CN112054676B - PID control method and system of Boost DC-DC converter - Google Patents

PID control method and system of Boost DC-DC converter Download PDF

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CN112054676B
CN112054676B CN202010972659.9A CN202010972659A CN112054676B CN 112054676 B CN112054676 B CN 112054676B CN 202010972659 A CN202010972659 A CN 202010972659A CN 112054676 B CN112054676 B CN 112054676B
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boost
converter
correction
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correction device
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CN112054676A (en
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孙跃
虞忠明
唐春森
王智慧
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Chongqing University
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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

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Abstract

The invention relates to the technical field of Boost DC-DC converters, and particularly discloses a PID control method and a system of a Boost DC-DC converter, wherein the method comprises the following steps: s1, modeling a Boost DC-DC converter by adopting a state space average method, and acquiring a duty ratio-output open-loop transfer function of the Boost DC-DC converter; s2, determining basic parameters of the Boost DC-DC converter, substituting the basic parameters into a duty ratio-output open-loop transfer function, and drawing a corresponding Bode graph; s3, determining a correction value according to a Bode diagram of the Boost DC-DC converter, and performing advanced correction on the Boost DC-DC converter by using a PD (potential difference) to enable the phase margin and the gain crossover frequency to reach a set value; s4, determining the output voltage steady-state effective value of the Boost DC-DC converter after PD correction; and S5, according to the output voltage steady-state effective value, performing advanced correction on the Boost DC-DC converter by using PI (proportional integral) to enable the output voltage steady-state effective value to reach a set value. The invention enables the Boost DC-DC converter to output the constant voltage direct current which reaches the required voltage value through the PID controller, and is efficient and accurate.

Description

PID control method and system of Boost DC-DC converter
Technical Field
The invention relates to the technical field of Boost DC-DC converters, in particular to a PID control method and a PID control system of a Boost DC-DC converter.
Background
The DC-DC converter is used for converting a direct current into another direct current with fixed voltage or adjustable voltage and comprises a direct current converting circuit and an indirect direct current converting circuit, wherein the direct current converting circuit is used for directly converting a direct current into another direct current, and the indirect direct current converting circuit is used for firstly converting the direct current into an alternating current and then converting the alternating current into the direct current. With the rapid development of the DC-DC switching power supply technology, the DC-DC switching power supply technology is more and more widely used in the industrial field due to its characteristics of high efficiency, high power and high reliability. The DC-DC switching power supply can realize the conversion from a high-voltage power supply to a low-voltage power supply, such as a Buck DC-DC converter; the transition from a low voltage power supply to a high voltage power supply may also be accomplished, for example, with a DC-DC Boost converter.
How to realize constant output from low-voltage direct current to high-voltage direct current still lacks an efficient and accurate control strategy at present.
Disclosure of Invention
The invention provides a PID control method and a system of a Boost DC-DC converter, which solve the technical problems that: how to realize the constant output from low-voltage direct current to high-voltage direct current efficiently and accurately.
In order to solve the technical problems, the invention provides a PID control method of a Boost DC-DC converter, which comprises the following steps:
s1, modeling a Boost DC-DC converter by adopting a state space average method, and acquiring a duty ratio-output open loop transfer function of the Boost DC-DC converter;
s2, determining basic parameters of the Boost DC-DC converter, substituting the basic parameters into the duty ratio-output open loop transfer function, and drawing a corresponding Bode graph;
s3, determining a correction amount according to a Bode diagram of the Boost DC-DC converter, and performing advanced correction on the Boost DC-DC converter by using an advanced PD correction device to enable the phase margin of the Boost DC-DC converter to be larger than a set value and the gain crossover frequency to reach the set value;
s4, determining the output voltage steady-state effective value of the Boost DC-DC converter after PD correction;
and S5, performing hysteresis correction on the Boost DC-DC converter by using a hysteresis PI correction device according to the output voltage steady-state effective value to enable the output voltage steady-state effective value to reach a set value.
