CN107370402B - Switching control method based on discrete Lyapunov function - Google Patents

Switching control method based on discrete Lyapunov function Download PDF

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CN107370402B
CN107370402B CN201710775514.8A CN201710775514A CN107370402B CN 107370402 B CN107370402 B CN 107370402B CN 201710775514 A CN201710775514 A CN 201710775514A CN 107370402 B CN107370402 B CN 107370402B
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current
voltage
vdc
sampling
rectifier
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CN107370402A (en
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杜贵平
杜发达
柳志飞
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South China University of Technology SCUT
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    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02MAPPARATUS 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
    • H02M7/00Conversion of ac power input into dc power output; Conversion of dc power input into ac power output
    • H02M7/02Conversion of ac power input into dc power output without possibility of reversal
    • H02M7/04Conversion of ac power input into dc power output without possibility of reversal by static converters
    • H02M7/12Conversion of ac power input into dc power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
    • H02M7/21Conversion of ac power input into dc power output without possibility of reversal 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
    • H02M7/217Conversion of ac power input into dc power output without possibility of reversal 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
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02MAPPARATUS 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
    • H02M1/00Details of apparatus for conversion
    • H02M1/0003Details of control, feedback or regulation circuits
    • H02M1/0012Control circuits using digital or numerical techniques

Abstract

The invention discloses a switching control method based on a discrete Lyapunov function, which belongs to the field of power electronic conversion technology and intelligent control, wherein the discrete Lyapunov function based on error terms of a controlled quantity and a reference quantity is defined according to a discrete mathematical model of a converter, a control law is obtained by a second Lyapunov stability theorem, different defined variables α are selected at a dynamic response stage and a steady state stage, and then a switching signal is output by PWM modulation.

