A DC-DC boost converter adaptive second-order sliding mode compound control method based on an extended state observer

Abstract

The application discloses a DC-DC step-up converter adaptive second-order sliding mode compound control method based on an extended state observer, and belongs to the field of electric vehicle power supply control. Under the control method, the output voltage of the switching power supply is high in stability and fast in tracking speed. Main steps are as follows: 1, a state space average method is used to model the step-up converter; 2, according to the mathematical model, a second-order sliding mode controller is designed to make the output voltage signal stably track an ideal signal; 3, a finite time extended state observer is constructed to estimate the lumped disturbance, and a second-order sliding mode compound controller is designed; 4, an adaptive law is designed and combined with the second-order sliding mode compound controller to obtain the DC-DC step-up converter compound control method. The application has the following advantages: 1, the vehicle can quickly respond under the disturbance condition, and the accuracy of the output voltage tracking the reference value is improved; 2, the control effect of the second-order sliding mode is significantly optimized, and the chattering problem is reduced.

Description

Technical Field

[0001] This invention belongs to the field of DC-DC converters for pure electric vehicles, and relates to an adaptive second-order sliding mode composite control method for DC-DC boost converters based on an extended state observer. Background Technology

[0002] Switching power supplies are a widely used technology in the field of power electronics, with DC-DC boost converters being one type, applied in various fields such as new energy vehicles. Due to the fluctuating and intermittent nature of new energy power supply, it can negatively impact the stability of the entire industrial system. Furthermore, load variations can also lead to power imbalances in the DC system. Therefore, controlling the power supply voltage is crucial, and DC-DC boost converters are a key means of maintaining power supply stability. In recent years, the most widely used control technology for DC-DC converters in the power electronics field is PID control. PID is a linear strategy, while a DC-DC converter is a time-varying nonlinear system. Nonlinear control techniques are needed to improve the output voltage speed, steady-state error, and anti-interference capability of the DC-DC converter, enabling it to produce a stable and efficient power supply. Sliding mode variable structure control is one such nonlinear control method, widely used in the power electronics field due to its advantages such as fast convergence speed, strong anti-interference capability, and ease of implementation.

[0003] The primary function of sliding mode control is to design a reasonable switching law that enables the system's moving point to reach a specific sliding surface within a finite time and perform sliding mode motion. However, in actual control, due to factors such as system inertia, time and space lag, the sliding mode cannot move precisely on the switching surface, but instead chatters back and forth along it. This chattering not only affects the system's control accuracy and increases energy loss, but can even excite high-frequency interference signals in the system, potentially causing instability. Therefore, chattering has long been considered a major factor hindering the practical application of sliding mode control technology in engineering.

[0004] In recent years, some scholars at home and abroad have proposed high-order sliding mode control methods through in-depth research on the dynamic characteristics of high-order sliding modes. This method explicitly includes the discontinuous control term in conventional sliding mode control on the higher-order derivatives of the sliding mode variable, while the actual control input is obtained by integrating the discontinuous control, thus obtaining a continuous sliding mode control law, which effectively reduces chattering.

[0005] Therefore, this invention designs a second-order sliding mode controller. To simultaneously improve the convergence speed and estimation accuracy of traditional estimators, a finite-time extended state observer is constructed using generalized super-twist technology. Unlike previously proposed observers, this one can observe disturbances very quickly. Furthermore, combining the designed controller with adaptive mechanisms effectively reduces chattering issues. Summary of the Invention

[0006] The purpose of this invention is to enable the output voltage to reach the reference value stably and quickly by designing an adaptive second-order sliding mode controller. To this end, an adaptive second-order sliding mode composite control method for a DC-DC boost converter based on an extended state observer is provided.

[0007] The present invention achieves the above-mentioned technical objectives through the following technical means.

[0008] An adaptive second-order sliding mode composite control method for a DC-DC boost converter based on an extended state observer is proposed, with the following specific steps:

[0009] Step 1: The boost converter is modeled using the state-space averaging method, and the boost converter is in continuous mode. The boost converter is modeled using the characteristics of capacitors and inductors.

[0010] Step 2: Based on the mathematical model in Step 1, design a second-order sliding mode controller using the relay-polynomial method to ensure that the output voltage signal can stably track the ideal signal.

[0011] Step 3: For the unknown lumped disturbance in the mathematical model of Step 2, construct a finite-time extended state observer to estimate it and give a second-order sliding mode composite controller.

