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CN115173701B - Adaptive continuous sliding mode control method for power converters based on zero-crossing detection - Google Patents

Adaptive continuous sliding mode control method for power converters based on zero-crossing detection Download PDF

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CN115173701B
CN115173701B CN202210868070.3A CN202210868070A CN115173701B CN 115173701 B CN115173701 B CN 115173701B CN 202210868070 A CN202210868070 A CN 202210868070A CN 115173701 B CN115173701 B CN 115173701B
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sliding mode
control law
control
zero
formula
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CN115173701A (en
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王艳敏
段广鑫
张伟琦
谷京昀
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Harbin Institute of Technology Shenzhen
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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
    • H02M1/00—Details of apparatus for conversion
    • H02M1/08—Circuits specially adapted for the generation of control voltages for semiconductor devices incorporated in static converters

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  • Power Engineering (AREA)
  • Feedback Control In General (AREA)

Abstract

一种基于过零检测的电力变换器自适应连续滑模控制方法，属于电力变换器的滑模控制技术领域。本发明针对现有电力变换器的滑模控制方法中，传统固定控制增益的技术手段无法收敛到期望的稳态误差的问题。包括在针对两个状态变量的传统一阶滑模面设计的基础上引入变换器系统状态的积分项，得到改进的滑模面s；在状态变量运动轨迹的第一阶段，设计控制律u1，使运动轨迹在有限时间内到达首次波峰位置点B；控制律u1具有固定控制增益；在第二阶段，设计控制律u2，使系统由首次波峰位置点B逐渐收敛到零位置点；控制律u2具有变控制增益的特征，两个状态变量的运动轨迹呈螺旋特征。本发明可保证系统稳态误差收敛到给定范围。

Figure 202210868070

An adaptive continuous sliding mode control method for a power converter based on zero-crossing detection belongs to the technical field of sliding mode control for power converters. The invention aims at the problem that the traditional technical means of fixed control gain cannot converge to the expected steady-state error in the existing sliding mode control method of the power converter. Including introducing the integral term of the converter system state on the basis of the traditional first-order sliding mode surface design for two state variables, and obtaining an improved sliding mode surface s; in the first stage of the state variable trajectory, design the control law u 1 , so that the trajectory reaches the first peak position point B within a limited time; the control law u 1 has a fixed control gain; in the second stage, the control law u 2 is designed so that the system gradually converges from the first peak position point B to the zero position point; The control law u 2 has the characteristics of variable control gain, and the trajectory of the two state variables presents a spiral characteristic. The invention can ensure that the steady-state error of the system converges to a given range.

Figure 202210868070

Description

Self-adaptive continuous sliding mode control method of power converter based on zero-crossing detection
Technical Field
The invention relates to a self-adaptive continuous sliding mode control method of a power converter based on zero-crossing detection, and belongs to the technical field of sliding mode control of power converters.
Background
At present, the sliding mode control mainly has the following problems:
1. influence of the buffeting problem of the first-order sliding mode on the electric energy quality of the power converter is transmitted:
at present, in the field of sliding mode control power converters, the traditional first-order sliding mode application is still mainly adopted. The first-order sliding mode is mainly applied by a linear sliding mode, a terminal sliding mode and a non-singular terminal sliding mode, and a sign function sgn (); however, when the actual system is implemented, because the switching frequency of the existing switching tube is limited, the theoretical infinity cannot be achieved, so that the symbol function sgn (the term) can induce the buffeting problem, the signal oscillation with limited amplitude limit value and limited frequency appears in the voltage and the current, the electric energy quality of the power converter is seriously affected, and a plurality of problems such as heating, accelerated aging, serious harmonic and the like of the power converter can be caused, so that the method is the focus of attention and research in the current industry.
2. Although the higher order sliding mode is considered as one of the most effective methods for suppressing buffeting at present, the control gain thereof is a fixed value at most. As the system converges to the equilibrium point, excessive control gain can reduce the dynamic and static control performance of the system, and also reduce the electrical energy quality of the power converter:
compared with the method of weakening buffeting by a boundary layer method, fuzzy control and the like, the high-order sliding mode is regarded as an effective method for essentially solving the buffeting problem. The control idea is based on the relative order concept by directly adding the switching control sgn () to the sliding mode variable higher derivative so that the actual control quantity is continuous through integration or low pass filtering. The current common algorithms include a twist algorithm, a Super-twist algorithm, a suboptimal algorithm, and the like. However, the control gain of the conventional high-order sliding mode control method is usually set to a fixed value, and the value of the control gain depends on transient performance in an initial stage or disturbance to be overcome; however, as the system trajectory goes toward the equilibrium point, the fixed control gain becomes critical to destroy the steady state performance of the system, and excessive control gain determined in the initial stage will bring about large steady state error and response time.
3. The high-order sliding mode is combined with the self-adaptive control, and the problem of fixed gain of the traditional high-order sliding mode can be solved through variable gain control. However, the existing adaptive methods are few, and most only consider stability indexes, so that the method cannot converge to the expected steady-state error:
in order to solve the problem of large steady-state error of the system caused by fixed control gain, a sliding mode control method for variable control gain is generated. Currently, the adaptive mechanism mainly comprises two types based on stability and based on a switching time principle. The former is based on the premise of ensuring the stability of the system, and certain specific control performance indexes such as steady-state errors and the like are less considered; the latter is mostly based on the switching time principle, the control concept of which follows the switching characteristics inherent in sliding mode control. However, the adaptive mechanism depends on the motion trail of the system tending to the balance point, and research on directly establishing the influence relationship of certain performance indexes such as gain change and steady-state error is not yet available, so that the key problems such as the variable gain mechanism, switching time, system stability and the like need to be studied in depth.
