CN116470755A - Continuous nonsingular terminal sliding mode control method of Buck converter - Google Patents
Continuous nonsingular terminal sliding mode control method of Buck converter Download PDFInfo
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- CN116470755A CN116470755A CN202310382508.1A CN202310382508A CN116470755A CN 116470755 A CN116470755 A CN 116470755A CN 202310382508 A CN202310382508 A CN 202310382508A CN 116470755 A CN116470755 A CN 116470755A
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Classifications
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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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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
- H02M1/00—Details of apparatus for conversion
- H02M1/0003—Details of control, feedback or regulation circuits
- H02M1/0038—Circuits or arrangements for suppressing, e.g. by masking incorrect turn-on or turn-off signals, e.g. due to current spikes in current mode control
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- Engineering & Computer Science (AREA)
- Power Engineering (AREA)
- Dc-Dc Converters (AREA)
Abstract
The invention discloses a continuous nonsingular terminal sliding mode control method of a Buck converter, which is mainly used for solving the problems of limited time stability and unmatched interference suppression of output voltage of the Buck converter. The invention establishes a state space average model aiming at the Buck converter working in an inductive current continuous mode, and a controller based on a supercoiled algorithm is designed to enable a sliding mode variable to be converged to zero in a limited time, and enable a system state to be converged to a balance point along a non-singular terminal sliding mode surface in the limited time, so that the limited time tracking of the Buck converter output voltage to a reference voltage is realized; based on the method, the non-matching interference of the Buck converter is estimated and compensated by a non-linear interference observer, so that the effective suppression of the non-matching interference is realized. The invention has simple form and strong practicability, can ensure that the Buck converter system realizes the limited time stability of output voltage under the condition of unmatched interference, and has wider engineering application prospect.
Description
Technical Field
The invention relates to a continuous nonsingular terminal sliding mode control method of a Buck converter based on a supercoiled algorithm and a nonlinear interference observer, and belongs to the technical field of power electronic control.
Background
The power electronics technology is a technology for performing power conversion and control using power electronics, and has important applications in industries such as smart grids, electrified transportation, and new energy distributed generation systems. The dc converter is a classical power electronic device for realizing dc voltage increase or decrease, and has a wide application in the power field, and can be divided into six structures according to functions, wherein the Buck converter and the Boost converter are two most basic forms, and the Buck-Boost, cuk, sepic and the Zeta converter are derived based on the two converters.
The Buck converter control strategy can be divided into linear control and nonlinear control, with the development of modern industrial technology, the traditional linear control strategy cannot meet application requirements, and some modern control methods are tried to be applied to Buck converter control, such as robust control, sliding mode control, fuzzy control, adaptive control and the like. The literature (Komurcugil H. Adaptive terminal slip-mode control strategy for DC-DC Buck converters [ J ]. ISAtranfection, 2012,51 (6): 673-681) applies terminal slip-mode control to Buck converters for the first time. In order to eliminate the influence of load disturbance, the literature (Wu B, yang J, wang J, et al, extended state observer based control for DC-DC Buck converters subject to mismatched disturbances [ C ]// Proceedings of the 33rd Chinese control conference.IEEE,2014:8080-8085.2014, nanjing, china: institute of Electrical and Electronics Engineers, 2014:8080-8085) designs an Extended State Observer (ESO) for a Buck converter, and effectively suppresses the influence of load disturbance on the Buck converter through disturbance compensation. Literature (Yang J, cui H, li S, et al, optimized active disturbance rejection control for DC-DC Buck converters with uncertainties using a reduced-order GPI observer [ J ]. IEEE Transactions on Circuits and Systems I: regular Papers,2017,65 (2): 832-841) designed a reduced order generalized proportional integral state observer for Buck converters, and on this basis designed an optimized ADRC method to improve the tracking performance of the controller in the presence of system uncertainty and disturbances.
The invention provides a continuous nonsingular terminal sliding mode control method of a Buck converter based on a supercoiled algorithm and a nonlinear interference observer, which aims to further improve the dynamic tracking performance of the output voltage of the Buck converter and improve the suppression capability of the system on unmatched interference.
Disclosure of Invention
The invention aims to: the continuous nonsingular terminal sliding mode control method of the Buck converter is designed based on a nonsingular terminal sliding mode surface, a supercoiled algorithm and a nonlinear interference observer and is mainly used for solving the problems of reference voltage finite time tracking and unmatched interference suppression in Buck converter control.