Further, the Boost DC-DC converter comprises a direct current power supply, an inductor, a diode, a load, an MOS (metal oxide semiconductor) tube and a capacitor;
the inductor, the diode and the load are sequentially connected between the positive electrode and the negative electrode of the direct current power supply, and the diode is in forward connection;
the drain electrode of the MOS tube is connected with the positive electrode end of the diode, the source electrode of the MOS tube is connected with the negative electrode end of the direct current power supply E, and the grid electrode of the MOS tube is connected with the on-off time controller;
the capacitor is connected between the negative electrode end of the diode and the negative electrode end of the direct current power supply;
the duty cycle-to-output open loop transfer function is expressed as:
Figure GDA0003088494670000021
wherein, L, C, R0Respectively representing the inductance, the capacitance, the inductance value, the capacitance value, and the like of the load,Resistance value, D represents duty ratio, U0Representing the required output voltage, s representing the complex frequency of the Boost DC-DC converter.
In step S3, the performing the lead correction on the Boost DC-DC converter by using a lead PD correction apparatus specifically includes:
s31, determining a phase correction value according to a Bode diagram of the Boost DC-DC converter, and performing phase lead correction on the Boost DC-DC converter by adopting a lead PD correction device without gain to enable the phase margin of the Boost DC-DC converter to be larger than a set value;
and S32, analyzing the Boost DC-DC converter after phase correction, and performing gain correction on the Boost DC-DC converter by using a correction device containing a gain k to enable the gain crossover frequency to reach a set value.
Further, the step S31 is specifically:
to make the phase margin larger than the set value, let the leading PD correction device increase the phase by θ, and the transfer function of the leading PD correction device without gain is:
Figure GDA0003088494670000031
and the index coefficient
Figure GDA0003088494670000032
Gain crossover frequency fgAnd the switching frequency fsThe relational expression of (A) is:
Figure GDA0003088494670000033
thus, the gain crosses the angular frequency ωg＝2πfg；
Maximum leading phase angular frequency omega of leading PD correcting devicem＝ωgThen, the turning frequency of the leading PD correction transpose is obtained as:
Figure GDA0003088494670000034
thus obtaining
Figure GDA0003088494670000035
T is a time constant;
substituting a and T into
Figure GDA0003088494670000036
The transfer function of the advanced PD correction apparatus without gain is obtained.
Further, the step S32 is specifically:
drawing a Bode diagram of the Boost DC-DC converter after phase correction, and determining the amplitude L (omega) of a gain crossover frequency point of the Boost DC-DC converterg) Then, after adding the gain k: l (omega)g) The k value is calculated as 0 in +20 lgk.
Further, the step S5 is specifically:
judging whether the steady-state effective value of the output voltage is smaller than a preset value, if not, not correcting, if so, performing voltage correction by adopting a hysteresis PI correction device, wherein the transfer function of the hysteresis PI correction device is as follows:
Figure GDA0003088494670000037
according to experience, there is a correction angular frequency ω ≦ 0.1 ωg。
The invention also provides a PID control system of the Boost DC-DC converter, which comprises the Boost DC-DC converter and a PID controller;
the PID controller is used for determining a correction amount according to a Bode diagram of the Boost DC-DC converter, and performing advanced correction on the Boost DC-DC converter by using an advanced PD correction device to enable the phase margin of the Boost DC-DC converter to be larger than a set value and the gain crossover frequency to reach the set value;
the PID controller is also used for carrying out hysteresis correction on the Boost DC-DC converter by using a hysteresis PI correction device according to the output voltage steady-state effective value to enable the output voltage steady-state effective value to reach a set value;
and the Boost DC-DC converter is used for converting an input initial direct-current voltage source into a Boost direct-current voltage source reaching a preset voltage value under the control of the PID controller.
Preferably, the circuit structure of the Boost DC-DC converter is as described in the above PID control system, and the duty ratio-output open loop transfer function is expressed as:
Figure GDA0003088494670000041
wherein, L, C, R0Respectively represent the inductance L, the capacitance C and the load R0Inductance, capacitance, resistance, U0Representing the required output voltage, s representing the complex frequency of the Boost DC-DC converter.
Specifically, the PID controller comprises a leading PD correction device and a lagging PI correction device;
the advanced PD correction device is used for determining a phase correction value according to a Bode diagram of the Boost DC-DC converter and carrying out phase and gain advanced correction on the Boost DC-DC converter to enable the phase margin of the Boost DC-DC converter to be larger than a set value and the gain crossover frequency to reach the set value;
and the lag PI correction device is used for correcting the voltage of the Boost DC-DC converter according to the output voltage steady-state effective value of the Boost DC-DC converter corrected by the lead PD correction device, so that the output voltage steady-state effective value reaches a set value.
