Method for controlling a boost converter having N switching units

Abstract

The present invention relates to a method for controlling a boost converter having N switching units using synchronous pulse width modulation, wherein N is a natural integer not equal to zero, the method comprising: measuring an input voltage (V 输入 ) and output voltage (V 输出 ) step; - determining an output vector (y) designed to define a representation of the linear state of the boost converter; - calculating a power change (P 输出 ) step; ‑ According to the second-order derivative of the output vector (y) #imgabs0# the power (P 输出 ) and the measured input voltage (V 输入 ) and output voltage (V 输出 ) to determine the N duty cycles (α k ) step; and ‑according to the determined duty cycle (α k ) to control the steps of each switching unit (k) of the converter.

Description

Technical Field

[0001] The present invention relates to a method for controlling a boost converter having N switching units.

[0002] The invention relates to a DC / DC boost converter, which is a step-up DC voltage converter. Background Art

[0003] In the field of hybrid or electric vehicles, a known solution is to use a boost converter 2 in an electrical assembly 10 including a drive motor 4, such as Figure 1 shown.

[0004] In such an electrical assembly 10 , the boost converter 2 is placed upstream of the voltage inverter 3 and the electric machine 4 , and is considered as a dynamic current source.

[0005] However, the boost converter 2 is positioned downstream of the power supply 1 and the input filter.

[0006] The boost converter 2 is a converter of the DC-DC type. Its purpose is therefore to supply a DC voltage greater than or equal to the voltage measured at the input terminals to the load being powered.

[0007] This type of converter is a non-minimum phase system. In fact, the transfer function relating the output voltage to the control, denoted H(s), appears to be zero in the complex plane with a positive real part.

[0008] Based on the small signal model development and linearization about a given stable operating point, the transfer function H(s) takes the following form:

[0009]

[0010] Among them, z1>0, p1<0, and p2<0 are the zeros and poles of the transfer function H(s) respectively.

[0011] Furthermore, the boost converter is a non-minimum phase system, where the output response is initially in antiphase with respect to the input change. The output tends to diverge before converging towards a stable point. This is known as the unstable phase of the output voltage. Furthermore, the relationship between its various states (on the one hand) and control (on the other hand) is nonlinear.

[0012] Accordingly, a general problem is to stably and quickly control a boost converter having N switching cells, where N is a non-zero natural integer.

[0013] It is worth noting that the document US 2017 / 0257038 A1 known in the prior art describes a method for controlling a boost converter with N phases, where N is a non-zero natural integer. The method aims to modify the chopping frequency of the system and add a phase shift between the control commands of the various units to avoid the resonant frequency of the DC bus. However, such a solution cannot achieve stable, dynamic and fast control.

[0014] Accordingly, it is a well-known problem to obtain a more stable and faster control of such a boost converter, rather than using control of cascaded loops which tend to limit the dynamic range of control of external disturbance effects. Summary of the invention

[0015] A method for controlling a boost converter having N switching units using synchronous pulse width modulation is provided, wherein N is a non-zero natural integer, the converter receiving a DC voltage V at an input terminal from a voltage source 输入 The output voltage is greater than or equal to the input voltage V 输入 The output voltage V 输出 , the method comprising:

[0016] -Measure the input voltage V of the boost converter 输入 and output voltage V 输出 Steps;

[0017] - a step of determining an output vector y designed for global linearization of the system of equations of the boost converter;

[0018] - Calculate the power change of the electrical load at the output of the converter Steps;

[0019] -According to the second derivative of the output vector y The derivative of the power of the electrical load And the measured input voltage V 输入 With the output voltage V 输出 The step of determining N duty cycles of the converter by the ratio of

[0020] - The step of controlling each switching unit of the converter according to the determined duty cycle.

[0021] Therefore, a control method can be obtained by controlling a converter having N switching units nonlinearly via global linearization and compensating for the nonlinearity by a control that ensures a stable asymptotic convergence of the error. This method allows the output voltage of the DC-DC converter (which is the voltage measured across the terminals of the decoupling capacitor at the input of the voltage inverter) to be regulated to a set point voltage set by the user, while ensuring the overall stability of the system and providing a relatively good reactivity and dynamic behavior of the control of external disturbance effects.