The technical scheme is as follows: in order to achieve the purpose of the invention, the following technical scheme is adopted: a Buck converter continuous nonsingular terminal sliding mode control method based on a supercoiled algorithm and a nonlinear interference observer comprises the following steps:
step 1: for an asynchronous Buck converter working in an inductive current continuous mode, a state space average method is used for establishing a mathematical model of the asynchronous Buck converter as follows:
wherein μ=1 represents that the switching element VT is on, μ=0 represents that the switching element VT is off; u (u) o Outputting voltage for the Buck converter; i.e L Is an inductive current; u (U) in Is a direct current power supply voltage; c is the capacitance value; l is the inductance value.
Let the expected output voltage of Buck converter be U ref ，0＜U ref ＜U in Is constant. Selecting an error value x of an output voltage of a Buck converter 1 And its first derivative x 2 Is a system state variable, namely:
x 1 ＝U ref -u o (2)
when state variable x 1 When converging to 0, the output voltage u of the Buck converter o Will converge to the desired value of the output voltage U ref . For state variable x 1 、x 2 Deriving and substituting the equation (1), wherein the system error state equation is as follows:
on the basis, the uncertainty and internal and external interference of the system are considered, and the error state equation of the system is as follows:
wherein d is 1 (t) is a mismatch interference; d, d 2 And (t) is the matched interference. Let the interference quantity d 1 (t) and d 2 (t) is slow time-varying interference, i.eCan be ignored. At the same time interfere with upper bound D 1 ＝sup t＞0 |d 1 (t)|、D 2 ＝sup t＞0 |d 2 (t) | is finite and known.
Step 2: the non-singular terminal sliding mode surface is designed aiming at the system shown in the formula (5):
wherein p and q are both odd numbers. And (3) solving a second derivative of the sliding mode surface to obtain the following steps of:
and (3) making:
the control law based on the supercoiled algorithm is designed as follows:
wherein the controller parameters lambda, p need to satisfy:
parameters C, K m And K M The upper and lower bounds of the uncertainty of the system are respectively:
O＜K m ≤|γ(x，t)|≤K M (13)
from literature (Li Peng, zheng Zhijiang. Super-twiddling algorithm convergence analysis based on a quadratic-like Lyapunov function [ J ]]Control and decision 2011,26 (06): 949-952.) it is known that the controller design of formula (10) can be such that within a limited timeThe system will then move along the designed nonsingular terminal slide face. Solving the formula (6) to obtain:
wherein x is 1 (t) is the state variable x at time t 1 Is a value of (2). Let t be the time required for the sliding mode variable s to converge to 0 s System state variable x 1 State x when converging to 0 from sliding mode variable s 1 (t s ) Moving to the equilibrium point x 1 Time t=0 NTSM From formula (14):
i.e. t NTSM Is limited, so that the sliding mode variable x is in a limited time 1 Can move to a balance point along a nonsingular terminal sliding mode surface, namely the output voltage u of the Buck converter o Can converge to the desired value U in a limited time ref Convergence time and x 1 (t s ) And the parameters beta and p/q of the sliding mode surface are related.
Step 3: set Buck converter mismatch interference d 1 Observed values of (2) areDefining a mismatch interference observation error e 1 The method comprises the following steps:
under the assumption of step 1, deriving the above formula:
and (3) making:
wherein l 1 To disturb the observer gain. Combined type (5), (16), (17) and (18)
Taking into account thatUnknown true value of term, let:
where z is the disturbance observer state variable. Integrating the formula (20);
from equation (21), the mismatch disturbance observations of the Buck converterThe method comprises the following steps:
the form of the mismatch interference observer is:
step 4: introducing a mismatching interference observation value into a system error state equation shown in the formula (5) to compensate, so as to obtain:
setting up using mismatched interference observationsCorrected state variable x 2 Is->From formula (24):
substituting formula (25) into a non-singular terminal sliding die surface shown in formula (6) to obtain:
as can be seen from equation (26), when the mismatch interference of the observer shown in equation (23) observes error e 1 When the total quantity is approximately equal to 0, the system can effectively inhibit the unmatched interference after the interference compensation is introduced, and the overall form of the controller is as follows;
in formula (27), β > 0, 1 < p/q < 2, l 1 > 0; the parameters λ, ρ are required to satisfy the constraints defined by the equations (8), (9), (11), (12), (13). When the interference quantity d is not matched 1 At 0, formula (27) will degenerate into the form determined by formulas (6) and (10). That is, when the system is not interfered, the design of the interference observer and the interference compensation quantity introduced by the interference observer in the non-singular terminal sliding mode surface do not influence the overall performance of the controller.
