Nonlinear Control Method of Interleaved Parallel Buck Converters Based on Extended State Observer

Abstract

The present invention discloses a nonlinear control method for an interleaved parallel Buck converter based on an extended state observer. The inner current loop adopts differential flat control, and the switching control law is obtained according to the state equation of the system. The outer voltage loop adopts global fast terminal sliding mode control, and the reference value of the inductor current of each phase is determined according to the sliding mode. The sliding mode control law does not contain a switching function, which reduces the difficulty of parameter adjustment. To further weaken the chattering caused by the sliding mode control, an extended state observer is used to estimate the total disturbance and compensate for the total disturbance. While ensuring the steady-state output and transient response speed of the system, the present invention realizes the current sharing control of each phase, and adopts the extended state observer to estimate the unknown total disturbance, so that the output can quickly follow the output expected value.

Description

Technical Field

[0001] The present invention belongs to the technical field of converters, and in particular relates to a nonlinear control method of an interleaved parallel Buck converter based on an extended state observer. Background Art

[0002] With the advancement of modern science, an increasing number of electronic devices require high-power, high-precision, low-output-ripple DC power supplies, such as microprocessor power modules, RF power amplifiers, and laser diodes. If independent switching power supplies are used, the switching transistors and diodes are limited by their power capacity, increasing switching stress and reducing the lifespan of the switching modules. Parallel technology divides the total power supply into several power modules, reducing switching losses in power devices and making it suitable for low-voltage, high-current applications. Interleaving technology delays the phase of N switching modules by 1 / N cycles, reducing output ripple. Interleaved parallel technology combines the advantages of both, making it suitable as a switching module for these high-precision devices and, as such, has become a hot topic of research among experts in recent years.

[0003] The key to current research in interleaved parallel technology is how to average the currents of each phase of a DC converter, maintaining system stability while ensuring good transient performance when subjected to internal and external disturbances. In recent years, a large number of papers have examined current-sharing control in interleaved parallel converters. Some use charge control, further broadening the load stability range and accelerating transient response. However, linear control has limited interference immunity. Nonlinear control methods such as differential flat control (DFBC), fuzzy control, and sliding mode control have been widely used in interleaved parallel converters due to their strong robustness and excellent transient performance.

[0004] Nonlinear control has a good control effect on the anti-interference performance and current sharing characteristics of the interleaved parallel converter. Among them, sliding mode control is rarely used in this system, and global fast sliding mode control (FTSM) not only has finite time convergence characteristics, but also ensures rapid convergence when the system is far from the equilibrium point. Summary of the Invention

[0005] The purpose of the present invention is to provide a nonlinear control method for an interleaved parallel Buck converter based on an extended state observer. The capacitor voltage outer loop adopts FTSM, and the inductor current inner loop adopts DFBC. While ensuring the steady-state output and transient response speed of the system, the current sharing control of each phase is achieved.

[0006] The technical solution adopted by the present invention is a nonlinear control method for an interleaved parallel Buck converter based on an extended state observer. The inner current loop adopts differential flat control, and the switching control law is obtained according to the state equation of the system. The outer voltage loop adopts global fast terminal sliding mode control, and the reference value of the inductor current of each phase is determined according to the sliding mode. The sliding mode control law does not contain a switching function, which reduces the difficulty of parameter adjustment. To further reduce the chattering caused by the sliding mode control, the extended state observer is used to estimate the total disturbance and compensate for the total disturbance. The specific steps include:

[0007] Step 1: Model the interleaved parallel Buck converter.

[0008] Step 2: Construct a dual closed-loop nonlinear controller system for interleaved parallel Buck converter control, including a capacitor voltage outer-loop controller based on global fast sliding mode control (FTSM), an inductor current inner-loop controller based on differential flat control (DFBC), and an extended state observer (ESO).

[0009] Step 3: Design the extended state observer ESO to observe and compensate the total disturbance term.

[0010] Step 4: The capacitor voltage outer loop adopts global fast sliding mode control to make the system state converge to the equilibrium state;

[0011] Step 5: The inner loop of the inductor current uses differential flat control to calculate the current sharing control law for each phase so that the inner loop current accurately follows the reference value, realizing nonlinear control of the interleaved parallel Buck converter.