[0022] Advantageously and in a non-limiting manner, when the converter comprises N>1 switching units, the step of determining N duty cycles comprises calculating the energy flow through each switching unit. Therefore, the calculations can be obtained taking into account the dynamic behavior of the converter.

[0023] Advantageously and in a non-limiting manner, the step of determining N duty cycles comprises:

[0024] - The energy flow of these switching cells is calculated from the second switching cell by applying the following formula The duty cycle (α1) of the first switch unit (k=1) is calculated by summing:

[0025]

[0026] Advantageously and in a non-limiting manner, the step of determining N duty cycles comprises calculating the duty cycle of each switching unit except the first switching unit from the calculated energy flow by applying the following set of equations:

[0027]

[0028] Advantageously and in a non-limiting manner, when the converter comprises a single switching unit, the step of determining the duty cycle comprises applying the following equation:

[0029]

[0030] Therefore, when the converter includes only one switching unit, a simpler procedure for calculating the duty cycle can be obtained.

[0031] Advantageously and in a non-limiting manner, the step of controlling each switching unit comprises generating, for each switching unit, a control signal which is a function of a logical comparison between the determined duty cycle and a high frequency symmetrical triangular carrier signal applying a chopping frequency to the converter. Advantageously and in a non-limiting manner, the comparison comprises:

[0032] For the first switch unit (k=1):

[0033] If α1≥carrier 1, then PWM1=1;

[0034] If not, PWM1 = 0;

[0035] For other switch units (k>1):

[0036] If α k ≥Carrier k , then PWM k =1;

[0037] If not, then PWM k =0;

[0038] Among them, the carrier k The phase offset from carrier 1 is 2qπ / N, where q is a natural integer multiple of 2.

[0039] Therefore, this control step is based on a simple logical comparison, which ensures a fast execution of this step.

[0040] Advantageously and in a non-limiting manner, the boost converter comprises, for each switching unit, an inductor, and the output vector is also calculated from the measured current of each inductor. Thus, the output vector can be calculated in a reliable manner.

[0041] Advantageously and in a non-limiting manner, the average value of the measured current of each inductor is obtained by sampling each of the N carriers used to generate the power switch chopping at a minimum or maximum value.

[0042] The invention also relates to an electrical component comprising a DC power supply, a boost converter having N switching units, a DC-AC voltage converter, an electric motor, and a device for controlling the boost converter designed to implement the method as described above. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Other characteristics and advantages of the invention will become apparent on reading the description presented hereinafter of a particular embodiment of the invention given by way of non-limiting example, with reference to the accompanying drawings, in which:

[0044] - Figure 1 is a schematic circuit diagram of a power supply according to the present invention;

[0045] - Figure 2 is a schematic diagram of a boost converter with N phases controlled according to a first embodiment of the present invention, where N is a non-zero natural integer, greater than 3 in this case.

[0046] - Figure 3is a schematic diagram of the steps of calculating the power variation at the output terminal of the boost converter according to the present invention;

[0047] - Figure 4 is a graphical representation of the steps of sampling current for a first embodiment of the present invention in an example with three interleaved switch cells;

[0048] - Figure 5 is a schematic diagram of a nonlinear control method according to a first embodiment of the present invention;

[0049] - Figure 6 is a schematic diagram of a single-stage boost converter controlled by a second embodiment of the present invention; and

[0050] - Figure 7 is a schematic diagram of a nonlinear control method according to a second embodiment of the present invention. DETAILED DESCRIPTION

[0051] In the first embodiment of the present invention, reference Figures 1 to 5 , a nonlinear control method by exact linearization using state feedback of a voltage step-up converter having “N” number of switching cells is described.

[0052] This method allows compensating for nonlinearities exhibited by the system it is desired to control.

[0053] The form of this compensation is associated with the structure of the system. For example, in order to compensate the nonlinear term (denoted as θ(x)) by subtraction, the control vector u and the nonlinear term θ(x) at the input of the system must appear together in the form of addition u+θ(x).

[0054] On the other hand, in order to compensate θ(x) by division, the control vector u and the nonlinear term must appear together in the form of multiplication u.θ(x).

