CN111641337A - Robust control method and system of direct current buck converter and power converter - Google Patents
Robust control method and system of direct current buck converter and power converter Download PDFInfo
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- 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 discloses a robust control method and a robust control system for a direct current buck converter and the direct current buck power converter. The method comprises the following steps: s1, acquiring voltage at two ends of a capacitor of the converter and current flowing through an inductor of the converter; s2, respectively calculating error variable z according to the acquired voltage and current1And z2Value z at time k1(k) And z2(k) (ii) a S3, setting the duty ratio of the on-off control signal of the switching tube of the converter as an actual control variable u, acquiring the value u (k) of the actual control variable u at the moment k, and setting the duty ratio of the on-off control signal of the switching tube of the converter as u (k), and returning to S1. The control method can effectively solve the problem of bus voltage oscillation caused by load nonlinear change, enables the power supply voltage to tend to be stable, has small calculated amount and simple and understandable algorithm, realizes robust control by combining the first inequality and the second inequality with a counter-step method, and has small amplification to the items needing amplification and small output oscillation.
Description
Technical Field
The present invention relates to a control method of a dc power converter, and more particularly, to a robust control method and control system of a dc buck converter, and a dc buck power converter.
Background
A power electronic system typically includes a plurality of subsystems, each subsystem being provided with a power supply unit, such as during operation of a low earth orbit satellite, the power supply units of each subsystem typically drawing power from a mains power supply. Different subsystems may have different voltage requirements, and most of the subsystems need to perform voltage reduction processing on the dc power supply, and in an actual situation, loads carried by the subsystems change nonlinearly, and the change of the loads may cause fluctuation of the output of the dc voltage reduction converter, thereby causing damage to the system. In these power electronic systems, therefore, a stable and reliable voltage supply is essential for their safe operation, and a dc-dc switching power converter is used to adapt the supply voltage on the load side to its requirements. Buck converter has been widely used as a basic adjustable step-down DC power supply, and has also occupied an important position in micro-grid systems, such as the power supply of DC motors, various satellite loads and other electronic devices. In the above background, it is crucial to the safe operation of the power electronic system that the Buck converter output voltage is stabilized by using an appropriate control method.
Early dc buck converter control methods were mostly based on linear control methods of a linearization model, some of which papers proposed passive damping strategies, such as adding the necessary capacitors or resistors to design the LC filter, which are simple and effective, but they are limited by physical constraints and expensive. In addition, the damping is also proposed to be increased in the early stage so as to stabilize the feeder line converter, but the damping is only suitable for a small-signal model and cannot ensure the stability of the bus voltage under the condition of large signals. It is clear that the control performance of these control methods deteriorates under the condition that the load exhibits a non-linear load characteristic. From a practical point of view, the resistance characteristic on the load side is practically uncertain and non-linear, especially when the load resistance is affected by temperature, the power of the device varies and thus the impedance varies. Therefore, there is a strong need for efficient controllers that seek smaller steady state errors, lower overshoot, faster dynamic response, and milder sensitivity to noise.
Later, in order to ensure the stability of the bus voltage under the condition of large signal, the nonlinear control technology is mostly adopted in the prior art to solve the problem. In recent years, with the development of advanced control theory, a great number of researchers and scholars continue to use nonlinear dynamics methods to conduct more extensive research on power electronic related circuits. For example, a non-linear disturbance observer (NDO) is an effective method for online estimation of uncertainty disturbance of a non-linear system, and provides a very effective solution for disturbance suppression and uncertainty compensation, which is a key objective in controller design, some documents use an (NDO) online estimation method to solve the problem of constant power load control in a Boost converter, but the method is only suitable for control of a problem of estimation of unknown constants, for example, a power value of a constant power load in the document shows a certain value in a state space model, and is not suitable for a non-linear load control system. Also, as some documents solve the nonlinear load problem in Buck converters with robust control using a discrete online identification method, this method still requires the maximum limit of known load variation. As another example, some documents use an adaptive control method to solve the control problem in the Boost converter, but this method also needs to assume that the load resistance is an unknown constant value, and cannot be used in the nonlinear load control problem. Therefore, a new control method is needed to solve the problem of controlling the time-varying nonlinear load well under the condition that the load variation limit is unknown.