[0012] The present invention is also characterized in that:

[0013] Step 1 is as follows:

[0014] The interleaved parallel Buck converter is connected to the input voltage, parallel capacitor C and resistive load R. The input voltage signal is v in , the voltage signal across the capacitor is v o The interleaved parallel Buck converter includes diodes D1, D2, power switches S1, S2, and inductors L1 and L2. S1 and S2 are turned on with a phase difference of 180 degrees. The current signals flowing through the inductors L1 and L2 are The superposition of i L ;

[0015] According to the structural characteristics of the interleaved parallel Buck converter, its state space average model is derived as follows:

[0016]

[0017] In formula (1): io is the load side current, and u1 and u2 are the on-duty cycles of the power switches S1 and S2 respectively, and u1 = u2.

[0018] Step 3 is as follows:

[0019] For a nonlinear time-varying system with disturbances, the expression is

[0020] x (n) =f(x(t),…,x (n-1) (t), w(t))+bu(t) (2)

[0021] In formula (2): are the system state variables, w(t) is the disturbance term, u(t) is the control variable, and b is the coefficient of the control variable;

[0022] Let x1=x in formula (2), x n =x (n-1) , and the system expansion term a(t) selects the unknown total disturbance f(x(t),…,x (n-1) (t), w(t)), therefore, formula (2) is expressed as:

[0023]

[0024] The state observation model of the system is obtained from formula (3):

[0025]

[0026] In formula (4), k1~k n+1 are the observer gains, g1(e1), g2(e1), …, g n+1 (e1) is a nonlinear function, and the observation values ​​z1, z2, ..., z n+1 will exactly follow the state variables x1, x2, ..., x n+1 ;

[0027] For a two-phase interleaved parallel Buck converter, there exists

[0028]

[0029] Let the output voltage deviation e=v o -V ref , where V ref is the expected value of the output voltage. By combining equations (1) and (5) and taking their derivatives, the nonlinear system can be transformed into a series linear system, that is,

[0030]

[0031] After formula (6) is expanded, it is expressed as:

[0032]

[0033] In formula (7): x1 = e; u(t)=[u1u2] T ;

[0034]

[0035] V ref is the expected value of output voltage;

[0036] Expand and estimate the load disturbance term a(t) in the above formula to obtain the third-order observer model:

[0037]

[0038] In formula (8), z1 and z2 are the observed values ​​of state variables x1 and x2, and z3 is the estimate of the total disturbance a(t);

[0039] The observer gains k1, k2, and k3 are selected according to the bandwidth configuration method, and in order to reduce the estimation bias of the observer system, the nonlinear function is designed as follows:

[0040]

[0041] Step 4 is as follows:

[0042] Based on ESO, the external disturbance of the system is compensated to eliminate the influence of external disturbance on the system. The global fast terminal sliding surface is selected as

[0043]

[0044] In formula (10): e q / p =|e| q / p sign(e), α and β are both greater than 0, q and p are both positive odd numbers and satisfy q <p<2q;

[0045] In order for the system to reach and maintain the sliding surface s, it is necessary to satisfy s = 0, at which point the terminal sliding attractor Assume that (0, 0) is the origin of the phase plane. Substituting equation (5) into equation (10), we have

[0046]

[0047] Substituting the output voltage deviation estimate in the extended state observer ESO designed in step 3 into equation (11), the inductor current reference value after the observer model can be obtained:

[0048]

[0049] Assume any initial state If it is not at the origin, then the initial state will always converge to the equilibrium state in a finite time on the sliding mode, and the required time is expressed as

[0050]

[0051] Therefore, the system state can be converged to the equilibrium state by adjusting the control parameters α, β, p, and q.

[0052] Step 5 is as follows:

[0053] When the interleaved parallel Buck converter is in steady-state current sharing, the inductor currents of each phase have the following relationship:

[0054]

[0055] In formula (16): i Lref1 、i Lref2 i L1 、i L2 Reference value of

[0056] Select the inductor current as the flat output y c and the state variable x c ,Right now

[0057] x c =y c =[i L1 i L2 ] T =ψ x (y c ) (17)

[0058] According to equations (1) and (17), the flat output y c The input variable u is composed of its derivative c The expression is

[0059]

[0060] Equations (17) and (18) meet the flatness requirements of the system, and the flat output y c Get the reference value y of the flat output cd =[i L1ref i L2ref ] T ;

[0061] when Accurately follow the reference trajectory When y c with y cd The deviation between, and the derivative and integral terms of the deviation have the following relationship:

[0062]

[0063] In formula (19): K1 and K2 are feedback gain matrices;

[0064] The control object is equivalent to a second-order system to eliminate the steady-state error, and the closed-loop transfer function of the system is:

[0065]

[0066] Combining equations (19) and (20), we get

[0067]

[0068] In formula (21): e c =y c -y cd ;

[0069] Therefore, from formula (21) we can get

[0070]

[0071] In formula (22): c is the damping ratio of the second-order system, ω nc is the oscillation frequency;

[0072] Combining equations (19) and (22), the differential term of the flat output variable is

[0073]

[0074] Substituting Equation (23) into Equation (17) we can obtain the current sharing control law for each phase.