Step 5: in the control system block diagram, z k-1 、w k-1 The upper right symbol k-1 in (a) represents the corresponding variable calculated in the previous control period, and Δt is the control period. The calculation flow of the control algorithm in a single control period is as follows:
1. based on the output voltage u measured by the voltage sensor o Inductance current i measured by current sensor L And an expected value of output voltage U ref Calculating state variable x 1 、x 2 ；
x 1 ＝U ref -u o (28)
2. According to state variable x 1 、x 2 And the disturbance observer state variable z of the last cycle k-1 、Computing System mismatch interference observations +.>
3. According to state variable x 1 、x 2 And mismatch interference observationsCalculating a sliding mode variable s;
4. variable w calculated from sliding mode variable s and last control period k-1 Calculating a controller output u;
W k ＝W k-1 -ρsign(s)ΔT (33)
5. the controller output u is subjected to amplitude limiting and then sent to a PWM signal generator to generate PWM signals, and the PWM signals are amplified and isolated by a photoelectric coupler and then used for controlling a switching element VT.
The beneficial effects are that: compared with the prior Buck converter output voltage control and anti-interference technical scheme, the invention has the following technical effects:
(1) The continuous nonsingular terminal sliding mode control method of the Buck converter based on the supercoiled algorithm and the nonlinear interference observer can enable the output voltage of the Buck converter to track an upper reference signal in a limited time.
(2) The continuous nonsingular terminal sliding mode control method of the Buck converter based on the supercoiled algorithm and the nonlinear interference observer can effectively inhibit the mismatch interference of the Buck converter system.
Drawings
FIG. 1 is a diagram of an ideal circuit configuration of an asynchronous Buck converter;
FIG. 2 is a block diagram of a control system according to the present invention;
FIG. 3 shows the simulation comparison test results of the control method (NTSMC+ST+NO) and the PI controller according to the present invention, wherein the control is performed from top to bottomOutput voltage u of Buck converter o A change curve;
FIG. 4 shows the simulation comparison experiment results of the control method (NTSMC+ST+NO) and the PI controller according to the present invention, wherein the inductor current i is from top to bottom L State variable x 1 State variable x 2 A change curve;
FIG. 5 shows simulation results of the control method (NTSMC+ST+NO) according to the present invention, in which sliding mode variables s and interference observations are respectively from top to bottomA change curve;
FIG. 6 shows the semi-physical simulation experiment result of the control method (NTSMC+ST+NO) designed by the present invention under the condition of NO interference, wherein the output voltages u of the Buck converter are respectively from top to bottom o Slip-mode variable s, controller output u, inductor current i L A change curve;
FIG. 7 shows the results of semi-physical simulation experiments of the control method (NTSMC+ST+NO) designed by the present invention under the condition of the system having matching and non-matching interference, respectively, the output voltages u of the Buck converter from top to bottom o Slip-mode variable s, controller output u, inductor current i L A change curve;
Detailed Description
The present invention is further illustrated in the following drawings and detailed description, which are to be understood as being merely illustrative of the invention and not limiting the scope of the invention.
The ideal circuit structure diagram of the asynchronous Buck converter is shown in figure 1, wherein VT is a switching element, which can be GRT, IGBT, MOSFET and other devices, L is an inductor, E is a direct current power supply, R is an equivalent load, C is a filter capacitor, and VD is a freewheeling diode. A block diagram of a control system designed according to this invention is shown in FIG. 2, where z k-1 、w k-1 The upper right symbol k-1 in (a) represents the corresponding variable calculated in the previous control period, and Δt is the control period. The control algorithm in a single control period calculates the flow as：
1. Based on the output voltage u measured by the voltage sensor o Inductance current i measured by current sensor L And an expected value of output voltage U ref Calculating state variable x 1 、x 2 ；
x 1 ＝U ref -u o (35)
2. According to state variable x 1 、x 2 And the disturbance observer state variable z of the last cycle k-1 、Computing System mismatch interference observations +.>
3. According to state variable x 1 、x 2 And mismatch interference observationsCalculating a sliding mode variable s;
4. variable w calculated from sliding mode variable s and last control period k-1 Calculating a controller output u;
W k ＝W k-1 -ρsign(s)ΔT (40)
5. the controller output u is subjected to amplitude limiting and then sent to a PWM signal generator to generate PWM signals, and the PWM signals are amplified and isolated by a photoelectric coupler and then used for controlling a switching element VT.