Disclosure of Invention
Aiming at the problem that the traditional technical means for controlling gain by fixed way can not be converged to the expected steady-state error in the sliding mode control method of the existing power converter, the invention provides a self-adaptive continuous sliding mode control method of the power converter based on zero-crossing detection.
The invention relates to a self-adaptive continuous sliding mode control method of a power converter based on zero-crossing detection, which comprises the following steps,
establishing a mathematical model of the Buck type DC-DC converter;
according to the mathematical model, introducing integral terms of the system state of the converter on the basis of the traditional first-order sliding mode surface design aiming at two state variables to obtain a sliding mode surface s containing the integral terms; the state variable is the voltage difference x between the actual output voltage and the target output voltage of the converter 1 And the rate of change x of the actual output voltage 2 ；
Dividing the motion trail of two state variables into two stages based on a sliding mode surface s containing integral items and a switching time principle, wherein the first stage is from an initial point A to a first wave crest position point B; the second stage from the first peak position point B to the zero position point;
in the first stage, a control law u is designed 1 Enabling the motion trail of the two state variables to reach a first wave crest position point B in a limited time; control law u 1 Having a fixed control gain;
in the second phase, design control law u 2 The motion trail of the two state variables is in spiral characteristics, and gradually converges to a zero position point from a first wave crest position point B; control law u 2 Having a variable control gain; and the variable control gain adaptively adjusts the amplitude value along with the number of zero crossing points of the sliding mode surface s detected in the sampling interval.
According to the self-adaptive continuous sliding mode control method of the power converter based on zero-crossing detection of the invention,
the initial mathematical model of the Buck type DC-DC converter is as follows:
Figure BDA0003759319990000021
i in L For the current flowing through the filter inductance, t is the timeL is a filter inductance, u is a control law, E is a direct current input voltage, v c The voltage is actually output by the converter, C is a capacitor, and R is a load resistor;
definition V ref For a target output voltage, the state variable x 1 ＝v c -V ref ，
Figure BDA0003759319990000022
Deforming the initial mathematical model to obtain a deformed mathematical model:
Figure BDA0003759319990000023
in the middle of
Figure BDA0003759319990000031
Is an intermediate variable +.>
Figure BDA0003759319990000032
According to the self-adaptive continuous sliding mode control method of the power converter based on zero-crossing detection of the invention,
transmission uniform-order sliding die surface s 0 The method comprises the following steps:
s 0 ＝c 1 x 1 +x 2 ，
in c 1 For the first design parameter c 1 >0；
Transmission uniform-order sliding mode surface s 0 Introducing integral terms of the system state of the converter to obtain a sliding mode surface s containing the integral terms:
Figure BDA0003759319990000033
in c 2 For the second design parameter c 2 >0。
According to the self-adaptive continuous sliding mode control method of the power converter based on zero-crossing detection, in the first stage, a control law u is set as the control law u 1 Control law u 1 The design process of (1) comprises:
definition of vectors
Figure BDA0003759319990000034
Wherein T is a sampling interval;
the formula for the slip plane s is modified as:
Figure BDA0003759319990000035
wherein,,
Figure BDA0003759319990000036
mu is an intermediate variable which is used as a reference,
Figure BDA0003759319990000037
design control law u 1 The method comprises the following steps:
Figure BDA0003759319990000038
where U is the fixed control gain.
According to the self-adaptive continuous sliding mode control method of the power converter based on zero-crossing detection, a control law u 1 The process of enabling the motion trail of the two state variables to reach the first wave crest position point B in a limited time comprises the following steps:
solving the second derivative of the sliding mode surface s with respect to time according to the formula of the sliding mode surface s after deformation:
Figure BDA0003759319990000039
wherein:
Figure BDA0003759319990000041
y 22 (μ)＝c 1 μ-μβ 1 ，
β 1 ＝1/RC，β 2 ＝ω 0 2 ＝1/LC；
defining four constants ζ 1 、ζ 2 、ζ 3 、ζ 4 Sum function Y 21 、Y 22 The following variable substitutions were made:
Figure BDA0003759319990000042
Figure BDA0003759319990000043
the following relationship is satisfied:
Figure BDA0003759319990000044
will control law u 1 The formula of (2) is substituted into the second derivative of the slip plane s with respect to time to obtain:
Figure BDA0003759319990000045
mu in the middle min K is a constant greater than 0, which is the minimum value of the intermediate variable μ;
further, the following is obtained:
Figure BDA0003759319990000046
according to
Figure BDA0003759319990000047
Both sides are multiplied by |s|, i.e. there is +.>
Figure BDA0003759319990000048
If true, then for two shapesThe motion trail of state variable is limited time t from initial point A 0 The first wave crest position point B is reached;
wherein t is 0 ＝t B -t A ，
Wherein t is A For the moment corresponding to the initial point A, t B The time corresponding to the first peak position point B.
According to the self-adaptive continuous sliding mode control method of the power converter based on zero-crossing detection, the fixed control gain U is as follows:
Figure BDA0003759319990000051
according to the self-adaptive continuous sliding mode control method of the power converter based on zero-crossing detection, in the second stage, a control law u is set as the control law u 2 Control law u 2 The design is as follows:
Figure BDA0003759319990000052
u in j To change the control gain, r 4 For presetting a fixed value to control gain r 4 >0。
According to the self-adaptive continuous sliding mode control method of the power converter based on zero crossing detection, the assignment method of the self-adaptive amplitude adjustment of the variable control gain comprises the following steps:
Figure BDA0003759319990000053
is N j For the j-th sampling interval T j The number of zero crossing points of the inner s is a reference value of the number of zero crossing points, and N is more than or equal to 2; Λ type 1 Sum lambda 2 Is two positive numbers, Λ 1 <Λ 2 ；T＝{T 1 ,T 2 ,...T i J=1, 2,3, … … i; i is the total number of sampling intervals; u (U) 0 Is control law u 2 Is set to the initial value of (1):
U 0 ＝[Y 21 (||w|| * ,|s(t 0 )|)+Y 22 u 1max +k]，
u in the formula 1max For control law u 1 Is the maximum value of (2):
Figure BDA0003759319990000054
according to the self-adaptive continuous sliding mode control method of the power converter based on zero-crossing detection, a control law u 2 The convergence range of the sliding die surface s is set as follows:
|s|≤[U 0 +(1+r 4 )μ max U j ]T 2 ，
mu in the middle max Is the maximum value of the intermediate variable mu.
