0103] The sliding surface is defined as Where k>0 is the integral gain.

[0104] Derivative the sliding surface to obtain:

[0105]

[0106] Indicates V dcref The derivative of represents the derivative of the sliding surface s.

[0107] In order to analyze the stability, the first Lyapunov candidate function is taken as:

[0108] Derivative the Lyapunov candidate function V1 and substitute the derivative (6) of the sliding surface to obtain:

[0109]

[0110] Indicates V dcref The derivative of represents the derivative of the Lyapunov candidate function V1, i d and i q Represents the component of the grid-side current on the dq axis, i dc represents the load current, and C represents the system capacitance.

[0111] The voltage outer loop control of the Vienna rectifier is performed based on the sliding mode controller to calculate the system control rate of the sliding mode controller:

[0112]

[0113] 3. Design of super-helical sliding mode controller

[0114] First, in this preferred embodiment, the supercoil algorithm is selected as:

[0115]

[0116] Where λ and η are switching term gains, and η>|d p |d p represents the lumped uncertainty of the system and d p (t)≤ρ, ρ is a positive constant, sign(·) is a sign function, represents the derivative of the sliding surface s, represents the derivative of the supercoil factor μ. The phase trajectory of the supercoil algorithm is as follows Figure 4 shown.

[0117] The switching control rate is designed based on the super-helical algorithm:

[0118]

[0119] The system control rate of the super-helical sliding mode controller is obtained based on the system control rate of the sliding mode controller and the switching control rate:

[0120]

[0121] Here, we verify the stability of the designed super-helical sliding mode controller as follows.

[0122] Derivative the Lyapunov candidate function (7), and then substitute the system control rate (12) of the super-helical sliding mode controller into it to obtain:

[0123]

[0124] In the above formula, the disturbance term dp(t) is defined as the lumped uncertainty of the system (including modeling errors and external disturbances), which is limited by the positive constant of the real system. Here, it is assumed that the bounds of dp(t) are given as:

[0125] d p (t)≤ρ (14)

[0126] Where p is a positive constant.

[0127] Therefore, as long as η>|d p |, you can make The Lyapunov function V1 is positive definite, and V1 is a negative definite function. According to the Lyapunov theorem, V1(t) is a continuously decreasing function that will reach an equilibrium point in a finite time. Therefore, the designed super-helical sliding mode control system is asymptotically stable.

[0128] 4. Design of a two-layer adaptive super-helical sliding mode controller

[0129] Because sliding mode control has unknown boundary information during the sliding phase due to uncertainty, a large switching gain is typically selected to ensure system robustness, resulting in "chattering" in the control system's transient state. To address this issue, the present invention proposes an adaptive law that can quickly obtain an appropriate switching gain during the sliding phase. This effectively addresses the "chattering" problem caused by excessively high switching gains while ensuring the robustness of the control system.

[0130] Taking into account the uncertainty of the system, the system uncertainty is introduced To reconstruct the supercoil algorithm:

[0131]

[0132] Where λ(t) and η(t) are the changes of switching term gain over time; s(t) represents the change of sliding surface over time; represents the uncertainty term in the super-helical sliding mode control law; Where L s (T) represents the time-varying gain and satisfies L s (t)>l s0 > 0, satisfying the bounded and differentiable constraints, Indicates L s (t), and s represents the sliding surface.

[0133] The reconstructed system control rate of the superhelical sliding mode controller is obtained based on the reconstructed superhelical algorithm:

[0134]

[0135] In actual control systems, the uncertainty is time-varying and difficult to know. Therefore, Equation (16) cannot be directly used in actual control systems. In order to solve this problem, we designed a double-layer adaptive law for super-helical sliding mode control to achieve the uncertainty Real-time estimation of the system control rate of the double-layer adaptive super-helical sliding mode controller designed by the double-layer adaptive law is:

[0136]

[0137] in and are the estimated values ​​of the switching term gains λ and η, is the time-varying gain L s (t) is an estimated value.

[0138] In a preferred embodiment of the present invention, the specific steps of designing the system control rate of the double-layer adaptive super-spiral sliding mode controller using the double-layer adaptive law are as follows.

