CN115411935A - Phase plane secant trajectory control method of Boost converter - Google Patents

Phase plane secant trajectory control method of Boost converter Download PDF

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CN115411935A
CN115411935A CN202210816773.1A CN202210816773A CN115411935A CN 115411935 A CN115411935 A CN 115411935A CN 202210816773 A CN202210816773 A CN 202210816773A CN 115411935 A CN115411935 A CN 115411935A
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output voltage
boost converter
control method
state
control
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陈章勇
刘海峰
陈勇
肖方波
李猛
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University of Electronic Science and Technology of China
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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

Abstract

The invention aims to provide a phase plane secant trajectory control method of a Boost converter, and belongs to the technical field of power electronics. The method divides the working state of the Boost converter into two conditions for different control: during the transient period, a TCOS method is adopted for control, namely, the on-state and the off-state of the switching tube are determined by using a state plane track, and the balance between recovery time and voltage deviation is well reflected; in a steady state process, an improved Active Disturbance Rejection Control (ADRC) control method is adopted to compensate uncertainty and disturbance in real time, and the robustness of the system to internal parameter disturbance and external disturbance is improved.

Description

Phase plane secant trajectory control method of Boost converter
Technical Field
The invention belongs to the technical field of power electronics, and particularly relates to a phase plane secant trajectory control method of a Boost converter.
Background
In recent years, due to the development of technology, research on power conversion has been unprecedented. The DC-DC converter is greatly applied to industrial production due to its characteristics of high efficiency, high power density, low EMI, and the like, for example: fuel cells in mobile devices, photovoltaic (PV) systems, lithium ion batteries in Hybrid Electric Vehicles (HEVs), and intelligent appliances. Among them, particularly, fuel cell hybrid vehicle systems require a Boost type DCDC converter because the output voltage of their large fuel cells should be adjusted to provide a stable direct voltage to a succeeding cascade device. On the other hand, it is much more difficult to control such a boost DCDC converter than a buck DCDC converter because the output voltage of the boost converter is higher than the input power voltage; on the other hand, the state variables of Boost converters are interrelated (including their input disturbances and parameter uncertainties) resulting in modeling and linearization difficulties; in addition, the boost converter also exhibits non-minimum phase characteristics, and such non-minimum phase characteristics exhibit phase lag in the system, and if the parameters of the boost converter, such as load resistance and voltage gain, change, the instability of the system is further aggravated, and a wide range of closed-loop bandwidth cannot be realized. Therefore, it is more difficult to control the boost type DCDC converter than the buck type.
In order to obtain a stable output voltage of the Boost converter, many control algorithms have been proposed to regulate the output voltage.
Aiming at the fact that a Boost converter is a nonlinear time-varying system, a small signal model is obtained through linearization around an accurate working point of a state space average model, and a classical control theory is introduced on the basis of the small signal model to design a controller. The linear controller is simple and convenient in design and easy to implement, but cannot process system parameter changes and large-signal transient changes;
whereas multi-loop current mode control uses the input inductor current for inner current loop regulation with high crossover frequency, and the output voltage is regulated by the slower outer voltage loop. The design of such controllers considers different loop gains and specific target operating points to evaluate the system performance, greatly improving the dynamic response of the system, but designing a dual-loop controller has great challenges, especially for the topology of high-order converters.
The controller is designed based on a linear system theory whether based on a small signal model or a multi-loop mode, and the controller has excellent performance only at a certain working point, and once the system deviates from a balance point, the interference suppression capability of the designed controller is reduced. Therefore, the linear control theory cannot effectively cope with the changes of the input power supply voltage of the Boost converter and the system parameters. In order to be able to cope with the non-linearity, wide input voltage and load variations inherent to DCDC converters and to ensure stability under any operating conditions and at the same time provide a fast transient response, many documents have introduced advanced control theories to overcome the deficiencies of linear systems for controller design.
The existence of the switch tube in the DCDC converter constitutes the variable structure characteristic of the system, so the Sliding Mode Control (SMC) technology is suitable for the Boost converter. SMC exhibits stable output voltage regulation in the presence of input voltage and output load disturbances, with faster dynamic response and less overshoot and undershoot than conventional PI control. However, the regulated output voltage of the SMC has high frequency ripple due to the sliding mode plane crossings. In addition, high-frequency vibration caused by the vibration on the switch surface is difficult to eliminate, and unmodeled dynamics of the system is easy to excite.
