CN110543662B - Method for optimizing parameters of wide-load-range non-minimum-phase-switch Boost converter - Google Patents
Method for optimizing parameters of wide-load-range non-minimum-phase-switch Boost converter Download PDFInfo
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Abstract
The invention provides a parameter optimization method for a wide-load-range non-minimum-phase switching Boost converter, which comprises the following steps of: based on a negative voltage transient mathematical model, deeply analyzing the relationship between the peak time of the negative voltage in a wide load range and circuit parameters including load resistance, inductance and capacitance, providing a step of parameter optimization design, and calculating the peak time t of the negative voltage under different parameters p And is compared with the time t of the negative regulation voltage peak value set by the system p,sd And comparing, and if the requirements are not met, continuing to perform optimization design until the requirements are met. And finally, the correctness and the rationality of theoretical analysis are verified by utilizing simulation and experimental results. The method can effectively restrain the negative regulation voltage, thereby improving the transient response speed of the system, is also suitable for other non-minimum phase wide-load-range switching DC-DC converters, and has the advantages of simplicity and higher engineering application value.
Description
Technical Field
The invention belongs to the technical field of a Boost converter parameter optimization method, and particularly relates to a wide-load-range non-minimum-phase-switch Boost converter parameter optimization method.
Background
With the increasing prominence of the energy crisis, new energy technologies such as photovoltaic and fuel cell have become the research hotspots nowadays. In these systems, there is a need for Boost converters that can operate over a wide load range and have good transient and steady state performance, and the mathematical model of the transient of the control variables of these converters to the output voltage contains one or more right half-plane zeros (RHPZ), referred to as a non-minimum phase system. The existence of RHPZ can lead to the phenomenon of negative regulation voltage of output voltage when the duty ratio of the converter is suddenly changed, the phenomenon of negative regulation can lead to the transient transition time of the system to be prolonged, and the system is easy to form positive feedback in the continuous time stage of the negative regulation voltage to cause the phenomenon of instability. Therefore, a lot of technologists are constantly searching for a method for improving the transient performance of the non-minimum phase switching Boost converter.
At present, the study of scholars at home and abroad on a non-minimum phase switch Boost converter mainly comprises circuit topology improvement and control strategy optimization design, and the methods improve the transient performance of the converter containing the RHPZ to a certain extent, but are complex. Analysis of a transient mathematical model of the non-minimum phase switch Boost converter shows that RHPZ is related to converter parameters, so that the situation that the transient performance is improved by suppressing the negative regulation voltage through reasonable design of the parameters of the non-minimum phase switch Boost converter can be explored. However, the existing technologies for improving the transient performance of the non-minimum phase switching Boost converter from the perspective of converter parameter optimization design are few, and especially how to design the parameters of the converter working in a wide load range lacks corresponding theoretical basis, so that the research on the parameter design of the converter in the wide load range is urgently needed to guide the development and development of the non-minimum phase switching Boost converter product.
The Boost converter is a typical non-minimum phase switch converter, and has the advantages of simple circuit topology, easy design of a driving circuit and the like, and is widely applied to systems such as new energy sources and the like. The prior art researches the parameter optimization design of the non-minimum phase Boost converter. For example, the method for designing the negative regulation voltage generation mechanism and the negative regulation voltage suppression parameter of the Boost converter is researched, and the method and the principle for designing the Boost converter parameter in a certain input voltage and load resistance dynamic range are provided. However, the influence of inductance, capacitance and load resistance on the transient performance of the non-minimum phase switching Boost converter is not fully considered, so that the parameter design of the non-minimum phase switching Boost converter in a wide load range cannot be guided. If the full dynamic range of the wide-load-range Boost converter is designed into an inductive Current Continuous Mode (CCM), the needed inductance is too large, so that the transient performance of the system is poor, and meanwhile, the system is unstable due to the serious negative regulation phenomenon; if the full dynamic range works in an inductive current discontinuous mode (DCM), the needed inductance is small, the transient response speed of the system can be improved, but due to the circuit topology particularity of the non-minimum phase Boost converter, the inductance is too small, the possibility of direct connection of an input power supply is increased, the peak current of the inductance is very large, the voltage stress of a switching tube is very large, and the ripple voltage of the system is very large. Thus for a non-minimum phase Boost converter operating over a wide load range, the full dynamic range can operate neither in CCM nor in DCM. How to design parameters to improve the transient performance of the system is the key of the parameter design of the wide-load-range non-minimum-phase Boost converter.