Disclosure of Invention
The invention aims to at least solve the technical problems in the prior art, and particularly innovatively provides a robust control method and a robust control system of a direct-current buck converter and the direct-current buck power converter.
In order to achieve the above object of the present invention, according to a first aspect of the present invention, there is providedA robust control method for a DC buck converter is provided, comprising: the following steps are repeatedly performed during the operation of the converter: step S1, obtaining the voltage across the capacitor of the converter and the current flowing through the inductor of the converter, and recording the voltage across the capacitor of the converter as the first state variable x1Noting the current through the inductor of the converter as a second state variable x2Setting the current time as k time, and making the first state variable x at k time1Has a value of x1(k) And a second state variable x2Has a value of x2(k) (ii) a Step S2, calculating a first error variable z1Value z at time k1(k)：
Calculating a second error variable z2Value z at time k2(k)：z2(k)＝x2(k) α (k), wherein,
representing a first state variable x1Let the virtual control variable α represent the second state variable x2α (k) denotes the second state variable x at the time k2A reference value of (d); step S3, setting the duty ratio of the on-off control signal of the switching tube of the converter as an actual control variable u, acquiring the value u (k) of the actual control variable u at the moment k, and setting the duty ratio of the on-off control signal of the switching tube of the converter as u (k), wherein u (k) is:
wherein,
l represents the inductance value of the inductance of the converter, E represents the supply voltage of the converter; c represents the capacitance value of the capacitor of the converter; k is a radical of2An adjustment parameter, k, representing the actual control variable u2>0；
Represents an upper conductance bound of the nonlinear load;
represents the derivative value of the time-varying function ξ (t) at the time k, ξ (k) represents the value of the time-varying function ξ (t) at the time k, ξ (t) satisfies
Representing an unknown but bounded constant, α (k) representing the state variable x at time k2A reference value of (d); return is made to step S1.
In a preferred embodiment of the present invention, the time-varying function ξ (t) is ξ (t) ═ Ae-λtWherein the time-varying function has a first coefficient A>0; second coefficient lambda of time-varying function>0。
In a preferred embodiment of the present invention, α (k) is obtained according to the following formula:
wherein e is1Denotes a set positive value constant, k1Adjustment parameter, k, representing virtual control variable α1>0；
For a first state variable x1Constant reference value of
The derivation is carried out by the derivation,
the value is 0.
In a preferred embodiment of the present invention, the α (k) calculation formula is constructed by:
step A, constructing a first Lyapunov function V1：
Step B, establishing a first inequality:
step C, based on the first inequality, making the first Lyapunov function V1Stable, virtual control variable α is designed to be:
In a preferred embodiment of the present invention, the obtaining u (k) calculation formula creating process includes:
step I, constructing a second Lyapunov function V2Comprises the following steps:
wherein z is2＝x2-α；
Step II, establishing a second inequality:
step III, based on the second inequality, making the second Lyapunov function V2And (5) stabilizing, and designing the actual control variable u as:
based on the above formula, obtain:
in order to achieve the above object, according to a second aspect of the present invention, there is provided a control system of a dc down-converter, comprising a voltage obtaining unit, a current obtaining unit, and a controller; the controller is respectively connected with the voltage acquisition unit and the current acquisition unit; the voltage acquisition unit detects voltages at two ends of a capacitor of the direct current buck converter; the current acquisition unit is used for detecting the current flowing through the inductor of the direct current buck converter; the controller outputs alternating switching signals to the on-off control end of a switching tube of the direct current buck converter; the controller executes the method of the invention to adjust the duty cycle of the switching signal.
In a preferred embodiment of the present invention, the controller includes a back-stepping robust control module and a PWM generator; the backstepping method robust control module executes the method to obtain the target duty ratio of the switching signal; the PWM generator acquires a target duty ratio and outputs a switching signal with the duty ratio of the target duty ratio to the on-off control end of the switching tube.
In order to achieve the above object, according to a third aspect of the present invention, there is provided a dc buck power converter, including a power supply, a switching tube, an inductor, a capacitor, and the control system of the present invention; the positive electrode of the power supply is connected with the source electrode of the switching tube, the drain electrode of the switching tube is connected with the first end of the inductor, the grid electrode of the switching tube is connected with the alternating switching signal output end of the control system, the second end of the inductor is connected with the first end of the capacitor, and the second end of the capacitor is connected with the negative electrode of the power supply; the control system obtains the current flowing through the inductor and the voltage at two ends of the capacitor, and adjusts the duty ratio of the switching signal output to the grid electrode of the switching tube.
