WO2020215517A1 - 基于分段延迟反馈控制的Buck-Boost变换器控制参数稳定域确定方法 - Google Patents
基于分段延迟反馈控制的Buck-Boost变换器控制参数稳定域确定方法 Download PDFInfo
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- WO2020215517A1 WO2020215517A1 PCT/CN2019/098332 CN2019098332W WO2020215517A1 WO 2020215517 A1 WO2020215517 A1 WO 2020215517A1 CN 2019098332 W CN2019098332 W CN 2019098332W WO 2020215517 A1 WO2020215517 A1 WO 2020215517A1
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
- H02M3/00—Conversion of dc power input into dc power output
- H02M3/02—Conversion of dc power input into dc power output without intermediate conversion into ac
- H02M3/04—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters
- H02M3/10—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
- H02M3/145—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal
- H02M3/155—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only
- H02M3/156—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only with automatic control of output voltage or current, e.g. switching regulators
-
- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
- H02M3/00—Conversion of dc power input into dc power output
- H02M3/02—Conversion of dc power input into dc power output without intermediate conversion into ac
- H02M3/04—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters
- H02M3/10—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
- H02M3/145—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal
- H02M3/155—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only
- H02M3/156—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only with automatic control of output voltage or current, e.g. switching regulators
- H02M3/158—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only with automatic control of output voltage or current, e.g. switching regulators including plural semiconductor devices as final control devices for a single load
- H02M3/1582—Buck-boost converters
-
- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
- H02M1/00—Details of apparatus for conversion
- H02M1/44—Circuits or arrangements for compensating for electromagnetic interference in converters or inverters
-
- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
- H02M1/00—Details of apparatus for conversion
- H02M1/0003—Details of control, feedback or regulation circuits
Definitions
- the invention belongs to the technical field of power electronics, and in particular relates to a method for determining the stability domain of a Buck-Boost converter control parameter based on segmented delay feedback control.
- Buck-Boost converter has been widely used because of its simple structure, wide input voltage range, and buck-boost control.
- the converter is a variable structure and strong nonlinear system, it will produce bifurcation and chaos under certain conditions, and cause problems such as excessive irregular electromagnetic noise and increased oscillation during the operation of the converter, which directly affects the converter’s performance. Stable operation. Therefore, it is of great significance to study effective chaos control methods for the converter to ensure the stable operation of the system.
- the present invention provides a method for determining the stability region of Buck-Boost converter control parameters based on segmented delay feedback control.
- the invention provides a method for determining the stability domain of Buck-Boost converter control parameters based on segmented delay feedback control.
- the specific steps include:
- Step 1 Taking the inductor current and capacitor voltage in the Buck-Boost converter as state variables, establish the state differential equations for the two different level states of the converter under the action of the pulse input voltage;
- Step 2 According to the difference of Buck-Boost converter input voltage, correct the inductor reference current in the converter to obtain a new inductor reference current;
- Step 3 Obtain the discrete iterative mapping model of the system according to the state differential equation described in step 1 and the new inductor reference current described in step 2;
- Step 4 According to the discrete iterative mapping model obtained in step 3, when the converter adopts segmented delay feedback control under the action of pulse input voltage, any given value of its control parameter k 1 can be selected to obtain the control parameters when the system is running stably k ranges from 2 (k 2min, k 2max);
- Step 5 Change the given value of the control parameter k 1 at a certain interval, and obtain the corresponding value range (k 2min , k 2max ) of the m groups of control parameters k 2 using the same method as described above;
- Step 6 According to the obtained upper limit k 2max and lower limit k 2min of the control parameter k 2 of m groups and the corresponding control parameter k 1 value, the upper limit k 2max and k 1 value are obtained by numerical fitting method respectively and the functional relationship between the lower limit value 2min k k 1, two function formulas by the area bounded control parameter k is the k stability region. 1 and 2, the stabilization domain arbitrarily selected. 1 and k Both k 2 values can ensure the stable operation of the system.
- the establishment of the state differential equation of the Buck-Boost converter in the step 1 specifically includes:
- L, C and R are the inductance, capacitance and load resistance in the converter respectively.
- the inductor reference current in the converter is corrected to obtain a new inductor reference current, which is specifically:
- I'ref is the revised new inductor reference current
- I ref is the initial value of the inductor reference current
- k 1 and k 2 are the control parameters when the converter input voltage is high level U in1 and low level U in2 respectively
- U C is the capacitor voltage
- T is the switching period of the power switch Q.
- Obtaining the discrete iterative mapping model of the system in the step 3 specifically includes:
- Step (3-1) the formula (1) - (3) of the time discrete differential equations state, respectively, and i n u n represents the inductor current and capacitor voltage at the time nT.
- the discrete equation is as follows:
- Equation (1) Discretization can be expressed as:
- Equation (2) Discretization can be expressed as:
- Equation (3) Discretization can be expressed as:
- Step (3-3) According to the power switch on time t n and the inductor current i n and the capacitor voltage u n at the time nT shown in formula (8), the discrete iterative mapping model of the system can be obtained, which is specifically expressed as:
- M 1 (I n cos( ⁇ t m )+a sin( ⁇ t m ))
- M 2 ( ⁇ I n +a ⁇ )cos( ⁇ t m )
- M 3 (a ⁇ - ⁇ I n )sin( ⁇ t m )
- t m Tt n
- I n represents the new inductor reference current at nT.