Disclosure of Invention
The invention provides a parameter optimization method for a wide-load-range non-minimum-phase-switch Boost converter, which is used for guiding the development and development of non-minimum-phase-switch Boost converter products.
The technical scheme of the invention is as follows: the parameter optimization method of the wide-load-range non-minimum-phase switching Boost converter comprises the following steps:
the method comprises the following steps: establishing a transient mathematical model from a Boost converter control variable to an output voltage in a continuous inductor current mode (CCM):
(1) the main parameters of the switch working circuit comprise an input voltage V i Load resistance R, output voltage V o Energy storage inductor L, filter capacitor C and ripple voltage V PP ，
The system damping ratio ζ obtained from equation (1) is:
(2) according to the analysis formula (1), the zero point (RHPZ) of the right half plane is related to the load resistance R of the Boost converter, the mathematical model can change along with the change of the load resistance value R of the converter, and the transient mathematical model of the negative regulation voltage when the duty ratio of the Boost converter changes suddenly is as follows:
in the formula, Δ d is the duty ratio variation;
(3) the inverse laplace transform is obtained from the formula (3), and the obtained negative regulated voltage time domain transient mathematical model of the switching converter is as follows:
in the formula (I), the compound is shown in the specification,
step two: in the energy storage inductor L, the filter capacitor C and the output voltage V o Under certain conditions, the Boost converter is at the input voltage [ V ] i,min ～V i,max ]And a load resistance [ R ] min ～R max ]When the dynamic range of (1) is changed, the peak time limit value t of the negative regulated voltage in the wide load range p Analysis of the conditions of the influencing factors of (1):
A. the time t of the peak value of the negative regulation voltage can be obtained by taking the derivative of the formula (4) with respect to the time t and making the derivative zero p Comprises the following steps:
t in the formula (5) p The first partial derivative of R can be obtained:
equation (6) equals zero available
In the formula, R k Is a critical load resistance;
r in the formula (7) k The system damping ratio obtained by substituting formula (2) is ζ 0.707;
the second partial derivative of R is obtained by using equation (5):
as can be seen from analytical formulae (6) and (8), t p Is a convex function with respect to R, which peaks when the system damping ratio ζ is 0.707, with R at the top k ，t p At wide load range variation, t p An extremum exists;
B. analysis of the critical load resistance R k It is known that R k In the input voltage dynamic range [ V ] i,min ～V i,max ]Has maximum and minimum values when V i ＝V i,max When R is k Reaches a minimum value at which R k ＝R k,min As shown in formula (9); when V is i ＝V i,min When R is k Reaches a maximum value when R k ＝R k,max As shown in the formula (10),
the load resistance R of the Boost converter changes within a certain range according to the load range [ R min ～R max ]And critical load resistance [ R ] k,min ～R k,max ]Different in magnitude relationship between R and t p The following may occur:
a. when the load resistance satisfies R max ≤R k,min Or R k,min ≤R max ≤R k,max Time, negative voltage peak time t p The first partial derivative of the load resistance R satisfies:
at this time t p Increases as R increases, when the load resistance value reaches R max Time t p Reaches a maximum value t of the time of the negative regulation voltage peak value p,max Comprises the following steps:
t in the formula (5) p To V i The derivative is taken to obtain:
from the equation (13), at the input voltage V i Dynamic range of variation, t p Following the input voltage V i Increases and decreases, so that in the input voltage and load resistance dynamic range, when the load resistance satisfies R max ≤R k,min The maximum value t of the time of the negative regulation voltage peak value in the dynamic range p,max And a minimum value t p,min Respectively as follows:
from the equation (2), the damping ratio range of the system satisfies:
0.707≤ζ min ＜ζ max ＜1
in the formula (I), the compound is shown in the specification,
when V is i ＝V i,min ，R＝R max When t is p Reaches a maximum value when V i ＝V i,max ，R＝R max When t is p Reaching a minimum value;
b. when the load resistance satisfies R min ≥R k,max Or R k,min ≤R min ≤R k,max When t is p The first derivative to R satisfies:
at this time t p Decreases as R increases when the load resistance reaches R min Time t p Reaches a maximum value, at which time t p Maximum value t of p,max Comprises the following steps:
from the formula (13), at the input voltage [ V ] i,min ～V i,max ]Within the range, the time t of negative regulation voltage peak value p At V i ＝V i,min When t is p Reaches a maximum value within the dynamic range t p Maximum value t of p,max And a minimum value t p,min Respectively as follows:
as can be seen from equation (2), the system damping ratio range in this dynamic range satisfies:
0＜ζ min ＜ζ max ≤0.707
when V is i ＝V i,min ，R＝R min When t is p Reaches a maximum value when V i ＝V i,max ，R＝R max When tp reaches a minimum value;
c. when the load resistance satisfies R min ≤R k,min And R is max ≥R k,max When t is p The second derivative to R satisfies:
when the load resistance satisfies R ≦ R k,max When t is p Increases with the increase of R, when the load resistance R is R k,max When t is p Reaches a maximum value, at which time t p Maximum value t of p,max Comprises the following steps:
when load resistance R ═ R k,max When the damping ratio zeta of the system is 0.707;
when the load resistance satisfies R>R k,max When t is p As R increases and decreases, the load resistance R ═ R max Time t p Reaches a minimum value, at which time t p Minimum value of t p,min,Rmax Comprises the following steps:
when the minimum load resistance satisfies R min ≤R k When t is p Decreases with decreasing R, where R is R min Time t p Reaches a minimum value at which t p Minimum value of t p,min,Rmin Comprises the following steps:
when the load resistance satisfies R min ≤R k,min And R is max ≥R k,max When t is p Minimum value of t p,min Comprises the following steps:
t p,min ＝min{t p,min,Rmax ，t p,min,Rmin } (22)
when the load resistance satisfies R min ≤R k,min And R is max ≥R k,max And taking into account the dynamic range of the input voltage [ V ] i,min ～V i,max ]When t is p Minimum value of t p,min Comprises the following steps:
when the load resistance satisfies R min ≤R k,min And R is max ≥R k,max Then, as can be seen from equation (4), the damping ratio range of the system in the dynamic range of the input voltage and the load resistance satisfies:
0＜ζ min ＜ζ max ＜1
when ζ is 0.707, t p Reaches a maximum value of
t p The minimum value of (A) is a load resistanceR min And R max Corresponding t p,min Minimum value of (1);
step three: optimally designing parameters of the switching converter:
B. analyzing parameters of load resistance R, inductance L and capacitance C to t p Influence of (2)
Deriving L from equation (5):
c is derived from equation (5):
as can be seen from the analytical expressions (24) and (25), t is larger as the inductance L is larger p The longer the filter capacitance C, the larger t p Longer, smaller L and C are advantageous for suppression of t p Thereby improving the transient performance of the system;
b: designing and optimizing parameters of the Boost converter in the wide load range:
1) setting a Q working frequency f of a switching tube;
2) c can be calculated by substituting the set f into the formula (26) min ，
In the formula, the value of lambda is 2-3;
3) will know the input voltage V i,max And a load R max Calculation of L by substitution formula (27) min ，
In the formula, the value of gamma is 1.2-1.5;
4) will give a given input voltage V i Range [ V ] i,min ～V i,max ]Load resistance R range [ R min ～R max ]、L min And C min The critical load resistance R is calculated by substituting equations (9) and (10) respectively k Range [ R ] k,min ～R k,max ]；
5) Will give a given load resistance R range R min ～R max ]And [ R ] k,min ～R k,max ]Comparing, judging whether the load resistance range meets the following three conditions, and calculating corresponding t p,max ；
(a) If the load resistance range R satisfies R k,min ≤R max ≤R k,max Or R max ≤R k,min Then, the maximum value t of the peak regulation time is calculated according to the formula (14) p,max ；
(b) If the load resistance R range satisfies R k,min ≤R min ≤R k,max Or R min ≥R k,max Then, t is calculated according to the formula (17) p,max ；
(c) If the load resistance R satisfies R min ≤R k,min And R is max ≥R k,max Then, t is calculated according to the formula (19) p,max ；
6) Will calculate t p,max The substitution formula (28) judges whether the result is true, if true, the step (7) is continued; if not, the load resistance R is reduced appropriately max The resistance value of the resistance sensor is designed from the step (3) again until the index requirement is met,
t P,max ≤t P,sd (28)
in the formula, t p,sd Negative regulation of the peak voltage time t for the system p A maximum set value;
7) verifying whether the designed inductance and capacitance meet the overall performance index requirements of the converter design volume, efficiency and electromagnetic compatibility, if not, adjusting f and designing from the step (1) again until the requirements are met under the condition that the switching frequency f is allowed;
step four: and carrying out simulation and experimental verification.
