An adaptive MPC control method for two-phase interleaved parallel DC-DC converters

Abstract

The present invention discloses an adaptive MPC control method for a two-phase staggered parallel DC-DC converter, which belongs to the field of on-board chargers. Under this control method, the output voltage of the system has high stability and fast tracking speed. The main steps are: 1. Establishing a dynamic model of the system, using the dynamic model to discretize it, and obtaining a discrete model of the system; 2. Establishing an observer module, estimating the state variables in the system, and obtaining the observed values ​​of the input voltage and the load resistance; 3. Establishing an MPC controller, in the voltage outer loop, obtaining the current reference value through the proportional link, and finally predicting the next moment of the model. The advantages of the present invention are: first, the system can quickly and automatically respond to disturbances in the load or input voltage, thereby improving the accuracy of the output voltage tracking the reference value; second, it significantly optimizes the control effect in the traditional MPC method, and reduces potential jitter and overshoot problems; third, the control method has a simple structure, a small amount of calculation, and is easy to implement.

Description

[0001] The present invention relates to the field of on-board chargers, and specifically utilizes a novel MPC control method to improve the dynamic and steady-state performance of a power converter, enhance the robustness of the system, and use an adaptive sliding mode observer to estimate unknown load resistance and input voltage to reduce costs, making it closer to practical applications. Background Art

[0002] In the field of DC-DC converters for pure electric vehicles, electric vehicles require charging stations. The output voltage of these stations is often low, and consumers are increasingly demanding fast charging. This requires a boost circuit. Boost power converters are a commonly used type of DC-DC switching power supply. Through certain control methods, they can convert unstable input voltages into higher, more stable output voltages. Their simple topology, minimal components, and excellent reliability have led to their widespread application in industries such as aerospace, energy, electric vehicles, and healthcare. Interleaved parallel boost circuits are particularly attractive, offering smaller size and lower current and output voltage ripple than single-phase boost circuits. Consequently, interleaved parallel boost circuits are increasingly favored in pure electric vehicles. Due to the nonlinear and non-minimum phase characteristics of boost circuits, a standard approach is to use a linear PWM-based PI control strategy. This can degrade the performance of linear controllers, making it impossible to directly control the output voltage using control methods that use the output voltage error as the output, such as input-output feedback linearization and backstepping. In other words, when the output voltage is used as the output, zero dynamics is unstable. Therefore, output voltage regulation should be implemented as current tracking, a method known as indirect control. Adaptive boost control is mostly indirect control. The present invention proposes a new model predictive control method. Using existing MPC, output voltage tracking can be easily achieved. In situations where unbiased tracking is required under various interferences such as load resistance, inductance, and input voltage, and where the system state is not necessarily fully measurable or physically difficult to measure, which requires significant cost, the present invention adds an adaptive rule observer method. The advantage of this solution is that it only requires a one-step prediction range to control the converter, has good transient response, and accurately tracks the actual values ​​of each state vector, input voltage, and load resistance.

[0003] MPC is a finite-horizon optimization method. Finite Control Set MPC (FCS MPC) is well-suited for DC power electronics. The boost converter is a typical DC power system, but its drawback is the computational complexity of solving the optimization problem. Therefore, one approach requires only one prediction step in the time domain, which offers the advantage of a constant switching frequency. Predictive control strategies have the advantage of not relying on an average model and can incorporate converter limitations, such as overcurrent, as system constraints in the formulation of the optimal control problem. Summary of the Invention

[0004] This invention provides an MPC control method for a two-phase interleaved parallel Boost converter based on an adaptive sliding mode observer. By observing various circuit states using the adaptive observer, the inductor current, output voltage, input voltage, and load observations in the circuit can accurately track their actual values. These observed values ​​are fed into the MPC controller, which generates a duty cycle, enabling the output voltage to stably and quickly reach a reference value. The specific steps are as follows:

[0005] Step 1: Establish a state space expression based on the working principle of the dual-phase interleaved parallel boost converter control system;

[0006] Step 2: Based on the mathematical model in the previous step, a sliding mode observer is established, and the input voltage and load resistance are designed as the adaptive parameters of the observer;

[0007] Step 3: Analyze the conditions that the MPC controller needs to meet, establish a discrete model of the interleaved parallel boost converter, and predict the output voltage and inductor current change trends at future times;

[0008] Step 4: Calculate the reference value of each phase inductor current based on the observed input voltage and load, and combine it with the sampled value to construct the system's target optimization function.

