An inverter control method based on double-layer adaptive super-helical backstepping sliding mode

Abstract

The present invention discloses an inverter control method based on a double-layer adaptive super-helical back-stepping sliding mode. The double-layer adaptive super-helical back-stepping sliding mode controller includes a stability function, a sliding surface, a rated model, a super-helical algorithm, and a double-layer adaptive law. A system dynamics model is established for a three-phase inverter, and a system back-stepping sliding mode controller model is designed by introducing a stability function, a virtual error, and a sliding surface, and the system is corrected layer by layer; on this basis, a super-helical algorithm is also introduced to make the control continuous in time, thereby improving the jitter phenomenon; finally, a double-layer adaptive law is added on the basis of the super-helical algorithm, and by reconstructing equivalent control, the equivalent value of the uncertain term is estimated in real time, the output of the controller is obtained, and the full-bridge switch of the three-phase inverter is controlled by signal through SVPWM. Compared with the prior art, the present invention further improves the jitter phenomenon and has stronger robustness and adaptability to parameter changes and load disturbances in the system.

Description

Technical Field

[0001] The present invention relates to the technical field of inverter control, and in particular to an inverter control method based on a double-layer adaptive super-helical backstepping sliding mode. Background Art

[0002] The development of renewable energy is a major trend at present. Different energy sources have different ways to convert them into electrical energy. Therefore, before being connected to the power grid, AC technology needs to be used to regulate the converted electrical energy according to different actual needs. Usually, most of the energy directly converted from renewable energy is difficult to maintain in a stable state. If certain regulatory measures are not taken when it is connected to the power grid, the power grid is easily damaged, affecting the power consumption of users.

[0003] In order to ensure the power quality of microgrids, various advanced control strategies are constantly applied to inverter control. Control strategy is the core to ensure the excellent output performance of inverters. Therefore, designing an adaptive control strategy in microgrid inverters that can meet the changes in working conditions within a certain range can make full use of the flexibility of power electronic converters and effectively reduce the cost of microgrid system design, which has important theoretical research value and engineering practice significance.

[0004] Common inverter control strategies include PI control, PR control, sliding mode control and backstepping control. Among them, PI control has a simple structure, strong adaptability and is easy to implement, but its parameter setting is complex, the control accuracy is relatively poor, and the real-time and robustness are difficult to meet the current high-quality AC power demand. If it is to be applied to microgrid inverters, it is still necessary to make some improvements; PR control can improve the waveform and improve the robustness of the system, but it will provide different PR control internal models when facing harmonics of different frequencies, which increases the complexity of the entire system; the sliding mode control method is a very practical nonlinear control method in the inverter field due to its fast dynamic response and strong robustness to parameter uncertainty and external interference, but the intermediate variables in the sliding mode control system may cause chattering, especially when operating at a finite frequency; backstepping control can be used to force nonlinear systems to behave like linear systems in new coordinate sets. The main advantage is that it has the flexibility to avoid eliminating useful nonlinearities and pursues the goals of stability and tracking. However, the traditional backstepping control scheme requires detailed system dynamic information, so people have increased research on improved backstepping control methods. Summary of the invention

[0005] Purpose of the invention: In order to solve the problems existing in the prior art, the present invention provides an inverter control method based on a double-layer adaptive super-helical backstepping sliding mode, introduces a sliding mode term, overcomes the interference to the model, improves the jitter phenomenon of the sliding mode by introducing a super-helical algorithm, and introduces a double-layer adaptive law in the super-helical algorithm to solve the problem that the switching gain is conservatively selected due to the unknown upper limit information of the uncertainty, resulting in serious jitter in the control system, so that the controller can achieve faster and more precise control.