The invention has the advantages that: the method can effectively restrain the negative regulation voltage by optimizing the parameters of the wide-load-range non-minimum-phase Boost converter, thereby improving the transient response speed of the system.
Drawings
FIG. 1 shows the experimental parameters of the present invention, L-5.2 mH, C-700. mu.F, R-5. omega., F-40 kHz, V i Results plot of 10V;
fig. 2 shows the experimental parameters of the present invention, L ═ 420 μ H, C ═ 700 μ F, R ═ 5 Ω, F ═ 40kHz, V i Results plot of 10V;
Detailed Description
The present invention will now be described more fully hereinafter with reference to the accompanying drawings, in which a person skilled in the art can, without any creative effort, fully implement the present invention.
The specific implementation mode of the invention is as follows: the parameter optimization method for the wide-load-range non-minimum-phase switching Boost converter comprises the following steps of:
the method comprises the following steps: establishing a transient mathematical model from a Boost converter control variable working in CCM to an output voltage:
(1) the main parameters of the switch working circuit comprise an input voltage V i Load resistance R, output voltage V o Energy storage inductor L, filter capacitor C and ripple voltage V PP ，
The system damping ratio ζ obtained from equation (1) is:
(2) according to the analysis formula (1), the zero point (RHPZ) of the right half plane is related to the load resistance R of the Boost converter, the mathematical model can change along with the change of the load resistance value R of the converter, and the transient mathematical model of the negative regulation voltage when the duty ratio of the Boost converter changes suddenly is as follows:
in the formula, Δ d is the duty ratio variation;
(3) the inverse laplace transform is obtained from the formula (3), and the obtained negative regulated voltage time domain transient mathematical model of the switching converter is as follows:
in the formula (I), the compound is shown in the specification,
step two: in the energy storage inductor L, the filter capacitor C and the output voltage V o Under certain conditions, the Boost converter is at the input voltage [ V ] i,min ～V i,max ]And a load resistance [ R ] min ～R max ]When the dynamic range of (1) is changed, the peak time limit value t of the negative regulated voltage in the wide load range p Analysis of the conditions of the influencing factors of (1):
A. the time t of the peak value of the negative regulation voltage can be obtained by taking the derivative of the formula (4) with respect to the time t and making the derivative zero p Comprises the following steps:
t in the formula (5) p The first partial derivative of R can be obtained:
equation (6) equals zero
In the formula, R k Is a critical load resistance;
r in the formula (7) k The system damping ratio obtained by substituting formula (2) is zeta 0.707;
the second partial derivative of R is obtained by using equation (5):
as can be seen from analytical formulae (6) and (8), t p Is a convex function with respect to R, which peaks when the system damping ratio ζ is 0.707, with R at the top k ，t p At wide load range variation, t p An extremum exists;
B. analysis of the critical load resistance R k It is known that R k In the input voltage dynamic range [ V ] i,min ～V i,max ]Has maximum and minimum values when V i ＝V i,max When R is k Reaches a minimum value when R k ＝R k,min As shown in formula (9); when V is i ＝V i,min When R is k Reaches a maximum value when R k ＝R k,max As shown in the formula (10),
the load resistance R of the Boost converter changes within a certain range according to the load range [ R min ～R max ]And critical load resistance [ R ] k,min ～R k,max ]Different in magnitude relationship between R and t p The following may occur:
a. when the load resistance satisfies R max ≤R k,min Or R k,min ≤R max ≤R k,max Time, negative voltage peak time t p The first partial derivative of the load resistance R satisfies:
at this time t p Increases as R increases, when the load resistance value reaches R max Time t p Reaches a maximum value t of the time of the negative regulation voltage peak value p,max Comprises the following steps:
t in the formula (5) p To V i The derivative is taken to obtain:
from the equation (13), at the input voltage V i Within the dynamic range of variation, t p With input voltage V i Increases and decreases, so that in the input voltage and load resistance dynamic range, when the load resistance satisfies R max ≤R k,min The maximum value t of the time of the negative regulation voltage peak value in the dynamic range p,max And a minimum value t p,min Respectively as follows:
as can be seen from equation (2), the damping ratio range of the system satisfies:
0.707≤ζ min ＜ζ max ＜1
in the formula (I), the compound is shown in the specification,
when V is i ＝V i,min ，R＝R max When t is p Reaches a maximum value when V i ＝V i,max ，R＝R max When t is p Reaching a minimum value;
b. when the load resistance satisfies R min ≥R k,max Or R k,min ≤R min ≤R k,max When t is p The first derivative to R satisfies:
at this time t p Decreases as R increases, when the load resistance reaches R min Time t p Reaches a maximum value, at which time t p Maximum value t of p,max Comprises the following steps:
from the formula (13), at the input voltage [ V ] i,min ～V i,max ]Within the range, the time t of negative regulation voltage peak value p At V i ＝V i,min When t is p Reaches a maximum value within the dynamic range t p Maximum value t of p,max And a minimum value t p,min Respectively as follows:
as can be seen from equation (2), the system damping ratio range in this dynamic range satisfies:
0＜ζ min ＜ζ max ≤0.707
when V is i ＝V i,min ，R＝R min When t is p Reaches a maximum value when V i ＝V i,max ，R＝R max When tp reaches a minimum value;
c. when the load resistance satisfies R min ≤R k,min And R is max ≥R k,max When t is p The second derivative to R satisfies:
when the load resistance satisfies R ≦ R k,max When t is p Increases with the increase of R, when the load resistance R is R k,max When t is p Reaches a maximum value, at which time t p Maximum value t of p,max Comprises the following steps:
when load resistance R ═ R k,max When the damping ratio zeta of the system is 0.707;
when the load resistance satisfies R>R k,max When t is p Decreases as R increases, and the load resistance R ═ R max Time t p Reaches a minimum value at which t p Minimum value of t p,min,Rmax Comprises the following steps:
when the minimum load resistance satisfies R min ≤R k When t is p Decreases with decreasing R, where R ═ R min Time t p Reaches a minimum value at which t p Minimum value of t p,min,Rmin Comprises the following steps:
when the load resistance satisfies R min ≤R k,min And R is max ≥R k,max When t is p Minimum value of t p,min Comprises the following steps:
t p,min ＝min{t p,min,Rmax ，t p,min,Rmin } (22)
when the load resistance satisfies R min ≤R k,min And R is max ≥R k,max And taking into account the dynamic range of the input voltage [ V ] i,min ～V i,max ]When t is p Minimum value t of p,min Comprises the following steps:
when the load resistance satisfies R min ≤R k,min And R is max ≥R k,max Then, as can be seen from equation (4), the damping ratio range of the system in the dynamic range of the input voltage and the load resistance satisfies:
0＜ζ min ＜ζ max ＜1
when ζ is 0.707, t p Reaches a maximum value of
t p Has a minimum value of the load resistance R min And R max Corresponding t p,min Minimum value of (1);
step three: optimally designing parameters of the switching converter:
a: analyzing parameters of load resistance R, inductance L and capacitance C to t p Influence of (2)
Deriving L from equation (5):
c is derived from equation (5):
as can be seen from the analytical expressions (24) and (25), t is larger as the inductance L is larger p The longer the filter capacitor C, the larger t p The longer, the smaller L and C are favorable for suppressing t p Thereby improving the transient performance of the system;
b: designing and optimizing parameters of the Boost converter in the wide load range:
1) setting a Q working frequency f of a switching tube;
2) c can be calculated by substituting the set f into the formula (26) min ，
In the formula, the value of lambda is 2-3;
3) will know the input voltage V i,max And a load R max Calculation of L by substitution formula (27) min ，
In the formula, the value of gamma is 1.2-1.5;
4) will give an input voltage V i Range [ V ] i,min ～V i,max ]Load resistance R range [ R min ～R max ]、L min And C min The critical load resistance R is calculated by substituting the formulas (9) and (10) respectively k Range [ R ] k,min ～R k,max ]；
5) Will give a given load resistance R range R min ～R max ]And [ R ] k,min ～R k,max ]Comparing, judging whether the load resistance range meets the following three conditions, and calculating corresponding t p,max ；
(a) If the load resistance range R satisfies R k,min ≤R max ≤R k,max Or R max ≤R k,min Then, the maximum value t of the peak regulation time is calculated according to the formula (14) p,max ；
(b) If the load resistance R range satisfies R k,min ≤R min ≤R k,max Or R min ≥R k,max Then, t is calculated according to the formula (17) p,max ；
(c) If the load resistance R satisfies R min ≤R k,min And R is max ≥R k,max Then, t is calculated according to the formula (19) p,max ；
6) Will calculate t p,max The substitution formula (28) judges whether the result is true, if true, the step (7) is continued; if not, the load resistance R is reduced appropriately max The resistance value of (3) is restartedThe design is carried out until the index requirements are met,
t P,max ≤t P,sd (28)
in the formula, t p,sd Negative regulation of the peak time t of the voltage for the system p A maximum set value;
7) verifying whether the designed inductance and capacitance meet the overall performance index requirements of the converter design volume, efficiency and electromagnetic compatibility, if not, adjusting f and designing from the step (1) again until the requirements are met under the condition that the switching frequency f is allowed;
step four: and carrying out simulation and experimental verification.
