A boost converter control method based on adaptive second-order sliding mode

Abstract

This invention discloses a Boost converter control method based on adaptive second-order sliding mode, belonging to the field of power electronic converters. This control method can suppress external disturbances, making the system insensitive to parameter uncertainties and improving system stability and robustness. The main steps are: 1. Considering the external disturbances and parameter uncertainties present in the actual operation of the Boost converter, a more realistic mathematical model is established; 2. Using voltage deviation as the sliding variable, a suitable sliding surface is designed to establish the equivalent sliding mode controller for the Boost converter; 3. An adaptive law is designed to establish an adaptive second-order sliding mode controller. The advantages of this invention are: First, the introduction of the adaptive law effectively handles system parameter uncertainties and unmodeled coupled perturbations, improving the system's anti-interference capability; Second, this control method improves steady-state accuracy and convergence speed, effectively reducing chattering problems.

Description

Technical Field

[0001] This invention relates to control technology for DC-DC power converter systems, belonging to the field of power electronic converter control. Specifically, it introduces an adaptive second-order sliding mode control method by introducing an adaptive law, which accelerates the response speed of the output voltage, enhances anti-interference capability, and reduces system chattering. Background Technology

[0002] With the rapid development of technology, switching power supplies have gone from being widely used in computers to being applied in various power electronics fields. There are many types of switching power supplies, and DC / DC converters are a very important component. They have been widely used in traditional industrial fields, such as for clean energy sources like fuel cells, wind power, and solar photovoltaic power generation, whose output power and voltage are easily affected by climate and load changes. It is essential to use DC / DC converters at their output terminals to provide stable output voltage. Currently, research on DC / DC converters generally falls into two directions: one is to study new converter topologies to improve power conversion efficiency; the other is to optimize existing control algorithms or design new control strategies with good control performance and strong robustness to achieve superior output performance and improve system efficiency and stability.

[0003] Boost converters, as a type of DC / DC converter, are typical time-varying nonlinear systems. They incorporate switching devices such as capacitors, inductors, diodes, MOSFETs, or IGBTs. Furthermore, the inaccurate modeling caused by their parasitic circuit parameters makes commonly used control methods, such as PID control, highly sensitive to parameter changes. Under large load variations, they are prone to slow dynamic response and output waveform distortion. Advanced nonlinear control strategies are crucial for ensuring the output voltage quality of DC converters. Numerous theoretical and experimental studies have shown that sliding mode control, as a variable-structure nonlinear control method, is highly adaptable to DC converters.

[0004] First-order sliding mode control has been extensively studied since its inception. However, because its control signal directly includes the switching term, the control effect depends on the selection of the sliding surface, which can lead to high-frequency chattering. To address these issues, higher-order sliding mode control methods have been proposed. These methods are characterized by the control input acting on the higher-order derivatives of the switching term. Second-order sliding mode control is a type of higher-order sliding mode control, exhibiting better robustness and stronger disturbance suppression capabilities compared to traditional control methods, thus making it a valuable area of ​​research. As a robust variable structure control method, sliding mode control demonstrates strong robustness against internal parameters and external disturbances. Its excellent robustness and transient response characteristics ensure good dynamic and static performance of the DC-DC converter even under large variations in input voltage or load. Summary of the Invention

[0005] The purpose of this invention is to propose a Boost converter control method based on adaptive second-order sliding mode. Leveraging its advantages of good anti-interference capability, fast output response speed, and strong robustness, this method combines adaptive and sliding mode control to precisely control the output voltage and disturbances of the Boost converter, thereby reducing system chattering and improving stability and dynamic / static performance. The specific technical solution is as follows:

[0006] A Boost converter control method based on adaptive second-order sliding mode includes the following steps:

[0007] Step 1: Consider the parameter uncertainties and external disturbances that exist in the actual Boost converter and establish a mathematical model. By the deviation between the actual output voltage and the ideal output voltage, the error state equation of the system is obtained.