[0009] Step 5: Minimize the objective optimization function constructed in step 5 and solve the control input based on the staggered parallel boost converter as the duty cycle input value at the next moment.

[0010] Furthermore, in step 1, the system state space expression is specifically expressed as follows:

[0011]

[0012] Among them, x1 and x2 represent i L1 、i L2 ; Z = V c -V ref , L1, L2 represent the equivalent inductance value of each phase in the circuit, C represents the equivalent capacitance value in the circuit, V ref Represents the output voltage reference value, and θ represents the reciprocal of the load resistance.

[0013] Furthermore, the capacitor voltage error Z information is fully considered, and a new state variable, the inductor current, is introduced.

[0014] Furthermore, in step 2, based on the system state space expression (1), the sliding mode observer is designed as follows:

[0015]

[0016] in, and are the estimated values ​​of x1, x2 and Z respectively; is an estimate of the input voltage; is the estimated value of θ; h1, h2, h3>0 are the observer gains.

[0017] Furthermore, the adaptive parameters designed on the observer and is given by the following adaptive law:

[0018]

[0019]

[0020] Among them, α1, α2>0 are adaptive gains.

[0021] Furthermore, in step 3, based on the system state space expression (1), a discrete model of the two-phase interleaved parallel Boost converter system is established as follows:

[0022]

[0023]

[0024] Among them, T s represents the sampling period, V in (k) represents the input voltage value at the sampling moment k, θ(k) represents the reciprocal of the load resistance at the sampling moment k, i L1 (k), i L2 (k) represents the inductor current sampling value of each phase at the kth sampling moment, Z(k) represents the difference between the output voltage sampling value and the input reference value at the kth sampling moment, and u1(k) and u2(k)∈(0, 1) represent the control input at the kth sampling moment of each phase.

[0025] Simplifying expressions (3) and (4) into a unified discrete model expression yields:

[0026] X i＝1，2 (k+1)=AX i (k)+BX i (k)u i (k)+Cu i (k)+D (5)

[0027] in

[0028]

[0029] Furthermore, in step 4, the reference value of the inductor current is expressed as follows:

[0030]

[0031] Based on the discrete mathematical model (5) of the system, the system optimization target cost function is constructed as follows:

[0032]

[0033] in, is the reference value of the state variable, is the difference value of the controller, is the ideal value of the controller, vector P c is the weight of the inductor current error and the output capacitor error, γ is the controller u i The weight of .

[0034] Furthermore, according to J when k→∞ u (X i (k+1),u i * )-J u (X i (k),u i )≤0, we can get P c Need to meet P c -(A+Bu i * ) T P c (A+Bu i *)≥0, its purpose is to pass the controller average value u i Make the value of the cost function tend to be minimum.

[0035] Furthermore, in step 5, based on the system's optimization target cost function (6), the optimal switching state u is selected by minimizing the associated cost function. i , we can get the following:

[0036]

[0037] c1(X i (k+1))=AX i (k)+DX i *

[0038] c2(X i (k+1))=BX i (k)+C

[0039] Among them, γ, u * 、P c 、Xi * is a known constant, which must satisfy γ>0, P c >0, c1(X i (k+1))、c2(X i (k+1)) is an intermediate variable.

[0040] The invention has the following beneficial technical effects:

[0041] The present invention designs a new MPC controller for a two-phase interleaved parallel Boost converter based on a sliding mode observer. Intuitively, it can improve the steady-state and dynamic performance of the system and greatly reduce the complexity of the algorithm. Microscopically, the sliding mode observer is used to observe the system state, achieving unbiased tracking while taking into account the changing trends of each state at future moments. Global finite-time stability and convergence are demonstrated through Simulink simulation in Matlab. The estimated value accurately tracks the actual measured value, eliminating interference due to load changes and unstable input voltage. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 This is the block diagram of the control system of the two-phase interleaved parallel Boost converter.

[0043] Figure 2 This is the waveform of the dual-phase interleaved parallel Boost converter during the startup phase.

[0044] Figure 3 This is the output voltage waveform of the dual-phase interleaved parallel Boost converter under sudden load change.

[0045] Figure 4 This is the sudden voltage change waveform of the two-phase interleaved parallel Boost converter.