- the converter adopts segmented delay feedback control under the action of the pulse input voltage, and its control parameter k 1 is any given value to obtain the control when the system is stable in operation.
- the value range of the parameter k 2 (k 2min , k 2max ) specifically includes the following steps:
- Step (4-1) Set system parameters, including: pulse input voltage high level U in1 , low level U in2 , the initial value of the inductor reference current I ref , the maximum number of iterations N, the initial value of the control parameter k 1 k 1.0 , the initial value of the control parameter k 2 k of 2.0, the control parameter k Ak 2 delta 2, B maximum number of repetitions, the initial value of the count variable q is 0;
- Step (4-2) Collect the pulse input voltage and capacitor voltage, and calculate the new reference current value of the inductor at nT according to the pulse input voltage level and formula (4):
- u n u n-1 respectively, and represent the time nT and (n + 1) at time T capacitor voltage;
- Step (4-3) Calculate the conduction time of the power switch in the nth switching cycle according to formula (8):
- I n represents the new inductor reference current at nT
- Step (4-4) According to formula (9), calculate (n+1) the inductor current i n+1 and the capacitor voltage u n+1 at time T:
- M 1 (I n cos( ⁇ t m )+a sin( ⁇ t m ))
- M 2 ( ⁇ I n +a ⁇ )cos( ⁇ t m )
- M 3 (a ⁇ - ⁇ I n )sin( ⁇ t m )
- t m Tt n
- I n represents the new inductor reference current at nT;
- Step (4-12): The control parameter k 2 is sequentially reduced by ⁇ k 2 on the basis of (k 2.0 -qB ⁇ k 2 ), and steps (4-2) to (4-5) are repeated to determine whether the system is operating stably, if so , Then set k 2max k 2 , and then execute step (4-13), otherwise execute step (4-14);
- Step (4-13): Control parameters k 2 sequentially reduced ⁇ k 2, repeat steps (4-2) through step (4-5), it is determined whether the stable operation of the system, and if so, then let k 2min k 2, until the system Until it can't run stably, then go to step (4-15);
- the given value of the control parameter k 1 is changed at a certain interval, and the corresponding value ranges (k 2min , k 2max ) of the m groups of control parameters k 2 are obtained using the same method described above.
- the value interval ⁇ k 1 of the control parameter k 1 and the specific data of the m group of parameters can be determined as required.
- a numerical fitting method is used to obtain the upper limit k 2max and k 2max respectively. 1 value and the functional relationship between the lower limit k 2min and k 1 value; the numerical fitting method preferentially adopts the least square method, and the obtained functional relationship is respectively:
- a 1 , b 1 , c 1 , d 1 are coefficients respectively, and the coefficients are determined by the least square method.
- a 2 , b 2 , c 2 , and d 2 are coefficients respectively, and the coefficients are determined by the least square method.
- FIG. 1 is a diagram of the main circuit topology of the Buck-Boost converter of the present invention
- Fig. 2 is a flowchart of a method for determining the stability region of Buck-Boost converter control parameters based on segmented delay feedback control provided by an embodiment of the present invention
- FIG. 3 is a numerical simulation flowchart for obtaining the value range (k 2min , k 2max ) of the control parameter k 2 when the system is stably operating according to an embodiment of the present invention
- FIG. 1 is a diagram of the main circuit topology of the Buck-Boost converter of the present invention.
- the converter includes pulse power U in (including high level U in1 , low level U in2 ), power switch Q, inductor L, capacitor C, diode D and load resistance R.
- FIG. 2 is a flow chart of a method for determining the stability region of Buck-Boost converter control parameters based on segmented delay feedback control provided by the present invention. The method includes the following steps:
- Step 1 Taking the inductor current and capacitor voltage in the Buck-Boost converter as state variables, establish the state differential equations for the two different level states of the converter under the action of the pulse input voltage;
- Step 2 According to the difference of Buck-Boost converter input voltage, correct the inductor reference current in the converter to obtain a new inductor reference current;
- Step 3 Obtain the discrete iterative mapping model of the system according to the state differential equation described in step 1 and the new inductor reference current described in step 2;
- Step 4 According to the discrete iterative mapping model obtained in step 3, when the converter adopts segmented delay feedback control under the action of pulse input voltage, any given value of its control parameter k 1 can be selected to obtain the control parameters when the system is running stably k ranges from 2 (k 2min, k 2ma);
- Step 5 Change the given value of the control parameter k 1 at a certain interval, and obtain the corresponding value range (k 2min , k 2max ) of the m groups of control parameters k 2 using the same method as described above;
- Step 6 According to the obtained upper limit k 2max and lower limit k 2min of the control parameter k 2 of m groups and the corresponding control parameter k 1 value, the upper limit k 2max and k 1 value are obtained by numerical fitting method respectively and the functional relationship between the lower limit value 2min k k 1, two function formulas by the area bounded control parameter k is the k stability region. 1 and 2, the stabilization domain arbitrarily selected. 1 and k Both k 2 values can ensure the stable operation of the system.
