CN110543662A - 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 parameter optimization design step, calculating the value of the peak time tp of the negative voltage under different parameter conditions, comparing the value with the peak time tp and sd of the negative voltage set by a system, and continuing the optimization design if the requirement is not met until the requirement is 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 Boost converter parameter optimization methods, 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 Vi, a load resistor R, an output voltage Vo, an energy storage inductor L, a filter capacitor C and a ripple voltage VPP,
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: under the condition that an energy storage inductor L, a filter capacitor C and an output voltage Vo are fixed, when the dynamic range of an input voltage [ Vi, min-Vi, max ] and a load resistor [ Rmin-Rmax ] of a Boost converter changes, analyzing the conditions of influence factors of a wide-load-range negative regulation voltage peak value time extreme value tp:
A. taking the derivative of the equation (4) with respect to the time t, and making the derivative zero, the peak time tp of the negative regulation voltage can be obtained as:
the first partial derivative of R with tp in equation (5) can be obtained:
Equation (6) equals zero available
in the formula, Rk is critical load resistance;
the system damping ratio ζ becomes 0.707 by substituting Rk in formula (7) for formula (2);
the second partial derivative of R is obtained by using equation (5):
as can be seen from analysis of equations (6) and (8), tp is a convex function with respect to R, and reaches a peak value when the system damping ratio ζ is 0.707, and reaches a peak value when R is Rk, and has an extreme value when tp varies in a wide load range;
B. analyzing the critical load resistor Rk, wherein Rk has a maximum value and a minimum value within the dynamic range [ Vi, min-Vi, max ] of the input voltage, and when Vi is Vi and max, Rk reaches the minimum value, and at this time, Rk is Rk and min, as shown in formula (9); when Vi is Vi, min, Rk reaches a maximum value, where Rk is Rk, max, as shown in equation (10),
the load resistance R of the Boost converter changes within a certain range, and according to different magnitude relations between the load range [ Rmin-Rmax ] and the critical load resistance [ Rk, min-Rk, max ], the influence of R on tp can occur as follows:
a. when the load resistance satisfies that Rmax is less than or equal to Rk, min or Rk, Rmax is less than or equal to min and is less than or equal to Rk, and max, the first-order partial derivative of the load resistance R by the peak time tp of the negative regulation voltage satisfies:
at this time, tp increases along with the increase of R, tp reaches a maximum value when the load resistance value reaches Rmax, and max of the maximum value tp of the peak time of the negative regulation voltage is:
The derivative of tp to Vi in equation (5) can be obtained:
as can be seen from equation (13), in the dynamic variation range of the input voltage Vi, tp decreases as the input voltage Vi increases, so that in the dynamic ranges of the input voltage and the load resistance, when the load resistance satisfies Rmax ≦ Rk, min, the maximum tp, max and the minimum tp, min of the peak time of the negative regulation voltage in the dynamic range are respectively:
as can be seen from equation (2), the damping ratio range of the system satisfies:
0.707≤ζ＜ζ＜1
in the formula (I), the compound is shown in the specification,
when Vi is Vi, min, and R is Rmax, tp reaches a maximum value, and when Vi is Vi, max, and R is Rmax, tp reaches a minimum value;
b. when the load resistance satisfies Rmin is more than or equal to Rk, max or Rk, min is more than or equal to Rmin and less than or equal to Rk, max, the first derivative of tp to R satisfies:
at this time, tp decreases with the increase of R, tp reaches a maximum value when the load resistance value reaches Rmin, and the maximum value tp, max of tp at this time is:
as can be seen from equation (13), in the range of the input voltage [ Vi, min to Vi, max ], when the peak time tp of the negative regulation voltage is Vi, min, tp reaches the maximum value, and the maximum value tp, max and the minimum value tp, min of tp in the dynamic range are:
as can be seen from equation (2), the system damping ratio range in this dynamic range satisfies:
0＜ζ＜ζ≤0.707
when Vi is Vi, min and R is Rmin, tp reaches a maximum value, and when Vi is Vi, max and R is Rmax, tp reaches a minimum value;
c. when the load resistance satisfies that Rmin is less than or equal to Rk, min and Rmax is greater than or equal to Rk, max, the second derivative of tp to R satisfies:
when the load resistance R is less than or equal to Rk and max, tp is increased along with the increase of R, when the load resistance R is equal to Rk and max, tp reaches a maximum value, and the maximum value tp and max of tp are as follows:
when the load resistance R is Rk, max, the damping ratio ζ of the system is 0.707;
when the load resistance satisfies R > Rk, max, tp decreases along with the increase of R, when the load resistance R is equal to Rmax, tp reaches a minimum value, and at the moment, tp and min are minimum values of tp, Rmax are as follows:
When the minimum load resistance satisfies that Rmin is less than or equal to Rk, tp is reduced along with the reduction of R, and when R is equal to Rmin, tp reaches a minimum value, at the moment, the minimum value tp, min of tp is as follows, Rmin is as follows:
When the load resistance satisfies that Rmin is less than or equal to Rk, min and Rmax is greater than or equal to Rk, max, the minimum value tp of tp is as follows:
t＝min{t，t} (22)
when the load resistance satisfies that Rmin is less than or equal to Rk, min and Rmax is greater than or equal to Rk, max, and the dynamic range [ Vi, min-Vi, max ] of the input voltage is considered, the minimum value tp of tp is as follows:
when the load resistance satisfies that Rmin is less than or equal to Rk, min and Rmax is greater than or equal to Rk, max, the system damping ratio range in the input voltage and load resistance dynamic range satisfies the following formula (4):
0＜ζ＜ζ＜1
when zeta is 0.707, tp reaches a maximum value, and the minimum value with the maximum value tp is the minimum value of tp and min corresponding to the load resistance Rmin and Rmax;
step three: optimally designing parameters of the switching converter:
B. analyzing the influence of the parameters of load resistance R, inductance L and capacitance C on tp
deriving L from equation (5):
c is derived from equation (5):
according to the analysis formulas (24) and (25), the larger the inductance L is, the longer tp is, the larger the filter capacitance C is, the longer tp is, and the smaller L and C are beneficial to inhibiting tp, so that the transient performance of the system is improved;
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) cmin can be calculated by using the set f-substituted equation (26),
in the formula, the value of lambda is 2-3;
3) Lmin is calculated by substituting known input voltages Vi, max and load Rmax into formula (27),
in the formula, the value of gamma is 1.2-1.5;
4) Respectively substituting given input voltage Vi ranges [ Vi, min-Vi, max ], load resistance R ranges [ Rmin-Rmax ], Lmin and Cmin into equations (9) and (10) to calculate critical load resistance Rk ranges [ Rk, min-Rk, max ];
5) Comparing a given load resistance R range [ Rmin-Rmax ] with [ Rk, min-Rk, max ], judging which of the following three conditions the load resistance range meets, and calculating corresponding tp and max;
(a) if the load resistance range R meets Rk, Rmax is more than or equal to min and is less than or equal to Rk, and max or Rmax is less than or equal to Rk and min, calculating the maximum value tp and max of the peak regulation time according to the formula (14);
(b) if the range of the load resistance R meets Rk, Rmin is less than or equal to Rm and min is less than or equal to Rk, and max or Rmin is greater than or equal to Rk and max, calculating tp and max according to the formula (17);
(c) If the load resistance R meets the condition that Rmin is less than or equal to Rk, min and Rmax is more than or equal to Rk, max, calculating tp and max according to the formula (19);
6) substituting the calculated tp and max into an equation (28) to judge whether the equation is established, and if the equation is established, continuing to carry out the step (7); if not, properly reducing the resistance value of the load resistor Rmax, and restarting the design from the step (3) until the index requirement is met,
t≤t (28)
in the formula, tp and sd are maximum set values of the peak time tp of the negative voltage regulation of the system;
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 invention 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 is a graph of the results of the experiment of the present invention with L-5.2 mH, C-700 μ F, R-5 Ω, F-40 kHz, and Vi-10V;
fig. 2 is a graph of the results of the experiment of the present invention with L420 μ H, C700 μ F, R5 Ω, F40 kHz, Vi 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 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 working in CCM to an output voltage:
(1) the main parameters of the switch working circuit comprise an input voltage Vi, a load resistor R, an output voltage Vo, an energy storage inductor L, a filter capacitor C and a ripple voltage VPP,