[0006] Technical solution: The present invention discloses an inverter control method based on a double-layer adaptive super-helical backstepping sliding mode, wherein the inverter is a three-phase full-bridge LC inverter, and the control method comprises the following steps:

[0007] Step 1: According to the filter inductor current and filter capacitor voltage of the three-phase full-bridge LC inverter, a system dynamics model of the three-phase inverter in the α-β coordinate system is constructed;

[0008] Step 2: According to the system dynamics model constructed in step 1, convert it into a second-order system, select the system state variables, add lumped uncertainties, and construct a new three-phase inverter equivalent system model;

[0009] Step 3: Based on the three-phase inverter equivalent system model constructed in step 2, the backstepping sliding mode algorithm is used to design the controller, and the stability function, virtual error and sliding mode surface are introduced to construct the backstepping sliding mode controller;

[0010] Step 4: Based on the backstepping sliding mode controller constructed in step 3, the super helical algorithm is used to ensure the continuity of control in time, improve the chattering phenomenon, optimize the backstepping sliding mode controller, and construct a super helical backstepping sliding mode controller;

[0011] Step 5: According to the super-helical backstepping sliding mode controller constructed in step 4, a double-layer adaptive law is added to construct a double-layer adaptive super-helical backstepping sliding mode controller, reconstruct the equivalent control, estimate the uncertainties in real time, and further improve the chattering phenomenon;

[0012] Step 6: Based on the double-layer adaptive super-helical backstepping sliding mode controller constructed in step 5, obtain the output of the controller and perform signal control on the full-bridge switch of the three-phase inverter through SVPWM.

[0013] Furthermore, the system dynamics model in the α-β coordinate system of step 1 is:

[0014]

[0015] Where: L and C represent the filter inductance and filter capacitance of the LC filter in the three-phase full-bridge LC inverter, r is the equivalent load of the loop, and are the currents on the inverter AC side inductance on the α-axis and β-axis respectively, and are the currents flowing through the load on the AC side of the inverter on the α-axis and β-axis respectively, and are the capacitor voltages on the AC side of the inverter on the α-axis and β-axis respectively, and are the voltages output by the inverter on the α-axis and β-axis respectively, u k =D i V dc =K PWM u conk , where the duty cycle in one switching cycle is D i =u con / V tri , the inverter equivalent gain is K PWM =V dc / V tri ,u con is the output control rate, V dc is the DC bus voltage, V tri is the amplitude of the high-frequency triangular carrier signal.

[0016] Furthermore, the second-order system in step 2 is:

[0017]

[0018] Select AC output voltage As the system status, select the control signal As the control input, the lumped uncertainty term is added to expand the disturbance parameters systematically, and a new three-phase inverter equivalent system model is constructed as follows:

[0019]

[0020] in: Output voltage for the state variable; a p1 =-r / L; a p2 =-1 / (LC); b p =K PWM / (LC);c p1 =-1 / C; c p2 = -r / (LC); a p1n ,a p2n ,b pn ,c p1n ,c p2n They are respectively p1 ,a p2 ,b p ,c p1 ,c p2Nominal value of Δa p1n ,Δa p2n ,Δb pn ,Δc p1n ,Δc p2n represents the uncertainty of system parameters; is the lumped uncertainty vector, where the disturbance term d p (t) is subject to the restriction of positive constants of the real system. Here, it is assumed that d p The limits of (t) are:

[0021] ||d p (t)||1≤ρ

[0022] Among them: ||·||1 represents a norm operator, and ρ is a positive constant.

[0023] Furthermore, the backstepping sliding mode controller in step 3 is designed as follows:

[0024]

[0025] e v =x 1d -x1

[0026]

[0027] e s =x 2d -x2

[0028]

[0029] Among them: a p1n ,a p2n ,b pn ,c p1n ,c p2n They are respectively p1 ,a p2 ,b p ,c p1 ,c p2 The nominal value of a p1 =-r / L; a p2 =-1 / (LC); b p =K PWM / (LC);c p1 =-1 / C; c p2 =-r / (LC); L and C represent the filter inductance and filter capacitance of the LC filter in the three-phase full-bridge LC inverter, r is the equivalent load of the loop, and the equivalent gain of the inverter is K PWM =V dc / V tri , V dc is the DC bus voltage, V triis the amplitude of the high-frequency triangular carrier signal; x 1d is the reference value of x1, x 2d is a stable function, x1 and x2 are the state variable output voltage and the derivative of the state variable respectively; to simplify the description, x1 is x(t), c1, c2 and k1 are positive constants, e v is the voltage error, x 2d is a stable function, e s is the virtual error, and s is the sliding surface.

[0030] Furthermore, the output control rate of the super-helical backstepping sliding mode controller in step 4 is designed as:

[0031]

[0032] Where λ and η are switching term gains, and η>|d p |,d p is the disturbance term, equivalent to d p (t), where sing(·) is a symbolic function to simplify the description, and the superhelix algorithm is designed as:

[0033]

[0034] Here, μ is an intermediate term in the superhelical equation.