[0139] First, define the equivalent value of the uncertainty term f(t) in the super-helical sliding mode control law:

[0140]

[0141] sign(s)| eq represents the average value of the switching term that maintains the control system state in the sliding mode, and η(t) represents the function of the switching term gain η changing with time. The equivalent value of the uncertainty term f(t) Real-time estimation can be performed using formula (18):

[0142]

[0143] where τ μ is the filter time constant, which is between the sampling time and 1.

[0144] The adaptive law of the switching gain in the reconstructed system control rate of the super-helical sliding mode controller of design formula (16) is:

[0145]

[0146] where λ0 and η0 are positive adjustable parameters, and is the estimated value of λ(t), is the estimated value of η(t), The estimated value of the time-varying gain L s (t).

[0147] Define the adjustment variable δ(t), increase or decrease the switching gain based on the sign direction of the adjustment variable δ(t), and adjust the change speed of the switching positive electrode according to the magnitude of the adjustment variable δ(t):

[0148]

[0149] where a is a positive adjustable parameter, and 0 < aη0 < 1, ε is the approaching error, taking a positive value.

[0150] Design an adaptive law for the time-varying gain L s (t):

[0151]

[0152]

[0153]

[0154]

[0155] where l s0 , r0, and γ are all positive adjustable parameters. When δ(t) = 0 ensure that the switching term gain is greater than the boundary value of the uncertain term, that is

[0156] Figure 5 is the control flowchart of the double-layer adaptive law adopted by the Vienna rectifier control method based on the double-layer adaptive super-twisting sliding mode of the present invention.

[0157] As Figure 5 shown, Equation (22) is the first-layer adaptive law, which changes the change direction of the time-varying gain in real time through the sign direction of the adjustment variable δ(t). When the sign of the adjustment variable δ(t) is positive, that is, when the switching term is greater than the uncertain term, according to Equation (22) reduce the time-varying gain L s (t); conversely, when the sign of the adjustment variable δ(t) is negative, that is, when the switching term is less than the uncertain term, according to Equation (22) increase the time-varying gain L s (t); The design of the first-layer adaptive law aims to make the uncertain term and the switching term approximately equal to suppress chattering and ensure the robustness of the control system in the sliding phase.

[0158] Formula (24) is the second-layer adaptive law, which changes the speed of the time-varying gain in real time according to the size of the adjustment variable δ(t). When the absolute value of the adjustment variable δ(t) is large, that is, when there is a large difference between the switching term and the uncertain term, according to formula (24) Increase the time-varying gain L s (t) the speed of change; on the contrary, when the absolute value of the adjustment variable δ(t) is small, that is, the difference between the switching term and the uncertain term is small, according to formula (24) Reduce the time-varying gain L s The second-layer adaptive law effectively reduces the control variable chattering amplitude under time-varying uncertainty conditions.

[0159] The switching gain in the aforementioned two-layer adaptive law addresses the difficulty of obtaining information about the upper bound of control system uncertainty by reconstructing equivalent control and estimating the equivalent value of the uncertainty term in real time. Based on the obtained equivalent value of the uncertainty term, the adaptive law is designed to make the switching term slightly larger than the equivalent value of the uncertainty term, effectively reducing the switching gain of the sliding mode control. The two-layer adaptive design comprehensively considers the adjustment direction and speed of the sliding mode switching gain, ensuring the robustness of the control system while quickly achieving a low switching gain.

[0160] As mentioned above, the system control rate of the double-layer adaptive super-helical sliding mode controller designed using the double-layer adaptive law is:

[0161]

[0162] 5. Verifying the Stability of the Double-Layer Adaptive Super-Helical Sliding Mode Controller

[0163] In order to verify the stability of the double-layer adaptive super-helical sliding mode controller constructed above, we perform the following verification steps.

[0164] Assumption: The system uncertainty term f(t satisfies the constraints:

[0165] |f(t)|≤a0<+∞ (26)

[0166] |f(t)|≤a1<+∞ (27)

[0167] Where a0 and a1 are the unknown upper bounds of the uncertain terms and their derivatives.