[0046] Figure 5 shows the waveforms obtained by the observer of the dual-phase interleaved parallel Boost converter. DETAILED DESCRIPTION

[0047] The present invention will be further described below with reference to the accompanying drawings.

[0048] The following describes the embodiments of the present invention through specific examples, and those skilled in the art can easily implement the embodiments according to the contents disclosed in this specification.

[0049] The topology used in the present invention is a dual-phase interleaved parallel Boost power converter, such as Figure 1 As shown, the components included are: DC voltage source V in , switch tube S i , diode D i 、Inductor L i, output capacitor C, load R. The MPC controller first establishes a continuous mathematical model, then discretizes it, and designs the controller through the cost function. The specific parameters are as follows: input voltage V in =15V, output voltage expected value V c =60V, inductor L1=L2=100μH, output capacitor C=680μF, load resistance R=18Ω, system frequency f s =100KHz.

[0050] A novel MPC control method for a two-phase interleaved parallel Boost converter based on an adaptive sliding mode observer is proposed. The implementation process of the method is as follows:

[0051] 1. Based on Figure 1 The system state space expression of the dual-phase interleaved parallel Boost power converter is as follows:

[0052]

[0053] Among them, x1 and x2 represent i L1 、i L2 ; Z = V c -V ref , V ref Represents the output voltage reference value, and θ represents the reciprocal of the load resistance.

[0054] The capacitor voltage error Z information is fully considered, and a new state variable, the inductor current, is introduced.

[0055] 2. Based on the system state space expression (1), a sliding mode observer is established. The specific design is as follows:

[0056]

[0057] in, and are the estimated values ​​of x1, x2 and Z respectively; is an estimate of the input voltage; is the estimated value of θ; h1, h2, h3>0 is the observer gain, let

[0058] 3. Design adaptive laws to observe adaptive parameters and The construction method is as follows:

[0059] First, subtract (2) from (1) to obtain the following model:

[0060]

[0061] According to the state variable error selected in model (3), the Lyapunov function is designed as:

[0062]

[0063] Among them, α1, α2>0 are adaptive gains;

[0064] According to the error model (3), the expression (4) is derived and analyzed according to the Lyapunov stability theory, we can get The expression is as follows:

[0065]

[0066] To make It depends on canceling the contents of the brackets in expression (5); thus giving the following adaptive law:

[0067]

[0068]

[0069] 4. Based on the system state space expression (1), a discrete model of the interleaved parallel Boost converter is established to predict the output voltage and inductor current variation trends at future moments. The discrete model is as follows:

[0070]

[0071]

[0072] Among them, T s represents the sampling period, V in (k) represents the input voltage value at the sampling moment k, θ(k) represents the reciprocal of the load resistance at the sampling moment k, i L1 (k), i L2 (k) represents the inductor current sampling value of each phase at the kth sampling moment, Z(k) represents the difference between the output voltage sampling value and the input reference value at the kth sampling moment, and u1(k) and u2(k)∈(0, 1) represent the control input at the kth sampling moment of each phase.

[0073] Simplifying expressions (6) and (7) into a unified discrete model expression yields:

[0074] X i＝1，2 (k+1)=AX i (k)+BX i (k)u i (k)+Cu i (k)+D (8) in

[0075] 5. Based on the circuit's input power being equal to the output power, the reference value of the inductor current is obtained. Add the ratio of the difference between the output voltage and the reference output voltage to the reference value of the inductor current, and the expression for the reference value of the inductor current is as follows:

[0076]

[0077] In order to keep the switching frequency constant, the prediction domain is 1. Based on the system discrete model (8), the target cost function of the system is constructed as follows:

[0078]

[0079] in, is the reference value of the state variable, is the difference value of the controller, is the ideal value of the controller, vector P c is the weight of the inductor current error and the output capacitor error, γ is the controller u i The weight of .

[0080] 6. In order to be able to change the controller average value u i To minimize the cost function, we need to design a suitable vector P c , the specific design method is:

[0081] First, define the steady-state error of the state variable: e(k+1)=X i (k+1)-X i * , in order to ensure J u (X(k+1),u * )-J u (X(k),u)=-e(k) T W c e(k)-γu i 2 <0, that is, when W c When ≥0, J u (X(k+1),u * )<J u (X(k),u), so that the system cost function can converge quickly. Among them, W c =P c -(A+Bu * ) T P c (A+Bu * ).