In summary, due to the adoption of the above technical scheme, the control method, the control system and the dc buck power converter of the invention have the following beneficial effects:
1) compared with the traditional algorithm such as a PID algorithm, the control method can effectively solve the problem of bus voltage oscillation caused by nonlinear change of the load, so that the power supply voltage tends to be stable.
2) Although the convergence rate of many control methods is high, the calculation amount is large, so that the resource overhead consumed for realizing the control methods is large, and the practical application of the control methods is greatly limited. The control method designed by the invention only needs to continuously iterate the actual control variable u, so that the error is finally bounded in a small range, the calculated amount is small, and the algorithm is simple and easy to understand.
3) According to Lyapunov theory and derivation of Lyapunov function, controller oscillation can be restrained in an initial stage due to the existence of xi (t) function, steady-state error can be reduced along with the reduction of xi (t) function, and finally the error between actual voltage and target voltage reaches a relatively small value.
4) In Backstepping robust control (robust control for short), attention is paid to adjustment of system design parameters and selection of inequalities is ignored, most researchers adopt classical transformation such as Young inequality and the like to ensure that a transformed expression is not negative when inequality transformation is carried out on an unknown function with an undetermined upper bound known sign and time variation, and then a non-negative term is subtracted from a derivative of a Lyapunov function of the system to ensure that the derivative is negative to achieve the effect of robust control. However, the traditional inequality Young inequality amplifies terms needing amplification too much, and output oscillation of the controller is easily caused.
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FIG. 1 is a schematic diagram of a prior art DC buck power converter;
fig. 2 is a schematic diagram of a dc buck power converter circuit according to an embodiment of the invention.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.
In the description of the present invention, it is to be understood that the terms "longitudinal", "lateral", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", and the like, indicate orientations or positional relationships based on those shown in the drawings, and are used merely for convenience of description and for simplicity of description, and do not indicate or imply that the referenced devices or elements must have a particular orientation, be constructed in a particular orientation, and be operated, and thus, are not to be construed as limiting the present invention.
In the description of the present invention, unless otherwise specified and limited, it is to be noted that the terms "mounted," "connected," and "connected" are to be interpreted broadly, and may be, for example, a mechanical connection or an electrical connection, a communication between two elements, a direct connection, or an indirect connection via an intermediate medium, and specific meanings of the terms may be understood by those skilled in the art according to specific situations.
The invention discloses a robust control method of a direct current buck converter, which repeatedly executes the following steps during the working period of the converter: step S1, obtaining the voltage across the capacitor of the converter and the current flowing through the inductor of the converter, and recording the voltage across the capacitor of the converter as the first state variable x1Noting the current through the inductor of the converter as a second state variable x2Setting the current time as k time, and making the first state variable x at k time1Has a value of x1(k) And a second state variable x2Has a value of x2(k) (ii) a Step S2, calculating a first error variable z1Value z at time k1(k)：
Calculating a second error variable z2Value z at time k2(k)：z2(k)＝x2(k) α (k), wherein,
representing a first state variable x1Let the virtual control variable α represent the second state variable x2α (k) denotes the second state variable x at the time k2A reference value of (d); step S3, changeThe duty ratio of on-off control signals of a switch tube of the device is an actual control variable u, the value u (k) of the actual control variable u at the moment k is obtained, and the duty ratio of the on-off control signals of the switch tube of the converter is set to be u (k), wherein u (k) is:
wherein,
l represents the inductance value of the inductance of the converter, E represents the supply voltage of the converter; c represents the capacitance value of the capacitor of the converter; k is a radical of2An adjustment parameter, k, representing the actual control variable u2>0；
The method comprises the steps that the upper conductance bound of a nonlinear load is represented, the load has a size range under normal working conditions (namely abnormal conditions such as open circuit and short circuit), so that the conductance of the load also has a numerical range, and the range of the conductance of the load is determined after the load is selected;
represents the derivative value of the time-varying function ξ (t) at the time k, ξ (k) represents the value of the time-varying function ξ (t) at the time k, ξ (t) satisfies
Representing an unknown but bounded constant, α (k) representing the state variable x at time k2A reference value of (d); return is made to step S1.