According to the self-adaptive continuous sliding mode control method of the power converter based on zero-crossing detection, the process for obtaining the convergence range of the sliding mode surface s comprises the following steps:
will control law u 2 Substituting the expression of s into the expression of s second derivative of the slip plane with respect to time, to obtain:
Figure BDA0003759319990000061
further deformation is as follows:
Figure BDA0003759319990000062
let i be 0 ∈[1,N j ]，j 0 ∈[1,N j ]And i 0 <j 0 Wherein i is 0 Is [1, N j ]One of all zero crossing points in the inner part, j 0 Is [1, N j ]Another zero crossing of all zero crossings in the inner, then:
s(t i0 )＝s(t j0 )＝0；
according to N.gtoreq.2, the time point t exists i0j0 ：t i0 <t i0j0 <t j0 So that
Figure BDA0003759319990000066
Presence;
according to the Lagrangian median theorem, at t and t i0j0 There is a time t of existence i0j0 ' the following relation is satisfied:
Figure BDA0003759319990000063
t is T j At any time of the sampling interval, and |t-t i0j0 |<T j ；
Similarly, at t and t i0 There is another time t i0 ' satisfy:
Figure BDA0003759319990000064
according to |t-t i0 |<T, the above deformation is:
Figure BDA0003759319990000065
and integrating the two ends at the same time to obtain the convergence range of the sliding mode surface s:
|s|≤[U 0 +(1+r 4 )μ max U j ]T 2 。
the invention has the beneficial effects that: the method is provided based on an online zero-crossing detection self-adaptive mechanism, can effectively inhibit the buffeting problem, and can ensure that the steady-state error of the system converges to a given range.
Firstly, establishing a mathematical model of a converter, improving a traditional sliding mode control algorithm from two aspects of a sliding mode surface and a control law, namely purposefully introducing an integral item of a system state into the design of the sliding mode surface, dividing a convergence track into two stages, and measuring the number of zero crossings of the sliding mode surface in real time; the expected steady-state error is incorporated into the design of the sliding mode control law, a low-pass filtering link is introduced, the continuous control law of the variable gain is deduced in stages under the constraint of a convergence track, and corresponding stability analysis is given.
Simulation and performance comparison experiments prove that the method has remarkable advantages compared with the prior art in the aspects of buffeting inhibition, response speed and control precision.
Drawings
FIG. 1 is a block diagram of a slip-mode control system of a Buck type DC-DC converter according to the present invention; the SMC controller in the figure represents a sliding mode controller; s is S w Is a controllable switch tube, VD is a current limiting diode, i C For the current flowing through the capacitor C,
FIG. 2 is a schematic diagram of a convergence process of an adaptive progressive sliding mode control corresponding to a motion profile of two state variables;
FIG. 3 is a schematic diagram of the number of zero crossings of s within a single sampling interval;
FIG. 4 is a schematic diagram of a simulation of actual output voltage for controlling a converter using three methods under nominal operating conditions in an exemplary embodiment;
FIG. 5 is a schematic diagram of inductor current simulation for controlling a converter using three methods under nominal operating conditions in an exemplary embodiment;
FIG. 6 is a schematic diagram of a control law for controlling a converter using three methods under nominal operating conditions in an exemplary embodiment;
FIG. 7 is a graph of N number of different zero crossings when three methods are used to control the converter under nominal conditions * A lower output voltage schematic;
FIG. 8 is a schematic diagram of a simulation of actual output voltage for controlling a converter using three methods under disturbance conditions in an embodiment;
FIG. 9 is a schematic diagram of inductor current simulation for controlling a converter using three methods under disturbance conditions in an embodiment;
FIG. 10 is a schematic diagram of a control law for controlling a converter using three methods under disturbance conditions in an embodiment.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
It should be noted that, without conflict, the embodiments of the present invention and features of the embodiments may be combined with each other.
The invention is further described below with reference to the drawings and specific examples, which are not intended to be limiting.
The invention provides a self-adaptive continuous sliding mode control method of a power converter based on zero-crossing detection, which is shown in the accompanying figure 1,
establishing a mathematical model of the Buck type DC-DC converter;
according to the mathematical model, introducing integral terms of the system state of the converter on the basis of the traditional first-order sliding mode surface design aiming at two state variables to obtain a sliding mode surface s containing the integral terms; the state variable is the voltage difference x between the actual output voltage and the target output voltage of the converter 1 And the rate of change x of the actual output voltage 2 ；
Dividing the motion trail of two state variables into two stages based on a sliding mode surface s containing integral items and a switching time principle, wherein the first stage is from an initial point A to a first wave crest position point B; the second stage from the first peak position point B to the zero position point;
in the first stage, a control law u is designed 1 Enabling the motion trail of the two state variables to reach a first wave crest position point B in a limited time; control law u 1 Having a fixed control gain;
in the second phase, design control law u 2 The motion trail of the two state variables is in spiral characteristics, and gradually converges to a zero position point from a first wave crest position point B; control law u 2 Having a variable control gain; the variable control gain is along with zero crossing points of the sliding mode surface s detected in the sampling intervalThe number adaptively adjusts the amplitude.
Power converter system modeling:
the method of the invention is applicable to various power converters such as DC-DC, AC-AC and the like. Fig. 1 is a block diagram of a system for slip-mode control of a Buck DC-DC converter. Controllable switch tube S w MOSFET and IGBT applications are often used in many cases, and pulse width modulation is often used. In the invention, the controllable switch tube is controlled by a designed control law u.