[0008] Step 2: Based on the system error state equation described in Step 1, select a suitable sliding surface and establish the sliding mode equivalent controller for the Boost converter;

[0009] Step 3: Based on the equivalent controller in Step 2, design a switching control function, introduce an adaptive law, and establish an adaptive second-order sliding mode controller to reduce chattering caused by external disturbances and parameter uncertainties.

[0010] Furthermore, in step one, considering the existing parameter uncertainties and external disturbances, the mathematical model of the Boost converter is obtained as follows:

[0011]

[0012] In the formula v i v0 is the input voltage, i is the output voltage. L It is the inductor current, L0, C0, R0, v i0 For L, C, R, v under ideal conditions i △L, △C, △R, △v i0 Representing L, C, R, and v respectively i The changes in d1(t) and d2(t) are bounded external disturbances. u is the system control input, and its value can be 0 or 1.

[0013] After simple mathematical calculations, the above can be rewritten as:

[0014]

[0015] Where W1(t) and W2(t) are equivalent disturbance quantities, expressed as follows:

[0016]

[0017] The established error state equation is:

[0018]

[0019] In the formula, v0 is the output voltage, v ref x1 is the reference voltage, x2 is the output voltage deviation, and x3 is the rate of change of voltage deviation.

[0020] Furthermore, in step two, based on the error state equation established in step one, the selected sliding surface is:

[0021] s = x1 + c∫x1d(t)

[0022] In the formula, c>0.

[0023] Differentiating the above equation, we get:

[0024]

[0025] The equivalent sliding mode controller is designed as follows:

[0026]

[0027] In the formula, v ref It is the reference voltage, i L It is the inductor current, R0 and C0 are ideal values, c is a normal value, and W2 is the equivalent disturbance.

[0028] Furthermore, in step three, based on the sliding mode equivalent controller established in step two, the designed switching control law is as follows:

[0029]

[0030] The adaptive second-order sliding mode controller is designed as follows:

[0031]

[0032] in,

[0033]

[0034] The adaptive law is designed as follows:

[0035]

[0036] In the formula, u eq It is an equivalent control term, u vss It is a switching control term, sgn is the sign function, β is the time-varying adjustable gain, and has λ is the filtering time constant, and k, η, τ, m1, and m2 are suitable positive constants, 0 < σ ≤ 1.

[0037] The beneficial effects of this invention are:

[0038] The adaptive second-order sliding mode control method designed in this invention can effectively enable the output voltage of the Boost converter to quickly track the reference voltage, improving steady-state accuracy and convergence speed. Furthermore, the introduction of the adaptive rate can effectively handle the uncertainty of system parameters and unmodeled coupled perturbations, enhance the anti-interference capability of the system, and effectively reduce the chattering problem caused by external disturbances and parameter uncertainties. Attached Figure Description

[0039] Figure 1 This is the system architecture diagram of the Boost converter.

[0040] Figure 2 This is the circuit schematic of a Boost converter.

[0041] Figure 3 This is a waveform diagram of the startup phase of the Boost converter.

[0042] Figure 4 This is a waveform diagram of the load-changing stage of the Boost converter.

[0043] Figure 5 This is a waveform diagram of the transformer stage of a Boost converter. Detailed Implementation

[0044] This invention discloses an adaptive second-order sliding mode control method for output voltage control of a Boost converter. To make the objectives, technical solutions, and beneficial effects of this invention clearer and more explicit, the invention will be further described below with reference to the accompanying drawings.

[0045] Figure 1 The diagram shown is the system architecture of the Boost converter, which includes: (1) a Boost converter model that fits the actual model; (2) an error state equation module; (3) an adaptive second-order sliding mode controller module; (4) an adaptive law module; and (5) a comparator module.

[0046] The parameters of the DC-DC boost converter used are shown in Table 1.

[0047] Table 1 Parameters of DC-DC boost converter

[0048] Input voltage <![CDATA[v i (V)]]> 12 inductance L(μH) 100 capacitance C(μF) 1000 resistance R(Ω) 50 Reference voltage <![CDATA[v ref (V)]]> 24

[0049] Combination Figure 1 and Figure 2 A Boost converter control method based on adaptive second-order sliding mode is characterized by the following implementation steps:

[0050] Step 1: Consider the parameter uncertainties and external disturbances that exist in the actual Boost converter and establish a mathematical model. By the deviation between the actual output voltage and the ideal output voltage, the error state equation of the system is obtained.