Preferably, the advanced PD correction apparatus performs phase correction on the Boost DC-DC converter according to the process described in the PID control method;
the advanced PD correction device performs gain correction on the Boost DC-DC converter according to the process of the PID control method;
and the hysteresis PI correction device performs voltage correction on the Boost DC-DC converter according to the process of the PID control method.
According to the PID control method and system for the Boost DC-DC converter, the gain crossover frequency, the phase margin and the output voltage steady-state effective value of the Boost DC-DC converter are subjected to closed-loop regulation through the PID controller, so that the Boost DC-DC converter outputs constant-voltage direct current reaching a required voltage value, and the method and system are efficient and accurate.
Drawings
Fig. 1 is a flowchart illustrating steps of a PID control method for a Boost DC-DC converter according to embodiment 1 of the present invention;
fig. 2 is a circuit topology diagram of a Boost DC-DC converter provided in embodiment 1 of the present invention;
fig. 3 is a circuit topology diagram of the Boost DC-DC converter shown in fig. 2 when V is turned on and off according to embodiment 1 of the present invention;
fig. 4 is a Bode diagram of the Boost DC-DC converter shown in fig. 2 after basic parameters are determined, according to embodiment 1 of the present invention;
fig. 5 is a Bode diagram of the Boost DC-DC converter shown in fig. 2 provided in embodiment 1 of the present invention after a correction device without gain is added;
fig. 6 is a Bode diagram of the Boost DC-DC converter shown in fig. 2 according to embodiment 1 of the present invention after a correction device with gain is added;
fig. 7 is a simulation model diagram of the Boost DC-DC converter shown in fig. 2 according to embodiment 1 of the present invention;
FIG. 8 is a state variable dynamic curve diagram of the simulation model shown in FIG. 7 provided in embodiment 1 of the present invention;
fig. 9 is a simulation model diagram of a correction device including a gain, which is added to the Boost DC-DC converter shown in fig. 2 according to embodiment 1 of the present invention;
fig. 10 is a simulation model diagram of adding a PID controller to the Boost DC-DC converter shown in fig. 2 according to embodiment 1 of the present invention;
FIG. 11 is a graph of output voltage waveforms in simulation of the simulation model shown in FIG. 10 according to embodiment 1 of the present invention;
fig. 12 is a schematic closed-loop control diagram of a PID control method of the Boost DC-DC converter according to embodiment 1 of the present invention.
Detailed Description
The embodiments of the present invention will be described in detail below with reference to the accompanying drawings, which are given solely for the purpose of illustration and are not to be construed as limitations of the invention, including the drawings which are incorporated herein by reference and for illustration only and are not to be construed as limitations of the invention, since many variations thereof are possible without departing from the spirit and scope of the invention.
Example 1
The PID control method of the Boost DC-DC converter provided by the embodiment of the invention, as shown in FIG. 1, comprises the following steps:
s1, modeling a Boost DC-DC converter by adopting a state space average method, and acquiring a duty ratio-output open loop transfer function of the Boost DC-DC converter;
s2, determining basic parameters of the Boost DC-DC converter, substituting the basic parameters into a duty ratio-output open loop transfer function, and drawing a corresponding Bode graph;
s3, determining a correction value according to a Bode diagram of the Boost DC-DC converter, and performing advanced correction on the Boost DC-DC converter by using an advanced PD correction device to enable the phase margin of the Boost DC-DC converter to be larger than a set value and the gain crossover frequency to reach the set value;
s4, determining the output voltage steady-state effective value of the Boost DC-DC converter after PD correction;
and S5, performing hysteresis correction on the Boost DC-DC converter by using a hysteresis PI correction device according to the output voltage steady-state effective value to enable the output voltage steady-state effective value to reach a set value.
It should be noted that, as shown in fig. 2, the Boost DC-DC converter targeted by the method of this embodiment includes a DC power supply E, an inductor L, a diode VD, and a load R0MOS tube V and capacitor C;
inductor L, diode VD and load R0The diode VD is connected between the positive pole and the negative pole of the direct current power supply E in sequence, and the diode VD is in forward connection; the drain electrode of the MOS tube V is connected with the positive electrode end of the diode VD, the source electrode is connected with the negative electrode end of the direct current power supply E, and the grid electrode is connected with the on-off time controller; the capacitor C is connected between the cathode terminal of the diode VD and the cathode terminal of the dc power supply E.