Further, in practical system applications, the power converter is operated in continuous current mode, i.e. inductor current i L Not equal to 0, and then based on kirchhoff's circuit law, establishing an initial mathematical model of the Buck DC-DC converter shown in fig. 1 as:
Figure BDA0003759319990000081
i in L For the current flowing through the filter inductor, t is time, L is filter inductor, u is control law, E is DC input voltage, v c The voltage is actually output by the converter, C is a capacitor, and R is a load resistor;
definition V ref For a target output voltage, the state variable x 1 ＝v c -V ref ，
Figure BDA0003759319990000082
Deforming the initial mathematical model to obtain a deformed mathematical model:
Figure BDA0003759319990000083
in the middle of
Figure BDA0003759319990000091
Is an intermediate variable +.>
Figure BDA0003759319990000092
Traditional first order sliding mode control: the design of the sliding mode controller comprises a sliding mode surface and a control law aiming at the mathematical model of the converter in the formula (2). Typically, a uniform slip-form surface s is imparted 0 The method comprises the following steps:
s 0 ＝c 1 x 1 +x 2 ， (3)
in c 1 For the first design parameter c 1 >0；
x 1 And x 2 The voltage and current can be directly obtained by measuring the voltage and the current by using a Hall sensor, and the method is simple and easy to realize. Once the inverter control system converges to the slip form surface s 0 =0, the dynamic and static performance of the system depends on
Figure BDA0003759319990000093
I.e. output voltage deviation
Figure BDA0003759319990000094
Asymptotically converges to zero in an exponential fashion, and the design parameter c 1 The larger the convergence speed of the system is, the faster it is.
In terms of control law, the design of the first-order sliding mode and the second-order sliding mode control law is required to meet the sliding mode arrival condition
Figure BDA0003759319990000095
To ensure system stability. The buffeting suppression mechanism based on relative order from the higher order slip mode is different from the two in that: the first order sliding mode SMC directly acts the switching control item sgn (DEG) on the first derivative of the sliding mode variable +.>
Figure BDA0003759319990000096
On to ensure a first order sliding mode s 0 The presence of =0, followed by equation (3), then the Buck converter output voltage bias and its derivative x are implemented 1 ＝x 2 =0, but there is a buffeting problem. For the second order sliding mode, taking the conventional Twisting algorithm as an example, the control law is generally designed as follows:
Figure BDA0003759319990000097
r 1 and r 2 Are all control gains, and r 1 >r 2 >0，r 1 、r 2 Is related to the response speed and steady state error of the system. It can be seen that since the switching control term sgn ()' appears at the first derivative of the control law
Figure BDA0003759319990000098
The actual output u is continuously formed through the integral action, which is why the Twisting algorithm effectively solves the buffeting problem. However, it should be noted that the gain r is controlled 1 And r 2 The overall process of system convergence to the origin remains unchanged, however, the closer to the origin, the larger the control gain will destroy the steady state performance of the system.
Improved adaptive second order SMC control:
in order to improve the conventional second-order sliding mode fixed control gain problem in formulas (3) and (4), the method is improved from the two aspects of a sliding mode surface and a control law.
Sliding mode surface design:
transmission uniform-order sliding mode surface s 0 Introducing integral terms of the system state of the converter to obtain a sliding mode surface s containing the integral terms:
Figure BDA0003759319990000099
in c 2 For the second design parameter c 2 >0。
In actual use, the first design parameter c 1 And a second design parameter c 2 And adjusting according to the use condition.
In the first stage, control law u is set as control law u 1 Control law u 1 The design process of (1) comprises:
definition of vectors
Figure BDA0003759319990000101
Wherein T is a sampling interval;
in combination with formula (2), formula (5) can be transformed into:
Figure BDA0003759319990000102
wherein,,
Figure BDA0003759319990000103
mu is an intermediate variable which is used as a reference,
Figure BDA0003759319990000104
control law design:
in the design of the control law u, the method of the invention divides the motion trail into two phases according to the system convergence process based on the switching time principle, as shown in fig. 2, namely, the 1 st phase is from the initial point A to the first peak position point B, the 2 nd phase is after the point B, and is divided into sampling intervals with equal interval T, which is expressed as { T } 1 ,T 2 ,...T i }. In particular, where the desired steady state error Δ is incorporated into the improvement of the conventional twist control law of equation (4), the two-stage control law u is decomposed into u 1 And u 2 The design process is as follows.
First stage, movement of point a to point B:
in FIG. 2, it is assumed that the time of the initial point A is t A The corresponding position is (t A ,s A ) The moment of the first wave crest position point B is t B The corresponding position is (t B ,s B ) And has
Figure BDA0003759319990000105
Comparative formula (4), design control law u 1 The method comprises the following steps:
Figure BDA0003759319990000106
where U is the fixed control gain.
The fixed control gain U is:
Figure BDA0003759319990000107
wherein k is>0 is a constant; the method comprises the steps of carrying out a first treatment on the surface of the Mu (mu) max And mu min The maximum and minimum values of μ are defined by equation (7), respectively.
Control law u 1 The process of enabling the motion trail of the two state variables to reach the first wave crest position point B in a limited time comprises the following steps:
similarly to equation (6), the second derivative of the sliding mode variable s with respect to time is further calculated according to the equation of the sliding mode surface s after deformation, and the switching control term sgn () is displayed, that is, the second derivative of the sliding mode surface s with respect to time can be derived from equation (6):
Figure BDA0003759319990000111
wherein:
Figure BDA0003759319990000112
y 22 (μ)＝c 1 μ-μβ 1 ， (10)
β 1 ＝1/RC，β 2 ＝ω 0 2 ＝1/LC；
for convenience of the following description, four constants ζ are defined by formulas (9) - (10) 1 、ζ 2 、ζ 3 、ζ 4 Sum function Y 21 、Y 22 The following variable substitutions were made:
Figure BDA0003759319990000113
Figure BDA0003759319990000114
the following relationship is satisfied:
Figure BDA0003759319990000115
theorem 1: for the Buck converter in the formula (2), if the design of the sliding mode surface is shown as the formula (5), the control law in the first stage is shown as the formulas (14) - (15), and the limited time of the system reaches the point B.
