A band observer limited sliding mode control method for direct-direct converter

Abstract

The application discloses a kind of band observer limited sliding mode control methods for direct-direct converter, it includes including introducing nonlinear conversion function to the mathematical model of direct-direct converter is restructured, according to the model of restructured direct-direct converter, the sliding mode controller of direct-direct converter is designed to control, the state variable and disturbance variable of direct-direct converter are designed to expand state observer, the state variable and disturbance variable of direct-direct converter are observed by expanding state observer, and the observation value of disturbance variable is introduced into sliding mode controller by feedforward compensation, to adjust the output of sliding mode controller.The application estimates and compensates the high-frequency disturbance and external disturbance unknown to system in real time by designing expanding state observer, reduces switching gain, reduces chattering, enhances the adaptive capacity of sliding mode controller to uncertain disturbance, to improve the robustness and control performance of system.

Description

Technical Field

[0001] This invention belongs to the field of power electronics technology, and specifically relates to a control method for DC-DC converters. Background Technology

[0002] In recent years, with the advancement of electronic technology, the design of DC-DC converters has become more efficient and flexible. Boost converters have received particular attention because they can achieve high-voltage boosting through simple circuits, and their output voltage can be easily adjusted. However, Boost converters in practical engineering are susceptible to various disturbances, including model errors, measurement errors, external interference, and unconsidered variables (such as inductor resistance and switching transistor on-resistance). Under various uncertainties, the system model will change, affecting controller performance and necessitating model updates and controller improvements. The nonlinear control properties of sliding mode control are naturally applicable to such DC-DC converters, thus attracting increasing attention. In traditional sliding mode control, increasing the switching gain often eliminates the influence of uncertainties and improves dynamic performance; however, as the switching gain increases, chattering becomes more severe. Therefore, a control method that can both eliminate the impact of uncertainties on controller performance and reduce chattering is urgently needed.

[0003] Currently, in order to solve the above problems, many academic papers and patents have been published and proposed corresponding solutions, such as:

[0004] 1. In patent application number 202210357931.1, entitled "A Sliding Mode Control Method for Multimodal Boost Converter Circuits Based on Genetic Algorithms," Qi Wenhai et al. constructed an effective sliding mode control strategy using genetic algorithms, enabling the sliding mode dynamics to be driven to the ideal minimum sliding region within a finite time. Simultaneously, it comprehensively considered the influence of parameter uncertainty, multimodal characteristics, and nonlinearity on the multimodal Boost converter circuit system, resulting in an accurate model that better matches the actual operating scenarios of the system and has a wide range of applications. However, the model established by this method is only applicable to multimodal Boost converter circuits and does not consider measurement errors or errors caused by variables.

[0005] 2. In the article entitled “Voltage and Current Double Closed-loop Terminal Sliding Mode Control of Buck Converters”, the authors WANG YM et al. proposed a voltage and current double closed-loop terminal sliding mode control method based on Buck circuit, which improved the overall performance of the system. However, only simulation results were given, and the design was relatively complex without experimental verification.

[0006] 3. Junxiao Wang et al. published “Finite-time disturbance observer based non-singular terminal sliding-mode control for pulse width modulation-based DC–DCbuck converters with mismatched load disturbances”, IET Power Electronics, 2016, 9(09): 1995-2002. They eliminated the unconventional characteristics of the system by combining a finite-time disturbance observer and a sliding-mode control method. However, in the design process, they only considered the impact of load disturbances on the system, and did not fully analyze the impact of input voltage fluctuations and perturbations of internal circuit parameters on the output voltage. Summary of the Invention

[0007] Considering that DC-DC converters in practical engineering are subject to various disturbances, and that increasing the switching gain in traditional sliding mode control often exacerbates chattering problems, the purpose of this invention is to propose an observer-restricted sliding mode control method for DC-DC converters, enabling the system to achieve stable and reliable operation when encountering large disturbances.

