CN109245518B - Fixed time sliding mode control method for buck type direct current converter - Google Patents

Fixed time sliding mode control method for buck type direct current converter Download PDF

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CN109245518B
CN109245518B CN201811065529.6A CN201811065529A CN109245518B CN 109245518 B CN109245518 B CN 109245518B CN 201811065529 A CN201811065529 A CN 201811065529A CN 109245518 B CN109245518 B CN 109245518B
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sliding mode
fixed time
buck
direct current
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CN109245518A (en
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陈强
钱宁
南余荣
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Zhejiang University of Technology ZJUT
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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
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance

Abstract

A fixed time sliding mode control method for a buck direct current converter comprises the following steps: step 1, establishing a system model of a buck direct current converter, and initializing a system state and control parameters; and 2, designing a fixed time sliding mode controller based on a fixed time sliding mode control theory, and designing a Lyapunov function. The invention realizes that the output voltage of the system converges to the expected reference output voltage in fixed time, and the upper bound of the convergence time is irrelevant to the initial value of the state variable of the system.

Description

Fixed time sliding mode control method for buck type direct current converter
Technical Field
The invention relates to a fixed time sliding mode control method for a buck direct current converter, in particular to a fixed time sliding mode control method for a buck direct current converter with system external interference.
Background
The basic topology is divided into a buck type direct current converter, a boost converter and a buck-boost converter, wherein the buck type direct current converter is also called as a buck converter and is widely used due to the characteristics of voltage reduction and the advantages of simple structure, high stability, easy analysis and the like.
In recent years, more and more new nonlinear control technologies are applied to the step-down type direct current converter, such as a backstepping method, fuzzy control, neural network control, sliding mode control and the like.
The traditional finite time sliding mode control can ensure the stability of the finite time of the system, but the upper bound of the convergence time of the traditional finite time sliding mode control is related to the initial value of the state variable of the system, namely when the initial value of the state variable of the system changes, the upper bound of the convergence time of the system also changes, and the convergence speed of the system is influenced. Therefore, how to eliminate the influence of the initial value of the system state quantity on the upper bound of the convergence time and improve the convergence speed of the system is a problem to be solved urgently in the application of sliding mode control in the buck direct current converter.
Disclosure of Invention
In order to solve the defects that the upper bound of the convergence time of the output voltage control method of the existing buck-type direct current converter is related to the initial value of the system state variable and the convergence speed of the system is slow, the invention provides a fixed time sliding mode control method of the buck-type direct current converter.
The technical scheme proposed for solving the technical problems is as follows:
a fixed-time sliding-mode control method for a buck-type direct-current converter comprises the following steps:
step 1, establishing a system model of a buck direct current converter, and initializing a system state and control parameters, wherein the process comprises the following steps:
1.1, the average model of the buck DC converter system is expressed in the form
Figure BDA0001798174530000021
Wherein, VoIs the output voltage, VinIs the input voltage iCIs the output capacitance current, L, C, R is the inductance, capacitance and load resistance, respectively; u is a control input;
1.2, define the State variable x1＝Vo-Vref，
Figure BDA0001798174530000027
The error dynamic equation of the buck DC converter is written into the following state space form
Figure BDA0001798174530000022
Wherein, VrefTo a desired reference output voltage, VrefIs a normal number;
step 2, designing a fixed time sliding mode controller, wherein the process is as follows:
2.1, designing the following fixed-time slip form surface
Figure BDA0001798174530000023
Wherein k is1，k2，a1，a2Is a normal number, 0 < a1＜1，a2＞1，
Figure BDA0001798174530000024
sgn (·) is a sign function;
according to equations (2) and (3), the derivative of the fixed-time slip-form surface s is
Figure BDA0001798174530000025
2.2 designing a fixed time sliding mode controller according to equation (4)
Figure BDA0001798174530000026
Wherein, α, β and lambda1、λ2Is a normal number, 0 < lambda1＜1，λ2＞1；
2.3 designing Lyapunov function
Figure BDA0001798174530000031
Wherein the content of the first and second substances,
Figure BDA0001798174530000032
derivative V to obtain
Figure BDA0001798174530000033
And substituting the formula (4) and the formula (5) into the formula (7) to obtain
Figure BDA0001798174530000034
Wherein the content of the first and second substances,
Figure BDA0001798174530000035
the determination system can be stable for a fixed time.
The invention adopts a fixed time sliding mode control method and designs a fixed time sliding mode controller to realize the rapid regulation of the output voltage of the buck DC converter.
The technical conception of the invention is as follows: aiming at the convergence speed problem of sliding mode control in a buck direct current converter system, the sliding mode surface of the fixed time terminal is adopted, the sliding mode controller of the fixed time is designed based on the sliding mode surface, and compared with the traditional sliding mode control, the upper bound of the convergence time of the system is irrelevant to the initial value of the state variable of the system, so that the influence of the initial value of the state variable of the system on the upper bound of the convergence time is eliminated, and the convergence of the output voltage of the system to the expected reference output voltage in the fixed time is realized.