First, the existence of the point B in FIG. 2 is demonstrated because it is the first peak position point, satisfying
Figure BDA0003759319990000116
For this purpose, formula (14) is substituted into formula (8), i.e., control law u 1 The formula of (2) is substituted into the second derivative of the slip plane s with respect to time and combined with formula (12), then there is
Figure BDA0003759319990000117
Mu in the middle min K is a constant greater than 0, which is the minimum value of the intermediate variable μ;
further, the following is obtained:
Figure BDA0003759319990000121
according to
Figure BDA0003759319990000122
Both sides are multiplied by |s|, i.e. there is +.>
Figure BDA0003759319990000123
If so, for the motion trail of the two state variables, a finite time t is set from any initial point A 0 The first wave crest position point B is reached;
wherein t is 0 ＝t B -t A ，
Wherein t is A For the moment corresponding to the initial point A, t B The time corresponding to the first peak position point B.
Further, in the second phase, the converging motion after point B:
in FIG. 2, when t>t B The system then enters a second stage of converging motion. Comparing the formula (5), setting the control law u as the control law u 2 Control law u 2 The design is as follows:
Figure BDA0003759319990000124
u in j To change the control gain, r 4 For presetting a fixed value to control gain r 4 >0。
The assignment method of the variable control gain self-adaptive adjustment amplitude comprises the following steps:
according to the variable control gain U j At T j The self-adaptive change is realized by detecting the zero crossing point s in the sampling interval, namely:
Figure BDA0003759319990000125
is N j For the j-th sampling interval T j The number of zero crossing points of the inner s is a reference value of the number of zero crossing points, and N is more than or equal to 2; Λ type 1 Sum lambda 2 Is two positive numbers, Λ 1 <Λ 2 ；T＝{T 1 ,T 2 ,...T i J=1, 2,3, … … i; i is the total number of sampling intervals; u (U) 0 Is control law u 2 Corresponds to the initial value of the first stage B point control law u 1 The maximum value is represented by formula (14):
U 0 ＝[Y 21 (||w|| * ,|s(t 0 )|)+Y 22 u 1max +k]， (20)
u in the formula 1max For control law u 1 Is set at the maximum value of (c), i w i * The upper limit of w is:
Figure BDA0003759319990000126
theorem 2: for the Buck converter of formula (2), if the improved sliding mode surface is designed as formula (5) and the variable gain control law of the second stage is designed as formulas (18) - (19), the control law u can be ensured 2 The convergence range of the sliding die surface s is set as follows:
|s|≤[U 0 +(1+r 4 )μ max U j ]T 2 ， (22)
mu in the middle max Is the maximum value of the intermediate variable mu.
The process of obtaining the convergence range of the slide face s includes:
will control law u 2 Substituting the expressions (18) - (19) into the second derivative expression (8) of the slip plane s with respect to time, yields:
Figure BDA0003759319990000131
from fig. 2, point B is the first peak position of the first stage and is also the point where the oscillation amplitude of the second stage is the largest. Thus, by combining formulas (8), (12), (13) and formulas (20), (21), then (23) can be further modified to:
Figure BDA0003759319990000132
by T j The sample interval is given as an example, and the analysis condition of the system zero crossing point in the single sample interval T is given. As in fig. 3, assume i 0 ∈[1,N j ]，j 0 ∈[1,N j ]And i 0 <j 0 Wherein i is 0 Is [1, N j ]One of all zero crossing points in the inner part, j 0 Is [1, N j ]Another zero crossing among all the zero crossings in the inner is known from fig. 3:
s(t i0 )＝s(t j0 )＝0；
because of the zero crossing point set pointN is equal to or greater than 2, meaning that at least two zero crossings occur within a single sampling interval T, a certain moment T must exist according to the Roel theorem i0j0 ：t i0 <t i0j0 <t j0 So that
Figure BDA0003759319990000136
Presence;
according to the Lagrangian median theorem, at t and t i0j0 There is a time t of existence i0j0 ' the following relational expression is satisfied by the formula (24):
Figure BDA0003759319990000133
wherein T is T j At any time of the sampling interval, and |t-t i0j0 |<T j ；
Similarly, at t and t i0 There is another time t i0 ' satisfy:
Figure BDA0003759319990000134
according to |t-t i0 |<T, formula (26) is deformed into:
Figure BDA0003759319990000135
and integrating the two ends at the same time to obtain the convergence range of the sliding mode surface s:
|s|≤[U 0 +(1+r 4 )μ max U j ]T 2 。
it should be particularly noted that during the second phase of motion of fig. 2, the amplitude of s becomes smaller as the system approaches the equilibrium point, and the number of zero crossings in the same sampling interval increases. From the formula (18), N j The magnitude relation to N affects the next sampling interval T j+1 Control gain U of (2) j+1 The choice of a given value N is therefore of vital importance. In practical systems, N may be determined experimentallyBy way of measurement, one can take the form of n=max {2Tf j +1}, where f j ＝N j and/T is the frequency of the experimentally measured s zero crossing point.
Specific examples:
in order to verify the superiority of the continuous sliding mode control method based on the self-adaptive mechanism of the online zero-crossing detection provided by the method in the aspects of buffeting inhibition, response speed and control precision, performance comparison is carried out on the continuous sliding mode control method with a second-order sliding mode method represented by a first-order sliding mode and a traditional twist algorithm, and the circuit parameters of the converter are shown in a table 1. For convenience of explanation, a first-order sliding mode method is represented by "1-SMC", a second-order sliding mode method represented by a traditional Twisting algorithm is represented by "2T-SMC", and a method of the invention is represented by "2 AT-SMC".