[0075] In step 5, the damping ratio ξ of the second-order system c and oscillation frequency ω nc The selection of determines the transient characteristics of the inner loop controller system. c When fixed, ω nc The larger the value, the faster the system responds, but nc It cannot be increased infinitely, the oscillation frequency ω is required for system stability nc Much smaller than the current loop system bandwidth ω s , that is, satisfying the following relationship

[0076] ω nc <<ω s =2πf s (24) In formula (24), f s is the system switching frequency.

[0077] The beneficial effects of the present invention are:

[0078] The present invention is based on an extended state observer (ESO)-based nonlinear control method for an interleaved parallel Buck converter, and adopts a capacitor voltage and inductor current dual-loop cascade structure. According to the nonlinear mathematical model of the system, the current inner loop adopts a DFBC strategy to derive the feedforward control law and error feedback control law of the differentially flat system. The voltage outer loop adopts an FTSM strategy, and uses ESO to estimate the unknown total disturbance. The current inner loop controller ensures that all phases of the system have equal current and compensates for output current ripple. The voltage outer loop controller reduces the sensitivity of the system to circuit parameter perturbations, making the system output smoother. Furthermore, since the FTSM control has the advantage of finite time convergence, the system has no steady-state error. The dynamic performance of the system in resisting load disturbances is optimized, and the robustness is enhanced. BRIEF DESCRIPTION OF THE DRAWINGS

[0079] Figure 1 This is the structure diagram of the interleaved parallel Buck converter;

[0080] Figure 2 It is a structural block diagram of the dual closed-loop nonlinear controller system of the present invention;

[0081] Figure 3 shows the output voltage waveforms of circuit parameters perturbations under different control strategies, where Figure 3(a) shows the output voltage waveform of circuit parameters perturbations under TSMFC control, and Figure 3(b) shows the output voltage waveform of circuit parameters perturbations under CDFBC control.

[0082] Figure 4 This is the steady-state simulation waveform diagram with a reference output voltage of 100V under the TSMFC control strategy;

[0083] Figure 5 It is the startup waveform of CPI, CDFBC and TSMFC;

[0084] Figure 6 is the output voltage waveform diagram of different control strategies against load disturbance, where Figure 6(a) is the output voltage waveform diagram under load disturbance, Figure 6(b) is the disturbance magnification diagram at 20ms, and Figure 6(c) is the disturbance magnification diagram at 50ms. DETAILED DESCRIPTION

[0085] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0086] The present invention is based on an extended state observer (ESO)-based nonlinear control method for an interleaved parallel Buck converter. The current inner loop adopts differential flat control, and a switching control law is derived based on the system's state equation. The voltage outer loop adopts global fast terminal sliding mode control, and the reference value of each phase inductor current is determined based on the sliding mode. Furthermore, the sliding mode control law does not contain a switching function, which reduces the difficulty of parameter adjustment. To further reduce chattering caused by the sliding mode control, an ESO is used to estimate and compensate for the total disturbance. The method specifically includes the following steps:

[0087] Step 1: Model the interleaved parallel Buck converter.

[0088] like Figure 1 As shown, the interleaved parallel Buck converter is connected with the input voltage, the parallel capacitor C and the resistive load R. The input voltage signal is v in , the voltage signal across the capacitor is v o The interleaved parallel Buck converter includes diodes D1, D2, power switches S1, S2, and inductors L1 and L2. S1 and S2 are turned on with a phase difference of 180 degrees. The current signals flowing through the inductors L1 and L2 are The superposition of i L ;

[0089] According to the structural characteristics of the interleaved parallel Buck converter, its state space average model is derived as follows:

[0090]

[0091] In formula (1): i o is the load side current, and u1 and u2 are the on-duty cycles of the power switches S1 and S2 respectively, and u1 = u2.