[0008] The present invention provides a constrained sliding mode control method with observer for a direct-to-direct-current converter, comprising the following steps:

[0009] 1) Introduce a nonlinear conversion function to reconstruct the mathematical model of the C / C converter;

[0010] 2) Based on the reconstructed mathematical model of the DC-DC converter, design a sliding mode controller to control the DC-DC converter;

[0011] 3) Design an extended state observer for the state variables and disturbance variables of the DC-DC converter;

[0012] 4) The state variables and disturbance variables of the DC-DC converter are observed by an extended state observer, and the observed values ​​of the disturbance variables are introduced into the sliding mode controller through feedforward compensation to adjust the output of the sliding mode controller.

[0013] Furthermore, the direct-to-direct-transformer mentioned in step 1) is a Boost converter, and the mathematical model of the reconstructed Boost converter is:

[0014]

[0015] In the formula, and It is the reconstructed state variable, v mIt is the measured value of the input voltage v of the Boost converter, i om The output current i of the Boost converter o The measured values; u is the duty cycle, d1 and d2 are interference variables, C and L are the nominal values ​​of the capacitor and inductor in the Boost converter, respectively; I min and I max The inductor current i in the Boost converter is respectively L The minimum and maximum allowable values, V max and V min The output voltage v in the Boost converter is respectively o The maximum and minimum allowable values ​​are given by x1 and x2, which are constrained state variables; η1 is the constrained transition variable corresponding to the constrained state variable x1, where x1∈R and I min <x1<I max η2 is the constrained constraint transformation variable corresponding to the constrained state variable x2, x2∈R and V min <x2<V max The introduced nonlinear transformation function is as follows:

[0016]

[0017] Furthermore, the sliding mode controller designed in step 2) is as follows:

[0018]

[0019] Where, m1=LI1(1-tanh 2 η1), I1=I max -I min ,

[0020] m2=CV1(1-tanh 2 η2), V1=V max -V min ,

[0021] α1=-ks-εsgn(s), where s is the nonlinear sliding surface, s=e1+ce2, c is the design constant, e1 and e2 are error variables, k is the design constant, and ε is the approach rate;

[0022] x2 * It is the reference value for the constrained state variable x2. is i o The first derivative, It is the first derivative of v;

[0023] α3=2vm2+2m2d1-2cm1i o+2cm1d2;

[0024] α4=-m2(V1 tanhη2+V2)+cm1(I1 tanhη1+I2), V2=V max +V min .

[0025] Furthermore, in step 3), designing the extended state observer includes:

[0026] Step S1: Assume that the disturbance variables d1 and d2 are first-order continuous and differentiable, and their derivatives are bounded, satisfying the following:

[0027]

[0028] Where M and N are positive constants, and The derivatives of the interference variables d1 and d2;

[0029] Step S2, assume the observation error vector ζ is:

[0030]

[0031]

[0032]

[0033] in ε1 and ε2 are the observed values ​​of variables x1, x2, d1, and d2, respectively, and ε1 and ε2 are positive proportional gains greater than 1;

[0034] Step S3, ζ i The derivative is:

[0035] Subscript i = 1, 2;

[0036] Where, ε i A is a positive proportional gain greater than 1; i and B i It is the system matrix, set as follows:

[0037]

[0038] Where, α 11 and α 12 α 21 and α 22 These are the observer gains, and they both satisfy the Hurwitz equation:

[0039] h1(s)=s 2 +α 11 s+α 12

[0040] h2(s)=s 2 +α 21 s+α 22 ;

[0041] Step S4, according to the formula:

[0042]

[0043] and in step S3 ζ i The derivative expression yields the following extended state observer:

[0044]

[0045]

[0046] Among them, v om For the output voltage v o The measured value, The measured value of inductor current i Lm The first derivative, and Observed values The first derivative.

[0047] The beneficial effects of this invention are:

[0048] 1. The present invention provides a restricted sliding mode control method with an observer for DC-DC converters. To address the problem that Boost converters may be affected by various disturbances in practical engineering, an extended state observer is designed to estimate and compensate for unknown high-frequency disturbances and external interferences in real time, reduce switching gain, reduce chattering, and enhance the adaptability of the sliding mode controller to uncertain disturbances, thereby improving the robustness and control performance of the system.