In the present embodiment, a first state variable x is set1And a second state variable x2Value x at time 01(0) And x2(0) Are all 0.
In this embodiment, in the prior art, the circuit structure of the dc buck power converter is generally as shown in fig. 1,the direct current power supply comprises a direct current power supply E, a switching tube S, a diode D, an inductor L and a capacitor C, wherein the positive output end of the power supply E is connected with the source electrode of the switching tube S, the grid electrode of the switching tube S is connected with the square wave signal (such as PWM) output end of a controller, the drain electrode of the switching tube S is respectively connected with the cathode of the diode D and the first end of the inductor L, the second end of the inductor L is connected with the first end of the capacitor C, and the second end of the capacitor C is connected with the negative output end of the power supply E. The first terminal of the capacitor C is the output terminal of the converter and can be connected with one or more loads R1、……、RnAnd the like.
In the embodiment, through a continuous iteration process, the on-off control signal duty ratio u (actual control variable) of the switching tube of the converter is adjusted, and finally the error z is caused1，z2And the method is bounded, so that robust control is realized under the condition that each subsystem has nonlinear load.
In the present embodiment, the time-varying function ξ (t) is preferably ξ (t) ═ Ae-λtWherein the time-varying function has a first coefficient A>0; second coefficient lambda of time-varying function>0。
In this embodiment, in order to ensure that the converter supplying power to each subsystem (e.g., subsystem of low earth orbit satellite system) can output stable voltage under the nonlinear variation of the load, the state space model of the converter is first converted into the standard form of the standard back-stepping method; secondly, the model takes the error between the state quantity and the reference quantity as a control object; then, a robust control algorithm is used according to the novel first inequality relation and the novel second inequality relation to ensure the stability of the system; and finally, ensuring the global asymptotic stability by a step-by-step back-stepping algorithm.
In a preferred embodiment, α (k) is obtained according to the following formula:
wherein e is1The positive value constant representing the setting can be selected according to experience; k is a radical of1Adjustment parameter, k, representing virtual control variable α1>0, can be selected according to experience;
for a first state variable x1Constant reference value of
The derivation is carried out by the derivation,
the value is 0.
In a preferred embodiment, the α (k) calculation formula is constructed by:
step A, constructing a first Lyapunov function V1：
Step B, establishing a first inequality:
step C, based on the first inequality, making the first Lyapunov function V1Stable, virtual control variable α is designed to be:
based on the above formula, obtain the formula
In this embodiment, preferably, the obtaining u (k) calculation formula creating process includes: step I, constructing a second Lyapunov function V2Comprises the following steps:
wherein z is2＝x2α, step II, establishing a second inequality:
step III, based on the second inequality, making the second Lyapunov function V2Stabilizing, designing the actual control variable uComprises the following steps:
based on the above formula, obtain:
in the present embodiment, based on the back-stepping method, the system stability is ensured by using the robust control algorithm based on the first inequality relationship and the second inequality relationship.
In the present embodiment, the detailed procedure for solving α (k) and u (k) is as follows:
under continuous signals, a typical dc BUCK power converter (e.g., BUCK) system with a non-linear load is modeled mathematically as follows:
since the design goal is to enforce the state variable x1，x2And gradually track its required value
And α, a new set of coordinate variables z is introduced1，z2：
Constructing a first Lyapunov function V1Comprises the following steps:
for the first Lyapunov function V1The derivation yields:
the following novel first inequality is established:
in order to minimize the steady-state error, the time-varying function ξ (t) is designed to satisfy the following condition:
ξ (t) function is Ae-λt，A>0，λ>0. To stabilize the Lyapunov function, the virtual control variables α are:
also, where k1The following condition k is satisfied for the design parameters1>0. Substituting (7) into (4) and arranging according to (5) to obtain:
constructing a second Lyapunov function V2Comprises the following steps:
to V2And obtaining by derivation:
similar to the above equation (4), the following inequality exists in equation (10):
to stabilize the designed Lyapunov function, u is designed to:
likewise, wherein k2The following condition k is satisfied for the design parameters2>0. Substituting u into (10) and obtaining according to (11):
to ensure global stability of the system, the overall Lyapunov function is constructed as:
V3＝V1+V2(14)
to V3The following equation is established by deriving the derivatives from equations (8) and (13):
to achieve the Lyapunov stability condition, a parameter k satisfying the following condition is selected1，k2：
Condition 1: k is a radical of1>0，k2>0. Due to Ae-λt，A>0，λ>0, 0 within the interval t → ∞<Ae-λt<A, then condition 2 can be obtained:
according to the conditions 1 and 2, the conclusion 1 is as follows:
conclusion 1: z is a radical of1、z2Is bounded. Known by the Lasalel theorem z1、z2For global consistent bounding, x is known from coordinate transformation1Bounded, α is about z1，x1，Ae-λtAccording to Ae in α-λt，A>0，λ>The functional property of 0 is:
from z1And x1The bounding property of (2) can be proved to be α bounded according to the clip approximation theorem, and x is known according to the coordinate transformation2There is a limit, because:
according to z1And x1Is bounded can be obtained
The boundedness of (A) can be proved by the same theory
Is bounded, so all variables of the system are bounded. The specific derivation implementation process and the proof process of the algorithm can deduce that the control method can stabilize the actual voltage of each subsystem of the low earth orbit satellite to be close to the target voltage under the condition of nonlinear load.