In order to verify the reasonability and feasibility of the parameter optimization method of the wide-load-range non-minimum-phase switching Boost converter, a typical Boost converter is provided for experimental verification, and parameters are shown in a table 1.
TABLE 1 Boost converter Circuit parameters
The converter parameters given in table 1 were designed according to the procedure:
(1) setting the switching frequency f to be 40 kHz;
(2) c is calculated from the formula (26) min 700 μ F (2 times margin selected);
(3) selection of R max When the value is 500 Ω, Lmin is calculated to be 5.2mH (1.2 times margin is selected) according to formula (27);
(4) the critical load resistance R can be calculated according to the given resistance range, the formulas (9) and (10) k Respectively are: r k,min ＝2.3Ω，R k,max ＝4.6Ω；
(5) According to the given load resistance R range [ R ] min ～R max ]And [ R ] k,min ～R k,max ]The relationship between R and V is shown when R is 5. omega. and V i T at 10V p Reaches a maximum value, at which time t p,max ＝3.2ms。
(6) Judging t p,max <t p,sd ，3.2Greater than 0.5 does not meet the requirements;
from the above calculation results, it can be seen that the load resistance R is selected max When the peak value of the voltage is 500 omega, the system negatively regulates the peak value time t p Too long, not meeting the setting requirements; reselecting R' max Recalculated from step (3) to give L of 40 Ω min ＝420μH，C min ＝700μF，R k,min ＝0.65Ω，R k,max 1.3 omega, when R is 5 omega, V i T at 10V p Reaches a maximum value, t p,max And 0.45ms, the negative regulation voltage suppression requirement is met.
Designing according to the steps according to the converter parameters given in the table 1, selecting f to be 80kHz under the condition that the switching frequency allows, repeatedly designing according to the design steps, and when R is allowed max When 500 Ω, C is calculated min ＝350μF，L min ＝2.6mH，R k,min ＝3.3Ω，R k,max 1.64 Ω; when R is 5 omega, V i T at 10V p Reaches a maximum value, at which time t p,max 1.6ms, obviously t p Too long to meet the requirements, selecting R' max 80 Ω, calculated to give L min ＝420μH，C min ＝350μF，R k,min ＝0.9Ω，R k,max 1.8 Ω; when R is 5 omega, V i T at 10V p Reaches a maximum value, at which time t p,max And 0.42ms, the negative regulation voltage suppression requirement is met.
Comparing the above analysis, it can be known that the dynamic range of the Boost converter operating in CCM can be expanded by increasing the switching frequency f, but the increase of the switching frequency f is limited by conditions such as controllers, components and electromagnetic interference.
A Boost converter experiment prototype is built to continuously verify the rationality, the power switch tube is IRF540, the power diode is 10TQ040, the controller is TMS320F28335, two groups of Boost converter parameters are respectively selected to carry out experiment contrastive analysis, and the two groups of parameters are respectively: (vi) 5.2mH, C700 μ F, R5 Ω, F40 kHz, V i 10V; the corresponding experimental results are shown in fig. 1; -420 μ H, 700 μ F, 5 Ω, 40kHz, V i The corresponding experimental results are shown in fig. 2, 10V.
Comparing the experimental results of fig. 1 and 2, it can be known that if the non-minimum phase Boost converter operating in the wide load range operates in the CISM in the full dynamic range, the converter may generate a severe negative voltage, and the transient performance of the system is poor; by reasonably optimizing and designing the parameters of the converter, the negative regulation voltage can be effectively inhibited, and the transient response speed of the system is improved.
While the preferred embodiments of the invention have been described, it is to be understood that the invention is not limited to the precise embodiments described, and that equipment and structures not described in detail are understood to be practiced as commonly known in the art; any simple modification, equivalent change and modification of the above embodiments according to the technical essence of the present invention by those skilled in the art can be made without departing from the technical scope of the present invention, and still fall within the protection scope of the technical solution of the present invention.