Sensorless control may provide system reliability and reduce system cost. Many estimation techniques are proposed in DCDC boost converters, such as: estimating sensorless display model predictive control of the inductive current through static approximation and extended Kalman filtering; or a discrete low-pass filter in each switching cycle to estimate the inductor current in the time domain. However, the estimation error still affects the regulation accuracy of the converter output voltage.
Disclosure of Invention
To comprehensively consider voltage deviation and recovery time, a split-line trajectory control based on the undershoot of the output voltage of a boost converter and the response time is proposed. Different from the traditional boundary control based on a natural track as a switch surface, a plurality of transient operating points are selected in the dynamic process from light load to heavy load jump, the switching-on track of the next transient operating point is a Secant of the switching-off track of the previous transient operating point, and the balance of voltage deviation and recovery time is realized through the control of a phase plane Secant track (trajector control of search in phase plane). However, because uncertainty and interference are ubiquitous in modern industrial systems, the conventional closed-loop control cannot obtain a satisfactory effect, and therefore, in order to compensate for uncertainty and interference in real time, active Disturbance Rejection Control (ADRC) is introduced in a steady-state process to improve the robustness of the system to internal parameter disturbance and external disturbance.
In order to achieve the purpose, the technical scheme of the invention is as follows:
a phase plane secant trajectory control of a Boost converter comprises the following steps:
step 1, judging whether a circuit of a Boost converter is in a steady state or a transient state, and if the circuit is in the transient state, entering a step 2; otherwise, entering step 3;
and 2, when the load jumps from light load to heavy load, selecting a transient working point in a dynamic process to comprehensively consider two indexes of output voltage undershoot and recovery time, and reaching a target working point based on a natural track of the on and off of the MOSFET switching tube, so that the system can reach a steady state theoretically only by two switching actions.
And 3, when the circuit is in a stable state, using an improved active disturbance rejection controller for control, wherein the active disturbance rejection controller is specifically,
Figure BDA0003740988590000021
in the above formula, k 1 And k 2 For the controller gain, y ref In order to achieve the desired output voltage,
Figure BDA0003740988590000022
respectively the output voltage and the inverse output voltage observed by the extended observer, b 0 In order to control the coefficients of the input,
Figure BDA0003740988590000023
is the estimated perturbation.
Further, the topology of the Boost converter includes: the circuit comprises an inductor (L), a capacitor (C), a switching tube (S1) and a diode (D1); the drain electrode of the switching tube (S1) is connected with one end of the inductor, and the source electrode of the switching tube (S1) is connected with the cathode of the input power supply; the anode of the diode (D1) is connected with one end of the inductor and the drain of the switch tube (S1), the cathode of the diode (D1) is connected with one end of the output capacitor (C), and the other end of the output capacitor (C) is connected with the negative electrode of the power supply.
Further, the output voltage of the Boost converter cannot be negative due to the presence of diodes in the circuit topology.
Further, the operation mode of the Boost converter during a steady state is a Continuous Conduction Mode (CCM).
Further, the control method is suitable for the condition that the load disturbance is small, namely the disturbance enables the output voltage of the converter to be not 0.
Further, the controller gain k 1 ＝w c 2 ,k 2 ＝2w c ，w c A controller gain parameterized for bandwidth.
In summary, due to the adoption of the technical scheme, the invention has the beneficial effects that:
1. the transient control method based on the natural track provided by the invention is switched to a proposed control method when the load is disturbed, and the on-off time of the switching tube is estimated by using state plane analysis, so that the state variable reaches a target working point in the shortest time on the basis of reducing the stress of the component.
Drawings
Fig. 1 is a simplified circuit schematic of a Boost converter;
wherein, (a) is a topology structure chart; (b) turning on an equivalent circuit diagram for the switching tube; and (c) is an equivalent circuit diagram of the switch tube.
Fig. 2 is a normalized trace diagram of the turn-on and turn-off of the MOSFET of the switching tube in the Boost converter.
Fig. 3 is a block diagram of the control method of the present invention.
FIG. 4 is a simplified optimal time dynamics control diagram of the present invention when the load is from light load to heavy load;
wherein, (a) is a phase trace diagram of output voltage and inductive current, (b) is an output voltage waveform, and (c) is an inductive current waveform.
Fig. 5 is a block diagram of an ADRC controller according to the present invention.
FIG. 6 is a simulation diagram of the output voltage of the present invention based on the digital optimal time dynamic control when the load is changed from light load to heavy load.
FIG. 7 is a simulation diagram of the variation of the inductor current waveform when the control method of the present invention is used during a load jump;
fig. 8 is a waveform diagram of a simulation of a conventional active disturbance rejection control.
Wherein, (a) is an output voltage simulation diagram; and (b) is an inductor current simulation diagram.
Fig. 9 is a time-optimized natural trajectory simulation waveform diagram.
Wherein, (a) is an output voltage simulation diagram; and (b) is an inductor current simulation diagram.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the embodiments and the accompanying drawings.