First, assume that the inductance L and the capacitance C are both large. When controllable switch MOWhen the S tube V is in an on state, the direct current power supply E charges the inductor L, and the charging current is constant to be IsWhile the voltage on the capacitor C is applied to the load R0And (5) supplying power. The output voltage u is larger due to the larger value of C0Substantially maintained at a constant value. Let V be in the on-state for tonAt off-state time of toffThe period T being Ton+toff. The energy accumulated on the inductor L in the on-state stage is E multiplied by Is×ton. When V is in the off state, the power source E and the inductor L together charge the capacitor C and provide energy to the load. During this time, the energy released by the inductor is (U)0-E)Is×toff，U0Representing the desired output voltage. When the circuit is in steady state, it is derived from the conservation of energy:
E×Is×ton＝(U0-E)×Is×toff (1)
and (3) after simplification:
Figure GDA0003088494670000071
wherein, T/Toff≥1。
It can be seen that the output voltage is higher than the input voltage and therefore the converter acts as a boost.
The Boost DC-DC converter has two working modes, namely an inductive current continuous working mode and an inductive current discontinuous working mode, the embodiment only analyzes the inductive current continuous mode, and the analysis method and the idea can also analyze the inductive current discontinuous mode. Under the continuous mode of inductive current, the working process of the circuit is divided into two steps of switching on and switching off of the switching tube V. When the switch tube V is conducted, the inductor L stores energy, and the load R is loaded at the moment0The power supply E is not used for supplying energy, but is supplied by the capacitor C. When the switch tube V is turned off, VD is conducted at the moment, and the power supply E and the inductor L simultaneously supply power to the load R0Power supply and capacitor C charging. In the continuous working mode, two topologies of the Boost circuit are shown in fig. 3, which are a topology when the switching tube V is turned on and a topology when the switching tube V is turned off.
For step S1:
in step S1, the Boost DC-DC converter system is modeled by using a state space averaging method. Let the state variable be x ═ is u0]TAnd u ═ E. The above analysis gave a value of [0, dT ]s]And [ dTs,Ts]The system state equations in the two time periods are respectively as follows:
Figure GDA0003088494670000081
Figure GDA0003088494670000082
wherein,
Figure GDA0003088494670000083
C1＝[0 0]，
Figure GDA0003088494670000084
C2＝[1 0]。
defined according to the state variable switching period average:
Figure GDA0003088494670000085
the notation d ═ 1-d can be given:
Figure GDA0003088494670000086
the same can be obtained:
Figure GDA0003088494670000087
therefore, the method comprises the following steps:
Figure GDA0003088494670000088
wherein A ═ dA1+(1-d)A2，Β＝dΒ1+(1-d)Β2，C＝dC1+(1-d)C2。
At steady state, there are
Figure GDA0003088494670000089
Namely:
Figure GDA00030884946700000810
obtaining:
Figure GDA00030884946700000811
here, ,
Figure GDA0003088494670000091
C＝[1-D 0]。
then, the steady state equation of the Boost DC-DC converter is obtained as follows:
Figure GDA0003088494670000092
Figure GDA0003088494670000093
to obtain a small-signal linear dynamic model, let:
Figure GDA0003088494670000094
substituting into a state space average equation and arranging to obtain:
Figure GDA0003088494670000095
neglecting the second-order alternating current small term, substituting into a steady-state equation to obtain a small-signal alternating current model as follows:
Figure GDA0003088494670000096
therefore, the ac small-signal state equation of the Boost DC-DC converter is:
Figure GDA0003088494670000097
in order to obtain the transfer function, the above equation of state is subjected to laplace transform to obtain:
Figure GDA0003088494670000098
obtaining by solution:
Figure GDA0003088494670000101
the transfer function that can be obtained is then as follows:
Figure GDA0003088494670000102
Figure GDA0003088494670000103
Figure GDA0003088494670000104
Figure GDA0003088494670000105
substituting the state equation to obtain a duty ratio-output open loop transfer function:
Figure GDA0003088494670000106
wherein, L, C, R0Respectively representing an inductance L, the capacitance C and a load R0D represents a duty ratio, U0Representing the desired output voltage and s representing the complex frequency of the Boost DC-DC converter.
For step S2:
the basic parameters of the Boost DC-DC converter determined in step S2 in this embodiment include L, C, R in equation (22)0、D、U0And substituting the basic parameters into the duty ratio-output open loop transfer function and drawing a corresponding Bode graph for later analysis.