Claims (1)
1. The parameter optimization design method for the wide-load-range non-minimum-phase-switching Boost converter is characterized by comprising the following steps of:
the method comprises the following steps: establishing a transient mathematical model from a Boost converter control variable working in an inductive current continuous mode to an output voltage:
(1) the parameters of the switch operating circuit include input voltage V i Load resistance R, output voltage V o Energy storage inductor L, filter capacitor C and ripple voltage V PP ，
The system damping ratio ζ obtained from equation (1) is:
(2) the right half-plane zero point in the transient mathematical model is related to the load resistance R of the switching converter by the analysis formula (1), the mathematical model can change along with the change of the load resistance value R carried by the converter, and the transient mathematical model of the negative regulation voltage when the duty ratio of the Boost converter changes suddenly is as follows:
in the formula, Δ d is the duty ratio variation;
(3) the inverse laplace transform is obtained from the formula (3), and the obtained negative regulated voltage time domain transient mathematical model of the switching converter is as follows:
in the formula (I), the compound is shown in the specification,
step two: in the energy storage inductor L, the filter capacitor C and the output voltage V o Under certain conditions, the Boost converter is at the input voltage [ V ] i,min ～V i,max ]And a load resistance [ R ] min ～R max ]When the dynamic range of (1) is changed, the peak time limit value t of the negative regulated voltage in the wide load range p Analysis of the conditions of the influencing factors of (1):
A. the time t of the peak value of the negative regulation voltage can be obtained by taking the derivative of the formula (4) with respect to the time t and making the derivative zero p Comprises the following steps:
t in the formula (5) p The first partial derivative of R can be obtained:
equation (6) equals zero available
In the formula, R k Is a critical load resistance;
r in the formula (7) k The system damping ratio obtained by substituting formula (2) is zeta 0.707;
the second partial derivative of R is obtained by using equation (5):
as can be seen from analytical formulae (6) and (8), t p Is a convex function with respect to R, which peaks when the system damping ratio ζ is 0.707, and the top is R ═ R k ，t p At wide load range variation, t p An extremum exists;
B. analysis of the critical load resistance R k It is known that R k In the input voltage dynamic range [ V ] i,min ～V i,max ]Has maximum and minimum values when V i ＝V i,max When R is k Reaches a minimum value when R k ＝R k,min As shown in formula (9); when V is i ＝V i,min When R is k Reaches a maximum value when R k ＝R k,max As shown in the formula (10),
the load resistance R of the Boost converter changes within a certain range according to the load range [ R min ～R max ]And critical load resistance [ R ] k,min ～R k,max ]Different in magnitude relationship between R and t p Can occur in order toThe following conditions:
a. when the load resistance satisfies R max ≤R k,min Or R k,min ≤R max ≤R k,max Time, negative voltage peak time t p The first partial derivative of the load resistance R satisfies:
at this time t p Increases as R increases, when the load resistance value reaches R max Time t p Reaches a maximum value t of the time of the negative regulation voltage peak value p,max Comprises the following steps:
t in the formula (5) p To V i The derivative is taken to obtain:
from the equation (13), at the input voltage V i Within the dynamic range of variation, t p With input voltage V i Increases and decreases, so that in the input voltage and load resistance dynamic range, when the load resistance satisfies R max ≤R k,min The maximum value t of the time of the negative regulation voltage peak value in the dynamic range p,max And a minimum value t p,min Respectively as follows:
as can be seen from equation (2), the damping ratio range of the system satisfies:
0.707≤ζ min ＜ζ max ＜1
in the formula (I), the compound is shown in the specification,
when V is i ＝V i,min ，R＝R max When t is p Reaches a maximum value when V i ＝V i,max ，R＝R max When t is p Reaching a minimum value;
b. when the load resistance satisfies R min ≥R k,max Or R k,min ≤R min ≤R k,max When t is p The first derivative to R satisfies:
at this time t p Decreases as R increases when the load resistance reaches R min Time t p Reaches a maximum value, at which time t p Maximum value t of p,max Comprises the following steps:
from the formula (13), at the input voltage [ V ] i,min ～V i,max ]Within the range, the time t of negative regulation voltage peak value p At V i ＝V i,min When t is p Reaches a maximum value within the dynamic range t p Maximum value t of p,max And a minimum value t p,min Respectively as follows:
as can be seen from equation (2), the system damping ratio range in this dynamic range satisfies:
0＜ζ min ＜ζ max ≤0.707
when V is i ＝V i,min ，R＝R min When t is p Reaches a maximum value when V i ＝V i,max ，R＝R max When the temperature of the water is higher than the set temperature,tp reaches a minimum value;
c. when the load resistance satisfies R min ≤R k,min And R is max ≥R k,max When t is p The second derivative to R satisfies:
when the load resistance satisfies R ≦ R k,max When t is p Increases with the increase of R, when the load resistance R is R k,max When t is p Reaches a maximum value, at which time t p Maximum value t of p,max Comprises the following steps:
when load resistance R ═ R k,max When the damping ratio zeta of the system is 0.707;
when the load resistance satisfies R > R k,max When t is p Decreases as R increases, and the load resistance R ═ R max Time t p Reaches a minimum value at which t p Minimum value of t p,min,Rmax Comprises the following steps:
when the minimum load resistance satisfies R min ≤R k When t is p Decreases with decreasing R, where R ═ R min Time t p Reaches a minimum value at which t p Minimum value of t p,min,Rmin Comprises the following steps:
when the load resistance satisfies R min ≤R k,min And R is max ≥R k,max When t is p Minimum value of t p,min Comprises the following steps:
t p,min ＝min{t p,min,Rmax ，t p,min,Rmin } (22)
when the load resistance satisfies R min ≤R k,min And R is max ≥R k,max And taking into account the dynamic range of the input voltage [ V ] i,min ～V i,max ]When t is p Minimum value of t p,min Comprises the following steps:
when the load resistance satisfies R min ≤R k,min And R is max ≥R k,max Then, as can be seen from equation (4), the damping ratio range of the system in the dynamic range of the input voltage and the load resistance satisfies:
0＜ζ min ＜ζ max ＜1
when ζ is 0.707, t p Reaches a maximum value of
t p Has a minimum value of the load resistance R min And R max Corresponding t p,min Minimum value of (1);
step three: optimally designing parameters of the switching converter:
A. analyzing parameters of load resistance R, inductance L and capacitance C to t p Influence of (2)
Deriving L from equation (5):
c is derived from equation (5):
as can be seen from analytical formulae (24) and (25), electricityThe greater the feeling L, t p The longer the filter capacitor C, the larger t p The longer, the smaller L and C are favorable for suppressing t p Thereby improving the transient performance of the system;
b: the parameter optimization design method of the wide-load-range Boost converter comprises the following steps:
1) setting a Q working frequency f of a power switch tube;
2) c can be calculated by substituting the set f into the formula (26) min ，
In the formula, the value of lambda is 2-3;
3) will know the input voltage V i,max And a load R max Calculation of L by substitution formula (27) min ，
In the formula, the value of gamma is 1.2-1.5;
4) will give an input voltage V i Range [ V ] i,min ～V i,max ]Load resistance R range [ R min ～R max ]、L min And C min The critical load resistance R is calculated by substituting the formulas (9) and (10) respectively k Range [ R ] k,min ～R k,max ]；
5) Will give a given load resistance R range R min ～R max ]And [ R ] k,min ～R k,max ]Comparing, judging whether the load resistance range meets the following three conditions, and calculating corresponding t p,max :
(a) If the load resistance range R satisfies R k,min ≤R max ≤R k,max Or R max ≤R k,min Then, the maximum value t of the peak regulation time is calculated according to the formula (14) p,max ；
(b) If the load resistance R range satisfies R k,min ≤R min ≤R k,max Or R min ≥R k,max Then, t is calculated according to the formula (17) p,max ；
(c) If the load resistance R satisfies R min ≤R k,min And R is max ≥R k,max Then, t is calculated according to the formula (19) p,max ；
6) Will calculate t p,max Judging whether the product is established or not by the substituted formula (28), and if so, continuing to carry out the step 7); if not, the load resistance R is reduced appropriately max The resistance value of the resistance sensor is designed from the step 3) again until the index requirement is met,
t P,max ≤t P,sd (28)
in the formula, t p,sd Negative regulation of the peak time t of the voltage for the system p A maximum set value;
7) verifying whether the designed inductance and capacitance meet the overall performance index requirements of the converter on design volume, efficiency and electromagnetic compatibility, if not, adjusting f and designing from the step 1) again until the requirements are met under the condition that the switching frequency f is allowed;
step four: and carrying out simulation and experimental verification.
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