The control method is designed for a Boost converter with a non-minimum phase (NMP) system, and a simplified circuit schematic diagram of the Boost converter is shown in figure 1. The circuit topology structure is as shown in fig. 1 (a), and includes: the circuit comprises an inductor (L), a capacitor (C), a switching tube (S1) and a diode (D1); the drain electrode of the switching tube (S1) is connected with one end of the inductor, and the source electrode of the switching tube (S1) is connected with the negative electrode of the input power supply; the anode of the diode (D1) is connected with one end of the inductor and the drain of the switching tube (S1), the cathode of the diode (D1) is connected with one end of the output capacitor (C), and the other end of the output capacitor (C) is connected with the negative electrode of the power supply; the output capacitor (C) is connected with the load (R) in parallel. Fig. 1 (b) and fig. 1 (c) are equivalent circuit diagrams of switching on or off of the switching tube MOSFET, respectively. When the switch tube MOSFET is switched on, the inductor current stores energy, and when the switch tube MOSFET is switched off, the energy stored in the inductor is transmitted to the load.
For the above-described transformer, in order to eliminate the dimension of the state variable to obtain generality, the variable is subjected to normalization processing,
Figure BDA0003740988590000031
t n ＝t*f o wherein V is r Is a reference voltage, f o In order to be the natural frequency of the frequency,
Figure BDA0003740988590000032
l and C are respectively inductance and capacitance, Z o In order to be a characteristic impedance,
Figure BDA0003740988590000033
when the switching tube is turned on (u = 1) and turned off (u = 0) (u refers to the state of the MOSFET switching tube and is also the control input of the system), according to KCL and KVL laws, the state equations of the inductor current and the output voltage are as follows,
Figure BDA0003740988590000034
Figure BDA0003740988590000035
wherein, V cc Is the input voltage i L Is the inductive current, v o Is the output voltage;
assuming that no power loss occurs during the operation of the Boost converter, the input power is equal to the output power, and the load line is defined as follows:
Figure BDA0003740988590000036
when the target operating voltage (output voltage equal to desired voltage) is normalized, the result is v on,t arget ＝1，
Figure BDA0003740988590000037
The target operating point of the converter is (v) on,target ,i Ln,target ) The determination can be made according to (3) and (4).
And obtaining the phase locus of the normalized inductive current and the normalized output voltage by an ordinary differential equation when the switch tube is switched on and off at the target working point:
Figure BDA0003740988590000041
wherein, when u =0, the phase locus of the inductor current and the output voltage is (V) ccn ,i on ) As a circle center, with a desired working point
Figure BDA0003740988590000042
To the center of a circle (V) ccn ,i on ) A circle with a radius; and u =1, the phase locus of the inductor current and the output voltage is the passing point
Figure BDA0003740988590000043
Has a slope of
Figure BDA0003740988590000044
A straight line of (c). As shown in fig. 2, the switching-on and switching-off tracks of the Boost converter are tangent at the target working point, and ideally, when the system reaches a steady state, the Boost converter performs high-frequency switching-on and switching-off near the target working point.
If the output voltage cannot be negative, and the Boost converter operates in Continuous Conduction Mode (CCM) during steady state.
A phase plane secant trajectory control method of a Boost converter is shown in a structural block diagram of fig. 3 and comprises the following steps:
step 1, judging whether a circuit of a Boost converter is in a steady state or a transient state, and if the circuit is in the transient state, entering step 2; otherwise, entering step 3;
and 2, when the load jumps from light load to heavy load, selecting a transient working point in a dynamic process to comprehensively consider two indexes of output voltage undershoot and recovery time, and reaching a target working point based on a natural track of the on and off of the MOSFET switch tube, so that the system can reach a steady state theoretically only by two switching actions. The specific process is shown in FIG. 4
As shown in fig. 4.A, when the load changes from light load to heavy load, the operating point 3 is the steady-state point at the next time, and the operating point 1 is the initial state point of the load jump process, which is also the steady-state operating point at the previous time. In order to comprehensively consider two indexes of voltage undershoot and recovery time, a transient operating point 2' is selected from the operating points 1 and 3. According to the derived on-off trajectories of the boost converter in the previous section, we can obtain that the on-off trajectories at the working point 3 are respectively:
Figure BDA0003740988590000045
Figure BDA0003740988590000046
wherein i on3 Is the load current at operating point 3.
Since the transient operating point 2 'is the middle point between the operating points 1 and 3, the transient operating point 2' has the coordinates of
Figure BDA0003740988590000047
The on and off trajectories at the transient point 2' are respectively:
Figure BDA0003740988590000048
Figure BDA0003740988590000051
according to the formula 6,8, by comparing the slope magnitudes of the opening traces at the working point 3 and the transient point 2, the relationship between the slope magnitudes is:
Figure BDA0003740988590000052
so, taking the transient operating point 2' as the initial point, the straight line of the slope of the on-trace at the operating point 3 intersects the off-trace at the transient operating point 2, i.e.: straight line 2'5 is the secant of the off-track at the transient operating point 2'. Based on the analysis of the above theory, we give the following two-stage switching control law:
Figure BDA0003740988590000053
fig. 4.a shows a phase trace of the inductor current and the output voltage for a two-stage switching control, and fig. 4.b and 4.c show a schematic diagram of the output voltage and the inductor current, respectively, as a function of time.