- L, C and R are the inductance, capacitance and load resistance in the converter respectively.
- the inductor reference current in the converter is corrected to obtain a new inductor reference current, which is specifically:
- I'ref is the revised new inductor reference current
- I ref is the initial value of the inductor reference current
- k 1 and k 2 are the control parameters when the converter input voltage is high level U in1 and low level U in2 respectively
- U C is the capacitor voltage
- T is the switching period of the power switch Q.
- Step (3-1) Discretize the state differential equation described in equations (1)-(3) in time to obtain:
- Equation (1) Discretization can be expressed as:
- Equation (2) Discretization can be expressed as:
- Equation (3) Discretization can be expressed as:
- the discrete iterative mapping model of the system can be expressed as:
- M 1 (I n cos( ⁇ t m )+a sin( ⁇ t m ))
- M 2 ( ⁇ I n +a ⁇ )cos( ⁇ t m )
- M 3 (a ⁇ - ⁇ I n )sin( ⁇ t m )
- t m Tt n
- I n represents the new inductor reference current at nT.
- FIG. 3 is a numerical simulation flowchart for obtaining the value range (k 2min , k 2max ) of the control parameter k 2 when the system is stably operating according to an embodiment of the present invention. Specific steps are as follows:
- Step (4-1) Set system parameters, including: pulse input voltage high level U in1 , low level U in2 , the initial value of the inductor reference current I ref , the maximum number of iterations N, the initial value of the control parameter k 1 k 1.0 , the initial value of the control parameter k 2 k of 2.0, the control parameter k Ak 2 delta 2, B maximum number of repetitions, the initial value of the count variable q is 0;
- Step (4-2) Collect the pulse input voltage and capacitor voltage, and calculate the new reference current value of the inductor at nT according to the pulse input voltage level and formula (4):
- u n u n-1 respectively, and represent the time nT and (n + 1) at time T capacitor voltage;
- Step (4-3) Calculate the conduction time of the power switch in the nth switching cycle according to formula (14):
- I n represents the new inductor reference current at nT
- Step (4-4) According to formula (15), calculate (n+1) the inductor current i n+1 and the capacitor voltage u n+1 at time T:
- M 1 (I n cos( ⁇ t m )+a sin( ⁇ t m ))
- M 2 ( ⁇ I n +a ⁇ )cos( ⁇ t m )