[0049] 2. The present invention provides a restrictive sliding mode control method with observer for DC-DC converters. By designing nonlinear restricted functions to model the Boost converter, the state variable (input current / output voltage) constraint problem of the Boost converter is transformed into a boundedness problem of nonlinear restricted functions. This solves the input current and output voltage constraint problems of the system and enables fast response for resistive loads and constant power loads (CPL), further ensuring the global stability and robustness of the system. Attached Figure Description

[0050] Figure 1 This is a flowchart of an ESO-based sliding mode control method applicable to Boost converters. The figure shows the structure of a typical Boost converter, which includes an inductor L, a switch S, a diode T, and a capacitor C.

[0051] Figure 2The Boost converter port has a CPL, and the CPL power P CPL In a randomly changing state, the added disturbance of the filter inductor's internal resistance is d1 = -0.1 × i L Observations at time and CPL power P CPL Output voltage v o Input current i L Waveform diagram.

[0052] Figure 3 To add a step CPL to the Boost converter port, add a filter capacitor with an internal resistance of r. C =0.05Ω, power value P CPL The CPL power P varies sequentially with power levels of 300W, 1200W, 2100W, 3000W, 2100W, 1200W, and 300W, at 0.05s intervals. CPL Observed values and Output voltage v o Input current i L Waveform diagram.

[0053] Figure 4 For the system at CPL power P CPL When the power is 2000W, the input inductor current i L With measurement error Δi L CPL power P at that time CPL Observed values and Output voltage v o Input current i L Waveform diagram.

[0054] Figure 5 For a Boost converter with CPL and a random disturbance d1 injected into the source side (d1 replaces the set of factors affecting the source-side model error), the disturbance d1 and the observed values ​​are equivalent to a random DC voltage source. Output voltage v o Input current i L Waveform diagram.

[0055] Figure 6 For a Boost converter with CPL and a random disturbance d2 injected into the load side (d2 replacing the ensemble factor of the load-side model error), the disturbance d2 and the observed values ​​are equivalent to a random current source. Output voltage v o Input current i L Waveform diagram.

[0056] Figure 7The perturbation d1 and the observed values ​​when a Boost converter with a CPL is simultaneously injected with random perturbations d1 and d2 (characterized by voltage and current sources, respectively) are given. Perturbation d2 and observed values Output voltage v o Input current i L Waveform diagram. Detailed Implementation

[0057] The present invention will be further described below with reference to the accompanying drawings and embodiments, but the present invention is not limited to the embodiments.

[0058] The observer-restricted sliding mode control method for a direct-to-direct-current converter in this embodiment includes the following steps:

[0059] 1) Introduce a nonlinear conversion function to reconstruct the mathematical model of the C / C converter.

[0060] Taking the direct-to-direct converter, specifically the Boost converter, as an example, in Figure 1 The paper presents the typical structure of a Boost converter. The state-space model of an ideal Boost converter is as follows:

[0061]

[0062] Among them, i L It is the inductor current, i o It is the output current, v o V is the output voltage, v is the input voltage, and u is the duty cycle.

[0063] Taking into account the influence of uncertainties, the above formula can be expressed as:

[0064]

[0065] The above equation can be simplified to:

[0066]

[0067] in,

[0068]

[0069] Where L and C are the nominal values ​​of inductor L and capacitor C in the Boost converter, respectively; v m and i Lm These are the input voltage v and inductor current i in the Boost converter. L The measured value; v om and i om They are v o and i o The measured values; Δv and Δi Lm They are v and i respectivelyLm Uncertain noise; Δv o and Δi o They are v o and i o Uncertain noise; ΔL and ΔC are the uncertain variables of inductance L and capacitance C, respectively; ε1 and ε2 are the effects of physical quantities not considered in the system modeling (such as the internal resistance of inductance and capacitance); d1 and d2 are disturbance variables, which include external disturbances, model errors, parameter changes and measurement errors.