And step 3, when the circuit is in a stable state, using an active disturbance rejection controller for control, wherein the active disturbance rejection controller is specifically,
Figure BDA0003740988590000054
in the above formula, k 1 And k 2 For the controller gain, y ref In order to achieve the desired output voltage,
Figure BDA0003740988590000055
respectively the output voltage and the inverse output voltage observed by the extended observer, b 0 In order to control the coefficients of the input,
Figure BDA0003740988590000056
is the estimated perturbation. The circuit structure block diagram is shown in fig. 5, an observation equation of the extended observer ESO is obtained according to an output equation of a controlled object (Boost converter), the ESO observes three values of output voltage, an output voltage derivative and partial disturbance respectively, and finally, the control input u of the extended observer ESO is obtained according to the PD control and disturbance values. In the figure, y ref Representing the desired output voltage, y being the output voltage, b o Is a coefficient of the control input u, b 1 Is the coefficient controlling the derivative of the input u, c is the time constant of the low-pass filter, z 1 Z2, z3 are observed values of the output voltage, the derivative of the output voltage, and the partial disturbance, respectively; the controller is a PD controller, the plant is a controlled object, and the Extended State observer is an Extended State observer;
the specific design process of the active disturbance rejection controller comprises the following steps:
the dynamic equation of the Boost converter is linearized and then processed into a form under an ADRC framework:
Figure BDA0003740988590000061
wherein the content of the first and second substances,
Figure BDA0003740988590000062
ξ (t) represents the net perturbation of the system internal and external perturbations, while y,
Figure BDA0003740988590000063
u,
Figure BDA0003740988590000064
respectively representing the output voltage, a first derivative of the output voltage, a second derivative of the output voltage, and controlling the input duty ratio and the derivatives;
to improve the efficiency of the extended observer, the pole information is incorporated into the extended observer (ESO) to alleviate the observation pressure, and equation 24 is expressed in the form of a nominal model as follows:
Figure BDA0003740988590000065
wherein
Figure BDA0003740988590000066
Let x1= y be the sum of,
Figure BDA0003740988590000067
x3= h, the state equation of the enhanced state space model is:
Figure BDA0003740988590000068
wherein
Figure BDA0003740988590000069
Is assumed to be bounded but unknown. The form of the ESO is:
Figure BDA00037409885900000610
wherein
Figure BDA00037409885900000611
Are the same as for y, respectively,
Figure BDA00037409885900000612
h estimate, [ w ] o1 ,w o2 ,w o3 ] T Is the observer gain. Let [ z) 1 ,z 2 ,z 3 ] T Is the output of the extended observer, then:
Figure BDA00037409885900000613
equation 15 reduces to:
Figure BDA00037409885900000614
wherein: u. of o ＝k 1 (r-z 1 )-k 2 z 2 ，[k 1 ,k 2 ]If it is the controller gain, the control input u is:
u＝(u o -z 3 )/b 0 (17)
based on bandwidth parameterization, with w respectively o And w c The observer and controller bandwidths are shown. The number of parameters to be adjusted in the ADRC scheme is simplified by using a parametric observer and controller gain. Selecting observer gain beta a1 ＝3w o ,β a2 ＝3w o 2 ,β a3 ＝w o 3 And a controller gain k 1 ＝w c 2 ,k 2 ＝2w c 。
Example 1
The control method is adopted to carry out control simulation on the Boost converter, and when the circuit parameters of the converter are shown in the table 1, the gains of the controller and the observer are selected to be w c ＝500rad/s,w o ＝4500rad/s。
Simulations of the voltage change from 5A to 10A (light to heavy) resistance are shown in fig. 6, and the change in dynamic process inductor current is shown in fig. 7. It can be seen from the above figure that the output voltage dynamic recovery time is about 1.13ms when the load jumps from 5A to 10A. The expected operating point of the output voltage is reached, the voltage undershoot maximum value is about 47.8V, and the voltage deviation is about 2.2V. After reaching the operating point, the switch is made to the active disturbance rejection controller, and the overall dynamic process is about 10ms due to the switching oscillation.
FIG. 8 is a graph of the output voltage waveform and the inductor current waveform of the active disturbance rejection controller, wherein the load is 10 Ω To 5 Ω When the change is carried out, the expected working point is reached in about 10ms, the voltage undershoot maximum value is about 46.8V, and the voltage deviation is about 3.2V.
Fig. 9 shows the output voltage and inductor current waveforms based on minimum recovery time in combination with an active disturbance rejection controller. Wherein the load is from 10 Ω To 5 Ω When the voltage is changed, the voltage reaching the expected working point is about 0.6ms, the time of the dynamic response of the system is about 8ms in consideration of the oscillation caused by switching, the minimum value of voltage undershoot is 46.87V, and the voltage deviation is about 3.13V.
Combining the above analysis methods, we have found that there is a respective superior performance between the two indicators of minimum voltage deviation and faster dynamic response, whether for active disturbance rejection control (fig. 8) or considering only the minimum recovery time (fig. 9). While the hierarchical switching control proposed herein better reflects the balance between recovery time and voltage deviation.
TABLE 1
Parameter(s) Value of
V cc 30V
V o 50V
f s 100KHz
L 500μH
C 1000μF
D 0.4
R 50Ω
Where mentioned above are merely embodiments of the invention, any feature disclosed in this specification may, unless stated otherwise, be replaced by alternative features serving equivalent or similar purposes; all of the disclosed features, or all of the method or process steps, may be combined in any combination, except mutually exclusive features and/or steps.