[0035] Furthermore, the double-layer adaptive super-helical backstepping sliding mode controller in step 5 is designed as follows:

[0036]

[0037] in, s(t) is the sliding surface, which can be abbreviated as s, L s (t) is a positive time-varying gain and satisfies L s (t)>l s0 > 0, satisfying the bounded and differentiable constraints, for the time-varying gain L s (t) The designed adaptive law is:

[0038]

[0039] The first layer of adaptive law:

[0040]

[0041] The second layer of adaptive law:

[0042] Among them, l s0 , r0 and γ are all positive adjustable parameters, δ is a variable, is the time-varying gain Ls The estimated value of (t) when δ(t) = 0 Ensure that the switching term gain is greater than the boundary value of the uncertain term, represents the uncertainty in the super-helical backstepping sliding mode control law, that is

[0043] Furthermore, the three-phase inverter full-bridge switch control signal obtained by the controller in step 6 is:

[0044] The u obtained based on the double-layer adaptive super-helical backstepping sliding mode controller α and u β As the input of SVPWM modulation strategy, six PWM signals are generated to control the switch control signals of six switching devices, so that the DC output voltage V dc Track the given value; adopt SVPWM modulation strategy, the switching frequency is equal to the sampling frequency.

[0045] Beneficial effects:

[0046] Firstly, the present invention introduces a sliding mode term to overcome the interference to the model because the traditional backstepping control method cannot guarantee robustness. Secondly, since the fundamental reason for the chattering of the sliding mode controller is the discontinuity of the control signal, in order to reduce the chattering, it is necessary to make the control signal more continuous, smooth and differentiable. The chattering phenomenon of the sliding mode is improved by introducing a superhelix algorithm. Finally, a two-layer adaptive law is introduced in the superhelix algorithm to solve the problem of serious chattering in the control system due to the conservative selection of switching gain due to unknown information on the upper bound of uncertainty. This allows the controller to achieve faster and more precise control. The specific effects are as follows:

[0047] 1. The inverter control strategy of the double-layer adaptive super-helical back-stepping sliding mode adopted by the present invention does not need to establish an accurate mathematical model of the inverter, and is particularly suitable for the control of high-frequency inverters with complex structures and time-varying parameters. It includes a stability function, a sliding surface, a rated model, a super-helical algorithm, and a double-layer adaptive law. The controller can estimate the equivalent value of the uncertain terms in real time, thereby reducing the influence of uncertain factors on error convergence and realizing adaptive control of the system output voltage.

[0048] 2. The back-stepping sliding mode controller used in the present invention is based on the three-phase output voltage u o The two-phase stationary coordinate vector obtained by Clark transformation is used as input, and the rated model of the system is designed according to the voltage error, virtual error and sliding surface. The stability function and virtual error are introduced to correct the system layer by layer, so that the controller has higher accuracy and robustness, and has better dynamic response performance.

[0049] 3. The superhelix algorithm adopted in the present invention can, on the one hand, make the system state return to the sliding surface within a finite time when it deviates from the sliding surface, thereby achieving the expected performance; on the other hand, the algorithm consists of two items, one is the integral of its discontinuous time derivative, and the other is the continuous function of the available sliding variable, so that the control signal acting on the system is uninterrupted, fundamentally avoiding the occurrence of chattering.

[0050] 4. The present invention introduces a double-layer adaptive law in the super-helical algorithm, and solves the problem of difficulty in obtaining the upper limit information of the uncertainty of the control system by reconstructing the equivalent control and estimating the equivalent value of the uncertainty term in real time, so that the switching term is slightly larger than the equivalent value of the uncertainty term, thereby effectively reducing the switching gain value of the backstepping sliding mode control, which can not only minimize the dependence on the boundary value of uncertainty, but also ensure that the system has good dynamic performance and improve the robustness of the system to parameter changes, load disturbances and voltage fluctuations. The adaptive design of the double-layer structure comprehensively considers the adjustment direction and adjustment speed of the sliding mode switching gain, which not only ensures the robustness of the control system, but also can quickly obtain a lower switching gain.