[0092] Step 2: Figure 2 As shown in the figure, a dual closed-loop nonlinear controller system is constructed for the control of interleaved parallel Buck converter, including a capacitor voltage outer loop controller based on global fast sliding mode control FTSM, an inductor current inner loop controller based on differential flat control DFBC, and an extended state observer ESO.

[0093] Step 3: Design the extended state observer ESO to observe and compensate the total disturbance term.

[0094] For a nonlinear time-varying system with disturbances, the expression is

[0095] x (n) =f(x(t),…,x (n-1) (t), w(t))+bu(t) (2)

[0096] In formula (2): are the system state variables, w(t) is the disturbance term, u(t) is the control variable, and b is the coefficient of the control variable;

[0097] Let x1=x in formula (2), x n =x (n-1) , and the system expansion term a(t) selects the unknown total disturbance f(x(t),…,x (n-1) (t), w(t)), therefore, formula (2) is expressed as:

[0098]

[0099] The state observation model of the system is obtained from formula (3):

[0100]

[0101] In formula (4), k1~k n+1 are the observer gains, g1(e1), g2(e1), …, g n+1 (e1) is a nonlinear function, and the observation values ​​z1, z2, ..., z n+1 will exactly follow the state variables x1, x2, ..., x n+1 ;

[0102] For a two-phase interleaved parallel Buck converter, there exists

[0103]

[0104] Let the output voltage deviation e=v o -V ref , where V ref is the expected value of the output voltage. By combining equations (1) and (5) and taking their derivatives, the nonlinear system can be transformed into a series linear system, that is,

[0105]

[0106] After formula (6) is expanded, it is expressed as:

[0107]

[0108] In formula (7): x1 = e; u(t)=[u1 u2] T ;

[0109]

[0110] V ref is the expected value of output voltage;

[0111] Expand and estimate the load disturbance term a(t) in the above formula to obtain the third-order observer model:

[0112]

[0113] In formula (8), z1 and z2 are the observed values ​​of state variables x1 and x2, and z3 is the estimate of the total disturbance a(t);

[0114] The observer gains k1, k2, and k3 are selected according to the bandwidth configuration method, and in order to reduce the estimation bias of the observer system, the nonlinear function is designed as follows:

[0115]

[0116] From the analysis of formula (8), it can be seen that the order of the observer after the expansion disturbance term does not increase compared with the original state equation, but is the same as the order of the original system, which reduces the number of observer gains and is conducive to obtaining accurate observation values.

[0117] Step 4: The capacitor voltage outer loop adopts global fast sliding mode control to make the system state converge to the equilibrium state;

[0118] External interference will cause chattering in the sliding mode control. Therefore, the external disturbance of the system is compensated based on ESO to eliminate the influence of external disturbance on the system. The global fast terminal sliding mode surface is selected as

[0119]

[0120] In formula (10): e q / p =|e|q / p sign(e), α and β are both greater than 0, q and p are both positive odd numbers and satisfy q <p<2q;

[0121] In order for the system to reach and maintain the sliding surface s, it is necessary to satisfy s = 0, at which point the terminal sliding attractor is the origin of the phase plane (0, 0), and substituting equation (5) into equation (10), we have

[0122]

[0123] Substituting the output voltage deviation estimate in the extended state observer ESO designed in step 3 into equation (11), the inductor current reference value after the observer model can be obtained:

[0124]

[0125] Assume any initial state If it is not at the origin, then the initial state will always converge to the equilibrium state in a finite time on the sliding mode, and the required time is expressed as

[0126]

[0127] Therefore, the system state can be quickly converged to the equilibrium state within a finite time by adjusting the control parameters α, β, p, and q.

[0128] Step 5: The inner loop of the inductor current uses differential flat control to calculate the current sharing control law for each phase, so that the inner loop current accurately follows the reference value, achieving nonlinear control of the interleaved parallel Buck converter.