In the embodiment, aiming at the problem of voltage fluctuation caused by nonlinear change of loads of various subsystems of a low-earth orbit satellite, a novel inequality is applied to a Lyapunov function, inequality transformation is carried out on terms needing amplification, and then based on the thought of a backstepping method, under the condition that the upper bound of the load conductance is known, a circuit system at the upper bound of the load conductance is stabilized through a control algorithm, so that the voltage fluctuation caused by the nonlinear change of the load resistance is reduced, the actual voltage is stabilized near a reference voltage value, and the purpose of robust control is achieved. According to the Lyapunov theory, controller oscillation can be restrained in the initial stage due to the function xi (t), and according to the formula (15) and the Lyapunov theory, the steady-state error can be reduced along with the reduction of the function xi (t), and finally the error between the actual voltage and the target voltage reaches a relatively small value. The algorithm also has the advantages of robustness, small-amplitude oscillation of the controller and simplicity and easiness in understanding.
In an application scenario of the present invention, a u iteration value is adaptively obtained, and the obtaining process specifically includes the following steps:
a) initializing u (k), L, C, E, iL(k)，VC(k)，x1(k)，x2(k)，
And α (k);
b) computing
z2(k)＝x2(k)-α(k)；
c) Computing
d) Obtaining u (k):
the invention also discloses a control system of the direct current buck converter, as shown in fig. 2, the system comprises a voltage obtaining unit, a current obtaining unit and a controller; the controller is respectively connected with the voltage acquisition unit and the current acquisition unit; the voltage acquisition unit detects the voltage at two ends of a capacitor of the direct current buck converter; the current acquisition unit is used for detecting the current flowing through the inductor of the direct current buck converter; the controller outputs alternating switching signals to the on-off control end of a switching tube of the direct current buck converter; the controller executes the control method to adjust the duty ratio of the switching signal.
In a preferred embodiment, as shown in fig. 2, the controller includes a back-step robust control module and a PWM generator; the backstepping method robust control module executes the control method to obtain the target duty ratio of the switching signal; the PWM generator acquires a target duty ratio and outputs a switching signal with the duty ratio as the target duty ratio to the on-off control end of the switching tube.
The invention also discloses a direct current buck power converter, which comprises a power supply, a switching tube, an inductor, a capacitor and a control system of the invention, as shown in figure 2; the positive pole of the power supply is connected with the source electrode of the switching tube, the drain electrode of the switching tube is connected with the first end of the inductor, the grid electrode of the switching tube is connected with the alternating switching signal output end of the control system, the second end of the inductor is connected with the first end of the capacitor, and the second end of the capacitor is connected with the negative pole of the power supply; the control system obtains the current flowing through the inductor and the voltage at two ends of the capacitor, and adjusts the duty ratio of the switching signal output to the grid electrode of the switching tube.
In the description herein, references to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
While embodiments of the invention have been shown and described, it will be understood by those of ordinary skill in the art that: various changes, modifications, substitutions and alterations can be made to the embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.