[0051] 5. The present invention adds an integral design to the sliding surface s. The traditional sliding mode reachability condition only ensures that the system reaches the switching surface from any point in the state space within a limited time. As for its motion trajectory, there is no provision, so it cannot guarantee that the system always meets the expected dynamic performance indicators in the entire arrival section. In order to solve this problem, the initial state of the integrator is set so that the initial state of the system is on the sliding surface from the beginning, thereby eliminating the arrival stage and improving the robustness of the control system. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 This is a system framework diagram of an inverter control strategy based on a double-layer adaptive super-helical backstepping sliding mode according to the present invention;

[0053] Figure 2 It is the phase trajectory diagram of the superhelix algorithm;

[0054] Figure 3 It is a simplified model diagram of an independent single-phase full-bridge inverter circuit;

[0055] Figure 4 The A-phase output voltage signal tracking waveform of the controller of the present invention under the rated working state;

[0056] Figure 5 is the THD value of phase A of the controller of the present invention under rated working condition;

[0057] Figure 6 The output voltage and current waveform of phase A of the controller of the present invention under nonlinear load;

[0058] Figure 7 is the THD value of phase A of the controller under nonlinear load;

[0059] Figure 8 The output voltage and current waveforms of the controller of the present invention under load mutation;

[0060] Fig. 9 It is the THD value of the output voltage of the controller of the present invention and the traditional SMC controller when the inductance parameters change. DETAILED DESCRIPTION

[0061] The present invention will be further described below in conjunction with the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and cannot be used to limit the protection scope of the present invention.

[0062] Reference Figure 1 The present invention discloses an inverter control method based on a double-layer adaptive super-helical back-stepping sliding mode, which is based on a three-phase inverter, and the three-phase inverter includes a DC source, a three-phase full-bridge topology, an LC filter, a load, and an SVPWM modulation module. A double-layer adaptive super-helical back-stepping sliding mode controller is designed on the basis of the three-phase inverter. The inverter tracks the three-phase output voltage in real time through the double-layer adaptive super-helical back-stepping sliding mode controller, and then uses the SVPWM algorithm to calculate the switching function to drive the switching devices T1, T2, T3, T4, T5, and T6 to work, so that the DC voltage V dc The inductor L is charged and discharged, and DC-AC conversion is achieved on the load side after filtering.

[0063] The present invention discloses an inverter control method based on a double-layer adaptive super-helical backstepping sliding mode, which mainly comprises the following steps:

[0064] Step 1: Establishment of mathematical model of three-phase LC inverter.

[0065] Reference Figure 1 The structure diagram of the three-phase LC inverter in the figure. dc is the DC bus voltage; the inverter unit is a three-phase bridge structure; the switch device adopts an IGBT with a commutation freewheeling diode; the filter unit adopts an LC filter; Z is the output load; and r is the loop equivalent load.

[0066] Since the three-phase inverter is decomposed into three completely independent control systems in the abc stationary coordinate system, there is no coupling correlation problem. In terms of control strategy, the three-phase inverter can also be controlled independently under the three-phase stationary coordinate system, so the three phases are divided into three single-phase full-bridge inverter circuits, and their equivalent models are as follows: Figure 3 As shown, where k = a, b, c.

[0067] Figure 3 middleu k , are the voltage output on the AC side and the capacitor voltage respectively; They are the current on the inductor and capacitor on the AC side and the current flowing through the load. Kirchhoff's law gives the loop and node equations:

[0068]

[0069]

[0070] Take the inductor current Capacitor voltage As the state parameter, we can get:

[0071]

[0072] From (3), the state equation of the three-phase inverter can be obtained as follows:

[0073]

[0074] The present invention adopts the SVPWM modulation algorithm, and needs to transform the vector coordinates from the abc coordinate system to the α-β coordinate system through Clarke transformation. Let x = i, u, then the transformation formula is:

[0075]

[0076] The mathematical expression of equation (4) can be transformed into the α-β coordinate system by equation (5), and two new sets of state equations are obtained:

[0077]

[0078] in: and are the currents on the inverter AC side inductance on the α-axis and β-axis respectively, and are the currents flowing through the load on the AC side of the inverter on the α-axis and β-axis respectively, and are the capacitor voltages on the AC side of the inverter on the α-axis and β-axis respectively, and are the voltages output by the inverter on the α-axis and β-axis respectively. k =D i V dc =K PWM u conk , where the duty cycle in one switching cycle is D i =u con / V tri , the inverter equivalent gain is K PWM =V dc / V tri ,ucon is the output control rate, V tri is the amplitude of the high-frequency triangular carrier signal. The inverter dynamic equation is obtained by deriving equation (6):