In order to verify the effectiveness and superiority of the control method designed by the invention, a MatLab/Simulink simulation experiment is used for comparing the control method (NTSMC+ST+NO) designed by the invention with a traditional PI control method, and basic parameters of an experiment platform are as follows: the inductor is 0.005H, the capacitor is 0.001F, the load resistance is 10Ω, the DC power supply voltage is 1000V, the PWM control signal frequency is 15KHz, and the control period is 0.001s.
In order to ensure the fairness of comparison, the control energy required by the two methods is kept at the same level through parameter adjustment in experiments, and parameters of a nonsingular terminal sliding mode controller based on a supercoiled algorithm and a nonlinear interference observer are set as follows: p/q=55/49, β=900, k 2 ＝0.009、M＝3.8、l 1 =50; PI controller parameter is set to K p ＝2.5×10 -4 、K i ＝3.1×10 -6 。
The expected value of the output voltage is set to 750V, the load resistance is set to 7.5 omega and 12.5 omega at 0.2s and 0.4s respectively, and as known from the system error state equation (5), the nominal value of the load resistance is set to be R, and the actual value is set to beThe amount of matched and unmatched interference introduced by load interference in the system is as follows:
controller output u and Buck converter output voltage u o The curve is shown in fig. 3; inductor current i L System state variable x 1 、x 2 The curve is shown in fig. 4; sliding mode variable s and mismatch interference estimation valueThe curve is shown in fig. 5. The key data of the simulation experiment are shown in table 1.
TABLE 1 simulation contrast experiment data of the control method (NTSMC+ST+NO) and the PI controller designed by the invention
As can be seen from the data in fig. 3, 4 and table 1, the control method of the present invention has shorter adjustment time and better dynamic performance than the PI controller at the same level of control energy; meanwhile, the dynamic drop and recovery time when the system is interfered are greatly reduced, and the system has good interference suppression capability. As can be seen from fig. 4 and 5, after the system state moves to the sliding surface under the action of the supercoiled algorithm, the system state x moves on the sliding surface 1 、x 2 Can converge to zero along the slip form surface.
As an implementation scheme, a Chahua VSM025A voltage sensor and a Chahua CSM025AY-100 current sensor are respectively used for measuring the output voltage and the inductance current of the Buck converter, and the output voltage and the inductance current are output to an a/D sampling module of the dsace real-time controller for analog-to-digital conversion; a control algorithm is operated in a Power PC processor to obtain a control signal, and the control signal is output as a PWM signal with a variable fixed frequency duty ratio through a PWM module of a dSPACE real-time controller; the PWM signal is isolated and amplified by the photoelectric coupler and then used for driving the switching element to regulate the amplitude of the output voltage of the Buck converter.
In order to verify the feasibility of the control method designed by the invention, the control algorithm is verified on a semi-physical experiment platform, and the basic parameters of the experiment platform are as follows: the inductor is 0.005H, the capacitor is 0.001F, the load resistance is 50Ω, the DC power supply voltage is 20V, the PWM control signal frequency is 15KHz, and the control period is 0.001s. The controller parameters are set as follows: p/q=55/49, β=2000, k 2 ＝0.05、M＝3、l 1 ＝100。
Under the condition that the system has no external interference, the output voltage reference values are respectively set to be 5V, 10V,5V, a modification interval of about 20s, a Buck converter output voltage U o A slip-mode variable s, a control quantity u and an inductance current i L The transformation curve is shown in fig. 6:
the observation shows that under the action of the controller, the output voltage of the Buck converter can rapidly and accurately track the reference signal, and meanwhile, the system state moves to the sliding mode surface and then keeps moving on the sliding mode surface.
Consider the case where there is a load disturbance to the system, which introduces both matched and unmatched disturbances in the system. The resistance values of the load resistors are respectively set to be 50 omega, 10 omega and 90 omega, the modification interval is about 20s, and the output voltage U of the Buck converter o A slip-mode variable s, a control quantity u and an inductance current i L The transformation curve is shown in fig. 7:
the observation shows that when the resistance value of the load resistor deviates from the rated value, under the regulation action of the controller, the output voltage of the Buck converter has no obvious fluctuation, namely the control method designed by the invention can simultaneously realize the effective inhibition of the matching interference and the unmatched interference.