[0082] Therefore, the weight matrix P cThe parameter design satisfies P c -(A+Bu * ) T P c (A+Bu * )≥0. This is easy to implement, so we can get

[0083] 7. Based on the system's objective cost function (9), an adaptive MPC controller for the two-phase interleaved parallel Boost converter is designed. The specific design is as follows:

[0084] The optimizer of this optimization problem minimizes the error of the next future state and the deviation of the input while satisfying the input constraints. In order to derive the optimal case of the cost function, the cost function is rewritten as:

[0085] J u (X(k+1),u)=[(BX(k)+C) T P C (BX(k)+C)+γ]u(k) 2

[0086] +[2(BX(k)+C) T P c (AX(k)+DX * )-2γ]u(k)

[0087] +(AX(k)+DX * ) T P C (AX(k)+DX * )-γu *

[0088] According to the cost function the optimal solution is The specific design of the adaptive MPC controller is as follows:

[0089]

[0090] The control parameters must meet the following requirements: 0<u i <1(i=1,2). c -(A+Bu * )≥0;

[0091] Design intermediate variables:

[0092] c1(X i (k+1))=AX i (k)+DX i *

[0093] c2(Xi (k+1))=BX i (k)+C

[0094] Among them, γ, u * 、P c 、X i * is a known constant, which must satisfy γ>0, P c >0, c1(X i (k+1))、c2(X i (k+1)) is an intermediate variable.

[0095] Example: The design is verified by the following simulation results:

[0096] The following compares four situations: when the system starts to respond to the system steady state, the output waveforms of the traditional MPC algorithm and the adaptive MPC algorithm are compared; when the system suddenly changes the load, the output waveforms of the traditional MPC algorithm and the new adaptive MPC algorithm are compared; when the system suddenly changes the voltage, the output waveforms of the traditional MPC algorithm and the adaptive MPC algorithm are compared.

[0097] Case 1: Waveforms of a two-phase interleaved parallel boost power converter during startup

[0098] like Figure 2 For a given voltage of 15V and an output voltage of 60V, the outputs of the novel MPC controller invented in this paper are compared with those of a traditional MPC controller. The system response speed, overshoot, and time to steady-state are compared. The simulation results show that the adaptive MPC controller outperforms the traditional MPC controller in terms of both dynamic and steady-state indicators, such as overshoot and response time.

[0099] Case 2: Sudden carrier waveform change in a dual-phase interleaved parallel boost power converter

[0100] like Figure 3 :like Figure 3 As shown in the figure, with a given voltage of 15V and an output voltage of 60V, the load resistance is suddenly changed from 18Ω to 30Ω, and the output voltage change at the instant of the load change is observed. The simulation graph shows that the adaptive MPC algorithm experiences an increase in output voltage at the instant of the load change, but subsequently maintains track of the target voltage. This error is lower than that of traditional MPC algorithms, and the output voltage tracking performance is also better than other controllers. The simulation results show that the adaptive MPC algorithm has significant advantages.

[0101] Case 3: Sudden voltage change waveform of dual-phase interleaved parallel boost power converter

[0102] like Figure 4:like Figure 4 As shown in the figure, with a given voltage of 15V and an output voltage of 60V, the input voltage is suddenly changed from 15V to 18V, and the output voltage change at the moment of transformation is observed. The simulation results show that the output voltage error of the adaptive MPC algorithm is slightly higher than that of the traditional MPC algorithm. The traditional MPC algorithm suffers from jitter, while the adaptive MPC algorithm effectively eliminates this shortcoming. The adaptive MPC also has a relatively fast convergence speed.

[0103] Case 4: Waveforms obtained by the observer of a two-phase interleaved parallel boost converter

[0104] As shown in Figure 5, when the given voltage is 15V and the output voltage is 60V, the load resistance is suddenly changed from 18Ω to 30Ω, and the input voltage is suddenly changed from 15V to 18V, Figure 5 (1) reflects the input voltage observation value change waveform, and Figure 5 (2) reflects the output load observation value change waveform. From the simulation results, it can be seen that the input voltage and output load reach a steady state in a very short time, and under the condition of variable load or variable voltage, the input voltage and output load change to the actual value in a step form.