- M 3 (a ⁇ - ⁇ I n )sin( ⁇ t m )
- t m Tt n
- I n represents the new inductor reference current at nT;
- Step (4-12): The control parameter k 2 is sequentially reduced by ⁇ k 2 on the basis of (k 2.0 -qB ⁇ k 2 ), and steps (4-2) to (4-5) are repeated to determine whether the system is operating stably, if so , Then set k 2max k 2 , and then execute step (4-13), otherwise execute step (4-14);
- Step (4-13): Control parameters k 2 sequentially reduced ⁇ k 2, repeat steps (4-2) through step (4-5), it is determined whether the stable operation of the system, and if so, then let k 2min k 2, until the system Until it can't run stably, then go to step (4-15);
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Abstract
本发明公开一种基于分段延迟反馈控制的Buck-Boost变换器控制参数稳定域确定方法。所述方法为:以Buck-Boost变换器中电感电流和电容电压为状态变量,针对该变换器在脉冲输入电压作用下的两种不同电平状态,分别建立其状态微分方程;根据Buck-Boost变换器输入电压的不同,对变换器中电感参考电流进行修正,从而得到新的电感参考电流;根据上述状态微分方程和新的电感参考电流,获得系统的离散迭代映射模型;根据上述离散迭代映射模型,获得变换器在脉冲输入电压作用下采用分段延迟反馈控制实现系统稳定运行时其控制参数上、下限值对应的函数关系式,由所得函数关系式即可确定相应控制参数的稳定域范围。
Description
本发明属于电力电子技术领域,尤其涉及一种基于分段延迟反馈控制的Buck-Boost变换器控制参数稳定域确定方法。
Buck-Boost变换器因具有结构简单、输入电压范围宽、可实现升降压控制等优点而得到了广泛的应用。然而该变换器因属变结构强非线性系统,在一定条件下会产生分岔与混沌现象,并导致变换器运行中产生不规则电磁噪声过大、振荡加剧等问题,直接影响到变换器的稳定运行。因此,针对变换器研究有效的混沌控制方法以确保系统的稳定运行具有重要意义。
目前国内外在有关Buck-Boost变换器的混沌控制方面已开展了系列研究,提出了诸如OGY控制方法、非线性分段二次函数反馈控制法、参数共振微扰法等多种控制方法,取得了较好的控制效果,但上述方法都是针对变换器在输入为稳态直流电压下存在的混沌现象提出的,当变换器直接采用PWM整流电源作为输入电源时,即变换器输入电压为PWM调制的脉冲输入电压时存在的混沌现象则研究较少,目前只提出了一种分段延迟反馈控制法,该方法虽取得了较好的控制效果,但存在控制参数整定困难等不足,如果其控制参数选择不合适,则不能达到预期的混沌控制效果。因此针对变换器在脉冲输入电压作用下采用分段延迟反馈控制法时,如何在保证系统稳定运行的前提下研究确定其控制参数的变化规律,并进而确定其控制参数的稳定域范 围,对于确保系统的稳定运行具有重要意义。
发明内容
为达到上述技术目标,本发明提供一种基于分段延迟反馈控制的Buck-Boost变换器控制参数稳定域确定方法。
本发明提供的一种基于分段延迟反馈控制的Buck-Boost变换器控制参数稳定域确定方法。具体步骤包括:
步骤1:以Buck-Boost变换器中电感电流和电容电压为状态变量,针对该变换器在脉冲输入电压作用下的两种不同电平状态,分别建立其状态微分方程;
步骤2:根据Buck-Boost变换器输入电压的不同,对变换器中电感参考电流进行修正,从而得到新的电感参考电流;
步骤3:根据步骤1所述状态微分方程和步骤2所述新的电感参考电流,获得系统的离散迭代映射模型;
步骤4:根据步骤3所得离散迭代映射模型,针对变换器在脉冲输入电压作用下采用分段延迟反馈控制时,对其控制参数k
1任取一给定值,获得实现系统稳定运行时控制参数k
2的取值范围(k
2min,k
2max);
步骤5:按一定间距改变控制参数k
1的给定值,采用上述同样的方法获得m组控制参数k
2相应的取值范围(k
2min,k
2max);
步骤6:根据所获得的m组控制参数k
2的上限值k
2max和下限值k
2min以及相应的控制参数k
1值,采用数值拟合方法分别获得上限值k
2max与k
1值以及下限值k
2min与k
1值间的函数关系式,由上述两个函数关系式所界定的区域即为控制参数k
1和k
2的稳定域,在该稳定域内任意选取的k
1和k
2值均能保证系统 的稳定运行。
所述步骤1中建立所述Buck-Boost变换器的状态微分方程,具体包括:
以Buck-Boost变换器中电感电流i
L和电容电压u
C为状态变量,针对变换器在脉冲输入电压作用下的两种不同电平状态并根据变换器中功率开关管Q的两种不同工作状态,分别建立其状态微分方程,具体为:
状态一:功率开关Q导通:
当变换器的脉冲输入电压为高电平U