The basic parameters of the present embodiment include: duty ratio D is 0.25, required output voltage U 010V, 20 μ H inductance L, 500 μ F capacitance C, 5V input dc voltage E, and load R 010 Ω, and 100 kHz. The control-output transfer function that can be obtained by substituting equation (22) is:
Figure GDA0003088494670000107
drawing the corresponding Bode graph is shown in fig. 4.
From the Bode plot of fig. 4, it can be seen that the phase margin is-5.34 °, and the gain crossover frequency is 2.84 × 104rad/s, and therefore lead correction is required. The lead correction will be performed with PD.
For step S3:
in this embodiment, in step S3, the performing the lead correction on the Boost DC-DC converter by using the lead PD correcting apparatus specifically includes the steps of:
s31, determining a phase correction value according to a Bode diagram of the Boost DC-DC converter, and performing phase lead correction on the Boost DC-DC converter by adopting a lead PD correction device without gain to enable the phase margin of the Boost DC-DC converter to be larger than a set value;
and S32, analyzing the Boost DC-DC converter after phase correction, and performing gain correction on the Boost DC-DC converter by using a correction device containing a gain k to enable the gain crossover frequency to reach a set value.
The step S31 specifically includes:
to make the phase margin larger than its set value by 45 ° (the phase correction amount is 50.34 °), the advance PD correction device increases the phase by an estimated value of θ to 70 °, and the transfer function of the advance PD correction device without gain is:
Figure GDA0003088494670000111
and the index coefficient
Figure GDA0003088494670000112
Gain crossover frequency fgAnd the switching frequency fsThe relational expression of (A) is:
Figure GDA0003088494670000113
thus, the gain crosses the angular frequency ωg＝2πfg＝1.26×105rad/s；
Maximum leading phase angular frequency omega of leading PD correcting devicem＝ωg＝1.26×105rad/s, then the turning frequency of the lead PD correction transpose is found to be:
Figure GDA0003088494670000114
thus obtaining
Figure GDA0003088494670000121
Time constant
Figure GDA0003088494670000122
Substituting a and T into
Figure GDA0003088494670000123
The transfer function of the advanced PD correction apparatus without gain is obtained as:
Figure GDA0003088494670000124
step S32 specifically includes:
drawing a Bode diagram for the Boost DC-DC converter after phase correction, and determining the amplitude L (omega) of the gain crossover frequency point of the Boost DC-DC converterg) Then, after adding the gain k: l (omega)g) The k value is calculated as 0 in +20 lgk.
More specifically, to determine the gain k, a Bode plot is first plotted after the correction device without gain is added to the original Boost DC-DC converter, as shown in fig. 5.
As can be seen from FIG. 5, when the correction device without gain k was added, the phase margin was 50.1 °, and the gain crossover frequency was 4.03 × 104rad/s. Therefore, the gain crossover frequency of the system should be 1.26 × 10 after adding gain k5rad/s, the amplitude of which is L (ω)g) -10.6dB, so, after k is added:
L(ωg)+20lgk＝0 (27)
k is obtained as 3.3884.
The PD correction device with gain k is thus obtained as follows;
Figure GDA0003088494670000125
the Boost DC-DC converter Bode after adding the gain k is plotted again as shown in fig. 6. As can be seen from fig. 6, when the PD correction apparatus including the gain k is added to the Boost DC-DC converter, the phase margin becomes 46 °, and the gain crossover frequency is 1.26 × 105rad/s, the set value is reached.
For step S4:
the MATLAB/Simulink simulation model before the Boost DC-DC converter system is not added with a PID controller is shown in FIG. 7, and the lower left is a measured amplitude (such as root mean square) display; at the lower right is a quiltAnd displaying the measured waveform. A MATLAB/Simulink toolbox is adopted to draw dynamic curves of various state variables of a Boost DC-DC converter before a controller is added, as shown in FIG. 8, and an output voltage u can be obtained from the graphs0The steady state has an effective value of 5.866V, less than 10V, in order to make u0The steady state effective value is 10V. According to the analysis of the steps S1-S3, a corresponding Simulink PD closed-loop control simulation module is obtained as shown in FIG. 9.