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: under the condition that an energy storage inductor L, a filter capacitor C and an output voltage Vo are fixed, when the dynamic range of an input voltage [ Vi, min-Vi, max ] and a load resistor [ Rmin-Rmax ] of a Boost converter changes, analyzing the conditions of influence factors of a wide-load-range negative regulation voltage peak value time extreme value tp:
A. taking the derivative of the equation (4) with respect to the time t, and making the derivative zero, the peak time tp of the negative regulation voltage can be obtained as:
The first partial derivative of R with tp in equation (5) can be obtained:
equation (6) equals zero available
In the formula, Rk is critical load resistance;
the system damping ratio ζ becomes 0.707 by substituting Rk in formula (7) for formula (2);
the second partial derivative of R is obtained by using equation (5):
as can be seen from analysis of equations (6) and (8), tp is a convex function with respect to R, and reaches a peak value when the system damping ratio ζ is 0.707, and reaches a peak value when R is Rk, and has an extreme value when tp varies in a wide load range;
B. analyzing the critical load resistor Rk, wherein Rk has a maximum value and a minimum value within the dynamic range [ Vi, min-Vi, max ] of the input voltage, and when Vi is Vi and max, Rk reaches the minimum value, and at this time, Rk is Rk and min, as shown in formula (9); when Vi is Vi, min, Rk reaches a maximum value, where Rk is Rk, max, as shown in equation (10),
the load resistance R of the Boost converter changes within a certain range, and according to different magnitude relations between the load range [ Rmin-Rmax ] and the critical load resistance [ Rk, min-Rk, max ], the influence of R on tp can occur as follows:
a. when the load resistance satisfies that Rmax is less than or equal to Rk, min or Rk, Rmax is less than or equal to min and is less than or equal to Rk, and max, the first-order partial derivative of the load resistance R by the peak time tp of the negative regulation voltage satisfies:
at this time, tp increases along with the increase of R, tp reaches a maximum value when the load resistance value reaches Rmax, and max of the maximum value tp of the peak time of the negative regulation voltage is:
the derivative of tp to Vi in equation (5) can be obtained:
as can be seen from equation (13), in the dynamic variation range of the input voltage Vi, tp decreases as the input voltage Vi increases, so that in the dynamic ranges of the input voltage and the load resistance, when the load resistance satisfies Rmax ≦ Rk, min, the maximum tp, max and the minimum tp, min of the peak time of the negative regulation voltage in the dynamic range are respectively:
as can be seen from equation (2), the damping ratio range of the system satisfies:
0.707≤ζ＜ζ＜1
in the formula (I), the compound is shown in the specification,
when Vi is Vi, min, and R is Rmax, tp reaches a maximum value, and when Vi is Vi, max, and R is Rmax, tp reaches a minimum value;
b. When the load resistance satisfies Rmin is more than or equal to Rk, max or Rk, min is more than or equal to Rmin and less than or equal to Rk, max, the first derivative of tp to R satisfies:
at this time, tp decreases with the increase of R, tp reaches a maximum value when the load resistance value reaches Rmin, and the maximum value tp, max of tp at this time is:
as can be seen from equation (13), in the range of the input voltage [ Vi, min to Vi, max ], when the peak time tp of the negative regulation voltage is Vi, min, tp reaches the maximum value, and the maximum value tp, max and the minimum value tp, min of tp in the dynamic range are:
as can be seen from equation (2), the system damping ratio range in this dynamic range satisfies:
0＜ζ＜ζ≤0.707
when Vi is Vi, min and R is Rmin, tp reaches a maximum value, and when Vi is Vi, max and R is Rmax, tp reaches a minimum value;
c. when the load resistance satisfies that Rmin is less than or equal to Rk, min and Rmax is greater than or equal to Rk, max, the second derivative of tp to R satisfies:
When the load resistance R is less than or equal to Rk and max, tp is increased along with the increase of R, when the load resistance R is equal to Rk and max, tp reaches a maximum value, and the maximum value tp and max of tp are as follows:
when the load resistance R is Rk, max, the damping ratio ζ of the system is 0.707;
when the load resistance satisfies R > Rk, max, tp decreases along with the increase of R, when the load resistance R is equal to Rmax, tp reaches a minimum value, and at the moment, tp and min are minimum values of tp, Rmax are as follows:
when the minimum load resistance satisfies that Rmin is less than or equal to Rk, tp is reduced along with the reduction of R, and when R is equal to Rmin, tp reaches a minimum value, at the moment, the minimum value tp, min of tp is as follows, Rmin is as follows:
when the load resistance satisfies that Rmin is less than or equal to Rk, min and Rmax is greater than or equal to Rk, max, the minimum value tp of tp is as follows:
t＝min{t，t} (22)
when the load resistance satisfies that Rmin is less than or equal to Rk, min and Rmax is greater than or equal to Rk, max, and the dynamic range [ Vi, min-Vi, max ] of the input voltage is considered, the minimum value tp of tp is as follows:
When the load resistance satisfies that Rmin is less than or equal to Rk, min and Rmax is greater than or equal to Rk, max, the system damping ratio range in the input voltage and load resistance dynamic range satisfies the following formula (4):
0＜ζ＜ζ＜1
when zeta is 0.707, tp reaches a maximum value, and the minimum value with the maximum value tp is the minimum value of tp and min corresponding to the load resistance Rmin and Rmax;
step three: optimally designing parameters of the switching converter:
a: analyzing the influence of the parameters of load resistance R, inductance L and capacitance C on tp
deriving L from equation (5):
c is derived from equation (5):
according to the analysis formulas (24) and (25), the larger the inductance L is, the longer tp is, the larger the filter capacitance C is, the longer tp is, and the smaller L and C are beneficial to inhibiting tp, so that the transient performance of the system is improved;
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) cmin can be calculated by using the set f-substituted equation (26),
in the formula, the value of lambda is 2-3;
3) lmin is calculated by substituting known input voltages Vi, max and load Rmax into formula (27),
in the formula, the value of gamma is 1.2-1.5;
4) respectively substituting given input voltage Vi ranges [ Vi, min-Vi, max ], load resistance R ranges [ Rmin-Rmax ], Lmin and Cmin into equations (9) and (10) to calculate critical load resistance Rk ranges [ Rk, min-Rk, max ];
5) comparing a given load resistance R range [ Rmin-Rmax ] with [ Rk, min-Rk, max ], judging which of the following three conditions the load resistance range meets, and calculating corresponding tp and max;
(a) If the load resistance range R meets Rk, Rmax is more than or equal to min and is less than or equal to Rk, and max or Rmax is less than or equal to Rk and min, calculating the maximum value tp and max of the peak regulation time according to the formula (14);
(b) if the range of the load resistance R meets Rk, Rmin is less than or equal to Rm and min is less than or equal to Rk, and max or Rmin is greater than or equal to Rk and max, calculating tp and max according to the formula (17);
(c) if the load resistance R meets the condition that Rmin is less than or equal to Rk, min and Rmax is more than or equal to Rk, max, calculating tp and max according to the formula (19);
6) substituting the calculated tp and max into an equation (28) to judge whether the equation is established, and if the equation is established, continuing to carry out the step (7); if not, properly reducing the resistance value of the load resistor Rmax, and restarting the design from the step (3) until the index requirement is met,
t≤t (28)
in the formula, tp and sd are maximum set values of the peak time tp of the negative voltage regulation of the system;
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) calculating Cmin as 700 μ F (selecting a 2-fold margin) according to equation (26);
(3) selecting Rmax to be 500 Ω, and calculating Lmin to be 5.2mH (selecting a margin of 1.2 times) according to formula (27);
(4) from the given resistance range and equations (9) and (10), the minimum and maximum values of the critical load resistance Rk can be calculated as: rk, min ═ 2.3 Ω, Rk, max ═ 4.6 Ω;
(5) from the given relationship between the load resistance R range [ Rmin to Rmax ] and [ Rk, min to Rk, max ], it is known that tp reaches a maximum value when R is 5 Ω and Vi is 10V, and tp and max are 3.2 ms.
(6) Judging that tp, max < tp, sd, 3.2 is more than 0.5 and cannot meet the requirement;
from the above calculation results, when the load resistance Rmax is selected to be 500 Ω, the peak time tp of the negative voltage regulation of the system is too long to meet the set requirement; re-selecting R' max to 40 Ω, re-calculating in step (3) to obtain Lmin to 420 μ H, Cmin to 700 μ F, Rk, min to 0.65 Ω, Rk, max to 1.3 Ω, tp to maximum when R to 5 Ω and Vi to 10V, tp, max to 0.45ms, and satisfying the negative regulation voltage suppression requirement.