[0055] The equation for a boost converter with N switching cells is as follows:

[0056]

[0057] Equation (1) can be written in the general form of the following affine nonlinear equation:

[0058]

[0059] Therefore, equation (2) becomes:

[0060]

[0061] in,

[0062] · is the vector of system state variables,

[0063] · represents the control vector considered as input to the system, α k is the switch S applied to the kth switch unit k The duty cycle, and 1-α k is the switching applied to the kth switching unit duty cycle.

[0064] f(X) and q(X) are infinitely differentiable nonlinear functions;

[0065] ·(L1,L2,...,L N ) and C 输出 are the inductance of each switching unit and the capacitor at the output of the boost converter;

[0066] ·i1,i2,...,i N and V 输出 are the current in each inductor and the voltage at the output of the boost converter, respectively;

[0067] ·P 输出 is the power of the dynamic load connected to the boost converter at the output.

[0068] The purpose of the method according to the invention is to control the energy flow from the voltage source at the input to the load at the output while reducing the voltage V at the output of the boost converter 输出 Adjust to the set point value (expressed as ).

[0069] The first step of the method consists in choosing an output vector (denoted y) that allows a global linearization of the system.

[0070] For the case of a converter with N arms, the following equation (4) allows obtaining the output vector of the globally linearized system with zero internal dynamics:

[0071]

[0072] The second step of the method consists in a series of successive derivations of the output vector y until a control vector u(t)=α is obtained. k＝l,...,N until:

[0073] First, the first-order derivative of equation (4) yields the following equation:

[0074]

[0075] This equation represents the losses incurred by the boost converter or its energy balance.

[0076] Subsequently, the second-order derivative of equation (4) yields the following equation:

[0077]

[0078] Then, the energy flow through each switching unit k is calculated. This allows, through equation (6), to obtain a system of N equations with N unknowns, from which the control α required for each cell k of a boost converter with N cells can be determined k .

[0079]

[0080] in, Among them, k>1.

[0081] Starting from the previous equation (7), determine the following:

[0082] The equation for controlling the first cell of a boost converter with N arms is:

[0083]

[0084] The equations for controlling the N-1 cells of the boost converter are:

[0085]

[0086] In order to obtain stable asymptotic tracking of the error, it is proposed:

[0087]

[0088] where {k′1, k′2, k′3} are the calibratable gains of the regulator of equation (10),

[0089] as well as

[0090]

[0091] where {k′1, k′2} are the calibratable gains of the regulator of equation (11), and

[0092] Ψ k =i1-i k ,and is the setpoint for the flow of the kth unit. More generally, a variable indexed as "ref" refers to the setpoint value of the corresponding variable.

[0093] Therefore, referring to equation (10), the control expressed by state feedback in equation (6) is The calculation includes:

[0094] - Proportional action on error

[0095] - acts on y and y ref Proportional action of the error between

[0096] - acts on y and y ref The integral action of the error between

[0097] Output vector y for set point ref and its derivatives The calculation of is obtained by the following equation:

[0098]

[0099] And among them:

[0100]

[0101] where η represents the efficiency of the system, which depends on the operating point, and N represents the number of units,

[0102] and:

[0103]

[0104] Reusing equations (8) and (9), it should be noted that in steady state, N duty cycles α k＝1,...,N converges towards the following final value:

[0105]

[0106] This expression corresponds to the open-loop transfer function (in other words, the static gain) of the boost converter.

[0107] To calculate the derivative of the output power refer to Figure 3 , perform the following variable transformations:

[0108]

[0109] in, yes Figure 3 The estimated output power is shown in . In steady state, it is expected to obtain:

[0110]

[0111] Likewise, reference Figure 3 , the change in output power is estimated by the following equation:

[0112]

[0113] Among them, {k p,k i} is the calibrable gain.

[0114] Therefore, the load power changes is obtained through a reduced-order observer.

[0115] Then, refer to Figure 4 , the method implements a step of sampling the currents to obtain an average value of these currents and generate a chopped wave.