in1时,系统状态微分方程为:
当变换器的脉冲输入电压为低电平U
in2时,系统状态微分方程为:
状态二:功率开关Q断开:
此时变换器工作状态与输入电压无关,其系统状态微分方程为:
所述步骤2中根据所述Buck-Boost变换器输入电压的不同,对变换器中电感参考电流进行修正,从而得到新的电感参考电流,具体为:
其中:I'
ref为修正后的新电感参考电流,I
ref为电感参考电流初值,k
1、k
2分别为变换器输入电压为高电平U
in1和低电平U
in2时的控制参数,u
C为电容电压,T为功率开关管Q的开关周期。
所述步骤3中获得所述系统的离散迭代映射模型,具体包括:
步骤(3-1):将式(1)-式(3)所述状态微分方程时间离散化,分别以i
n和u
n表示在nT时刻的电感电流和电容电压。离散方程具体如下:
式(1)离散化可表示为:
式(2)离散化可表示为:
式(3)离散化可表示为:
步骤(3-2):根据nT时刻的电感电流、脉冲输入电压以及式(4)所示新电感参考电流,得到变换器中功率开关管第n个开关周期的导通时间t
n为:
其中:U
in为变换器输入电压(当变换器输入电压为高电平时,U
in=U
in1;当变换器输入电压为低电平时,U
in=U
in2),I
n表示nT时刻新电感参考电流,即:
步骤(3-3):根据式(8)所示功率开关管导通时间t
n及nT时刻的电感电流i
n和电容电压u
n,可得系统的离散迭代映射模型,具体表示为:
其中:M
1=(I
ncos(ωt
m)+a sin(ωt
m)),M
2=(τI
n+aω)cos(ωt
m),M
3=(aτ-ωI
n)sin(ωt
m),
t
m=T-t
n,I
n表示nT时刻新电感参考电流。
所述步骤4中根据所述系统离散迭代映射模型,针对变换器在脉冲输入电压作用下采用分段延迟反馈控制,对其控制参数k
1任取一给定值,获取实现系统稳定运行时控制参数k
2的取值范围(k
2min,k
2max),具体包括如下步骤:
步骤(4-1):设置系统参数,包括:脉冲输入电压高电平U
in1、低电平U
in2,电感参考电流初值I
ref,最大迭代次数N,控制参数k
1的初始值k
1.0,控制参数k
2的初始值k
2.0,控制参数k
2的增量Δk
2,最大重复次数B,计数变量q的初始值为0;
步骤(4-2):采集脉冲输入电压和电容电压,根据脉冲输入电压电平并由公式(4)计算nT时刻电感的新参考电流值:
其中:u
n和u
n-1分别表示nT时刻和(n+1)T时刻的电容电压;
步骤(4-3):根据公式(8)计算第n个开关周期内功率开关管的导通时间:
其中:I
n表示nT时刻新电感参考电流,U
in为变换器输入电压(当变换器输入电压为高电平时,U
in=U
in1;当变换器输入电压为低电平时,U
in=U
in2);
步骤(4-4):根据公式(9),计算(n+1)T时刻的电感电流i
n+1和电容电压u
n+1:
其中:M
1=(I
ncos(ωt
m)+a sin(ωt
m)),M
2=(τI
n+aω)cos(ωt
m),M
3=(aτ-ωI
n)sin(ωt
m),
t
m=T-t
n,I
n表示nT时刻新电感参考电流;
步骤(4-5):判断系统的输出响应i
n+1和u
n+1是否与i
n和u
n相等,若是,则表示系统运行稳定,执行步骤(4-7),否则执行步骤(4-6);
步骤(4-6):判断迭代次数n是否小于最大迭代次数N,若是,则n加1,然后返回步骤(4-2);否则执行步骤(4-9);
步骤(4-7):控制参数k
2在(k
2.0+qBΔk
2)的基础上依次增加Δk
2,重复步骤(4-2)~步骤(4-5),判断系统是否稳定运行,若是,则令k
2max=k
2,直到系统不能稳定运行为止,然后执行步骤(4-8);
步骤(4-8):控制参数k
2在(k
2.0-qBΔk
2)的基础上依次减小Δk
2,重复步骤(4-2)~步骤(4-5),判断系统是否稳定运行,若是,则令k
2min=k
2,直到系统不能稳定运行为止,然后执行步骤(4-15);
步骤(4-9):控制参数k
2在(k
2.0+qBΔk
2)的基础上依次增加Δk
2,重复步骤(4-2)~步骤(4-5),判断系统是否稳定运行,若是,则令k
2min=k
2,然 后执行步骤(4-10),否则执行步骤(4-11);
步骤(4-10):控制参数k
2依次增加Δk
2,重复步骤(4-2)~步骤(4-5),判断系统是否稳定运行,若是,则令k
2max=k
2,直到系统不能稳定运行为止,然后执行步骤(4-15);
步骤(4-11):判断重复次数是否小于B次,若是,则返回步骤(4-9),否则执行步骤(4-12);
步骤(4-12):控制参数k
2在(k
2.0-qBΔk
2)的基础上依次减小Δk
2,重复步骤(4-2)~步骤(4-5),判断系统是否稳定运行,若是,则令k
2max=k
2,然后执行步骤(4-13),否则执行步骤(4-14);
步骤(4-13):控制参数k
2依次减小Δk
2,重复步骤(4-2)~步骤(4-5),判断系统是否稳定运行,若是,则令k
2min=k
2,直到系统不能稳定运行为止,然后执行步骤(4-15);
步骤(4-14):判断重复次数是否小于B次,若是,则返回步骤(4-12),否则计数变量q增加1,然后返回步骤(4-2);
步骤(4-15):根据所得控制参数k
2的上限值k
2max和下限值k
2min,即获得实现系统稳定运行时控制参数k
2的取值范围(k
2min,k
2max)。
所述步骤5中,按一定间距改变控制参数k
1的给定值,采用上述同样的方法获得m组控制参数k
2相应的取值范围(k
2min,k