[0079]

[0080] Select capacitor voltage As system status, control signal As the control input, the following state equation can be obtained:

[0081]

[0082] in: is the state variable output voltage, which is abbreviated as x1 below to simplify the description;

[0083] ap1=-rL;a p2 =-1(LC); b p =K PWM (LC); cp1 = -1C;

[0084] c p2 =-r(LC); ap1n, ap2n, bpn, cp1n, cp2n are the nominal values ​​of ap1, ap2, bp, cp1, cp2 respectively; Δa p1n ,Δa p2n ,Δb pn ,Δc p1n ,Δc p2n represents the uncertainty of system parameters; is the lumped uncertainty vector. Equation (8) can be written as the following integral chain form:

[0085]

[0086] x1 and x2 are the state variable output voltage and the derivative of the state variable respectively.

[0087] Step 2: Backstepping sliding mode controller design;

[0088] Step 1: To achieve voltage tracking, define the error variable:

[0089] e v =x 1d -x1(10)

[0090] where x 1d is the reference value of x1.

[0091] Take the first Lyapunov candidate function as:

[0092]

[0093] A stable function x can be designed 2d for:

[0094]

[0095] Where k1 is a positive constant.

[0096] Step 2: Introduce virtual error:

[0097] e s =x 2d -x2 (13)

[0098] The designed sliding surface is:

[0099]

[0100] Where c1 and c2 are positive constants.

[0101] Take the second Lyapunov candidate function as:

[0102]

[0103] According to equations (10), (12) and (13), we can obtain:

[0104]

[0105]

[0106] The control rate of the design system rated model is:

[0107]

[0108] Step 3: Design of super-helical backstepping sliding mode controller.

[0109] The super spiral algorithm used in this paper is designed as follows:

[0110]

[0111] Where μ is an intermediate term in the superhelix equation. λ and η are switching term gains, and η>|d p |, sing(·) is the sign function. The switching control law is designed as:

[0112]

[0113] Therefore, the output control rate of the super-helical backstepping sliding mode controller is designed as:

[0114]

[0115] Deriving equation (15), and then substituting control law (21) into it, we can obtain:

[0116]

[0117] As long as η>d p , you can make Established, d p is the disturbance term, which is equivalent to d p (t). The Lyapunov function V2 is positive definite, and V2 is a negative definite function. According to the Lyapunov theorem and the Barbalat theorem, V2(t) is a continuously decreasing function and will reach an equilibrium point in a finite time. Therefore, the designed super-helical backstepping sliding mode control system is asymptotically stable.

[0118] Step 4: Design of a two-layer adaptive super-helical backstepping sliding mode controller.

[0119] In the sliding stage, the boundary information of the sliding mode control is unknown. In order to ensure the robust performance of the system, a larger switching gain η is usually selected, which causes "jittering" in the transient process of the control system. To address this problem, this paper designs an adaptive law that can quickly obtain the appropriate switching gain in the sliding stage, so as to effectively solve the "jittering" problem caused by excessive switching gain while ensuring the robustness of the control system.

[0120] Considering the uncertainty of the system, we introduce Reconstruct (19) as:

[0121]

[0122] in represents the uncertainty in the super-helical backstepping sliding mode control law; s(t) is the sliding surface, which can be abbreviated as s, L s (t) is a positive time-varying gain and satisfies L s (t)>l s0 >0, satisfying the bounded and differentiable constraints.

[0123] From formula (23), it can be concluded that the super-helical backstepping sliding mode control law designed in this paper is:

[0124]

[0125] In actual control systems, the uncertainty term f(t) is time-varying and difficult to obtain. Therefore, equation (24) cannot be directly used in actual control systems. To solve this problem, this paper designs a super-helical backstepping sliding mode control adaptive law to achieve real-time estimation of the uncertainty term f(t).

[0126] Define the equivalent value of the uncertainty term f(t)

[0127]

[0128] where sign(s)| eq Represents the average value of the switching term that maintains the control system state in sliding mode. Real-time estimation can be performed using formula (26):

[0129]

[0130] where τ μ is the filter time constant, which is between the sampling time and 1.