The simulation shows that the output voltage value is still less than 10V, so that a hysteresis PI correction device is also needed to perform voltage correction. The transfer function of the PI element is as follows:
Figure GDA0003088494670000131
according to experience, there is generally a correction angular frequency ω ≦ 0.1 ωgHere, ω may be 800rad/s, and the transfer function of the PI element is obtained as:
Figure GDA0003088494670000132
thus, a complete PID closed-loop control simulation model is shown in fig. 10, and a corresponding output voltage waveform obtained through simulation is shown in fig. 11. As can be seen from fig. 11, the output voltage reached the specified requirement of 10V.
The closed loop control process of the entire method can be summarized as shown in fig. 12. Wherein G isvd(s) is the DC-DC duty cycle,
Figure GDA0003088494670000133
to the output
Figure GDA0003088494670000134
The transfer function of (2), i.e. equation (22), Gm(s) is the transfer function of the PWM pulse width modulator, H(s) is the transfer function of the feedback voltage divider network, Gc(s) is the transfer function of the compensation network (PID controller). Vref(s) denotes a reference signal, B(s) denotes a feedback signal, and E(s) denotes an error signal. Wherein G isc(s)＝Gc1(s)+Gc2(s)。
The whole process is that the real phase margin, the gain crossover frequency and the output voltage steady-state effective value V0(s) transmitting the error value E(s) and the set value thereof to a feedback voltage division network H(s), generating a corresponding feedback signal B(s) according to the error signal by the feedback voltage division network H(s), and generating a corresponding feedback signal B(s) in a reference signal Vref(s) are fed back to the compensation network Gc(s), compensation network Gc(s) outputting a corresponding voltage signal Vc(s), modulating by a PWM pulse width modulator, inputting into a Boost DC-DC converter, and outputting voltage after boosting change, thereby forming closed-loop control.
It should be noted that the Boost DC-DC converter to which the present invention is applied is not limited to the circuit configuration shown in fig. 2, and other modifications made on the basis of fig. 2 are also applicable.
According to the PID control method for the Boost DC-DC converter, provided by the embodiment of the invention, the gain crossover frequency, the phase margin and the output voltage steady-state effective value of the Boost DC-DC converter are subjected to closed-loop regulation through a PID controller (an advanced PD correction device and a lag PI correction device), so that the Boost DC-DC converter outputs constant-voltage direct current reaching a required voltage value, and the method is efficient and accurate.
Example 2
The embodiment of the invention provides a PID control system of a Boost DC-DC converter, which is applied to the PID control method in the embodiment 1 and comprises the Boost DC-DC converter and a PID controller;
the PID controller is used for determining a correction amount according to a Bode diagram of the Boost DC-DC converter, and performing advanced correction on the Boost DC-DC converter by using an advanced PD correction device to enable the phase margin of the Boost DC-DC converter to be larger than a set value and the gain crossover frequency to reach the set value;
the PID controller is also used for carrying out hysteresis correction on the Boost DC-DC converter by using a hysteresis PI correction device according to the output voltage steady-state effective value to enable the output voltage steady-state effective value to reach a set value;
the Boost DC-DC converter is used for converting an input initial direct current voltage source into a Boost direct current voltage source reaching a preset voltage value under the control of the PID controller.
Specifically, the PID controller comprises a leading PD correction device and a lagging PI correction device;
the advanced PD correction device is used for determining a phase correction value according to a Bode diagram of the Boost DC-DC converter and carrying out phase and gain advanced correction on the Boost DC-DC converter to enable the phase margin of the Boost DC-DC converter to be larger than a set value and the gain crossover frequency to reach the set value;
and the lag PI correction device is used for correcting the voltage of the Boost DC-DC converter according to the output voltage steady-state effective value of the Boost DC-DC converter corrected by the lead PD correction device, so that the output voltage steady-state effective value reaches a set value.
Preferably, the advanced PD correction apparatus performs phase correction on the Boost DC-DC converter according to the PID control method of embodiment 1;
the advanced PD correction device performs gain correction on the Boost DC-DC converter according to the PID control method of the embodiment 1;
the hysteresis PI correction device performs voltage correction on the Boost DC-DC converter according to the PID control method of embodiment 1.
The PID control process has been described in detail in embodiment 1, and the detailed control process of the PID controller in this embodiment is not described again.
The above embodiments are preferred embodiments of the present invention, but the present invention is not limited to the above embodiments, and any other changes, modifications, substitutions, combinations, and simplifications which do not depart from the spirit and principle of the present invention should be construed as equivalents thereof, and all such changes, modifications, substitutions, combinations, and simplifications are intended to be included in the scope of the present invention.