[0070] Introducing a nonlinear transformation function:

[0071]

[0072] Among them, I min and I max The inductor current i in the Boost converter is respectively L The minimum and maximum allowable values, V max and V min The output voltage v in the Boost converter is respectively o The maximum and minimum allowable values, x1 and x2 are constrained state variables, x1∈R and I min <x1<I max x2∈R and V min <x2<V max η1 is the constrained constraint transformation variable corresponding to the constrained state variable x1, and η2 is the constrained constraint transformation variable corresponding to the constrained state variable x2.

[0073] The mathematical model for reconstructing the Boost converter is as follows:

[0074]

[0075] In the formula, and It is the reconstructed state variable, v m It is the measured value of the input voltage v of the Boost converter, i om The output current i of the Boost converter o The measured value; u is the duty cycle.

[0076] 2) Based on the reconstructed mathematical model of the DC-DC converter, design the sliding mode controller for controlling the DC-DC converter as follows:

[0077]

[0078] Where, m1=LI1(1-tanh 2 η1), I1=I max -I min ,

[0079] m2=CV1(1-tanh 2 η2), V1=V max -V min ,

[0080] α1=-ks-εsgn(s), where s is the nonlinear sliding surface, s=e1+ce2, c is the design constant, e1 and e2 are error variables, k is the design constant, and ε is the approach rate;

[0081] x2 * It is the reference value for the constrained state variable x2. is i o The first derivative, It is the first derivative of v;

[0082] α3=2vm2+2m2d1-2cm1i o +2cm1d2;

[0083] α4=-m2(V1 tanhη2+V2)+cm1(I1 tanhη1+I2), V2=V max +V min .

[0084] Depend on Figure 1 As shown in the sliding mode control method flowchart, the output of the sliding mode controller serves as the input of the pulse width modulator. The pulse signal modulated by the pulse width modulator is output to the switching transistor of the Boost converter to control the switching transistor's on / off state.

[0085] As can be seen from the reconstructed mathematical model of the Boost converter and the above α3 expression, to achieve precise control of the Boost converter, it is necessary to accurately obtain the precise values ​​of the disturbance variables d1 and d2 and perform real-time compensation in order to improve the robustness and stability of the system.

[0086] 3) Since disturbance variables d1 and d2 are usually not directly measurable, this step designs an extended state observer to monitor the state and disturbance variables in real time. The design of the extended state observer includes:

[0087] Step S1: Assume that the disturbance variables d1 and d2 are first-order continuous and differentiable, and their derivatives are bounded, satisfying the following:

[0088]

[0089] Where M and N are positive constants, and Let be the derivatives of the disturbance variables d1 and d2.

[0090] The above assumptions are prerequisites for designing an ESO, and these assumptions are generally satisfied in practical Boost converter systems. The reasons are as follows:

[0091] Parasitic resistance in a circuit introduces passivity, and passive components consume energy. Examples include inductors, capacitors, resistors, power supply internal resistance, and semiconductor resistors.

[0092] The input power supply has limited capacity. Due to the limited voltage and current, the output power is also limited.

[0093] Inductors have a saturation limit. All inductors have a saturation current; beyond this saturation current, the inductance will decrease sharply, and its current handling capacity will be reduced.

[0094] Step S2: Assume the observation error vector is ζ = [ζ1, ζ1] T .

[0095] in:

[0096]

[0097]

[0098] in ε1 and ε2 are the observed values ​​of variables x1, x2, d1, and d2, respectively, and ε1 and ε2 are positive proportional gains greater than 1.

[0099] Step S3: Utilize ESO technology, ζ i The derivative of (i = 1, 2) can be described as:

[0100]

[0101] Where, ε i A is a positive proportional gain greater than 1; i and B i It is the system matrix, set as follows:

[0102]

[0103] Where, α 11 α 12 α 21 and α 22 These are the observer gains, and they both satisfy the Hurwitz equation:

[0104] h1(s)=s 2 +α 11 s+α 12

[0105] h2(s)=s 2 +α 21 s+α 22 .

[0106] Step S4: Based on the expression for the Boost converter under interference conditions and the above ζ i The derivative expression for (i = 1, 2) yields the following extended state observer:

[0107]

[0108]

[0109] in, The measured value of inductor current i Lm The first derivative, and Observed values The first derivative.