2max)。所述控制参数k
1的取值间距Δk
1和m组参数的具体数据可根据需要进行确定。
所述步骤6中,根据所述m组控制参数k
2的上限值k
2max和下限值k
2min以及相应的控制参数k
1值,采用数值拟合方法分别获得上限值k
2max与k
1 值以及下限值k
2min与k
1值间的函数关系式;所述数值拟合方法优先采用最小二乘法,所获得的函数关系式分别为:
(1)控制参数k
2上限值k
2max与k
1值间的函数关系式为:
式中:a
1、b
1、c
1、d
1分别为系数,所述系数采用最小二乘法进行确定。
(2)控制参数k
2下限值k
2min与k
1值间的函数关系式为:
式中:a
2、b
2、c
2、d
2分别为系数,所述系数采用最小二乘法进行确定。
图1为本发明Buck-Boost变换器的主电路拓扑结构图
图2为本发明实施例提供的一种基于分段延迟反馈控制的Buck-Boost变换器控制参数稳定域确定方法流程图
图3为本发明实施例提供的一种获得实现系统稳定运行时控制参数k
2的取值范围(k
2min,k
2max)的数值仿真流程图
下面结合附图和实施例对本发明做进一步具体的说明。
参见图1,为本发明Buck-Boost变换器的主电路拓扑结构图。该变换器包括脉冲电源U
in(包括高电平U
in1、低电平U
in2)、功率开关Q、电感L、电容C、二极管D和负载电阻R。
参见图2,为本发明提供的一种基于分段延迟反馈控制的Buck-Boost变换器控制参数稳定域确定方法流程图。所述方法包括如下步骤:
步骤1:以Buck-Boost变换器中电感电流和电容电压为状态变量,针对该变换器在脉冲输入电压作用下的两种不同电平状态,分别建立其状态微分方程;
步骤2:根据Buck-Boost变换器输入电压的不同,对变换器中电感参考电流进行修正,从而得到新的电感参考电流;
步骤3:根据步骤1所述状态微分方程和步骤2所述新的电感参考电流,获得系统的离散迭代映射模型;
步骤4:根据步骤3所得离散迭代映射模型,针对变换器在脉冲输入电压作用下采用分段延迟反馈控制时,对其控制参数k
1任取一给定值,获得实现系统稳定运行时控制参数k
2的取值范围(k
2min,k
2ma);
步骤5:按一定间距改变控制参数k
1的给定值,采用上述同样的方法获得m组控制参数k
2相应的取值范围(k
2min,k
2max);
步骤6:根据所获得的m组控制参数k
2的上限值k
2max和下限值k
2min以及相应的控制参数k
1值,采用数值拟合方法分别获得上限值k
2max与k
1值以及下限值k
2min与k
1值间的函数关系式,由上述两个函数关系式所界定的区域即为控制参数k
1和k
2的稳定域,在该稳定域内任意选取的k
1和k
2值均能保证系统的稳定运行。
步骤1的实现方式:
以Buck-Boost变换器中电感电流i
L和电容电压u
C为状态变量,针对变换器在脉冲输入电压作用下的两种不同电平状态并根据变换器中功率开关管Q的两种不同工作状态,分别建立其状态微分方程,具体为:
状态一:功率开关Q导通:
当变换器的脉冲输入电压为高电平U
in1时,系统状态微分方程为:
当变换器的脉冲输入电压为低电平U
in2时,系统状态微分方程为:
状态二:功率开关Q断开:
此时变换器工作状态与输入电压无关,其系统状态微分方程为:
步骤2的实现方式:
根据所述Buck-Boost变换器输入电压的不同,对变换器中电感参考电流进行修正,从而得到新的电感参考电流,具体为:
其中:I'
ref为修正后的新电感参考电流,I
ref为电感参考电流初值,k
1、k
2分别为变换器输入电压为高电平U
in1和低电平U
in2时的控制参数,u
C为电容电压,T为功率开关管Q的开关周期。
步骤3的实现方式:
步骤(3-1):将式(1)-式(3)所述状态微分方程时间离散化,可得:
x(n+1)=G
1x(n)+H
1U
in1 (5)
x(n+1)=G
1x(n)+H
1U
in2 (6)
x(n+1)=G
2x(n) (7)
计算可知:
分别以i
n和u
n表示在nT时刻的电感电流和电容电压。离散方程具体如下:
式(1)离散化可表示为:
式(2)离散化可表示为:
式(3)离散化可表示为:
步骤(3-2):根据nT时刻的电感电流、脉冲输入电压、式(4)所示新电感参考电流以及式(10)所表示的离散化方程,可得:
对式(13)求解得到变换器中功率开关管第n个开关周期的导通时间t
n为:
其中:U
in为变换器输入电压(当变换器输入电压为高电平时,U
in=U
in1;当变换器输入电压为低电平时,U
in=U
in2),I
n表示nT时刻新电感参考电流,即:
步骤(3-3):根据式(14)所示功率开关管导通时间t
n及nT时刻的电感电流i
n和电容电压u
n,以及式(10)-式(12),可得(nT+t
n)时刻的电感电流i=I
n,电容电压
功率开关管关断时间t
m=T-t
n,从而可得(n+1)T时刻的电感电流
电容电压
故系统的离散迭代映射模型可表示为:
其中:M
1=(I
ncos(ωt
m)+a sin(ωt
m)),M
2=(τI
n+aω)cos(ωt
m),M
3=(aτ-ωI
n)sin(ωt
m),
t
m=T-t
n,I
n表示nT时刻新电感参考电流。
步骤4的实现方式。
参见图3,为本发明实施例提供的一种获得实现系统稳定运行时控制参 数k
2的取值范围(k
2min,k
2max)的数值仿真流程图。具体步骤如下:
步骤(4-1):设置系统参数,包括:脉冲输入电压高电平U
in1、低电平U
in2,电感参考电流初值I
ref,最大迭代次数N,控制参数k
1的初始值k
1.0,控制参数k