[0131] The adaptive law of switching gain in the super-helical backstepping sliding mode control law of design formula (24) is:

[0132]

[0133] where λ0 and η0 are positive adjustable parameters, and is the time-varying gain L s (t) is an estimated value.

[0134] Define a new variable δ as:

[0135]

[0136] Where a is a positive adjustable parameter, and 0<aη0<1, ε is the approach error and takes a positive value.

[0137] For the time-varying gain L s (t) The designed adaptive law is:

[0138]

[0139] The first layer of adaptive law:

[0140]

[0141] The second layer of adaptive law:

[0142] Among them 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,

[0143] Formula (30) is the first-level adaptive law. By judging the sign of δ, the direction of change of the time-varying gain is changed in real time. When the switching term is greater than the uncertainty term, the switching gain is reduced; conversely, when the switching term is less than the uncertainty term, the switching gain is increased. The first-level adaptive law is designed to make the uncertainty term and the switching term close to equal, so as to suppress chattering and ensure that the control system maintains robustness during the sliding stage.

[0144] Formula (32) is the second-level adaptive law, which changes the speed of the time-varying gain in real time according to the size of δ. That is, when there is a large difference between the switching term and the uncertain term, the adjustment speed of the switching gain is accelerated, and when the difference between the switching term and the uncertain term is small, the adjustment speed of the switching gain is slowed down. The second-level adaptive law effectively reduces the control variable jitter amplitude under time-varying uncertainty conditions.

[0145] In summary, the double-layer adaptive super-helical backstepping sliding mode control rate of the three-phase inverter can be designed as:

[0146]

[0147] Step 5: Proof of stability of the double-layer adaptive super-helical backstepping sliding mode control strategy.

[0148] Assumption: The system uncertainty term f(t) satisfies the constraints:

[0149] |f(t)|≤a0<+∞ (34)

[0150] |f(t)|≤a1<+∞ (35)

[0151] Where a0 and a1 are the unknown upper bounds of the uncertain terms and their derivatives.

[0152] Theorem: For a three-phase inverter system with uncertainty, when the control rate is designed as equation (33) and the adaptive law of the switching gain is designed as equations (29)-(32), the system will converge within a finite time.

[0153] Proof: First, the stability of the reconstructed superhelix algorithm in equation (23) is analyzed. Define a new variable matrix:

[0154]

[0155] Substituting equation (36) into equation (23), for the case of s≠0, we can obtain:

[0156]

[0157] in because but satisfy Substituting formula (27) into formula (37) can be rearranged as:

[0158]

[0159] in

[0160] Construct the third Lyapunov function V3 = χ T Pχ, it can be concluded that χ1 and χ2 can converge to the equilibrium point in a finite time, that is, equation (36) will reach the equilibrium point (s,μ) = (0,0) in a finite time. Substituting s = μ = 0 into equation (23), it can be obtained that in a finite time Therefore, the super-helical backstepping sliding mode control of equation (23) tends to be stable.

[0161] Next, we prove that the designed adaptive law shown in equations (29)-(32) can satisfy condition.

[0162] Define new variables:

[0163]

[0164] because Then we can rewrite formula (28) as:

[0165]

[0166] Construct the fourth Lyapunov function:

[0167]

[0168] According to formula (40) and formula (29)-(32), we can know:

[0169]

[0170] From formula (31) and formula (39), we can get:

[0171]

[0172] From equations (42) and (43), we can differentiate both ends of equation (41) with respect to time and obtain:

[0173]

[0174] because Therefore, δ(t) and φ(t) are both 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 (27), we can get:

[0175]

[0176] Since 0<aη0<1, then:

[0177]

[0178] Since φ(t) is bounded and therefore and is bounded. From formula (28), we can see that:

[0179]

[0180] Since δ(t) is bounded, the adaptive gain So far, the theorem has been proved.

[0181] In summary, for the three-phase inverter system, the use of the double-layer adaptive super-helical backstepping sliding mode control described in this paper can make the system converge within a finite time even when system uncertainty occurs, ensuring the asymptotic stability of the system while reducing the "jittering" phenomenon.