Claims (9)

1. A PID control method of a Boost DC-DC converter is characterized by comprising the following steps:
s1, modeling a Boost DC-DC converter by adopting a state space average method, and acquiring a duty ratio-output open-loop transfer function of the Boost DC-DC converter;
s2, determining basic parameters of the Boost DC-DC converter, substituting the basic parameters into the duty ratio-output open loop transfer function, and drawing a corresponding Bode graph;
s3, determining a correction amount according to a Bode diagram of the Boost DC-DC converter, and performing advanced correction on the Boost DC-DC converter by using an advanced PD correction device to enable the phase margin of the Boost DC-DC converter to be larger than a set value and the gain crossover frequency to reach the set value;
s4, determining the output voltage steady-state effective value of the Boost DC-DC converter after PD correction;
s5, performing hysteresis correction on the Boost DC-DC converter by using a hysteresis PI correction device according to the output voltage steady-state effective value to enable the output voltage steady-state effective value to reach a set value;
the step S5 specifically includes:
judging whether the steady-state effective value of the output voltage is smaller than a set value, if not, not correcting, if so, performing voltage correction by adopting a hysteresis PI correction device, wherein the transfer function of the hysteresis PI correction device is as follows:
Figure FDA0003107964680000011
according to experience, there is a correction angular frequency ω ≦ 0.1 ωgAnd s represents the complex frequency of the Boost DC-DC converter, and the gain crossover angular frequency omegag＝2πfg，fgRepresenting the gain crossover frequency.
2. The PID control method of a Boost DC-DC converter as claimed in claim 1, wherein:
the Boost DC-DC converter comprises a direct-current power supply, an inductor, a diode, a load, an MOS (metal oxide semiconductor) tube and a capacitor;
the inductor, the diode and the load are sequentially connected between the positive electrode and the negative electrode of the direct current power supply, and the diode is in forward connection;
the drain electrode of the MOS tube is connected with the positive electrode end of the diode, the source electrode of the MOS tube is connected with the negative electrode end of the direct-current power supply, and the grid electrode of the MOS tube is connected with the on-off time controller;
the capacitor is connected between the negative electrode end of the diode and the negative electrode end of the direct current power supply;
the duty cycle-output open loop transfer function is expressed as:
Figure FDA0003107964680000021
wherein, L, C, R0Respectively representing the inductance, capacitance and resistance of the inductor, the capacitor and the load, D representing the duty ratio, U representing the duty ratio0Representing the required output voltage, s representing the complex frequency of the Boost DC-DC converter.
3. The PID control method according to claim 2, wherein the step S3 of performing the advanced correction on the Boost DC-DC converter by using an advanced PD correction apparatus includes the steps of:
s31, determining a phase correction value according to a Bode diagram of the Boost DC-DC converter, and performing phase lead correction on the Boost DC-DC converter by adopting a lead PD correction device without gain to enable the phase margin of the Boost DC-DC converter to be larger than a set value;
and S32, analyzing the Boost DC-DC converter after phase correction, and performing gain correction on the Boost DC-DC converter by using a correction device containing a gain k to enable the gain crossover frequency to reach a set value.
4. The PID control method of a Boost DC-DC converter according to claim 3, wherein the step S31 specifically comprises:
to make the phase margin larger than the set value, let the leading PD correction device increase the phase by θ, and the transfer function of the leading PD correction device without gain is:
Figure FDA0003107964680000022
and the index coefficient
Figure FDA0003107964680000023
Gain crossover frequency fgAnd the switching frequency fsThe relational expression of (A) is:
Figure FDA0003107964680000031
thus, the gain crosses the angular frequency ωg＝2πfg；
Maximum leading phase angular frequency omega of leading PD correcting devicem＝ωgThen, the turning frequency of the leading PD correction transpose is obtained as:
Figure FDA0003107964680000032
thus obtaining
Figure FDA0003107964680000033
T is a time constant;
substituting a and T into
Figure FDA0003107964680000034
The transfer function of the advanced PD correction apparatus without gain is obtained.
5. The PID control method of a Boost DC-DC converter according to claim 4, wherein the step S32 specifically comprises:
drawing a Bode diagram of the Boost DC-DC converter after phase correction, and determining the amplitude L (omega) of a gain crossover frequency point of the Boost DC-DC converterg) Then, after adding the gain k: l (omega)g) The k value is calculated as 0 in +20 lgk.