[0051] like Figure 2 The schematic diagram of the DC-DC boost converter circuit shown is used to derive the state-space average model of the system under ideal conditions, based on its working principle:

[0052]

[0053] Among them, v i It is a DC voltage source, i L V0 is the inductor current, L is the output voltage, C is the inductance, and R is the load. u is a switching quantity, with values ​​of 1 and 0 indicating the switching transistor is on or off.

[0054] Considering the parameter uncertainties and external disturbances present in practical work, the state-space average model can be rewritten as follows:

[0055]

[0056] In the formula, L0, C0, R0, v i0 For L, C, R, v under ideal conditions i ΔL, ΔC, ΔR, Δv i0 Representing L, C, R, and v respectively i The changes in d1(t) and d2(t) are bounded external disturbances.

[0057] The above formula can be simplified as follows:

[0058]

[0059] Where W1(t) and W2(t) are equivalent disturbance quantities, expressed as follows:

[0060]

[0061] The established error state equation is:

[0062]

[0063] In the formula, v0 is the output voltage, v ref x1 is the reference voltage, x2 is the output voltage deviation, and x3 is the rate of change of voltage deviation.

[0064] Step 2: Based on the system error state equation described in Step 1, select a suitable sliding surface and establish the sliding mode equivalent controller for the Boost converter.

[0065] The selected sliding surface is:

[0066] s = x1 + c∫x1d(t)

[0067] In the formula, c>0.

[0068] Differentiating the above equation, we have:

[0069]

[0070] The equivalent sliding mode controller is designed as follows:

[0071]

[0072] In the formula, v ref It is the reference voltage, i L It is the inductor current, R0 and C0 are ideal values, c is a normal value, and W2 is the equivalent disturbance.

[0073] Step 3: Based on the equivalent controller in Step 2, design a switching control function, introduce an adaptive law, and establish an adaptive second-order sliding mode controller to reduce chattering caused by external disturbances and parameter uncertainties.

[0074] The designed switching control item is:

[0075]

[0076] The adaptive second-order sliding mode controller is designed as follows:

[0077]

[0078] in,

[0079]

[0080] The adaptive law is designed as follows:

[0081]

[0082] In the formula, u eq It is an equivalent control term, u vss It is a switching control term, sgn is the sign function, β is the time-varying adjustable gain, and has λ is the filtering time constant, and k, η, τ, m1, and m2 are suitable positive constants, 0 < σ ≤ 1.

[0083] Example: The method of the present invention is verified by the following simulation results:

[0084] The following comparisons are given in three scenarios: during the system startup phase, a comparison of the output waveforms of the adaptive second-order sliding mode control method (ASOSM) of this invention with the PID algorithm and the first-order sliding mode algorithm (FOSM); a comparison of the output waveforms of the PID algorithm, the first-order sliding mode algorithm, and the control method of this invention when the load resistance is changed; and a comparison of the output waveforms of the PID algorithm, the first-order sliding mode algorithm, and the control method of this invention when the input voltage is changed.

[0085] Scenario 1: Comparison of DC-DC boost converter startup phase

[0086] like Figure 3 Given an input voltage of 12V and a reference output voltage of 24V, a comparison of the adaptive second-order sliding mode control method of this invention with the PID algorithm and the first-order sliding mode algorithm in terms of overshoot and response speed is presented. The comparison diagram during the startup phase shows that the adaptive second-order sliding mode control method of this invention not only has a faster response speed than the other two algorithms, but also exhibits no overshoot and good robustness, demonstrating that the control method of this invention has excellent dynamic and steady-state performance.