[0182] Figure 4 This is the output voltage waveform tracking effect of phase A when the controller of the present invention is started under rated working conditions. It can be seen from the figure that the double-layer adaptive super-helical backstepping sliding mode control strategy has a fast stabilization speed. After the system is stable, the output voltage waveform is smooth, and the amplitude and frequency basically obey the given values ​​without static error.

[0183] Figure 5 This is the harmonic analysis of the output voltage of phase A when the controller of the present invention is started under the rated working state. It can be seen from the figure that when the nominal inductance of the filter is L=1.4mH, the THD of the proposed control strategy is 0.45%, and the harmonic content is low. Therefore, the controller of the present invention has excellent performance under linear load.

[0184] Figure 6 The steady-state output voltage and current waveforms of phase A of the controller under nonlinear load of the present invention can be seen from the figure that when the control strategy proposed in this article faces nonlinear load, the voltage and current waveforms are stable and smooth, and the tracking effect basically obeys the given zero static error.

[0185] Figure 7 This is the output voltage harmonic analysis of phase A of the controller under nonlinear load of the present invention. It can be seen from the figure that the THD of the proposed control strategy is 0.96%, which effectively suppresses the harmonics of the output voltage and output current and stabilizes the voltage and current waveforms to make them comply with the national grid standards. Therefore, the controller of the present invention has excellent robustness under nonlinear loads.

[0186] When the load changes, the system adjustment time is one of the criteria for measuring the dynamic response of the system. The shorter the adjustment time and the smaller the overshoot, the better the dynamic response of the system. Given a rated system load of 18Ω, in the load disturbance simulation experiment, the system first switches from full load to half load at 0.155s, and then returns to full load at 0.255s. Figure 8 The simulated waveforms of the voltage and current of phase A of the controller of the present invention when the load changes suddenly are shown in the figure. It can be seen from the waveforms in the figure that when the load changes, the system can recover to a stable state in about 1ms, indicating that the control strategy proposed by the present invention has a good resistance to load disturbances and excellent robustness.

[0187] The aging of power devices and the influence of the environment will cause changes in system parameters. The value of the filter inductance L is one of the important circuit parameters in the three-phase inverter and has a great influence on the output voltage control performance. In order to verify the robustness of the control strategy proposed in this invention to parameter changes, a simulation condition is designed in which the actual filter inductance changes from 90% to 110% of the nominal value of 1.4mH. Fig. 9 The output voltage THD values ​​when the inductance parameters of ASTBSMC and SMC change are shown. It can be seen that when the inductance value changes, the proposed ASTBSMC changes the output voltage THD value from 0.56% to 0.41%, while the THD value of SMC changes from 2.82% to 1.11%. Therefore, it is concluded that compared with the traditional SMC, the control strategy proposed in the present invention has better robustness when the inductance changes.

[0188] The technical means disclosed in the scheme of the present invention are not limited to the technical means disclosed in the above-mentioned implementation mode, but also include technical schemes composed of any combination of the above-mentioned technical features. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications are also regarded as the protection scope of the present invention.