[0110] Based on the ESO method, it can be known that when α 11 α 12 α 21 and α 22 When the error is large enough, the perturbation estimation error will converge to 0.

[0111] 4) The state variables and disturbance variables of the DC-DC converter are observed by an extended state observer, and the observed values ​​of the disturbance variables are introduced into the sliding mode controller through feedforward compensation to adjust the output of the sliding mode controller.

[0112] The stability of the extended state observer proposed in this embodiment is then demonstrated:

[0113] Taking matrix A as an example: According to Lyapunov's stability theorem, when the system matrix A is a Hurwitz matrix, there must exist a positive definite matrix P that satisfies:

[0114] PA+A T P = -I

[0115] Here, matrix I is the identity matrix.

[0116] Define the Lyapunov function of the observer as:

[0117] V(ζ)=ζ T Pζ

[0118] In the combined step S3, ζ i The derivative expression for (i = 1, 2) and the observations in step S4 The expression, differentiated with respect to V(ζ), yields:

[0119]

[0120] in, The second derivative of d1, λ1 is P T The largest eigenvalue of P.

[0121] From the above formula, we can see that:

[0122]

[0123] From the above two equations, we can obtain:

[0124]

[0125]

[0126] Define Ω = {ζ|ζ∈R} 3 If V(ζ)≤δ1}, where δ1 is an arbitrarily small positive constant, then we can choose a sufficiently large ε1 to satisfy:

[0127]

[0128]

[0129] definition For any ζ∈C u For all Ω, V(ζ) > δ1. Since ε1 and δ1 are negatively correlated, when M, λ1, and L remain constant, an increase in ε1 leads to a decrease in δ1. Therefore, ε1 can be appropriately amplified to make δ1 almost equal to zero, which means that Ω can be infinitesimally small, and thus ζ in Ω can be adjusted to be as small as possible. u If Ω can be infinite, then the following always holds:

[0130]

[0131] According to Lyapunov's stability theory and the above equation, the designed estimator is asymptotically stable. Furthermore, as V(ζ) approaches ∞, ||η|| approaches 0, therefore the observation error approaches 0, and the closed-loop system is globally stable.

[0132] The observer-restricted sliding mode control method for direct-to-direct converters described in this embodiment is then verified through simulation:

[0133] Simulation Verification 1: Boost Converter under various uncertain disturbances, considering a constant power load (CPL) at the Boost converter port, setting the initial state i... L (0) = 0.001A, v o (0) = 270V, which satisfies the initial conditions for restricted control. Set the CPL power P. CPL In a randomly changing state, the added disturbance of the filter inductor's internal resistance is d1 = -0.1 × i L Output voltage reference value v orefThe voltage is 270V, the converter input voltage v is 120V, and the switching frequency f is... s The frequency is 100kHz, the inductance L is 1mH, the capacitance C is 0.47mF, and the adaptive sliding mode coefficients 1, 2, and 3 (c,k,ε) are 5, 1×10⁻⁶ ... 4 0.1, Input current lower limit and upper limit threshold I min I max 0A, 26A, lower and upper threshold voltages V respectively min V max 250V, 280V respectively, observer 1 gain 1 and 2 (α) 11 ,α 12 ) are 1×10 4 and 1×10 10 Observer 2 gain 1 and 2 (α) 21 ,α 22 ) are 1×10 4 and 1×10 10 Power range P CPL The power rating is 300-3000W. Figure 2 CPL power P CPL In a randomly changing state, the added disturbance of the filter inductor's internal resistance is d1 = -0.1 × i L Observations at time and CPL power P CPL Output voltage v o Input current i L Waveform diagram.

[0134] from Figure 2 As can be seen from (a), observer 1 can observe system disturbances, combined with Figure 2 (d) It can be seen that the observed values The result is equal to d1, indicating that observer 1 is correctly designed and has good tracking performance. Figure 2 (b) shows P CPL With P CPL The change in voltage v indicates the change in the system output voltage. o It consistently maintains a voltage around 270V, with fluctuations within the range of [-0.15, +15], exhibiting rapid response. System state v o and i L All are within the restricted range.