The invention has simple form and strong practicability, can ensure that the Buck converter system realizes the limited time stability of output voltage under the condition of unmatched interference, and has wider engineering application prospect.
The technical means disclosed by the scheme of the invention is not limited to the technical means disclosed by the embodiment, and also comprises the technical scheme formed by any combination of the technical features. It should be noted that modifications and adaptations to the invention may occur to one skilled in the art without departing from the principles of the present invention and are intended to be within the scope of the present invention.
Claims (5)
1. A continuous nonsingular terminal sliding mode control method of a Buck converter is characterized by comprising the following steps:
step 1: establishing a mathematical model by using a state space average method aiming at the Buck converter in a continuous mode of working and inductive current; and a system error state equation considering the system uncertainty and internal and external interference is given;
step 2: aiming at the system error state equation in the step 1, a nonsingular terminal sliding mode surface and a control law based on a supercoiled algorithm are designed, so that a sliding mode variable s can be converged to 0 in a limited time, and a system state variable x is formed 1 、x 2 The sliding mode surface can be converged to a balance point along the sliding mode surface in a limited time; i.e. the output voltage u of the Buck converter o Convergence to the desired value of the output voltage U for a limited time ref ；
Step 3: designing a nonlinear interference observer aiming at a system error state equation in the step 1, and estimating the system mismatch interference;
step 4: based on the unmatched interference observation value obtained by the nonlinear interference observer in the step 3, introducing interference compensation in the controller designed in the step 2, and realizing effective suppression of unmatched interference.
2. The continuous nonsingular terminal sliding mode control method of the Buck converter according to claim 1, wherein the Buck converter state space model in the step 1 is established as follows:
wherein μ=1 represents that the switching element VT is on, μ=0 represents that the switching element VT is off; u (u) o Outputting voltage for the Buck converter; i.e L Is an inductive current; u (U) in Is a direct current power supply voltage; c is the capacitance value; l is an inductance value; system state variable x 1 、x 2 The error values and the first derivatives thereof are respectively selected as output voltages, namely:
x 1 ＝U ref -u 。
when state variable x 1 When converging to 0, the output voltage u of the Buck converter o Will converge to the desired value of the output voltage U ref The method comprises the steps of carrying out a first treatment on the surface of the For state variable x 1 、x 2 Deriving and substituting the mathematical model of the Buck converter, and taking the uncertainty of the system and the internal and external interference into consideration, wherein the state equation of the system error is as follows:
where u is the controller output, d 1 (t) is a mismatch interference; d, d 2 And (t) is the matched interference.
3. The method for controlling the sliding mode of the continuous nonsingular terminal of the Buck converter according to claim 1, wherein the sliding mode surface of the nonsingular terminal in the step 2 is designed as follows:
wherein p and q are both odd numbers; the control law based on the supercoiled algorithm is designed as follows:
wherein the controller parameters lambda, p need to satisfy:
parameters C, K in the above m And K M The upper and lower bounds of the uncertainty of the system are respectively:
O＜K m ≤|γ(x，t)|≤K M
wherein:
4. the continuous nonsingular terminal sliding mode control method of Buck converter according to claim 1, wherein the nonlinear disturbance observer in the step 3 is designed as follows:
wherein l 1 To disturb the observer gain.
5. The method for continuous nonsingular terminal sliding mode control of Buck converter according to claim 1, wherein the overall form of the controller for introducing interference compensation in step 4 is:
wherein, beta is more than 0, p/q is more than 1 and less than 2, l 1 > 0; the parameters lambda, p need to meet the constraints in step 2.
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN117410953A (en) * | 2023-10-27 | 2024-01-16 | 陕西理工大学 | Design method of controller of bipolar direct-current micro-grid voltage balancer |
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| CN117410953A (en) * | 2023-10-27 | 2024-01-16 | 陕西理工大学 | Design method of controller of bipolar direct-current micro-grid voltage balancer |
| CN117410953B (en) * | 2023-10-27 | 2024-05-10 | 陕西理工大学 | Design method of controller of bipolar direct-current micro-grid voltage balancer |
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