[0012] Step 4: Construct an adaptive law based on the equivalent control method, and combine the controller designed in Step 3 with the adaptive law to obtain a composite control strategy for DC-DC boost converter based on the adaptive second-order sliding mode control method.

[0013] Furthermore, in step 1, a mathematical model is performed on the step-up transformer. Assuming the converter system is in an ideal state, the mathematical model of the system when the switching transistor is turned on is:

[0014]

[0015] The mathematical model of the system when the switching transistor is turned off is:

[0016]

[0017] Combining formulas (1) and (2), the average model of the boost converter is:

[0018]

[0019] Considering the uncertainties and external disturbances in the average mode, the dynamic model in formula (3) is:

[0020]

[0021] Where i L V0 is the inductor current, V0 is the capacitor output voltage, C is the capacitor, L is the inductor, R is the load resistance, and V0 is the capacitor output voltage. g The input voltage is V, G is a switch, which is represented by "1" and "0" to indicate on and off respectively. g0 R0 and R0 correspond to the nominal values ​​of the supply voltage and output load, respectively. w1(t) and w2(t) are time-varying, unknown, finite disturbance functions that are continuously differentiable, with their first derivatives bounded above. They are expressed as follows: and

[0022] Furthermore, in step 2, a controller for the second-order sliding mode is designed;

[0023] The error function has the following form:

[0024] s = V0 - V ref

[0025] Where V ref It is the expected value of the output voltage;

[0026] Specifically, the switching function G can be obtained by differentiating the error function.

[0027]

[0028] Furthermore, by taking the derivative of the error function, we can obtain...

[0029]

[0030] in It is regarded as a virtual controller;

[0031] It should be noted that when constructing the error function in this way, the switching function G, as the actual controller, will be the integral of the virtual controller u, which can reduce control chattering and improve control performance.

[0032] i L V0, w1(t), and w2(t) are all bounded, so let as well as They are i L From the maximum value of V0, we can derive the following inequality:

[0033]

[0034] Based on the above formula, a suitable constant can be found.

[0035]

[0036] It can be concluded that Therefore, this second-order system satisfies the assumptions of second-order sliding mode, and the second-order sliding mode controller has the following form:

[0037]

[0038] in It is regarded as a virtual controller, where s is the error function, β2 is the control gain, β1 determines the speed at which the system state approaches the sliding mode, and β1 and β2 are positive real numbers;

[0039] Furthermore, the switching function

[0040] Furthermore, in step 3, a finite-time extended state observer is designed;

[0041] The finite-time extended state observer of the lumped disturbance w1(t) can be constructed as follows:

[0042]

[0043] Among them l 11 and l 12 These are the parameters of the finite-time extended state observer, where V0 is the capacitor output voltage. It is an estimate of V0. It is an estimate of w1(t), and e1 is... The error is V0, C is the capacitance, R0 is the nominal value of the output load, G is the switching function, and f is the capacitance. 11 (e1) and f 12 (e1) is a nonlinear function;

[0044] Based on the generalized super-twisting technique, the nonlinear function f 11 (e1) and f 12 (e1) can be designed as follows:

[0045]

[0046] Where k1 is a positive real number;

[0047] Similarly, to estimate the lumped disturbance w2(t), the finite-time extended state observer is:

[0048]

[0049] Among them l 21 and l 22These are the parameters of the finite-time extended state observer, i L For inductor current, is i L The estimated value, It is an estimate of w2(t), V g0 It is the nominal value of the supply voltage, e2 is and i L The error, f 21 (e1) and f 22 (e1) is a nonlinear function;

[0050] Based on the generalized super-twisting technique, the nonlinear function f 21 (e1) and f 22 (e1) can be designed as

[0051]

[0052] Where k2 is a positive real number;

[0053] Compared to traditional extended state observers, finite-time extended state observers introduce fractional powers and an additional adjustable parameter k1; when the estimation error is far from the origin, the linear term l 11 and l 12 The high-speed exponential convergence characteristic of the equation can make the estimation error converge quickly to the vicinity of the origin; then, other nonlinear terms in the equation are given; Equations (8) and (10) can guarantee that the estimation error converges to zero from the neighborhood of the origin in a finite time.

[0054] Furthermore, in step 3, based on the finite-time extended state observer, the second-order sliding mode composite controller has the following form:

[0055]

[0056] in, β1 and β2 are positive real numbers, s is the error function, and G(t) is the switching function.