Claims

1. An inverter control method based on double-layer adaptive super-helical backstepping sliding mode, characterized in that: The inverter is a three-phase full-bridge LC inverter, and the control method comprises the following steps: Step 1: According to the filter inductor current and filter capacitor voltage of the three-phase full-bridge LC inverter, a system dynamics model of the three-phase inverter in the α-β coordinate system is constructed; The system dynamics model in the α-β coordinate system is: Where: L and C represent the filter inductance and filter capacitance of the LC filter in the three-phase full-bridge LC inverter, r is the equivalent load of the loop, and are the currents on the inverter AC side inductance on the α-axis and β-axis respectively, and are the currents flowing through the load on the AC side of the inverter on the α-axis and β-axis respectively, and are the capacitor voltages on the AC side of the inverter on the α-axis and β-axis respectively, and are the voltages output by the inverter on the α-axis and β-axis respectively, u k =D i V dc =K PWM u conk , where the duty cycle in one switching cycle is D i =u con / V tri , the inverter equivalent gain is K PWM =V dc / V tri ,u con is the output control rate, V dc is the DC bus voltage, V tri is the amplitude of the high-frequency triangular carrier signal; Step 2: According to the system dynamics model constructed in step 1, convert it into a second-order system, select the system state variables, add lumped uncertainties, and construct a new three-phase inverter equivalent system model; The second-order system is: Select AC output voltage As the system status, select the control signal As the control input, the lumped uncertainty term is added to expand the disturbance parameters systematically, and a new three-phase inverter equivalent system model is constructed as follows: in: is the state variable output voltage, which is abbreviated as x1 below to simplify the description; a p1 =-r / L; a p2 =-1 / (LC); b p =K PWM / (LC);c p1 =-1 / C; c p2 = -r / (LC); a p1n ,a p2n ,b pn ,c p1n ,c p2n They are respectively p1 ,a p2 ,b p ,c p1 ,c p2 Nominal value of Δa p1n ,Δa p2n ,Δb pn ,Δc p1n ,Δc p2n represents the uncertainty of system parameters; is the lumped uncertainty vector, where d p (t) is subject to the restriction of positive constants of the real system. Here, it is assumed that d p The limits of (t) are: ‖d p (t)‖1≤ρ Among them: ||·||1 represents a norm operator, ρ is a positive constant; Step 3: Based on the three-phase inverter equivalent system model constructed in step 2, the backstepping sliding mode algorithm is used to design the controller, and the stability function, virtual error and sliding mode surface are introduced to construct the backstepping sliding mode controller; The backstepping sliding mode controller is designed as: And v =x 1d -x1 e s =x 2d -x2 Where: x 1d is the reference value of x1, x 2d is a stable function, x1 and x2 are the state variable output voltage and the derivative of the state variable respectively; c1, c2 and k1 are positive constants, e v is the voltage error, e s is the virtual error, s(t) is the sliding surface, which can be abbreviated as s; Step 4: Based on the backstepping sliding mode controller constructed in step 3, the super helical algorithm is used to ensure the continuity of control in time, improve the chattering phenomenon, optimize the backstepping sliding mode controller, and construct a super helical backstepping sliding mode controller; The output control rate of the super-helical backstepping sliding mode controller is designed as: Where λ and η are switching term gains, and η>|d p |,d p To simplify the description, it is equivalent to d p (t), sing(·) is the symbolic function, and the superhelix algorithm is designed as: Where μ is an intermediate term in the superhelix equation; Step 5: According to the super-helical backstepping sliding mode controller constructed in step 4, a double-layer adaptive law is added to construct a double-layer adaptive super-helical backstepping sliding mode controller, reconstruct the equivalent control, estimate the uncertainties in real time, and further improve the chattering phenomenon; The design of the double-layer adaptive super-helical backstepping sliding mode controller is: in, L s (t) is a positive time-varying gain and satisfies L s (t)>l s0 >0; Define the equivalent value of the uncertainty term f(t) where sign(s)| eq represents the average value of the switching term that maintains the control system state in sliding mode, To perform a real-time estimate: Among them, τ μ is the filtering time constant, which is between the sampling time and 1; The adaptive law of switching gain in the designed super-helical backstepping sliding mode control law is: Among them, λ0 and η0 are positive adjustable parameters, and is the time-varying gain L s (t) is an estimated value; Define a new variable δ as: Among them, a is a positive adjustable parameter, and 0<aη0<1, ε is the approach error and takes a positive value; Satisfying the bounded and differentiable constraints, for the time-varying gain L s (t) The designed adaptive law is: The first layer of adaptive law: The second layer of adaptive law: Among them, l s0 , r0 and γ are all positive adjustable parameters, δ is a variable, is the time-varying gain L s The estimated value of (t) when δ(t) = 0 Ensure that the switching term gain is greater than the boundary value of the uncertain term, represents the uncertainty in the super-helical backstepping sliding mode control law, that is Step 6: Based on the double-layer adaptive super-helical backstepping sliding mode controller constructed in step 5, obtain the output of the controller and use SVPWM to control the full-bridge switch of the three-phase inverter.

2. The inverter control method based on double-layer adaptive super-helical backstepping sliding mode according to claim 1 is characterized in that: The three-phase inverter full-bridge switch control signal obtained by the controller in step 6 is: The u obtained based on the double-layer adaptive super-helical backstepping sliding mode controller α and u β As the input of SVPWM modulation strategy, six PWM signals are generated to control the switch control signals of six switching devices, so that the DC output voltage V dc Track the given value; adopt SVPWM modulation strategy, the switching frequency is equal to the sampling frequency.

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