Claims (8)
1. A robust control method for a dc buck converter, characterized by repeatedly performing the following steps during operation of the converter:
step S1, obtaining the voltage across the capacitor of the converter and the current flowing through the inductor of the converter, and recording the voltage across the capacitor of the converter as the first state variable x1Noting the current through the inductor of the converter as a second state variable x2Setting the current time as k time, and making the first state variable x at k time1Has a value of x1(k) And a second state variable x2Has a value of x2(k)；
Step S2, calculating a first error variable z1Value z at time k1(k)：
Calculating a second error variable z2Value z at time k2(k)：z2(k)＝x2(k) α (k), wherein,
representing a first state variable x1Let the virtual control variable α represent the second state variable x2α (k) denotes the second state variable x at the time k2A reference value of (d);
step S3, setting the duty ratio of the on-off control signal of the switching tube of the converter as an actual control variable u, acquiring the value u (k) of the actual control variable u at the moment k, and setting the duty ratio of the on-off control signal of the switching tube of the converter as u (k), wherein u (k) is:
wherein,
l represents the inductance value of the inductance of the converter, E represents the supply voltage of the converter; c represents the capacitance value of the capacitor of the converter; k is a radical of2An adjustment parameter, k, representing the actual control variable u2>0；
Represents an upper conductance bound of the nonlinear load;
represents the derivative value of the time-varying function ξ (t) at the time k, ξ (k) represents the value of the time-varying function ξ (t) at the time k, ξ (t) satisfies
Representing an unknown but bounded constant, α (k) representing the state variable x at time k2A reference value of (d);
return is made to step S1.
2. A robust control method for a dc buck converter as claimed in claim 1, wherein said time varying function ξ (t) is:
ξ(t)＝Ae-λtwherein the time-varying function has a first coefficient A>0; second coefficient lambda of time-varying function>0。
3. The robust control method of a dc buck converter according to claim 1, wherein α (k) is obtained according to the following equation:
wherein e is1Denotes a set positive value constant, k1Adjustment parameter, k, representing virtual control variable α1>0；
For a first state variable x1Constant reference value of
The derivation is carried out by the derivation,
the value is 0.
4. The robust control method of a dc buck converter according to claim 3, wherein the α (k) calculation formula is constructed by:
step A, constructing a first Lyapunov function V1：
Step B, establishing a first inequality:
step C, based on the first inequality, making the first Lyapunov function V1Stable, virtual control variable α is designed to be:
based on the above formula, obtain the formula
5. The robust control method of a dc buck converter according to claim 1, wherein obtaining u (k) calculation formula creation process includes:
step I, constructing a second Lyapunov function V2Comprises the following steps:
wherein z is2＝x2-α；
Step II, establishing a second inequality:
step III, based on the second inequality, making the second Lyapunov function V2And (5) stabilizing, and designing the actual control variable u as:
based on the above formula, obtain:
6. a control system of a DC buck converter is characterized by comprising a voltage acquisition unit, a current acquisition unit and a controller;
the controller is respectively connected with the voltage acquisition unit and the current acquisition unit; the voltage acquisition unit detects voltages at two ends of a capacitor of the direct current buck converter; the current acquisition unit is used for detecting the current flowing through the inductor of the direct current buck converter; the controller outputs alternating switching signals to the on-off control end of a switching tube of the direct current buck converter;
the controller performs the method of any of claims 1-5 to adjust the duty cycle of the switching signal.
7. The control system of a dc buck converter according to claim 6, wherein the controller includes a back-step robust control module and a PWM generator;
the backstepping robust control module executes the method of one of claims 1 to 5 to obtain a target duty cycle of the switching signal;
the PWM generator acquires a target duty ratio and outputs a switching signal with the duty ratio of the target duty ratio to the on-off control end of the switching tube.
8. A dc buck power converter comprising a power supply, a switching transistor, an inductor, a capacitor, and the control system of claim 6 or 7;
the positive electrode of the power supply is connected with the source electrode of the switching tube, the drain electrode of the switching tube is connected with the first end of the inductor, the grid electrode of the switching tube is connected with the alternating switching signal output end of the control system, the second end of the inductor is connected with the first end of the capacitor, and the second end of the capacitor is connected with the negative electrode of the power supply;
the control system obtains the current flowing through the inductor and the voltage at two ends of the capacitor, and adjusts the duty ratio of the switching signal output to the grid electrode of the switching tube.
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