Description

Switching control method based on discrete Lyapunov function
Technical Field
The invention relates to a single-phase voltage type PWM rectification technology, in particular to a switching control method based on a discrete Lyapunov function, and belongs to the technical field of power electronic current transformation.
Background
Along with the development of economy, the demand of a high-power direct-current power supply rises year by year, the input current harmonic of the traditional uncontrollable and phase-controlled power supply is large, the influence of low power factor on a power grid is large, and the current response is slow, so that the production and life requirements cannot be met; the voltage-type PWM rectifier can fundamentally eliminate input current harmonics and has a unity power factor, and thus is a major concern in the current power electronics field.
According to the control method based on the discrete lyapunov function, when the defined variable α is zero, namely traditional deadbeat control is carried out, and the deadbeat control depends on a mathematical model of a controlled object, so that the influence of the accuracy of the controlled object parameter on the control performance is large, the current is unstable and distorted due to the fact that inductance parameter drift, sampling inaccuracy and the like are caused when a single-phase PWM rectifier is applied, the robustness is poor, and when the defined variable α is not zero, the steady-state control performance of the system is good, the robustness is strong, but the problem of low dynamic response speed exists.
Disclosure of Invention
Aiming at the defects of the existing control strategy, the invention aims to provide a switching control method based on a discrete Lyapunov function. The method obtains a control law based on the Lyapunov stability second theorem, combines the advantages of dead-beat control and the feedforward-feedback characteristic of model prediction control, and has the advantages of high dynamic response speed, good control performance, strong robustness and the like.
The purpose of the invention can be realized by the following technical scheme.
A switching control method based on a discrete Lyapunov function selects different definition variables α in a dynamic response stage and a steady state stage, and then outputs a switching signal through PWM modulation, and specifically comprises the steps of (1) obtaining a grid voltage e, an input current i and a voltage Vdc at two ends of a direct current side capacitor C through sampling, (2) obtaining a reference current i through PI control by a voltage outer ring, (3) defining the discrete Lyapunov function to obtain a control law of a rectifier alternating current side, selecting different α parameters according to a converter state, and (4) outputting a switching signal S (k) through a PWM modulation unit and acting on a switching tube.
Further, in the step (1), a phase-locked circuit is utilized to obtain a zero crossing point of the power grid voltage, the DSP calculates the power grid period in real time according to the zero crossing point of the power grid voltage, changes the control period according to the power grid period, and calculates the power grid voltage value e according to the zero crossing point of the power grid voltage and converts the power grid voltage value e into a digital signal; and sampling an input current value i by using a current Hall sensor, sampling a direct-current voltage value Vdc at two ends of a direct-current side capacitor C of a rectification module by using a voltage division method, and converting the direct-current voltage value Vdc into a digital signal.
Further, in the step (2), the difference between the sampled dc-side output voltage Vdc and the command dc voltage Vdc _ ref is regulated by PI, the difference between the output dc voltage Vdc and the command dc voltage Vdc _ ref is used as the input of a voltage outer ring, the voltage outer ring is controlled by PI, the PI regulator outputs the amplitude of the reference current, and the reference current amplitude is multiplied by the grid voltage phase information to obtain the reference current i.
Further, in step (3), according to the second theorem of Lyapunov stability, a discrete Lyapunov function is defined asThereby obtaining the control law of the AC side of the rectifier at the moment of k +1Selecting a steady state error value △ H when | Vdc-Vdc _ ref>△ H, when α is set to 0, it is desirable that the dynamic response speed is fast, and when | Vdc-Vdc _ ref-<△ H, α is more than 0, α is selected within the range of α epsilon [0.1,0.75 ∈ ]]In order to reduceSteady state error, and system robustness enhancement.
Compared with the prior art, the invention has the beneficial effects that:
1. the input current ripple of the alternating current side of the single-phase voltage type PWM rectifier is low, and the system can realize unit power factor operation;
2. the system dynamic response speed is high;
3. the system robustness is good.
Drawings
FIG. 1 is a schematic diagram of a novel control method of a single-phase PWM rectifier based on a discrete Lyapunov function according to the present invention;
FIG. 2 is a Bode plot of the current inner loop closed loop transfer function G (z) of the present invention as a function of α;
fig. 3 is a graph of the control convergence speed ρ and α according to the present invention.
FIG. 4 is a simulated waveform of voltage and current on the switching control AC side based on Lyapunov discrete function, to which the present invention is applied
Fig. 5 is a simulation waveform of the switching control direct current side output voltage based on the Lyapunov discrete function to which the invention is applied.
Detailed Description
Embodiments of the present invention will be further described with reference to the accompanying drawings and specific examples, but the invention is not limited thereto, and it should be noted that those skilled in the art can realize or understand the embodiments without specific details.
The switching control method based on the discrete Lyapunov function in the embodiment mainly comprises the following steps:
(S1) obtaining the zero crossing point of the power grid voltage by using a phase-locked circuit, calculating the power grid period in real time by the DSP according to the zero crossing point of the power grid voltage, changing the control period according to the power grid period, calculating the power grid voltage value e according to the zero crossing point of the power grid voltage, and converting the power grid voltage value e into a digital signal;
(S2) sampling an input current value i by using a current Hall sensor, sampling a direct current voltage value Vdc at two ends of a direct current side capacitor C of the single-phase voltage type PWM rectification module by adopting a voltage division method, and converting the direct current voltage value Vdc into a digital signal;
(S3) taking the difference between the output direct current voltage Vdc and the instruction direct current voltage Vdc _ ref as the input of a voltage outer ring, wherein the voltage outer ring adopts PI control, a PI regulator outputs the amplitude of reference current, and the amplitude of the reference current is multiplied by the phase information of the grid voltage to obtain the reference current i x;
(S4) defining a discrete Lyapunov function to obtain a control law of the alternating current side of the rectifier, and selecting different α parameters according to the state of the converter, wherein the parameters are as follows:
A) e is single-phase alternating voltage; ls and R are respectively an alternating current side inductor and an equivalent resistor thereof; vr is the rectifier AC side voltage; i is the rectifier AC side current; c is a direct current side capacitor; vdc is the output voltage of the direct current side; rLIs a purely resistive load.
The mathematical model of the single-phase PWM rectifier AC measurement can be expressed as:
assuming that the system sampling frequency is T, the formula (1) is rewritten into a discrete form:
i (k) sample values representing the current at sampling times k; e (k) represents the sampling value of the alternating voltage at the sampling time k; i (k +1) represents the predicted current at time k +1 at the time k samples; vr (k +1) represents the voltage on the ac side of the rectifier at the sampling instant k + 1.
B) Defining the variable x (k) as the error between the current sample value and the reference value at the sampling moment k as follows:
x(k)=i(k)-i*(k) (3)
according to the second theorem of Lyapunov stability, and based on the error value of the current sampling value and the current reference value of the single-phase PWM rectifier, a discrete Lyapunov function L (x (k)) is defined as follows:
the Lyapunov functions of the k sampling time and the k +1 sampling time are respectively as follows:
the increment Δ L (x (k)) of the Lyapunov function at adjacent times is:
C) to ensure the stability of the system, according to the Lyapunov second theorem of stability, to ensure that Δ L (x (k)) < ═ 0 order:
i(k+1)-i*(k+1)=α[i(k)-i*(k)](7)
fig. 2 is a Bode diagram showing a current inner loop closed loop transfer function g (z) varying with α, and fig. 3 is a graph of a relationship between a control convergence speed ρ and α. it can be seen from fig. 2 and fig. 3 that the larger α is, the smaller the steady state error is, the smaller the overshoot of the unit step response is, and the slower the control convergence speed is, so a steady state error value △ H is selected, when | Vdc-Vdc _ ref | > △ H, α is made to be 0, the desired dynamic response speed is fast, when | Vdc-Vdc _ ref | < △ H, α is made to be greater than 0, and according to the Bode diagram, the selection range of the | Vdc-Vdc _ ref | < △ H of the α is α ∈ [0.1,0.75], in order to reduce the steady state error and enhance the robustness of the.
By combining formula (2) and formula (7), the control law Vr (k +1) on the ac side of the rectifier at the sampling time k +1 can be obtained as follows:
(S5) outputting a switching signal S (k) through the PWM modulation unit and acting on the switching tube.
In step (S2), the output dc voltage (Vdc) is sampled by using resistance voltage division, and isolated by using HCPL-7840, and then the sampled voltage is adapted to the voltage range of the DSP sampling port by using an operational amplifier.
Preferably, the algorithm calculation can be performed by a texas instruments 2000 series DSP processor.
In step (S3), the difference between the output dc voltage (Vdc) and the command dc voltage (Vdc _ ref) is used as the input of the voltage outer loop, the voltage outer loop adopts PI control, the PI regulator outputs the amplitude of the reference current, and the reference current amplitude is multiplied by the grid voltage phase information to obtain the reference current i.
As shown in fig. 4, the ac network side voltage e and the ac current i are in phase, and the input power factor is high and is approximately 1; and the robustness is good. As can be seen from fig. 5, the system has a fast dynamic response speed.
Various modifications, additions and substitutions for the specific embodiments described herein may be made by those skilled in the art without departing from the spirit and scope of the invention, which is within the ambit of the following claims. The technical scope of the present invention is not limited to the above-described embodiments.