[0057] Furthermore, in step 4, an adaptive law is designed;

[0058] The second-order composite controller (9) designed in step 3 is modified as follows:

[0059]

[0060] The variable gain β2(t) is obtained from the following adaptive law.

[0061]

[0062]

[0063]

[0064]

[0065] Where β1 is a positive real number, s is the error function, G(t) is the switching function, β2(t) is the variable gain, ξ is the adaptive gain, M is a positive real number, σ is the state variable, h is a positive real number, and [sign(s)] is the variable value of β1. av k is the average value of the high-frequency signal. - ,k + λ0, λ1, and λ2 are constants greater than zero, representing the upper and lower bounds of the gain k(t), respectively. -1 These are internal auxiliary variables; z0 and z1 are [sign(s)]. av and Symbol [x] + Represented as:

[0066]

[0067] The invention has the following beneficial technical effects:

[0068] This invention presents an adaptive second-order sliding mode composite control method for a DC-DC boost converter based on an extended state observer. First, a second-order sliding mode controller is designed based on the mathematical model of the boost converter. To simultaneously improve the convergence speed and estimation accuracy of traditional estimators, the second-order sliding mode controller is further improved by incorporating a generalized super-twist technique to construct a finite-time extended state observer, which can observe disturbances very quickly. The designed controller is then combined with the adaptive technique proposed in this invention to further reduce chattering and energy loss. Attached Figure Description

[0069] Figure 1 Block diagram of the control scheme for the boost converter

[0070] Figure 2 This is the waveform during the startup phase of the boost converter.

[0071] Figure 3 This is the output voltage waveform of a boost converter under sudden load changes.

[0072] Figure 4 This is the waveform of the boost converter controller. Detailed Implementation

[0073] The invention will now be further described with reference to the accompanying drawings.

[0074] The following specific examples illustrate the implementation of the present invention, and those skilled in the art can easily implement it based on the content disclosed in this specification.

[0075] The boost topology used in this invention is as follows: Figure 1 As shown, the components included are: DC voltage source V g The components include: switching transistor S, diode D, inductor L, output capacitor C, and load R. Specific parameters are as follows: Input voltage V g =12V, expected output voltage V ref =24V, inductance L=120uH, output voltage C=1000uF, load resistance R=150Ω, system frequency f s =100kHz.

[0076] An adaptive second-order sliding mode composite control method for a DC-DC boost converter based on an extended state observer. The implementation process of the method is as follows:

[0077] 1. Perform mathematical modeling of the step-up transformer. Assuming the converter system is in an ideal state, the mathematical model of the system when the switching transistor is turned on is:

[0078]

[0079] The mathematical model of the system when the switching transistor is turned off is:

[0080]

[0081] Combining formulas (1) and (2), the average model of the boost converter is:

[0082]

[0083] Considering the uncertainties and external disturbances in the average mode, the dynamic model in formula (3) is:

[0084]

[0085] Where i L V0 is the inductor current, V0 is the capacitor output voltage, C is the capacitor, L is the inductor, R is the load resistance, and V0 is the capacitor output voltage. g The input voltage is V, G is a switch, which is represented by "1" and "0" to indicate on and off respectively. g0 R0 and R0 correspond to the nominal values ​​of the supply voltage and output load, respectively. w1(t) and w2(t) are time-varying, unknown, finite disturbance functions that are continuously differentiable, with their first derivatives bounded above. They are expressed as follows: and

[0086] 2. The error function has the following form:

[0087] s = V0 - V ref

[0088] Where V ref It is the expected value of the output voltage;

[0089] Specifically, the switching function G can be obtained by differentiating the error function.

[0090]

[0091] Furthermore, by taking the derivative of the error function, we can obtain...

[0092]

[0093] in It is regarded as a virtual controller;

[0094] It should be noted that when constructing the error function in this way, the switching function G, as the actual controller, will be the integral of the virtual controller u, which can reduce control chattering and improve control performance.

[0095] i L V0, w1(t), and w2(t) are all bounded. Let... as well as They are i L From the maximum value of V0, we can derive the following inequality:

[0096]

[0097] Based on the above formula, a suitable constant can be found.