[0135] Simulation Verification 2: The difference from Simulation Verification 1 is that the CPL power P... CPL When the random change state is changed to a step CPL, the power value P CPLThe power output is changed sequentially from 300W, 1200W, 2100W, 3000W, 2100W, 1200W, and 300W, with an interval of 0.05s. The disturbance caused by adding a filter inductor is replaced by adding a filter capacitor with an internal resistance of r. C =0.05Ω. Figure 3 To add a step CPL to the Boost converter port, add a filter capacitor with an internal resistance of r. C =0.05Ω, power value P CPL The CPL power P varies sequentially with power levels of 300W, 1200W, 2100W, 3000W, 2100W, 1200W, and 300W, at 0.05s intervals. CPL Observed values and Output voltage v o Input current i L Waveform diagram.

[0136] from Figure 3 The observations of observer 1 can be seen in (b). The value is always 0. Observer 2's observation is non-zero at each step transition, which matches the characteristics of capacitor internal resistance, indicating a correct design. From Figure 3 (c) and 3(d) show that the system still operates within the limited range under the condition of capacitor internal resistance disturbance, with good performance and rapid response.

[0137] Simulation Verification 3: The difference from Simulation Verification 1 is: CPL power P CPL The system is changed from a state of random variation to a state of CPL power P CPL When the power is 2000W, the input inductor current i L With measurement error Δi L . Figure 4 For the system at CPL power P CPL When the power is 2000W, the input inductor current i L With measurement error Δi L CPL power P at that time CPL Observed values and Output voltage v o Input current i L Waveform diagram.

[0138] from Figure 4 (a) It can be seen that Δi L It varies randomly between the interval [-0.5, 0.9]. Figure 4 (b) represents the perturbation observations, which are observation errors generated on the input side. The value is 0, and the sensed value is 0. The error value is converted into an equivalent voltage and fed back to the system control loop. Figure 4 As can be seen in (c) and 4(d), although there is an input state i L Error Δi L However, through perturbation After receiving feedback, output the actual value i. L It can keep the system output stable at around 270V, with good adjustment effect, fast response speed, and all system state variables operating within the limited range.

[0139] Simulation Verification 4: The difference from Simulation Verification 1 is: CPL power P CPL The random change state is changed to a Boost converter with CPL, and a random disturbance d1 is injected into the source side. Figure 5 For a Boost converter with CPL and a random disturbance d1 injected into the source side (d1 replaces the set of factors affecting the source-side model error), the disturbance d1 and the observed values ​​are equivalent to a random DC voltage source. Output voltage v o Input current i L Waveform diagram.

[0140] from Figure 5 It can be seen that the random disturbance d1 varies randomly in the interval [-22, 27], and the observed values ​​of the designed observer... It can always track d1, providing system feedback and disturbance compensation. Furthermore, the output voltage v is maintained during the step switching between 300W and 3000W of the CPL. o The voltage consistently remained around 270V, fluctuating within the range [269.5, 272.3] with minimal ripple. The system performed well throughout the entire large disturbance, with the inductor current i... L and output voltage v o All results were within the preset range, and the system responded quickly and achieved good tracking results.

[0141] Simulation Verification 5: The difference from Simulation Verification 1 is: CPL power P CPL The system is changed from a randomly changing state to a Boost converter with CPL, and a random disturbance d2 is injected into the load side. Figure 6 For a Boost converter with CPL and a random disturbance d2 injected into the load side (d2 replacing the ensemble factor of the load-side model error), the disturbance d2 and the observed values ​​are equivalent to a random current source. Output voltage v o Input current i L Waveform diagram.

[0142] from Figure 6 It can be seen that the random disturbance d2 varies randomly in the range [-0.38A, -1.02A], and the observed values... It can always track random disturbance d2 and provide feedback and disturbance compensation to the system. When the CPL power jumps between 300W and 3000W, the output voltage v o It can consistently maintain a stable voltage around 270V, with a maximum surge voltage of 272.7V, a maximum overshoot σ of 1%, and low ripple. The inductor current i during the disturbance process... L and output voltage v o All parameters are within the preset range, and the system has a fast response and strong robustness.