designing according to the steps according to the converter parameters given in table 1, selecting F to be 80kHz under the condition that the switching frequency allows, repeating the designing according to the designing steps, and when Rmax to be 500 Ω, calculating to obtain Cmin to be 350 μ F, Lmin to be 2.6mH, Rk, min to be 3.3 Ω, and Rk, max to be 1.64 Ω; when R is 5 Ω and Vi is 10V, tp reaches a maximum value, where tp and max are 1.6ms, and tp is too long and not satisfactory, R' max is 80 Ω, and Lmin is 420 μ H, Cmin is 350 μ F, Rk, min is 0.9 Ω, Rk and max is 1.8 Ω; when R is 5 Ω and Vi is 10V, tp reaches a maximum value, and at this time tp and max are 0.42ms, which satisfies the negative regulation voltage suppression requirement.
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: l5.2 mH, C700 μ F, R5 Ω, F40 kHz, Vi 10V; the corresponding experimental results are shown in fig. 1; the corresponding experimental results are shown in fig. 2, where L is 420 μ H, C is 700 μ F, R is 5 Ω, F is 40kHz, and Vi is 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 method of 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 main parameters of the switch working circuit comprise an input voltage Vi, a load resistor R, an output voltage Vo, an energy storage inductor L, a filter capacitor C and a ripple voltage VPP,
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: under the condition that an energy storage inductor L, a filter capacitor C and an output voltage Vo are fixed, when the dynamic range of an input voltage [ Vi, min-Vi, max ] and a load resistor [ Rmin-Rmax ] of a Boost converter changes, analyzing the conditions of influence factors of a wide-load-range negative regulation voltage peak value time extreme value tp:
A. taking the derivative of the equation (4) with respect to the time t, and making the derivative zero, the peak time tp of the negative regulation voltage can be obtained as:
the first partial derivative of R with tp in equation (5) can be obtained:
equation (6) equals zero available
in the formula, Rk is critical load resistance;
The system damping ratio ζ becomes 0.707 by substituting Rk in formula (7) for formula (2);
The second partial derivative of R is obtained by using equation (5):
as can be seen from analysis of equations (6) and (8), tp is a convex function with respect to R, and reaches a peak value when the system damping ratio ζ is 0.707, and reaches a peak value when R is Rk, and has an extreme value when tp varies in a wide load range;
B. analyzing the critical load resistor Rk, wherein Rk has a maximum value and a minimum value within the dynamic range [ Vi, min-Vi, max ] of the input voltage, and when Vi is Vi and max, Rk reaches the minimum value, and at this time, Rk is Rk and min, as shown in formula (9); when Vi is Vi, min, Rk reaches a maximum value, where Rk is Rk, max, as shown in equation (10),
the load resistance R of the Boost converter changes within a certain range, and according to different magnitude relations between the load range [ Rmin-Rmax ] and the critical load resistance [ Rk, min-Rk, max ], the influence of R on tp can occur as follows:
a. When the load resistance satisfies that Rmax is less than or equal to Rk, min or Rk, Rmax is less than or equal to min and is less than or equal to Rk, and max, the first-order partial derivative of the load resistance R by the peak time tp of the negative regulation voltage satisfies:
at this time, tp increases along with the increase of R, tp reaches a maximum value when the load resistance value reaches Rmax, and max of the maximum value tp of the peak time of the negative regulation voltage is:
the derivative of tp to Vi in equation (5) can be obtained:
As can be seen from equation (13), in the dynamic variation range of the input voltage Vi, tp decreases as the input voltage Vi increases, so that in the dynamic ranges of the input voltage and the load resistance, when the load resistance satisfies Rmax ≦ Rk, min, the maximum tp, max and the minimum tp, min of the peak time of the negative regulation voltage in the dynamic range are respectively:
as can be seen from equation (2), the damping ratio range of the system satisfies:
0.707≤ζ＜ζ＜1
in the formula (I), the compound is shown in the specification,
when Vi is Vi, min, and R is Rmax, tp reaches a maximum value, and when Vi is Vi, max, and R is Rmax, tp reaches a minimum value;
b. when the load resistance satisfies Rmin is more than or equal to Rk, max or Rk, min is more than or equal to Rmin and less than or equal to Rk, max, the first derivative of tp to R satisfies:
at this time, tp decreases with the increase of R, tp reaches a maximum value when the load resistance value reaches Rmin, and the maximum value tp, max of tp at this time is:
as can be seen from equation (13), in the range of the input voltage [ Vi, min to Vi, max ], when the peak time tp of the negative regulation voltage is Vi, min, tp reaches the maximum value, and the maximum value tp, max and the minimum value tp, min of tp in the dynamic range are:
as can be seen from equation (2), the system damping ratio range in this dynamic range satisfies:
0＜ζ＜ζ≤0.707
when Vi is Vi, min and R is Rmin, tp reaches a maximum value, and when Vi is Vi, max and R is Rmax, tp reaches a minimum value;
c. When the load resistance satisfies that Rmin is less than or equal to Rk, min and Rmax is greater than or equal to Rk, max, the second derivative of tp to R satisfies:
when the load resistance R is less than or equal to Rk and max, tp is increased along with the increase of R, when the load resistance R is equal to Rk and max, tp reaches a maximum value, and the maximum value tp and max of tp are as follows:
when the load resistance R is Rk, max, the damping ratio ζ of the system is 0.707;
when the load resistance satisfies R > Rk, max, tp decreases along with the increase of R, when the load resistance R is equal to Rmax, tp reaches a minimum value, and at the moment, tp and min are minimum values of tp, Rmax are as follows:
when the minimum load resistance satisfies that Rmin is less than or equal to Rk, tp is reduced along with the reduction of R, and when R is equal to Rmin, tp reaches a minimum value, at the moment, the minimum value tp, min of tp is as follows, Rmin is as follows:
when the load resistance satisfies that Rmin is less than or equal to Rk, min and Rmax is greater than or equal to Rk, max, the minimum value tp of tp is as follows:
t＝min{t，t} (22)
when the load resistance satisfies that Rmin is less than or equal to Rk, min and Rmax is greater than or equal to Rk, max, and the dynamic range [ Vi, min-Vi, max ] of the input voltage is considered, the minimum value tp of tp is as follows:
when the load resistance satisfies that Rmin is less than or equal to Rk, min and Rmax is greater than or equal to Rk, max, the system damping ratio range in the input voltage and load resistance dynamic range satisfies the following formula (4):
0＜ζ＜ζ＜1
when zeta is 0.707, tp reaches a maximum value, and the minimum value with the maximum value tp is the minimum value of tp and min corresponding to the load resistance Rmin and Rmax;
step three: optimally designing parameters of the switching converter:
A. analyzing the influence of the parameters of load resistance R, inductance L and capacitance C on tp
Deriving L from equation (5):
c is derived from equation (5):
according to the analysis formulas (24) and (25), the larger the inductance L is, the longer tp is, the larger the filter capacitance C is, the longer tp is, and the smaller L and C are beneficial to inhibiting tp, so that the transient performance of the system is improved;
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) cmin can be calculated by using the set f-substituted equation (26),
in the formula, the value of lambda is 2-3;
3) lmin is calculated by substituting known input voltages Vi, max and load Rmax into formula (27),
in the formula, the value of gamma is 1.2-1.5;
4) respectively substituting given input voltage Vi ranges [ Vi, min-Vi, max ], load resistance R ranges [ Rmin-Rmax ], Lmin and Cmin into equations (9) and (10) to calculate critical load resistance Rk ranges [ Rk, min-Rk, max ];
5) comparing a given load resistance R range [ Rmin-Rmax ] with [ Rk, min-Rk, max ], judging which of the following three conditions the load resistance range meets, and calculating corresponding tp and max;
(a) if the load resistance range R meets Rk, Rmax is more than or equal to min and is less than or equal to Rk, and max or Rmax is less than or equal to Rk and min, calculating the maximum value tp and max of the peak regulation time according to the formula (14);
(b) if the range of the load resistance R meets Rk, Rmin is less than or equal to Rm and min is less than or equal to Rk, and max or Rmin is greater than or equal to Rk and max, calculating tp and max according to the formula (17);
(c) If the load resistance R meets the condition that Rmin is less than or equal to Rk, min and Rmax is more than or equal to Rk, max, calculating tp and max according to the formula (19);
6) substituting the calculated tp and max into an equation (28) to judge whether the equation is established, and if the equation is established, continuing to carry out the step (7); if not, properly reducing the resistance value of the load resistor Rmax, and restarting the design from the step (3) until the index requirement is met,
t≤t (28)
in the formula, tp and sd are maximum set values of the peak time tp of the negative voltage regulation of the system;
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.
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