[0098]

[0099] It can be concluded that Therefore, this second-order system satisfies the assumptions of second-order sliding mode, and the second-order sliding mode controller has the following form:

[0100]

[0101] in It is regarded as a virtual controller, where s is the error function, β2 is the control gain, β1 determines the speed at which the system state approaches the sliding mode, and β1 and β2 are positive real numbers;

[0102] Furthermore, switching functions

[0103] 3. Design a finite-time extended state observer. A finite-time extended state observer for a lumped disturbance w1(t) can be constructed as follows:

[0104]

[0105] Among them l 11 and l 12 These are the parameters of the finite-time extended state observer, where V0 is the capacitor output voltage. It is an estimate of V0. It is an estimate of w1(t), and e1 is... The error is V0, C is the capacitance, R0 is the nominal value of the output load, G is the switching function, and f is the capacitance. 11 (e1) and f 12 (e1) is a nonlinear function;

[0106] Based on the generalized super-twisting technique, the nonlinear function f 11 (e1) and f 12 (e1) can be designed as follows:

[0107]

[0108] Where k1 is a positive real number;

[0109] Similarly, to estimate the lumped disturbance w2(t), the finite-time extended state observer is:

[0110]

[0111] Among them l 21 and l 22 These are the parameters of the finite-time extended state observer, i L For inductor current, is i L The estimated value, It is an estimate of w2(t), V g0 It is the nominal value of the supply voltage, e2 is and i L The error, f 21 (e1) and f 22 (e1) is a nonlinear function;

[0112] Based on the generalized super-twisting technique, the nonlinear function f 21 (e1) and f 22 (e1) can be designed as

[0113]

[0114] Where k2 is a positive real number.

[0115] Compared to traditional extended state observers, finite-time extended state observers introduce fractional powers and an additional adjustable parameter k1. When the estimation error deviates far from the origin, the linear term l... 11 and l 12The high-speed exponential convergence property of the equation allows the estimation error to converge quickly to the vicinity of the origin. Then, other nonlinear terms in the equation are given. Equations (8) and (10) can guarantee that the estimation error converges to zero from the neighborhood of the origin in a finite time.

[0116] 4. Based on the finite-time expansion observer designed in step 2, the second-order sliding mode composite controller has the following form:

[0117]

[0118] in, β1 and β2 are positive real numbers, s is the error function, and G(t) is the switching function.

[0119] 5. Design an adaptive law.

[0120] According to step 3, the second-order sliding mode composite controller (9) is modified as follows:

[0121]

[0122] The variable gain β2(t) is obtained from the following adaptive law.

[0123]

[0124]

[0125]

[0126]

[0127] Where β1 is a positive real number, s is the error function, G(t) is the switching function, β2(t) is the variable gain, ξ is the adaptive gain, M is a positive real number, σ is the state variable, h is a positive real number, and [sign(s)] is the variable value of β1. av k is the average value of the high-frequency signal. - ,k + λ0, λ1, and λ2 are constants greater than zero, representing the upper and lower bounds of the gain k(t), respectively. -1 These are internal auxiliary variables; z0 and z1 are [sign(s)]. av and Symbol [x] + Represented as:

[0128]

[0129] Example: The design is validated using the following simulation results:

[0130] The following comparisons are given for three scenarios: from system startup (when the system begins to respond) to steady state, comparing the output waveforms of the second-order sliding mode algorithm and the adaptive second-order sliding mode composite controller; when the system suddenly changes its load, comparing the output waveforms of the second-order sliding mode algorithm and the adaptive second-order sliding mode composite controller; and for the system controller G, comparing the output waveforms of the second-order sliding mode algorithm and the adaptive second-order sliding mode composite controller.

[0131] Case 1: Waveform during the startup phase of the boost power converter

[0132] like Figure 2 : At the input voltage V g =12V, expected output voltage V ref At 24V, the outputs of the adaptive second-order sliding mode composite controller and the second-order sliding mode controller are compared, and the system response speed and steady-state time are compared. Simulation results show that the system response speed and steady-state time are not significantly different, but it can be seen that the adaptive second-order sliding mode composite controller is superior to the second-order sliding mode controller.

[0133] Scenario 2: The boost power converter suddenly changes its carrier waveform

[0134] like Figure 3 The load resistance was suddenly changed from 150Ω to 300Ω, and the output voltage change was observed instantaneously. The simulation results show that the output voltage of the adaptive second-order sliding mode composite controller consistently tracks the target voltage of 24V under varying load conditions. Furthermore, when the load resistance increases, the overshoot voltage is smaller than that of the second-order sliding mode controller, indicating that the adaptive second-order sliding mode composite controller has load-resistance capabilities.