[0087] Scenario 2: Comparison of DC-DC boost converters during load change stages

[0088] like Figure 4 Given an input voltage of 12V and a reference output voltage of 24V, the load undergoes a sudden change at t = 0.25s, with the load resistance decreasing from 50Ω to 25Ω. The comparison chart of the load change stages shows that when the load resistance changes abruptly, both the PID and first-order sliding mode exhibit chattering, and the load change amplitude is higher than that of the adaptive second-order sliding mode. This demonstrates that the adaptive second-order sliding mode control method of this invention has smaller overshoot and a faster steady-state time compared to the other two algorithms, and can effectively suppress chattering caused by disturbances.

[0089] Scenario 3: Comparison of the transformation stages of a DC-DC boost converter

[0090] like Figure 5 Given an input voltage of 12V and a reference output voltage of 24V, the input voltage undergoes a sudden change at t = 0.25s, jumping from 12V to 15V. The comparison graph of the transformation stages shows that when the input voltage changes abruptly, the transformation amplitude of the adaptive second-order sliding mode is smaller than that of the PID and first-order sliding mode algorithms. This demonstrates that the adaptive second-order sliding mode control method of this invention has a faster response speed, better stability, and effectively mitigates the impact of chattering compared to the other two algorithms. Overall, the second-order sliding mode control method in this invention is superior to the first-order sliding mode and PID algorithms.

[0091] The embodiments of the present invention have been shown and described above, but are not intended to limit the scope of protection of the present invention. Any obvious modifications, substitutions and variations that can be made by those skilled in the art without departing from the principles and rules of the present invention shall fall within the scope of protection of the present invention.

Claims

1. A Boost converter control method based on adaptive second-order sliding mode, characterized in that: Step 1: Consider the parameter uncertainties and external disturbances that exist in the actual Boost converter and establish a mathematical model. By the deviation between the actual output voltage and the ideal output voltage, the error state equation of the system is obtained. Step 2: Based on the system error state equation described in Step 1, select a suitable sliding surface and establish the sliding mode equivalent controller for the Boost converter; Step 3: Based on the equivalent controller in Step 2, design a switching control function, introduce an adaptive law, and establish an adaptive second-order sliding mode controller to reduce chattering caused by external disturbances and parameter uncertainties in the system. In step three, the adaptive second-order sliding mode controller is designed as follows: in, In the formula, u eq It is an equivalent control term, u vss This is the switching control term, where sgn is the sign function, β is the time-varying adjustable gain, λ is the filtering time constant, k > 0, 0 < σ ≤ 1; and the time-varying adjustable gain β has a positive constant value. β and Satisfying Relationship: β and Let represent the upper and lower bounds of β, respectively; the value of σ affects the second-order sliding mode. If σ is 1, the system will reach an exponentially stable second-order sliding mode. If σ is 0.5, the system will realize the second-order sliding mode with the greatest probability. The adaptive law is designed as follows: In the formula, η, τ, m1, and m2 are appropriate positive constants.

2. The Boost converter control method based on adaptive second-order sliding mode according to claim 1, characterized in that, In step one, the mathematical model of the Boost converter with parameter uncertainties and external disturbances is established as follows: Rewriting the above equation in the form of a state-space model, its expression is: in, In the formula, i L It is the inductor current, v0 is the output voltage, L0, C0, R0, v i0 For L, C, R, v under ideal conditions i ΔL, ΔC, ΔR, Δv i0 Representing L, C, R, and v respectively i The change u is the system control input, which takes the values ​​0 and 1; d1(t) and d2(t) are bounded external disturbances; and W1(t) and W2(t) are equivalent disturbance quantities. The error state equation of the system is then: In the formula, v0 is the output voltage, v ref x1 is the reference voltage, x2 is the output voltage deviation, and x3 is the rate of change of voltage deviation.

3. The Boost converter control method based on adaptive second-order sliding mode according to claim 1, characterized in that, In step two, the design steps for the sliding mode equivalent controller are as follows: Select the sliding surface as follows s = x1 + c∫x1d(t) In the formula, c > 0; Differentiating with respect to the sliding surface, we have The sliding mode equivalent controller is designed as follows: In the formula, v ref It is the reference voltage, i L It is the inductor current, R0 and C0 are ideal values, c is a normal value, and W2 is the equivalent disturbance.

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