The invention has the beneficial effects that: the convergence of the system output voltage to the expected reference output voltage within a fixed time is realized, the upper bound of the convergence time is irrelevant to the initial value of the system state variable, and the influence of the initial value of the system state variable on the upper bound of the system convergence time is eliminated.
Drawings
FIG. 1 is a basic flow of the algorithm of the present invention;
FIG. 2 shows the initial value of the state variable as x1(0)＝-5，x2(0) When the voltage is equal to 0, the control system outputs a voltage response curve;
FIG. 3 shows the initial value of the state variable as x1(0)＝-9，x2(0) When the value is 0, the control system outputs a tracking error;
FIG. 4 shows the initial value of the state variable being x1(0)＝-5，x2(0) 0, outputting the control signal of the invention;
FIG. 5 shows the initial value of the state variable as x1(0)＝-9，x2(0) 0, the control signal of the present invention is output.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
Referring to fig. 1-5, a fixed-time sliding-mode control method of a buck-type dc converter includes the steps of:
step 1, establishing a system model of a buck direct current converter, and initializing a system state and control parameters, wherein the process comprises the following steps:
1.1, the average model of the buck DC converter system is expressed in the form
Figure BDA0001798174530000041
Wherein, VoIs the output voltage, VinIs the input voltage iCIs the output capacitance current, L, C, R is the inductance, capacitance and load resistance, respectively; u is a control input;
1.2, define the State variable x1＝Vo-Vref，
Figure BDA0001798174530000045
The error dynamic equation of the buck DC converter can be written into the following state space form
Figure BDA0001798174530000042
Wherein, VrefTo a desired reference output voltage, VrefIs a normal number;
step 2, designing a fixed time sliding mode controller, wherein the process is as follows:
2.1, designing the following fixed-time slip form surface
Figure BDA0001798174530000043
Wherein k is1，k2，a1，a2Is a normal number, 0 < a1＜1，a2＞1，
Figure BDA0001798174530000044
sgn (·) is a sign function;
according to equations (2) and (3), the derivative of the fixed-time slip-form surface s is
Figure BDA0001798174530000051
2.2 designing a fixed time sliding mode controller according to equation (4)
Figure BDA0001798174530000052
Wherein, α, β and lambda1、λ2Is a normal number, 0 < lambda1＜1，λ2＞1；
2.3 designing Lyapunov function
Figure BDA0001798174530000053
Wherein the content of the first and second substances,
Figure BDA0001798174530000054
derivative V to obtain
Figure BDA0001798174530000055
And substituting the formula (4) and the formula (5) into the formula (7) to obtain
Figure BDA0001798174530000056
Wherein the content of the first and second substances,
Figure BDA0001798174530000057
the determination system can be stable for a fixed time.
In order to verify the effectiveness of the method, the invention carries out a simulation experiment on the control effect of the fixed-time sliding mode controller represented by the formula (5), and sets the initial conditions and part of parameters in the simulation experiment, namely:in the system equation, L is 1mH, C is 1mF, R is 10 omega, and Vin＝10V，Vref5V. The control parameter in the formulae (3) and (5) is a1＝7/9，a2＝1.7，k1＝k2＝0.1，λ1＝0.6，λ21.7, α - β -0.04, and system state variable initial value x1(0)＝-5，x2(0)＝0。
FIG. 2 and FIG. 4 show the initial value of the system state variable as x1(0)＝-5，x2(0) The simulation effect graph when the value is 0. FIG. 3 and FIG. 5 show the initial value of the system state variable as x1(0)＝-9，x2(0) The simulation effect graph when the value is 0. As can be seen from fig. 2, the convergence time of the output voltage of the system controlled by the fixed-time sliding mode is almost the same as that of the limited-time sliding mode, and the convergence time is 0.023 s. As can be seen from fig. 3, the convergence time of the output voltage of the system controlled by the fixed time sliding mode is 0.024s, and the convergence time of the limited time sliding mode is 0.029 s. As can be seen from fig. 2 and fig. 3, the fixed-time sliding-mode control method for the buck dc converter according to the present invention can achieve fast and effective tracking of the actual system output voltage to the desired reference output voltage. As can be seen from fig. 4, the convergence time of the system control signal under the fixed time sliding mode control is almost the same as that of the finite time sliding mode, and the convergence time is 0.023 s. As can be seen from fig. 5, the convergence time of the system control signal controlled by the fixed time sliding mode is 0.024s, and the convergence time of the system control signal controlled by the finite time sliding mode is 0.029 s. In a whole view, the convergence speed of the output voltage of the system controlled by the sliding mode relative to the fixed time is slightly influenced by the initial value change of the system, and the convergence time of the state variable of the controlled system is basically unchanged. The fixed time sliding mode control method of the buck DC converter can ensure that the tracking error of the system is stably converged to a balance point in fixed time, and eliminates the influence of the initial value of the system state on the upper bound of the convergence time of the system.
While the foregoing has described a preferred embodiment of the invention, it will be appreciated that the invention is not limited to the embodiment described, but is capable of numerous modifications without departing from the basic spirit and scope of the invention as set out in the appended claims. The proposed control scheme is effective for buck dc converters, and under the action of the proposed controller, fast convergence of the output voltage of the buck dc converter within a fixed time is achieved.