[0168] Theorem: For a Vienna rectifier system with uncertainty, when the system control rate of the dual-layer adaptive super-spiral sliding mode controller is designed as Equation (25) and the adaptive law of the switching gain is designed as Equations (21)-(24), the system will converge within a finite time.

[0169] Proof: First, analyze the stability of the reconstructed superhelix algorithm in equation (15). Define a new variable matrix:

[0170]

[0171] Where χ1, χ2 represent the vectors in the variable matrix χ, s represents the sliding surface; Substituting equation (28) into equation (15), for the case of s≠0, we can obtain:

[0172]

[0173] in because but satisfy Substituting formula (19) into formula (29) can be rearranged as:

[0174]

[0175] in

[0176] Construct the second Lyapunov function V2 = χ T Pχ, it can be concluded that χ1, χ2 can converge to the equilibrium point in a finite time, that is, Equation (28) will reach the equilibrium point (s, μ) = (0, 0) in a finite time. Substituting s = μ = 0 into Equation (15), it can be obtained that in a finite time Therefore, the super-helical sliding mode controller of formula (15) tends to be stable.

[0177] Next, we prove that the designed adaptive law shown in Equations (21)-(24) can satisfy condition.

[0178] Define a new variable:

[0179]

[0180] because Then we can rewrite formula (20) as:

[0181]

[0182] Construct the third Lyapunov function:

[0183]

[0184] According to formula (32) and formula (21)-(24), we can know that:

[0185]

[0186] From formula (23) and formula (31), we can get:

[0187]

[0188] From equations (34) and (35), we can differentiate both ends of equation (33) with respect to time and obtain:

[0189]

[0190] because Therefore, both δ(t) and φ(t) are bounded. According to the LaSalle invariance principle, when t→∞, δ(t)→0. Therefore, there exists a finite time t0 such that for all times t>t0, |δ(t)|<ε / 2. Then, from Equation (19), we can obtain:

[0191]

[0192] Since 0<aη0<1, then:

[0193]

[0194] Since φ(t) is bounded, and therefore and is bounded. From formula (20), we can see that:

[0195]

[0196] Since δ(t) is bounded, the adaptive gain It also remains bounded. Thus, it can be seen that the dual-layer adaptive super-spiral sliding mode controller of the present invention is stable. Therefore, it can be demonstrated that for the Vienna rectifier, using the dual-layer adaptive super-spiral sliding mode controller described herein, the system can converge within a finite time even when system uncertainties occur, ensuring asymptotic stability while reducing chattering.

[0197] 6. Designing a PI Controller

[0198] Design a PI controller based on the mathematical model of the Vienna rectifier. Figure 1-2 The Vienna rectifier shown in FIG. 1 has an inner loop controller design similar to that of a conventional rectifier. Due to the presence of the grid angular frequency ω and the system input inductance L, the system dq axis power variables are mutually coupled. To achieve better current control, a feedforward decoupling control method is used in a preferred embodiment of the present invention to design a PI controller based on the mathematical model of the Vienna rectifier:

[0199]

[0200] k p 、k i Respectively represent the proportional and integral parameters of the PI controller, u d and u q Represent the components of the voltage vector on the dq axis, i dref1 and i qref1 Respectively represent the reference value of current on the dq axis, e d and e q They represent the components of the grid-side voltage on the dq axis, ω represents the grid angular frequency, i d and i q represents the component of the grid-side current on the dq axis, L represents the system input inductance, and δ represents the sliding mode surface.

[0201] 7. Implementing PWM Control of Vienna Rectifier

[0202] The control rate obtained in the voltage outer loop based on the double-layer adaptive super-spiral sliding mode controller is used as the input of the current inner loop to obtain a voltage signal, and a PWM control signal is generated based on the voltage signal to control the switching device of the Vienna rectifier, so that the DC output voltage of the Vienna rectifier tracks a given value.