[0143] Simulation Verification 6: The difference from Simulation Verification 1 is: CPL power P CPL The random change state is changed to a Boost converter with CPL, and random disturbances d1 and d2 are injected at the same time. Figure 7 The perturbation d1 and the observed values ​​when a Boost converter with a CPL is simultaneously injected with random perturbations d1 and d2 (characterized by voltage and current sources, respectively) are given. Perturbation d2 and observed values Output voltage v o Input current i L Waveform diagram.

[0144] from Figure 7 It can be seen that d1 randomly fluctuates in the interval [-11, 21], and d2 randomly fluctuates in the interval [-0.4, 1.18]. Regardless of how d1 and d2 change, the observer can track the random disturbances. When the CPL power jumps between 300W and 3000W, the output voltage v... o It can consistently maintain a voltage near the reference voltage of 270V, with a maximum surge voltage of 273.3V and a maximum overshoot σ of 1.2%. The inductor current i remains constant throughout the entire disturbance process. L and output voltage v o All parameters are within the preset range, and the system has a fast response and strong anti-interference capability.

[0145] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention, but technical solutions that do not depart from the spirit and scope of the present invention should be covered within the scope of the claims of the present invention.

Claims

1. A constrained sliding mode control method with observer for a direct-to-direct-current converter, characterized in that: Including the following steps: 1) Introduce a nonlinear conversion function to reconstruct the mathematical model of the C / C converter; 2) Based on the reconstructed mathematical model of the DC-DC converter, design a sliding mode controller to control the DC-DC converter; 3) Design an extended state observer for the state variables and disturbance variables of the DC-DC converter; 4) The state variables and disturbance variables of the DC-DC converter are observed by an extended state observer, and the observed values ​​of the disturbance variables are introduced into the sliding mode controller through feedforward compensation to adjust the output of the sliding mode controller; The direct-to-direct ... In the formula, and It is the reconstructed state variable, v m It is the measured value of the input voltage v of the Boost converter, i om The output current i of the Boost converter o The measured values; u is the duty cycle, d1 and d2 are interference variables, C and L are the nominal values ​​of the capacitor and inductor in the Boost converter, respectively; I min and I max The inductor current i in the Boost converter is respectively L The minimum and maximum allowable values, V max and V min The output voltage v in the Boost converter is respectively o The maximum and minimum allowable values ​​are given by x1 and x2, which are constrained state variables; η1 is the constrained transition variable corresponding to the constrained state variable x1, where x1 ∈ R and I min < x1 < I max η2 is the constrained transition variable corresponding to the constrained state variable x2, where x2 ∈ R and V min < x2 < V max The introduced nonlinear transformation function is as follows: ； The sliding mode controller designed in step 2) is as follows: in, , , ， ， Where s is a nonlinear sliding surface, , Here, e1 and e2 are the design constants, and k is the design constant. It is the rate of approximation; x2 * It is the reference value for the constrained state variable x2. is i o The first derivative, It is the first derivative of v; ； ， ； In step 3), designing the extended state observer includes: Step S1: Assume that the disturbance variables d1 and d2 are first-order continuous and differentiable, and their derivatives are bounded, satisfying the following: Where M and N are positive constants, and The derivatives of the interference variables d1 and d2; Step S2, assume the observation error vector ζ is: z=[z1, z2] T , ， in ε1 and ε2 are the observed values ​​of variables x1, x2, d1, and d2, respectively, and ε1 and ε2 are positive proportional gains greater than 1; Step S3, ζ i The derivative is: The subscripts i = 1, 2; Where, ε i A is a positive proportional gain greater than 1; i and B i It is the system matrix, set as follows: Where, α 11 and α 12 α 21 and α 22 These are the observer gains, and they both satisfy the Hurwitz equation: h1(s) = s 2 + a 11 s + a 12 h2(s) = s 2 + α 21 s + α 22 ; Step S4, according to the formula: and in step S3 ζ i The derivative expression yields the following extended state observer: Among them, v om For the output voltage v o The measured value, The measured value of inductor current i Lm The first derivative, , , and Observed values The first derivative.

Images