Claims (1)

1. A fixed time sliding mode control method of a buck direct current converter is characterized by comprising the following steps: the control method comprises the following steps:
step 1, establishing a system model of a buck direct current converter, and initializing a system state and control parameters, wherein the process comprises the following steps:
1.1, the average model of the buck DC converter system is expressed in the form
Figure FDA0002354419640000011
Wherein, VoIs the output voltage, VinIs the input voltage iCIs the output capacitance current, L, C, R is the inductance, capacitance and load resistance, respectively; u is a control input;
1.2, define the State variable x1＝Vo-Vref，
Figure FDA0002354419640000016
The error dynamic equation of the buck DC converter is written into the following state space form
Figure FDA0002354419640000012
Wherein, VrefTo a desired reference output voltage, VrefIs a normal number;
step 2, designing a fixed time sliding mode controller, wherein the process is as follows:
2.1, designing the following fixed-time slip form surface
Figure FDA0002354419640000013
Wherein k is1，k2，a1，a2Is a normal number, 0 < a1＜1，a2＞1，
Figure FDA0002354419640000014
sgn (·) is a sign function;
according to equations (2) and (3), the derivative of the fixed-time slip-form surface s is
Figure FDA0002354419640000015
2.2 designing a fixed time sliding mode controller according to equation (4)
Figure FDA0002354419640000021
Wherein, α, β and lambda1、λ2Is a normal number, 0 < lambda1＜1，λ2＞1；
2.3 designing Lyapunov function
Figure FDA0002354419640000022
Wherein the content of the first and second substances,
Figure FDA0002354419640000023
derivative V to obtain
And substituting the formula (4) and the formula (3) into the formula (7) to obtain
Figure FDA0002354419640000024
Figure FDA0002354419640000025
Wherein the content of the first and second substances,
Figure FDA0002354419640000026
when in use
Figure FDA0002354419640000027
The decision system can be stable for a fixed time.
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