6. A PID control system of a Boost DC-DC converter is characterized in that: the system comprises a Boost DC-DC converter and a PID controller;
the PID controller is used for determining a correction amount according to a Bode diagram of the Boost DC-DC converter, and performing advanced correction on the Boost DC-DC converter by using an advanced PD correction device to enable the phase margin of the Boost DC-DC converter to be larger than a set value and the gain crossover frequency to reach the set value;
the PID controller is also used for carrying out hysteresis correction on the Boost DC-DC converter by using a hysteresis PI correction device according to the output voltage steady-state effective value to enable the output voltage steady-state effective value to reach a set value;
the Boost DC-DC converter is used for converting an input initial direct-current voltage source into a Boost direct-current voltage source reaching a preset voltage value under the control of the PID controller;
the voltage correction process of the Boost DC-DC converter by the hysteresis PI correction device is as follows:
judging whether the steady-state effective value of the output voltage is smaller than a set value, if not, not correcting, if so, performing voltage correction by adopting a hysteresis PI correction device, wherein the transfer function of the hysteresis PI correction device is as follows:
Figure FDA0003107964680000041
according to experience, there is a correction angular frequency ω ≦ 0.1 ωgAnd s represents the complex frequency of the Boost DC-DC converter, and the gain crossover angular frequency omegag＝2πfg，fgRepresenting the gain crossover frequency.
7. The PID control system of a Boost DC-DC converter as claimed in claim 6, wherein:
the Boost DC-DC converter comprises a direct-current power supply, an inductor, a diode, a load, an MOS (metal oxide semiconductor) tube and a capacitor;
the inductor, the diode and the load are sequentially connected between the positive electrode and the negative electrode of the direct current power supply, and the diode is in forward connection;
the drain electrode of the MOS tube is connected with the positive electrode end of the diode, the source electrode of the MOS tube is connected with the negative electrode end of the direct-current power supply, and the grid electrode of the MOS tube is connected with the on-off time controller;
the capacitor is connected between the negative electrode end of the diode and the negative electrode end of the direct current power supply;
the duty cycle-output open loop transfer function is expressed as:
Figure FDA0003107964680000042
wherein, L, C, R0Respectively representing the inductance, capacitance and resistance of the inductor, the capacitor and the load, D representing the duty ratio, U representing the duty ratio0Representing the required output voltage, s representing the complex frequency of the Boost DC-DC converter.
8. The PID control system of a Boost DC-DC converter as claimed in claim 7, wherein: the PID controller comprises a leading PD correction device and a lagging PI correction device;
the advanced PD correction device is used for determining a phase correction value according to a Bode diagram of the Boost DC-DC converter and carrying out phase and gain advanced correction on the Boost DC-DC converter to enable the phase margin of the Boost DC-DC converter to be larger than a set value and the gain crossover frequency to reach the set value;
and the lag PI correction device is used for correcting the voltage of the Boost DC-DC converter according to the output voltage steady-state effective value of the Boost DC-DC converter corrected by the lead PD correction device, so that the output voltage steady-state effective value reaches a set value.
9. The PID control system of a Boost DC-DC converter as claimed in claim 8, wherein:
the process of the leading PD correcting device for carrying out phase correction on the Boost DC-DC converter is as follows:
to make the phase margin larger than the set value, let the leading PD correction device increase the phase by θ, and the transfer function of the leading PD correction device without gain is:
Figure FDA0003107964680000051
and the index coefficient
Figure FDA0003107964680000052
Gain crossover frequency fgAnd the switching frequency fsThe relational expression of (A) is:
Figure FDA0003107964680000053
thus, the gain crosses the angular frequency ωg＝2πfg；
Maximum leading phase angular frequency omega of leading PD correcting devicem＝ωgThen, the turning frequency of the leading PD correction transpose is obtained as:
Figure FDA0003107964680000054
thus obtaining
Figure FDA0003107964680000055
T is a time constant;
substituting a and T into
Figure FDA0003107964680000056
Obtaining a transfer function of the advanced PD correction device without gain;
the process of performing gain correction on the Boost DC-DC converter by the leading PD correction device is as follows:
drawing a Bode diagram of the Boost DC-DC converter after phase correction, and determining the amplitude L (omega) of a gain crossover frequency point of the Boost DC-DC converterg) Then, after adding the gain k: l (omega)g) The k value is calculated as 0 in +20 lgk.
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