[0203] In a preferred embodiment of the present invention, a space vector pulse width modulation (SVPWM) strategy can be used to control the switching devices of the Vienna rectifier. Any known SVPWM method can be used, and this application will not further elaborate on it. Of course, in other preferred embodiments of the present invention, any other suitable PWM control method can also be used, and all such methods fall within the scope of protection of the present invention.

[0204] In summary, the Vienna rectifier control method based on a dual-layer adaptive super-helical sliding mode of the present invention does not require the establishment of a precise mathematical model. It is particularly suitable for controlling high-frequency Vienna rectifiers with complex structures and time-varying parameters. The super-helical algorithm enables the rectifier to return to the sliding mode surface within a finite time, thereby achieving the expected performance. It also makes the switching signal continuous, fundamentally avoiding the occurrence of chattering. It can estimate the equivalent value of the uncertain terms in real time, thereby reducing the impact of uncertainties on error convergence, achieving adaptive control of the system output voltage, ensuring good dynamic performance, and improving the system's robustness to parameter changes, load disturbances, and voltage fluctuations. The adaptive design of the dual-layer structure comprehensively considers the adjustment direction and speed of the sliding mode switching gain, ensuring the robustness of the control system while quickly achieving a low switching gain. It is highly robust to unbalanced networks, distorted networks, and parameter uncertainty. It outperforms traditional nonlinear control strategies such as sliding mode controllers, backstepping control, and feedback linearization in terms of fast response speed, rapid convergence, small steady-state error, strong robustness, and reduced chattering.

[0205] A further preferred embodiment of the present invention discloses a Vienna rectifier control system based on a double-layer adaptive super-spiral sliding mode, comprising a voltage outer loop double-layer adaptive super-spiral sliding mode control module, a current inner loop PI feedforward decoupling control module and a PWM control module.

[0206] The voltage outer loop dual-layer adaptive super-spiral sliding mode control module is used to design a dual-layer adaptive super-spiral sliding mode controller based on the mathematical model of the Vienna rectifier and obtain the system control rate of the dual-layer adaptive super-spiral sliding mode controller. The current inner loop PI feedforward decoupling control module is used to use the control rate obtained in the voltage outer loop of the PI controller based on the dual-layer adaptive super-spiral sliding mode controller as the input of the current inner loop of the PI controller to obtain a voltage signal, and generate a PWM control signal based on the voltage signal. The PWM control module controls the switching devices of the Vienna rectifier based on the PWM control signal so that the DC output voltage of the Vienna rectifier tracks a given value.

[0207] In a preferred embodiment of the present invention, the voltage outer loop double-layer adaptive super-spiral sliding mode control module is further used to obtain a mathematical model of the Vienna rectifier in a two-phase rotating coordinate system; define a sliding mode surface based on the DC bus voltage error, and design a sliding mode controller based on the mathematical model and the sliding mode surface; design a super-spiral sliding mode controller based on the super-spiral algorithm and the sliding mode controller, and introduce system uncertainty into the super-spiral sliding mode controller to design the double-layer adaptive super-spiral sliding mode controller and obtain the system control rate of the double-layer adaptive super-spiral sliding mode controller.

[0208] Those skilled in the art will appreciate that the voltage outer loop dual-layer adaptive super-spiral sliding mode control module, current inner loop PI feedforward decoupling control module, and PWM control module described herein correspond one-to-one with the steps of the dual-layer adaptive super-spiral sliding mode Vienna rectifier control method of the present invention. Based on the teachings of the present invention and common knowledge in the art, those skilled in the art will be able to construct the aforementioned dual-layer adaptive super-spiral sliding mode Vienna rectifier control system and achieve its technical effects, and therefore will not be elaborated upon here.

[0209] Although the present invention is described by way of specific embodiments, it will be understood by those skilled in the art that various modifications and equivalent substitutions may be made to the present invention without departing from the scope of the present invention. Furthermore, various modifications may be made to the present invention for specific circumstances or materials without departing from the scope of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed, but is intended to encompass all embodiments falling within the scope of the claims.