[0135] Case 3: Waveform of controller G of boost power converter

[0136] like Figure 4 : At the input voltage V g =12V, expected output voltage V ref At 24V, observe the simulation diagrams of the adaptive second-order sliding mode composite controller and the second-order sliding mode controller. The simulation results show that the adaptive second-order sliding mode composite controller exhibits significantly less chattering than the second-order sliding mode controller, thus reducing energy loss.

[0137] The detailed descriptions listed above are merely specific descriptions of feasible embodiments of the present invention, and are not intended to limit the scope of protection of the present invention. All equivalent embodiments or modifications made without departing from the spirit of the present invention should be included within the scope of protection of the present invention.

Claims

1. An adaptive second-order sliding mode composite control method for a DC-DC boost converter based on an extended state observer, characterized in that, Includes the following steps: Step 1: The boost converter is modeled using the state-space averaging method, and the boost converter is in continuous mode. The boost converter is modeled using the characteristics of capacitors and inductors. Step 2: Based on the mathematical model in Step 1, design a second-order sliding mode controller using the relay-polynomial method to ensure that the output voltage signal can stably track the ideal signal. Step 3: For the unknown lumped disturbance in the mathematical model of Step 2, construct a finite-time extended state observer to estimate it and give a second-order sliding mode composite controller. Step 4: Construct an adaptive law based on the equivalent control method, and combine the controller designed in Step 3 with the adaptive law to obtain an adaptive second-order sliding mode composite control method for DC-DC boost converter based on an extended state observer. In step 3, the first lumped disturbance The finite-time extended state observer is constructed as follows: （5）； in and These are the parameters of a finite-time extended state observer. This is the output voltage of the capacitor. yes The estimated value, yes The estimated value, yes and The error, For capacitors, This is the nominal value of the output load. It is a switching function. and It is a nonlinear function; Based on the generalized super-twisting technique, nonlinear functions and Designed as follows: （6）； in It is a positive real number; Estimated total perturbation in episode 2 The finite-time extended state observer is: （7）； in and These are the parameters of a finite-time extended state observer. For inductor current, yes The estimated value, yes The estimated value, It is the nominal value of the power supply voltage. yes and The error, and It is a nonlinear function. It is an inductor; Based on the generalized super-twisting technique, nonlinear functions and Designed as follows: （8）； in It is a positive real number.

2. The method according to claim 1, characterized in that, Step 1, the modeling process of the boost converter, is as follows: Assuming the converter system is in an ideal state, the mathematical model of the system when the switching transistor is turned on is: （1）； The mathematical model of the system when the switching transistor is turned off is: （2）； Combining formulas (1) and (2), the average model of the boost converter is: （3）； Considering the uncertainties and external disturbances in the average mode, the dynamic model in formula (3) is changed to: （4）； in For inductor current, This is the output voltage of the capacitor. For capacitors, For inductance, The resistance of the load. Input voltage, It's a switching function, which uses "1" and "0" to represent on and off respectively. and These correspond to the nominal values ​​of the supply voltage and the output load, respectively. and It is a time-varying, unknown, finite perturbation function that is continuously differentiable and whose first derivative is bounded above, and is expressed as follows: and .

3. The method according to claim 2, characterized in that, A mathematical model of the step-up transformer is established, and the error function has the following form: ; in It is the expected value of the output voltage; Taking the derivative of the error function yields the switching function G: ； Furthermore, by differentiating the error function, we can obtain: ； in It is regarded as a virtual controller; When constructing the error function in this way, it can reduce control chattering and improve control performance.

4. The method according to claim 3, characterized in that, In step 2, the second-order sliding mode controller has the following form: ; in It is considered as a virtual controller, where s is the error function. To control the gain, The speed at which the system state approaches the sliding mode determines the speed at which the system state approaches the sliding mode. It is a positive real number; Switching function .

5. A method according to claim 4, characterized in that, In step 3, the second-order sliding mode composite controller has the following form: （9）； in , and Let be a positive real number, and s be the error function. (t) is the switching function, and x1 and x2 are error function variables.

6. A method according to claim 5, characterized in that, In step 4, the design process of the adaptive law is as follows: The second-order sliding mode composite controller (9) is rewritten as follows: ； Among them, variable gain Obtained from the following adaptive law: ， ； in, Let be a positive real number, and s be the error function. (t) is the switching function. It is a variable gain. For adaptive gain, It is a positive real number. For state variables, It is a positive real number. This is the average value of the high-frequency signal. These are constants greater than zero, representing the gains. The upper and lower bounds, , , It is a constant greater than zero. It is an internal auxiliary variable. and They are and ,symbol Represented as: .

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