Table 1 circuit parameters of the converter
Figure BDA0003759319990000141
For the Buck converter in the formula (2), the sliding mode surfaces of the 1-SMC and the 2T-SMC adopt the form of the formula (3), and the design parameter c 1 Selected as 100,1-SMC control law designed as u=0.5 [ sgn(s) -1]In an actual system, hysteresis modulation is mostly adopted to relieve buffeting, wherein the hysteresis width is 0.01; control gain r in equation (4) of 2T-SMC 1 Take 240, r 2 Taking 120; for the 2AT-SMC method provided by the invention, the sliding mode surface parameter c in the formula (5) 1 Still take 100, c 2 Taking 0.001, the control gain U of the first stage of equation (14) is taken to be 75, and the design parameters of the second stage of equations (18) - (19) are selected to be r 4 ＝0.541，Λ 1 ＝2，Λ 2 ＝4，N*＝8，T＝25μs。
The control performance of the Buck converter under the action of three methods is compared by taking two conditions of rated working conditions and input voltage disturbance as examples.
(1) Rated operating mode:
the control performance pairs of the three methods under rated conditions are shown in fig. 4 to 7 and table 2, wherein fig. 4 is the output voltage v c And FIG. 5 shows the inductor current i L As can be seen from the simulation results of (2), the three methods all realize two methodsConvergence control of the output voltage v c Converging to a given value V ref =5v, where the steady state error of 1-SMC is 13.01mV maximum, next 2T-SMC is 6.04mV,2at-SMC steady state performance is optimal, steady state error is only 1.03mV. Comparing equations (3) and (5), the method of the present invention achieves good results due to the 2AT-SMC method introducing integral terms of system state into the design of the slip-form surface. AT the same time, the system convergence speed under the control of 2AT-SMC is the fastest, which is only 0.042s, and the effect obtained by the invention is attributed to the variable gain control function of the 2AT-SMC method in combination with the comparison of the control law u of FIG. 6. Further, as shown in fig. 2, equation (14) and theorem 1, it can be seen that the initial motion trajectory of the system of the present invention oscillates maximally in the first stage, which also explains the reason that the amplitude of the control law u of 2AT-SMC is maximized in this stage; and then in the second stage, the amplitude of the second-order SMC is the smallest in the three methods along with the trend convergence of the system, particularly, the control law u of 1-SMC has obvious buffeting phenomenon, and even if hysteresis modulation is adopted for relieving, the second-order SMC buffeting inhibition performance such as 2T-SMC and 2AT-SMC is not good. Further, in fig. 7, three different zero crossing set points N are selected, 2,4,8, corresponding to output voltage steady state errors of 12.15mV,6.43mV, and 1.03mV, respectively. According to n=max {2Tf j From the formula +1, N can be found * The larger the zero crossing point is, the faster the frequency of detection is, the better the variable gain control performance of the 2AT-SMC method is, and further the influence of an online zero crossing point self-adaptive mechanism on the system performance is proved.
TABLE 2 comparison of Voltage and Current Performance under rated conditions
Figure BDA0003759319990000151
(2) Disturbance condition
Taking the disturbance of the input voltage E as an example, let us assume a jump from 10V to 12V at t=1s, and then back to 10V at t=2s, simulation pairs such as fig. 8 to 10 and table 3.
Comparing the rated condition of fig. 4 to 7 with the disturbance condition of fig. 8 to 10, three methods can be seen to output voltage v to the Buck converter c Inductor current i L And control law uThe effect is consistent due to the superiority of the sliding mode robust control. Specifically, the voltage v is output at t=1s c By taking disturbance as an example for analysis, it can be seen that the response speed of the 2AT-SMC of the method of the present invention is fastest, the response speed is recovered to the equilibrium state about 1.015s, the convergence time of the 2T-SMC and the 1-SMC method are respectively 1.038s and 1.042s, and the former start phase oscillates, which is due to the fact that the conventional second order sliding mode method selects the fixed gain to be natural, the comparison of the control law u in fig. 10 can also explain the reason of oscillation, namely, when the disturbance occurs AT t=1s, the control law u of the two second order SMCs of the 2T-SMC and the 2AT-SMC is close in size, but the control gain of the 2AT-SMC method provided by the present invention can be adaptively reduced along with the convergence process, while the 2T-SMC of the conventional fixed gain is always maintained AT a larger value, and the output voltage v is further enabled c Oscillations are generated during the rapid convergence process.
TABLE 3 comparison of Voltage and Current Performance under disturbance conditions
Figure BDA0003759319990000161
Based on the performance comparison of the Buck converter under the rated working condition and the disturbance working condition, the superiority of the 2AT-SMC based on the online zero-crossing detection self-adaptive mechanism in buffeting inhibition, response speed and control precision is demonstrated, and the output voltage quality of the converter is improved.
Although the invention herein has been described with reference to particular embodiments, it is to be understood that these embodiments are merely illustrative of the principles and applications of the present invention. It is therefore to be understood that numerous modifications may be made to the illustrative embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention as defined by the appended claims. It should be understood that the different dependent claims and the features described herein may be combined in ways other than as described in the original claims. It is also to be understood that features described in connection with separate embodiments may be used in other described embodiments.