[0116] A high frequency signal (which is dedicated to the chopping of each switching unit and is represented as PWM k＝1,...,N ) through the control signal (denoted as α k＝1,...,N ) is generated by a logical comparison between a high frequency symmetrical triangular signal (called a carrier) applied to the chopping frequency of the power converter. In addition, there is one carrier per switching unit.

[0117] Each carrier wave is phase-shifted from each other by 2qπ / N, where q is a natural integer multiple of 2 and N is the number of the switching unit.

[0118] However, when the switch unit is numbered 1, the following logic is followed:

[0119] If α1≥carrier 1, then PWM1=1;

[0120] If not, PWM1=0.

[0121] When the switch unit is numbered 2, the following logic is followed:

[0122] If α2 ≥ carrier 2, then PWM2 = 1;

[0123] If not, PWM2=0,

[0124] The phase of carrier 2 is offset from that of carrier 1 by 2π / N.

[0125] When the switch unit is numbered 3, the following logic is followed:

[0126] If α3 ≥ carrier 3, then PWM3 = 1;

[0127] If not, PWM3=0,

[0128] The phase of carrier 3 is offset from that of carrier 1 by 4π / N.

[0129] When the switch unit is numbered k, the following logic is followed:

[0130] If α k ≥Carrier k , then PWM k =1;

[0131] If not, then PWM k =0,

[0132] Among them, the carrier k The phase offset from carrier 1 is 2qπ / N.

[0133] Therefore, each current (expressed as k >) can be captured by sampling at the minimum (or maximum) value of each carrier. The sampled signal (denoted as trig k ) is in phase with its corresponding carrier.

[0134] This method—available only for frameworks using FPGA-type hardware targets—avoids the use of current filtering methods that introduce delays in the control that need to be compensated.

[0135] The sampling signal of the current measured in the inductor occurs at the minimum or maximum value of the carrier so as to obtain the mean component of the current without adding any delay caused by filtering the real signal in the case of using a low-pass digital filter.

[0136] In a second embodiment of the present invention, for a boost converter having a single switching unit (also referred to as a single-stage boost converter), reference is made to Figure 1 as well as Figure 6 and Figure 7 , the method includes the same main implementation steps, but their calculation mode can be simplified.

[0137] The equation for this single-stage boost converter is as follows:

[0138]

[0139] Equation (19) can be written in the general form of the following affine nonlinear equation:

[0140]

[0141] Therefore, equation (20) becomes:

[0142]

[0143] in,

[0144] · is the vector of system state variables,

[0145] · represents the control vector considered as the input to the system, α1 is the switch S applied to the switching unit a The duty cycle of the switch is 1-α1, and 1-α1 is applied to the switch unit. duty cycle.​

[0146] f(X) and g(X) are infinitely differentiable nonlinear functions;

[0147] L1 and C 输出 They are the inductor and capacitor for boosting voltage respectively;

[0148] i1 and V 输出 are the current in the inductor and the voltage at the output of the boost, respectively;

[0149] ·P 输出 is the power of the dynamic load connected to the boost converter at the output.

[0150] Therefore, the purpose of the method according to the present embodiment is to control the energy flow from the voltage source at the input to the load at the output via a single regulation loop while simultaneously reducing the voltage V at the output of the boost converter 输出 Adjust to the set point value (expressed as ).

[0151] The first step of the method consists in selecting an output vector to allow a global linearization of the system.

[0152] The following equation (22) - representing the output vector allowing global linearization of the system of equations (21) - allows obtaining the output vector of the globally linearized system for the case of a single-stage boost converter:

[0153]

[0154] The second step of the method consists in carrying out a reference transformation through a series of successive derivatives until a control vector u(t)=α appears. k＝1,...,N until:

[0155] First, the first-order derivative of equation (22) yields the following equation:

[0156]

[0157] This equation represents the losses incurred by the boost converter.

[0158] Subsequently, the second-order derivative of equation (22) yields the following equation:

[0159]

[0160] Starting from above, an equation for the duty cycle α1 is derived such that:

[0161]

[0162] in,

[0163] However, in steady state (at constant power), the duty cycle α1 converges towards the following final value:

[0164]

[0165] Therefore, the duty cycle calculated dynamically in (25) converges asymptotically and stably towards equation (26) in the steady state.