2的初始值k
2.0,控制参数k
2的增量Δk
2,最大重复次数B,计数变量q的初始值为0;
步骤(4-2):采集脉冲输入电压和电容电压,根据脉冲输入电压电平并由公式(4)计算nT时刻电感的新参考电流值:
其中:u
n和u
n-1分别表示nT时刻和(n+1)T时刻的电容电压;
步骤(4-3):根据公式(14)计算第n个开关周期内功率开关管的导通时间:
其中:I
n表示nT时刻新电感参考电流,U
in为变换器输入电压(当变换器输入电压为高电平时,U
in=U
in1;当变换器输入电压为低电平时,U
in=U
in2);
步骤(4-4):根据公式(15),计算(n+1)T时刻的电感电流i
n+1和电容电压u
n+1:
其中:M
1=(I
ncos(ωt
m)+a sin(ωt
m)),M
2=(τI
n+aω)cos(ωt
m),M
3=(aτ-ωI
n)sin(ωt
m),
t
m=T-t
n,I
n表示nT时刻新电感参考电流;
步骤(4-5):判断系统的输出响应i
n+1和u
n+1是否与i
n和u
n相等,若是, 则表示系统运行稳定,执行步骤(4-7),否则执行步骤(4-6);
步骤(4-6):判断迭代次数n是否小于最大迭代次数N,若是,则n加1,然后返回步骤(4-2);否则执行步骤(4-9);
步骤(4-7):控制参数k
2在(k
2.0+qBΔk
2)的基础上依次增加Δk
2,重复步骤(4-2)~步骤(4-5),判断系统是否稳定运行,若是,则令k
2max=k
2,直到系统不能稳定运行为止,然后执行步骤(4-8);
步骤(4-8):控制参数k
2在(k
2.0-qBΔk
2)的基础上依次减小Δk
2,重复步骤(4-2)~步骤(4-5),判断系统是否稳定运行,若是,则令k
2min=k
2,直到系统不能稳定运行为止,然后执行步骤(4-15);
步骤(4-9):控制参数k
2在(k
2.0+qBΔk
2)的基础上依次增加Δk
2,重复步骤(4-2)~步骤(4-5),判断系统是否稳定运行,若是,则令k
2min=k
2,然后执行步骤(4-10),否则执行步骤(4-11);
步骤(4-10):控制参数k
2依次增加Δk
2,重复步骤(4-2)~步骤(4-5),判断系统是否稳定运行,若是,则令k
2max=k
2,直到系统不能稳定运行为止,然后执行步骤(4-15);
步骤(4-11):判断重复次数是否小于B次,若是,则返回步骤(4-9),否则执行步骤(4-12);
步骤(4-12):控制参数k
2在(k
2.0-qBΔk
2)的基础上依次减小Δk
2,重复步骤(4-2)~步骤(4-5),判断系统是否稳定运行,若是,则令k
2max=k
2,然后执行步骤(4-13),否则执行步骤(4-14);
步骤(4-13):控制参数k
2依次减小Δk
2,重复步骤(4-2)~步骤(4-5),判断系统是否稳定运行,若是,则令k
2min=k
2,直到系统不能稳定运行为止, 然后执行步骤(4-15);
步骤(4-14):判断重复次数是否小于B次,若是,则返回步骤(4-12),否则计数变量q增加1,然后返回步骤(4-2);
步骤(4-15):根据所得控制参数k2的上限值k2max和下限值k2min,即获得实现系统稳定运行时控制参数k2的取值范围(k2min,k2max)。
Claims (7)
- 一种基于分段延迟反馈控制的Buck-Boost变换器控制参数稳定域确定方法,包括以下步骤:步骤1:以Buck-Boost变换器中电感电流和电容电压为状态变量,针对该变换器在脉冲输入电压作用下的两种不同电平状态,分别建立其状态微分方程;步骤2:根据Buck-Boost变换器输入电压的不同,对变换器中电感参考电流进行修正,从而得到新的电感参考电流;步骤3:根据步骤1所述状态微分方程和步骤2所述新的电感参考电流,获得系统的离散迭代映射模型;步骤4:根据步骤3所得离散迭代映射模型,针对变换器在脉冲输入电压作用下采用分段延迟反馈控制时,对其控制参数k 1任取一给定值,获得实现系统稳定运行时控制参数k 2的取值范围(k 2min,k 2ma);步骤5:按一定间距改变控制参数k 1的给定值,采用上述同样的方法获得m组控制参数k 2相应的取值范围(k 2min,k 2max);步骤6:根据所获得的m组控制参数k 2的上限值k 2max和下限值k 2min以及相应的控制参数k 1值,采用数值拟合方法分别获得上限值k 2max与k 1值以及下限值k 2min与k 1值间的函数关系式,由上述两个函数关系式所界定的区域即为控制参数k 1和k 2的稳定域,在该稳定域内任意选取的k 1和k 2值均能保证系统的稳定运行。
- 根据权利要求1所述的一种基于分段延迟反馈控制的Buck-Boost变换器控制参数稳定域确定方法,其特征在于:所述步骤1中建立所述Buck-Boost 变换器的状态微分方程,具体包括:以Buck-Boost变换器中电感电流i L和电容电压u C为状态变量,针对变换器在脉冲输入电压作用下的两种不同电平状态并根据变换器中功率开关管Q的两种不同工作状态,分别建立其状态微分方程,具体为:状态一:功率开关Q导通:当变换器的脉冲输入电压为高电平U in1时,系统状态微分方程为:当变换器的脉冲输入电压为低电平U in2时,系统状态微分方程为:状态二:功率开关Q断开:此时变换器工作状态与输入电压无关,其系统状态微分方程为:
- 根据权利要求1所述的一种基于分段延迟反馈控制的Buck-Boost变换器控制参数稳定域确定方法,其特征在于:所述步骤3中获得所述系统的离散迭代映射模型,具体包括:步骤(3-1):将式(1)-式(3)所述状态微分方程时间离散化,分别以i n和u n表示在nT时刻的电感电流和电容电压。离散方程具体如下:式(1)离散化可表示为:式(2)离散化可表示为:式(3)离散化可表示为:步骤(3-2):根据nT时刻的电感电流、脉冲输入电压以及式(4)所示新电感参考电流,得到变换器中功率开关管在第n个开关周期的导通时间t n为:步骤(3-3):根据式(8)所示功率开关管导通时间t n及nT时刻的电感电流i n和电容电压u n,可得系统的离散迭代映射模型,具体表示为:
- 根据权利要求1所述的一种基于分段延迟反馈控制的Buck-Boost变换器控制参数稳定域确定方法,其特征在于:所述步骤4中根据所述系统离散迭代映射模型,针对变换器在脉冲输入电压作用下采用分段延迟反馈控制,对其控制参数k 1任取一给定值,获取实现系统稳定运行时控制参数k 2的取值范围(k 2min,k 2max),具体包括如下步骤:步骤(4-1):设置系统参数,包括:脉冲输入电压高电平U in1、低电平U in2,电感参考电流初值I ref,最大迭代次数N,控制参数k 1的初始值k 1.0,控制参数k 2的初始值k 2.0,控制参数k 2的增量Δk 2,最大重复次数B,计数变量q的初始值为0;步骤(4-2):采集脉冲输入电压和电容电压,根据脉冲输入电压电平并由公式(4)计算nT时刻电感的新参考电流值:其中:u n和u n-1分别表示nT时刻和(n-1)T时刻的电容电压;步骤(4-3):根据公式(8)计算第n个开关周期内功率开关管的导通时间:其中:I n表示nT时刻新电感参考电流,U in为变换器输入电压(当变换器输入电压为高电平时,U in=U in1;当变换器输入电压为低电平时,U in=U in2);步骤(4-4):根据公式(9),计算(n+1)T时刻的电感电流i n+1和电容电压u n+1:其中:M 1=(I ncos(ωt m)+a sin(ωt m)),M 2=(τI n+aω)cos(ωt m),M 3=(aτ-ωI n)sin(ωt m), t m=T-t n,I n表示nT时刻新电感参考电流;步骤(4-5):判断系统的输出响应i n+1和u n+1是否与i n和u n相等,若是,则表示系统运行稳定,执行步骤(4-7),否则执行步骤(4-6);步骤(4-6):判断迭代次数n是否小于最大迭代次数N,若是,则n加1,然后返回步骤(4-2);否则执行步骤(4-9);步骤(4-7):控制参数k 2在(k 2.0+qBΔk 2)的基础上依次增加Δk 2,重复步骤(4-2)~步骤(4-5),判断系统是否稳定运行,若是,则令k 2max=k 2,直到系统不能稳定运行为止,然后执行步骤(4-8);步骤(4-8):控制参数k 2在(k 2.0-qBΔk 2)的基础上依次减小Δk 2,重复 步骤(4-2)~步骤(4-5),判断系统是否稳定运行,若是,则令k 2min=k 2,直到系统不能稳定运行为止,然后执行步骤(4-15);步骤(4-9):控制参数k 2在(k 2.0+qBΔk 2)的基础上依次增加Δk 2,重复步骤(4-2)~步骤(4-5),判断系统是否稳定运行,若是,则令k 2min=k 2,然后执行步骤(4-10),否则执行步骤(4-11);步骤(4-10):控制参数k 2依次增加Δk 2,重复步骤(4-2)~步骤(4-5),判断系统是否稳定运行,若是,则令k 2max=k 2,直到系统不能稳定运行为止,然后执行步骤(4-15);步骤(4-11):判断重复次数是否小于B次,若是,则返回步骤(4-9),否则执行步骤(4-12);步骤(4-12):控制参数k 2在(k 2.0-qBΔk 2)的基础上依次减小Δk 2,重复步骤(4-2)~步骤(4-5),判断系统是否稳定运行,若是,则令k 2max=k 2,然后执行步骤(4-13),否则执行步骤(4-14);步骤(4-13):控制参数k 2依次减小Δk 2,重复步骤(4-2)~步骤(4-5),判断系统是否稳定运行,若是,则令k 2min=k 2,直到系统不能稳定运行为止,然后执行步骤(4-15);步骤(4-14):判断重复次数是否小于B次,若是,则返回步骤(4-12),否则计数变量q增加1,然后返回步骤(4-2);步骤(4-15):根据所得控制参数k 2的上限值k 2max和下限值k 2min,即获得实现系统稳定运行时控制参数k 2的取值范围(k 2min,k 2max)。
- 根据权利要求1所述的一种基于分段延迟反馈控制的Buck-Boost变换器控制参数稳定域确定方法,其特征在于:所述步骤5中,按一定间 距改变控制参数k 1的给定值,采用上述同样的方法获得m组控制参数k 2相应的取值范围(k 2min,k 2max)。所述控制参数k 1的取值间距Δk 1和m组参数的具体数据可根据需要进行确定。
- 根据权利要求1所述的一种基于分段延迟反馈控制的Buck-Boost变换器控制参数稳定域确定方法,其特征在于:所述步骤6中,根据所述m组控制参数k 2的上限值k 2max和下限值k 2min以及相应的控制参数k 1值,采用数值拟合方法分别获得上限值k 2max与k 1值以及下限值k 2min与k 1值间的函数关系式;所述数值拟合方法优先采用最小二乘法,所获得的函数关系式分别为:(1)控制参数k 2上限值k 2max与k 1值间的函数关系式为:式中:a 1、b 1、c 1、d 1分别为系数,所述系数采用最小二乘法进行确定。(2)控制参数k 2下限值k 2min与k 1值间的函数关系式为:式中:a 2、b 2、c 2、d 2分别为系数,所述系数采用最小二乘法进行确定。
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