[0105] The simulation results show that the new MPC controller performs better than other controllers. The series of detailed descriptions listed above are only specific descriptions of feasible implementation methods of the present invention and are not intended to limit the scope of protection of the present invention. All equivalent implementation methods or modifications that do not depart from the spirit of the present invention are included in the scope of protection of the present invention.

Claims

1. An adaptive MPC control method for a two-phase interleaved parallel DC-DC converter, characterized in that: The following steps are involved: Step 1: Establish a state space expression based on the working principle of the dual-phase interleaved parallel boost converter control system; Step 2: Based on the mathematical model in the previous step, a sliding mode observer is established, and the input voltage and load resistance are designed as the adaptive parameters of the observer; Step 3: Analyze the conditions that the MPC controller needs to meet, establish a discrete model of the interleaved parallel boost converter, and predict the output voltage and inductor current change trends at future times; Step 4: Calculate the reference value of each phase inductor current based on the observed input voltage and load, and combine it with the sampled value to construct the system's target optimization function. Step 5: Minimize the objective optimization function constructed in step 5 and solve the control input of the interleaved parallel boost converter as the duty cycle input value at the next moment; In step 1, the system state space fully considers the capacitor voltage error Z information, and then introduces a new state variable inductor current. The expression is specifically expressed as follows: Among them, x1 and x2 represent i L1 、i L2 ; Z=V c -V ref , L1, L2 represent the equivalent inductance value of each phase in the circuit, C represents the equivalent capacitance value in the circuit, V ref Represents the output voltage reference value, θ represents the reciprocal of the load resistance; In step 3, based on the system state space expression (1), the discrete model of the two-phase interleaved parallel Boost converter system is established as follows: Among them, T s represents the sampling period, V in (k) represents the input voltage value at the sampling moment k, θ(k) represents the reciprocal of the load resistance at the sampling moment k, i L1 (k), i L2 (k) represents the inductor current sampling value of each phase at the kth sampling moment, Z(k) represents the difference between the output voltage sampling value and the input reference value at the kth sampling moment, u1(k), u2(k)∈(0,1) represent the control input of each phase at the kth sampling moment; Simplifying expressions (3) and (4) into a unified discrete model expression yields: X i＝1，2 (k+1)=AX i (k)+BX i (nest i (k)+Cu i (k)+D (5) in 2. The adaptive MPC control method for a two-phase interleaved parallel DC-DC converter according to claim 1, characterized in that: In step 2, based on the system state space expression (1), the sliding mode observer is designed as follows: in, and are the estimated values ​​of x1, x2 and Z respectively; is the estimated value of the input voltage; h1, h2, h3>0 are the observer gains.

3. The adaptive MPC control method for a two-phase interleaved parallel DC-DC converter according to claim 2, characterized in that: Adaptive parameters designed on sliding mode observer and is given by the following adaptive law: Among them, α1, α2>0 are adaptive gains, is an estimate of θ.

4. The adaptive MPC control method for a two-phase interleaved parallel DC-DC converter according to claim 1, characterized in that: In step 4, the reference value of the inductor current is expressed as follows: Based on the discrete mathematical model (5) of the system, the system optimization target cost function is constructed as follows: in, is the reference value of the state variable, is the difference value of the controller, is the ideal value of the controller, vector P c is the weight of the inductor current error and the output capacitor error, γ is the controller u i The weight of .

5. The adaptive MPC control method for a two-phase interleaved parallel DC-DC converter according to claim 4, characterized in that: The system's optimization objective cost function (6) is based on J when k→∞. u (X i (k+1),u i * )-J u (X i (k),u i )≤0, we can get P c Need to meet P c -(A+Bu i * ) T P c (A+Bu i * )≥0, its purpose is to pass the controller average value u i Make the value of the cost function tend to be minimum.

6. The adaptive MPC control method for a two-phase interleaved parallel DC-DC converter according to claim 5, characterized in that: In step 5, based on the system's optimization objective cost function (6), the optimal switching state u is selected by minimizing the associated cost function. i , we can get the following: c1(X i (k+1))=AX i (k)+D-X i * c2(X i (k+1))=BX i (k)+C Among them, γ, u * 、P c 、X i * is a known constant, which must satisfy γ>0, P c >0, c1(X i (k+1))、c2(X i (k+1)) is an intermediate variable.

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