Claims (3)

1.一种基于过零检测的电力变换器自适应连续滑模控制方法，其特征在于包括，1. A power converter adaptive continuous sliding mode control method based on zero-crossing detection, characterized in that comprising, 建立Buck型DC-DC变换器的数学模型；Establish the mathematical model of Buck type DC-DC converter; 根据所述数学模型，在针对两个状态变量的传统一阶滑模面设计的基础上引入变换器系统状态的积分项，得到包含积分项的滑模面s；所述状态变量为变换器实际输出电压与目标输出电压的电压差x1和实际输出电压的变化率x2；According to the mathematical model, the integral term of the converter system state is introduced on the basis of the traditional first-order sliding mode surface design for two state variables, and the sliding mode surface s including the integral term is obtained; the state variable is the actual value of the converter The voltage difference x 1 between the output voltage and the target output voltage and the change rate x 2 of the actual output voltage; 基于包含积分项的滑模面s和切换时间原理，将两个状态变量的运动轨迹分为两个阶段，第一阶段由初始点A到首次波峰位置点B；第二阶段由首次波峰位置点B到零位置点；Based on the sliding mode surface s including the integral term and the principle of switching time, the trajectory of the two state variables is divided into two stages, the first stage is from the initial point A to the first peak position point B; the second stage is from the first peak position point B to the zero position point; 在第一阶段，设计控制律u1，使两个状态变量的运动轨迹在有限时间内到达首次波峰位置点B；控制律u1具有固定控制增益；In the first stage, the control law u 1 is designed so that the trajectories of the two state variables reach the first peak position point B within a limited time; the control law u 1 has a fixed control gain; 在第二阶段，设计控制律u2，使两个状态变量的运动轨迹呈螺旋特征，由首次波峰位置点B逐渐收敛到零位置点；控制律u2具有变控制增益；所述变控制增益随采样区间内检测的滑模面s的过零点个数自适应调节幅值；In the second stage, the control law u 2 is designed so that the motion trajectories of the two state variables exhibit spiral characteristics, and gradually converge from the first peak position point B to the zero position point; the control law u 2 has a variable control gain; the variable control gain Adaptively adjust the amplitude according to the number of zero-crossing points of the sliding mode surface s detected in the sampling interval; Buck型DC-DC变换器的初始数学模型为：The initial mathematical model of the Buck type DC-DC converter is:
Figure QLYQS_1
Figure QLYQS_1
 式中iL为流过滤波电感的电流，t为时间，L为滤波电感，u为控制律，E为直流输入电压，vc为变换器实际输出电压，C为电容，R为负载电阻；where i L is the current flowing through the filter inductor, t is time, L is the filter inductor, u is the control law, E is the DC input voltage, v c is the actual output voltage of the converter, C is the capacitor, and R is the load resistance; 定义Vref为目标输出电压，则状态变量x1＝vc-Vref，
Figure QLYQS_2
Define V ref as the target output voltage, then the state variable x 1 =v c -V ref ,
Figure QLYQS_2
 将初始数学模型变形，获得变形后数学模型：Deform the initial mathematical model to obtain the deformed mathematical model:
Figure QLYQS_3
Figure QLYQS_3
 式中
Figure QLYQS_4
为中间变量，/>
Figure QLYQS_5
In the formula
Figure QLYQS_4
as an intermediate variable, />
Figure QLYQS_5
 传统一阶滑模面s0为：The traditional first-order sliding mode surface s 0 is: s0＝c1x1+x2，s 0 =c 1 x 1 +x 2 , 式中c1为第一设计参数，c1>0；In the formula, c 1 is the first design parameter, c 1 >0; 对传统一阶滑模面s0引入变换器系统状态的积分项，得到包含积分项的滑模面s：
Figure QLYQS_6
Introduce the integral term of the converter system state to the traditional first-order sliding mode surface s 0 , and obtain the sliding mode surface s including the integral term:
Figure QLYQS_6
 式中c2为第二设计参数，c2>0；In the formula, c 2 is the second design parameter, c 2 >0; 在第一阶段，设定控制律u为控制律u1，控制律u1的设计过程包括：In the first stage, the control law u is set as the control law u 1 , and the design process of the control law u 1 includes: 定义矢量
Figure QLYQS_7
define vector
Figure QLYQS_7
 式中T为采样区间；In the formula, T is the sampling interval; 将滑模面s的公式变形为：Transform the formula of the sliding surface s into:
Figure QLYQS_8
Figure QLYQS_8
 其中，
Figure QLYQS_9
in,
Figure QLYQS_9
 μ为中间变量，
Figure QLYQS_10
μ is an intermediate variable,
Figure QLYQS_10
 设计控制律u1为：The design control law u 1 is:
Figure QLYQS_11
Figure QLYQS_11
 式中U为固定控制增益；where U is the fixed control gain; 控制律u1使两个状态变量的运动轨迹在有限时间内到达首次波峰位置点B的过程包括：The process of the control law u1 making the trajectory of the two state variables reach the first peak position point B within a limited time includes: 根据变形后滑模面s的公式，求解滑模面s对时间的二阶导数：According to the formula of the deformed sliding mode surface s, solve the second derivative of the sliding mode surface s with respect to time:
Figure QLYQS_12
Figure QLYQS_12
 式中：In the formula:
Figure QLYQS_13
Figure QLYQS_13
 y22(μ)＝c1μ-μβ1，y 22 (μ)=c 1 μ−μβ 1 , β1＝1/RC，β2＝ω0 2＝1/LC；β 1 =1/RC, β 2 =ω 0 2 =1/LC; 定义四个常量ζ1、ζ2、ζ3、ζ4和函数Y21、Y22进行以下变量替换：Define four constants ζ 1 , ζ 2 , ζ 3 , ζ 4 and functions Y 21 , Y 22 to perform the following variable substitutions:
Figure QLYQS_14
Figure QLYQS_14
Figure QLYQS_15
Figure QLYQS_15
 满足以下关系式：Satisfy the following relation:
Figure QLYQS_16
Figure QLYQS_16
 将控制律u1的公式代入滑模面s对时间的二阶导数，得到：Substituting the formula of the control law u 1 into the second derivative of the sliding surface s with respect to time, we get:
Figure QLYQS_17
Figure QLYQS_17
 式中μmin为中间变量μ的最小值，k为大于0的常数；In the formula, μ min is the minimum value of the intermediate variable μ, and k is a constant greater than 0; 进一步，得到：Further, get:
Figure QLYQS_18
Figure QLYQS_18
 根据
Figure QLYQS_19
两边同乘s，即有/>
Figure QLYQS_20
成立，则对于两个状态变量的运动轨迹，从初始点A在有限时间t0内到达首次波峰位置点B；according to
Figure QLYQS_19
Multiply both sides by s, that is, />
Figure QLYQS_20
is established, then for the trajectory of the two state variables, from the initial point A to the first peak position point B within a limited time t 0 ; 其中t0＝tB-tA，where t 0 =t B -t A , 其中tA为初始点A对应的时刻，tB为首次波峰位置点B对应的时刻；Where t A is the time corresponding to the initial point A, and t B is the time corresponding to the first peak position point B; 第一阶段固定控制增益U为：The fixed control gain U of the first stage is:
Figure QLYQS_21
Figure QLYQS_21
 在第二阶段，设定控制律u为控制律u2，控制律u2设计为：In the second stage, the control law u is set as the control law u 2 , and the control law u 2 is designed as:
Figure QLYQS_22
Figure QLYQS_22
 式中Uj为变控制增益，r4为预设固定值控制增益，r4>0；In the formula, U j is the variable control gain, r 4 is the preset fixed value control gain, r 4 >0; 所述变控制增益自适应调节幅值的赋值方法包括：The method for assigning the variable control gain adaptive adjustment amplitude includes:
Figure QLYQS_23
Figure QLYQS_23
 式中Nj为第j个采样区间Tj内s的过零点个数，N*为过零点个数的参考值，N*≥2；Λ1和Λ2是两个正数，Λ1<Λ2；T＝{T1,T2,...Ti}，j＝1,2,3,……i；i为采样区间的总个数；U0是控制律u2的初始值：In the formula, N j is the number of zero-crossing points of s in the jth sampling interval T j , N* is the reference value of the number of zero-crossing points, N*≥2; Λ 1 and Λ 2 are two positive numbers, Λ 1 < Λ 2 ; T={T 1 ,T 2 ,...T i }, j=1,2,3,...i; i is the total number of sampling intervals; U 0 is the initial value of control law u 2 : U0＝[Y21(||w||*,|s(t0)|)+Y22u1max+k]，U 0 ＝[Y 21 (||w|| * ,|s(t 0 )|)+Y 22 u 1max +k], 式中u1max为控制律u1的最大值：where u 1max is the maximum value of control law u 1 :
Figure QLYQS_24
Figure QLYQS_24
 2.根据权利要求1所述的基于过零检测的电力变换器自适应连续滑模控制方法，其特征在于，控制律u2使滑模面s的收敛范围为：2. the power converter adaptive continuous sliding mode control method based on zero-crossing detection according to claim 1, is characterized in that, control law u 2 makes the convergence range of sliding mode surface s be: |s|≤[U0+(1+r4)μmaxUj]T2，|s|≤[U 0 +(1+r 4 )μ max U j ]T 2 , 式中μmax为中间变量μ的最大值。Where μ max is the maximum value of the intermediate variable μ. 3.根据权利要求2所述的基于过零检测的电力变换器自适应连续滑模控制方法，其特征在于，获得滑模面s的收敛范围的过程包括：3. the power converter adaptive continuous sliding mode control method based on zero-crossing detection according to claim 2, is characterized in that, the process of obtaining the convergence range of sliding mode surface s comprises: 将控制律u2的表达式代入滑模面s对时间的二阶导数表达式中，得到：Substituting the expression of the control law u 2 into the expression of the second derivative of the sliding surface s with respect to time, we get:
Figure QLYQS_25
Figure QLYQS_25
 进一步变形为：Further transformed into:
Figure QLYQS_26
Figure QLYQS_26
 假设i0∈[1,Nj]，j0∈[1,Nj]，且i0<j0，其中i0为[1,Nj]内所有过零点其中一个过零点，j0为[1,Nj]内所有过零点其中另一个过零点，则：Suppose i 0 ∈[1,N j ], j 0 ∈[1,N j ], and i 0 <j 0 , where i 0 is one of all zero-crossing points in [1,N j ], j 0 is All the zero-crossing points in [1,N j ] and the other zero-crossing point, then: s(ti0)＝s(tj0)＝0；s(t i0 )=s(t j0 )=0; 根据N*≥2，存在时间点ti0j0：ti0<ti0j0<tj0，使得
Figure QLYQS_27
存在；According to N*≥2, there exists a time point t i0j0 : t i0 <t i0j0 <t j0 , such that
Figure QLYQS_27
exist; 根据拉格朗日中值定理，在t与ti0j0内存在时间ti0j0′，满足下面关系式：According to the Lagrangian median value theorem, there exists a time t i0j0 ′ within t and t i0j0 , which satisfies the following relationship:
Figure QLYQS_28
Figure QLYQS_28
 t是Tj采样区间的任意时刻，且|t-ti0j0|＜Tj；t is any moment in the sampling interval of T j , and |tt i0j0 |<T j ; 同理，在t与ti0间还存在另一时刻ti0′满足：Similarly, there is another moment t i0 ′ between t and t i0 that satisfies:
Figure QLYQS_29
Figure QLYQS_29
 根据|t-ti0|<T，上式变形为：According to |tt i0 |<T, the above formula is transformed into:
Figure QLYQS_30
Figure QLYQS_30
 对上式两端同时求积分，获得滑模面s的收敛范围：Integrate both ends of the above formula at the same time to obtain the convergence range of the sliding mode surface s: |s|≤[U0+(1+r4)μmaxUj]T2。|s|≤[U 0 +(1+r 4 )μ max U j ]T 2 .
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