[0166] This expression corresponds to the open-loop transfer function of the boost converter 2 (in other words, the static gain).

[0167] To obtain asymptotic exponential tracking, the following is proposed:

[0168] Calculate control vector The second derivative of :

[0169]

[0170] in, and is obtained by the previously presented equation (23). Therefore, the general form of the first regulator is determined so that:

[0171]

[0172] Where {k′1, k′2, k′3} is the calibratable gain of the regulator.

[0173] Therefore, referring to equation (28), The calculation of (which corresponds to control by state feedback) includes:

[0174] - Proportional action on error

[0175] - acts on y and y ref Proportional action of the error between

[0176] - acts on y and y ref The integrating action of the error between

[0177] In addition, ref and The calculation of is performed as follows:

[0178]

[0179] in,

[0180]

[0181] Here, η represents the efficiency of the system, which depends on the operating point.

[0182] in addition,

[0183]

[0184] and the change in the derivative of the power at the estimated output

[0185] Perform the following variable transformations:

[0186]

[0187] And, it is expected to obtain in the steady state:

[0188]

[0189] From here, estimate the change in output power by:

[0190]

[0191] Among them, k p and k i is the calibrable gain.

Claims

1. A method for controlling a boost converter (2) having N switching units in a synchronous pulse width modulation mode, wherein: N is a non-zero natural integer, and the boost converter receives a DC voltage from a voltage source at an input terminal as an input voltage V 输入 The output voltage is greater than or equal to the input voltage V 输入 The output voltage V 输出 , the method comprising: -Measure the input voltage V of the boost converter (2) 输入 and output voltage V 输出 Steps; - A step of determining the output vector y designed for global linearization of the system of equations of the boost converter (2) by the following formula: Among them, L1,L2,...,L N and C 输出 are the inductance of each switching unit and the capacitance at the output of the boost converter, i1,i2,...,i N is the current measured in each inductor; - Calculate the power change of the electrical load at the output of the boost converter Steps; -According to the second derivative of the output vector y The derivative of the power of the electrical load And the measured input voltage V 输入 With the output voltage V 输出 The ratio of the N duty cycles α of the boost converter is determined by k steps; and -According to the determined duty cycle α k To control the steps of each switch unit (k) of the boost converter (2).

2. The method of claim 1, wherein when the boost converter comprises N>1 switch units (k), The step of determining N duty cycles includes calculating the energy flow through each switching unit (k) 3. The method according to claim 2, characterized in that The step of determining N duty cycles comprises: - The energy flow of these switching cells is calculated from the second switching cell by applying the following formula The duty cycle α1 of the first switch unit (k=1) is calculated by summing:

4. The method according to any one of claims 2 and 3, characterized in that The step of determining N duty cycles includes applying the following set of equations based on the calculated energy flow To calculate the duty cycle of each switch unit except the first switch unit (k>1):

5. The method of claim 1, when the boost converter comprises a single switching unit, characterized in that: The step of determining the duty cycle involves applying the following equation:

6. The method according to any one of claims 1 to 3, characterized in that The step of controlling each switch unit includes: generating a control signal PWM for each switch unit. k , the control signal is determined by the duty cycle α k＝1，...，N A high frequency symmetrical triangular carrier signal carrier wave which applies a chopping frequency to the boost converter (2) k A logical comparison function between .

7. The method according to claim 6, characterized in that The comparison includes: For the first switch unit (k=1): If α1v carrier 1, then PWM1 = 1; If not, PWM1 = 0; For other switch units (k>1): If α k ≥Carrier k , then PWM k =1; If not, then PWM k =0; Among them, the carrier k The phase offset from carrier 1 is 2qπ / N, where q is a natural integer multiple of 2.

8. The method according to claim 6, characterized in that Each inductor L k The measured current i k The average value of is obtained by sampling each of the N carriers used to generate the power switch chopping at the minimum value or the maximum value.

9. An electrical component (10) comprising a DC power supply (1), a boost converter (2) having N switching units, a DC-AC voltage converter (3), an electric motor (4), and a device for controlling the boost converter designed to implement the method according to any one of claims 1 to 8.

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