[0210] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A Vienna rectifier control method based on a double-layer adaptive super-helical sliding mode, characterized in that: include: Step S1, designing a double-layer adaptive super-spiral sliding mode controller based on a mathematical model of a Vienna rectifier and obtaining a system control rate of the double-layer adaptive super-spiral sliding mode controller; Step S2: designing a PI controller based on the mathematical model of the Vienna rectifier; Step S3, using the control rate obtained in the voltage outer loop based on the double-layer adaptive super-spiral sliding mode controller as the input of the current inner loop to obtain a voltage signal, and generating a PWM control signal based on the voltage signal to control the switching devices of the Vienna rectifier, so that the DC output voltage of the Vienna rectifier tracks a given value; The step S1 further comprises: Step S11, obtaining a mathematical model of the Vienna rectifier in a two-phase rotating coordinate system; Step S12: defining a sliding mode surface based on the DC bus voltage error, and designing a sliding mode controller based on the mathematical model and the sliding mode surface; Step S13: designing a super helical sliding mode controller based on the super helical algorithm and the sliding mode controller, introducing system uncertainty into the super helical sliding mode controller to design the double-layer adaptive super helical sliding mode controller and obtain the system control rate of the double-layer adaptive super helical sliding mode controller.

2. The Vienna rectifier control method based on double-layer adaptive super-helical sliding mode according to claim 1 is characterized in that: The step S11 further comprises: Step S111: The switching sequence of the switching devices of the Vienna rectifier is set to the switching function S j To express: Among them S j is the potential state of phases a, b, and c of the Vienna rectifier; i j is the current of phases a, b, and c, where j = a, b, c; Step S112: Convert the mathematical model of the Vienna rectifier in the three-phase stationary coordinate system into the two-phase rotating coordinate system to obtain the mathematical model of the Vienna rectifier in the two-phase rotating coordinate system. in, V dc Indicates the DC bus voltage, S d and S q Represent the components of the potential state on the dq axis respectively; e d and e q They represent the components of the grid-side voltage on the dq axis, L represents the system input inductance, C represents the system capacitance, r represents the equivalent resistance, ω represents the grid angular frequency, and i d and i q Represents the component of the grid-side current on the dq axis, i dc Indicates the load current.

3. The Vienna rectifier control method based on double-layer adaptive super-helical sliding mode according to claim 1, characterized in that: The step S12 further comprises: Step S121: define the DC bus voltage error as z=V dc -V dcref , where V dcref Indicates the reference value of DC bus voltage, V dc Indicates the DC bus voltage; Step S122: define the sliding surface as Where k>0 is the integral gain; Step S123: Derivative the sliding surface and select the Lyapunov candidate function And derive the Lyapunov candidate function V1 and substitute the derivative of the sliding surface to obtain: Indicates V dcref The derivative of represents the derivative of the Lyapunov candidate function V1, i d and i q Represents the component of the grid-side current on the dq axis, i dc represents the load current, and C represents the system capacitance; Step S124: Perform voltage outer loop control of the Vienna rectifier based on the sliding mode controller to calculate the system control rate of the sliding mode controller:

4. The Vienna rectifier control method based on double-layer adaptive super-helical sliding mode according to claim 3 is characterized in that: The step S13 further comprises: Step S131: Select the supercoil algorithm as: Where λ and η are switching term gains, and η>|d p |, sign(·) is the sign function, d p represents the lumped uncertainty of the system and d p (t)≤ρ, ρ is a positive constant, represents the derivative of the sliding surface s, represents the derivative of the supercoil factor μ; Step S132: Design a switching control rate based on the superhelical algorithm: Step S133: Obtain the system control rate of the super-helical sliding mode controller based on the system control rate of the sliding mode controller and the switching control rate: Step S134: Introducing system uncertainty To reconstruct the supercoil algorithm: Where λ(t) and η(t) are the changes of switching term gain over time; s(t) represents the change of sliding surface over time; represents the uncertainty term in the super-helical sliding mode control law; L s (t) represents the time-varying gain and satisfies L s (t)>l s0 >0, satisfying the bounded and differentiable constraints, Indicates L s The derivative of (t), s represents the sliding surface, l s0 is a positive adjustable parameter; Step S135: Obtain the reconstructed system control rate of the superhelical sliding mode controller based on the reconstructed superhelical algorithm: Step S136: The system control rate of the double-layer adaptive super-helical sliding mode controller is designed by using a double-layer adaptive law: in and are the estimated values ​​of the switching term gains λ and η, is the time-varying gain L s (t) is an estimated value.