Claims (2)

1. A switching control method based on a discrete Lyapunov function is characterized in that different definition variables α are selected in a dynamic response stage and a steady state stage, and then a switching signal is output through PWM modulation, and the method specifically comprises the steps of (1) obtaining grid voltage, input current and direct current voltage Vdc at two ends of a direct current side capacitor C through sampling, specifically obtaining a zero crossing point of the grid voltage through a phase-locked circuit, calculating a grid period in real time according to the zero crossing point of the grid voltage through a DSP, changing the control period according to the grid period, calculating the grid voltage according to the zero crossing point of the grid voltage, converting the grid voltage into a digital signal, sampling input current through a current Hall sensor, sampling the direct current voltage Vdc at two ends of the direct current side capacitor C of a rectifier through a voltage division method, and converting the direct current voltage Vdc into the digital signal, (2) obtaining a reference current i through PI control by adopting an outer ring, (3) defining the discrete Lyapunov function, obtaining a control law on the alternating current side of:
according to the second theorem of Lyapunov stability, a discrete Lyapunov function is defined asThereby obtaining the control law of the AC side of the rectifier at the sampling moment of k +1Selecting a steady state error value △ H when | Vdc-Vdc _ ref>△ H, Vdc _ ref is a DC-directed voltage, α is 0, and it is desirable that dynamic response speed is fast when | Vdc-Vdc _ ref-<△ H, α is more than 0, α is selected within the range of α epsilon [0.1,0.75 ∈ ]]The purpose is to reduce steady-state error and enhance the robustness of the system;
let e be the grid voltage; ls and R are respectively an alternating current side inductor and an equivalent resistor thereof; vr is the control law of the voltage at the alternating current side of the rectifier; i is an input current; c is a direct current side capacitor; rLIs a pure resistive load;
the mathematical model of the ac side of the single-phase PWM rectifier can be expressed as:
assuming that the system sampling frequency is T, the formula (1) is rewritten into a discrete form:
i (k) sample values representing the current at sampling times k; e (k) represents the sampling value of the grid voltage at the sampling moment k;
i (k +1) represents the predicted current at k +1 sample times; vr (k +1) represents the control law of the rectifier alternating current side at the sampling moment of k + 1;
defining the variable x (k) as the error between the current sample value and the reference value at the sampling moment k as follows:
x(k)=i(k)-i*(k) (3)
according to the second theorem of Lyapunov stability, and based on the error value of the current sampling value and the current reference value of the single-phase PWM rectifier, a discrete Lyapunov function L (x (k)) is defined as follows:
the Lyapunov functions of the k sampling time and the k +1 sampling time are respectively as follows:
the increment Δ L (x (k)) of the Lyapunov function at adjacent times is:
to ensure the stability of the system, according to the Lyapunov second theorem of stability, to ensure that Δ L (x (k)) < ═ 0 order:
i(k+1)-i*(k+1)=α[i(k)-i*(k)](7)
the control law Vr (k +1) on the ac side of the rectifier at the sampling time k +1 is obtained by integrating formula (2) and formula (7) as follows:
(4) based on the control law of the alternating current side of the rectifier, the PWM modulation unit outputs a switching signal S (k) and acts on a switching tube.
2. The switching control method based on the discrete Lyapunov function according to claim 1, characterized in that: in the step (2), the difference between the sampled direct current voltage Vdc and the command direct current voltage Vdc _ ref is regulated through PI, the difference between the direct current voltage Vdc and the command direct current voltage Vdc _ ref is used as the input of a voltage outer ring, the voltage outer ring adopts PI control, the PI regulator outputs the amplitude of the reference current, and the amplitude of the reference current is multiplied by the phase information of the grid voltage to obtain the reference current i.
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