Claims (6)

1. A phase plane secant trajectory control method of a Boost converter is characterized by comprising the following steps:
step 1, judging whether a circuit of a Boost converter is in a steady state or a transient state, and if the circuit is in the transient state, entering a step 2; otherwise, entering step 3;
and 2, when the load jumps from light load to heavy load, selecting a transient working point in a dynamic process to comprehensively consider two indexes of output voltage undershoot and recovery time, and reaching a target working point based on a natural track of the on and off of the MOSFET switching tube, so that the system can reach a steady state theoretically only by two switching actions.
And 3, when the circuit is in a stable state, using an improved active disturbance rejection controller for control, wherein the active disturbance rejection controller is specifically,
Figure FDA0003740988580000011
in the above formula, k 1 And k2 is the controller gain, y ref In order to achieve the desired output voltage,
Figure FDA0003740988580000012
respectively the output voltage and the inverse output voltage observed by the extended observer, b 0 In order to control the coefficients of the input,
Figure FDA0003740988580000013
is the estimated perturbation.
2. The digital optimal time dynamics control method of claim 1, wherein the topology of the Boost converter comprises: the circuit comprises an inductor, a capacitor, a switching tube and a diode; the drain electrode of the switching tube is connected with one end of the inductor, and the source electrode of the switching tube is connected with the negative electrode of the input power supply; the anode of the diode is connected with one end of the inductor and the drain of the switching tube, the cathode of the diode is connected with one end of the output capacitor, and the other end of the output capacitor is connected with the negative electrode of the power supply.
3. The phase plane secant trajectory control method of claim 1, wherein an output voltage of the Boost converter cannot be negative.
4. The phase plane secant trajectory control method of claim 1, wherein an operation mode of the Boost converter during a steady state is a continuous conduction mode.
5. The phase plane secant trajectory control method of claim 1, wherein the load disturbance causes the output voltage of the converter to be other than 0.
6. The phase plane secant trajectory control method of claim 1, wherein the controller gain k 1 ＝w c 2 ,k 2 ＝2w c ，w c A controller gain parameterized for bandwidth.
CN202210816773.1A 2022-07-12 2022-07-12 Phase plane secant trajectory control method of Boost converter Pending CN115411935A (en)

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