5. The Vienna rectifier control method based on double-layer adaptive super-helical sliding mode according to claim 4 is characterized in that: The step S136 further includes: Step S1361: define the equivalent value of the uncertainty term f(t) in the super-helical sliding mode control law: sign(s)| eq represents the average value of the switching term that maintains the control system state in the sliding mode; η(t) represents the function of the switching term gain η changing with time; Step S1362: Design the adaptive law of the switching gain in the reconstructed system control rate of the super-helical sliding mode controller as follows: where λ0 and η0 are positive adjustable parameters, and is the estimated value of λ(t), is the estimated value of η(t), is the time-varying gain L s (t) estimated value; Step S1363: define a regulating variable δ(t), increase or decrease the switching gain based on the sign direction of the regulating variable δ(t), and adjust the change speed of the switching positive pole according to the magnitude of the regulating variable δ(t): Where a is a positive adjustable parameter, and 0<aη0<1, ε is the approximation error, which takes a positive value.

6. The Vienna rectifier control method based on double-layer adaptive super-helical sliding mode according to claim 5, characterized in that: The step S1363 further includes: Step S13631: For the time-varying gain L s (t) Design adaptive law: where l s0 , r0 and γ are all positive adjustable parameters. When δ(t)=0 Ensure that the switching item gain is greater than the boundary value of the uncertain item, that is, Step S13632: When the sign of the adjustment variable δ(t) is positive, Reduce the time-varying gain L s (t), and when the sign of the adjustment variable δ(t) is negative, according to Increase the time-varying gain L s (t); Step S13633: When the absolute value of the adjustment variable δ(t) is large, Increase the time-varying gain L s (t), when the absolute value of the adjustment variable δ(t) is small, according to Reduce the time-varying gain L s The rate of change of (t).

7. The Vienna rectifier control method based on a double-layer adaptive super-helical sliding mode according to any one of claims 1 to 6, characterized in that: The step S2 further includes designing a PI controller based on a mathematical model of the Vienna rectifier: k p 、k i Respectively represent the proportional and integral parameters of the PI controller, u d and u q Represent the components of the voltage vector on the dq axis, i dref1 and i qref1 Respectively represent the reference value of current on the dq axis, e d and e q They represent the components of the grid-side voltage on the dq axis, ω represents the grid angular frequency, i d and i q represents the component of the grid-side current on the dq axis, L represents the system input inductance, and s represents the sliding mode surface.

8. A Vienna rectifier control system based on a double-layer adaptive super-helical sliding mode, characterized in that: include: A voltage outer loop double-layer adaptive super-spiral sliding mode control module is used to design a double-layer adaptive super-spiral sliding mode controller based on a mathematical model of a Vienna rectifier and obtain a system control rate of the double-layer adaptive super-spiral sliding mode controller; a current inner loop PI feedforward decoupling control module, configured to use the control rate obtained in the voltage outer loop of the PI controller based on the double-layer adaptive super-helical sliding mode controller as an input to the current inner loop of the PI controller to obtain a voltage signal, and generate a PWM control signal based on the voltage signal; a PWM control module, configured to control the switching device of the Vienna rectifier based on the PWM control signal so that the DC output voltage of the Vienna rectifier tracks a given value; The voltage outer loop double-layer adaptive super-spiral sliding mode control module is further used to obtain a mathematical model of the Vienna rectifier in a two-phase rotating coordinate system; define a sliding mode surface based on a DC bus voltage error, and design a sliding mode controller based on the mathematical model and the sliding mode surface; design a super-spiral sliding mode controller based on a super-spiral algorithm and the sliding mode controller, and introduce system uncertainty into the super-spiral sliding mode controller to design the double-layer adaptive super-spiral sliding mode controller and obtain the system control rate of the double-layer adaptive super-spiral sliding mode controller.

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