[0129] Differential flat control was first proposed by Filess in 1995. (1) ,…,y (n) To linearly represent the original state variable x and input variable u,

[0130] Assume that there is a nonlinear system whose model can be expressed as

[0131]

[0132] And the flat output y can be found, and the state variable x and input u can be expressed as

[0133]

[0134] Then the system is said to be flat. In formula (15), a and b are the derivative orders of the flat output y, and x∈R m , u∈R n , y∈R n , m, n are positive integers, ψ x (·),ψ u (·) are all mapping functions;

[0135] The current inner loop adopts the DFBC method to ensure that the inductor current is flat and quickly follows the reference value of the current. When the interleaved parallel Buck converter is in steady-state current sharing, the inductor current of each phase has the following relationship

[0136]

[0137] In formula (16): i Lref1 、i Lref2 i L1 、i L2 Reference value of

[0138] According to the design requirement of flat output of inner loop inductor current, the inductor current is selected as the flat output quantity y c and the state variable xc ,Right now

[0139] x c =y c =[i L1 i L2 ] T =ψ x (y c ) (17)

[0140] According to equations (1) and (17), the flat output y c The input variable u is composed of its derivative c The expression is

[0141]

[0142] From the analysis of formula (15), we can see that formula (17) and formula (18) meet the flatness requirements of the system, and the flat output y c Get the reference value y of the flat output cd =[i L1ref i L2ref ] T ;

[0143] when Accurately follow the reference trajectory When y c with y cd The deviation between, and the derivative and integral terms of the deviation have the following relationship:

[0144]

[0145] In formula (19): K1 and K2 are feedback gain matrices;

[0146] The control object is equivalent to a second-order system to eliminate the steady-state error, and the closed-loop transfer function of the system is:

[0147]

[0148] Combining equations (19) and (20), we get

[0149]

[0150] In formula (21): e c =y c -y cd ;

[0151] Therefore, from formula (21) we can get

[0152]

[0153] In formula (22): cis the damping ratio of the second-order system, ω nc is the oscillation frequency;

[0154] Combining equations (19) and (22), the differential term of the flat output variable is

[0155]

[0156] Substituting Equation (23) into Equation (17) yields the current sharing control law for each phase, and the current inner loop is combined with the master-slave control method to ensure the current sharing effect.

[0157] From the analysis of formula (23), we can see that the system is stable when K1 and K2 are positive definite matrices, and the damping ratio of the second-order system is ξ c and oscillation frequency ω nc The selection of determines the transient characteristics of the inner loop controller system. c When fixed, ω nc The larger the value, the faster the system responds, but nc It cannot be increased infinitely, the oscillation frequency ω is required for system stability nc Much smaller than the current loop system bandwidth ω s , that is, satisfying the following relationship

[0158] ω nc <<ω s =2πf s (twenty four)

[0159] In formula (24), f s is the system switching frequency.

[0160] Simulation Verification

[0161] To verify the effectiveness and superiority of the proposed extended state observer-based nonlinear control method for an interleaved parallel Buck converter, this method was applied to a two-phase interleaved parallel Buck converter. A PSIM simulation model was established, and the proposed terminal sliding mode flat control (TSMFC) strategy was used for the control. The control strategy was compared with traditional cascade PI (CPI) control and cascade differential flat control (CDFBC).

[0162] (1) Parameter selection

[0163] According to the interleaved parallel Buck converter operating in low ripple, high current applications, the circuit parameters are designed as shown in Table 1:

[0164] Table 1 Circuit parameters of two-phase interleaved parallel Buck converter

[0165]

[0166] From Equation (12), we can see that the voltage loop control parameters α and β determine the speed at which the system converges to the equilibrium state, and the selection of q and p will affect the robustness of the system to internal and external disturbances. Therefore, the controller parameters are shown in Table 2.

[0167] Table 2 Controller parameters

[0168]

[0169] Current reference value i of traditional CPI control Lref The expression of CPI control is indirectly determined by the expected value of the output voltage of the voltage loop:

[0170] u1=k pi (i Lref -i L1 )+k ii ∫(i Lref -i L1 )dt (25)

[0171] u2=k pi (i Lref -i L2 )+k ii ∫(i Lref -i L2 )dt (26)

[0172] in

[0173] i Lref =k pv (V ref -v o )+k iv ∫(V ref -v o )dt (27)

[0174] In formulas (25) to (27): k pi 、k ii They are the proportional and integral coefficients of the current loop, k pv 、k iv are the proportional and integral coefficients of the voltage loop respectively.

[0175] According to the requirements of dynamic performance, the current loop PI parameter is selected as k pi =0.1, k ii =1.25; Based on the requirements of the closed-loop system for steady-state performance, the voltage loop PI parameter is selected as k pv =0.2, k iv When =1000, the phase margin is about 45°. In the CDFBC control strategy, the current loop parameters are consistent with the TSMFC inner loop parameters, and the voltage loop bandwidth is selected as 12566 rad / s.

[0176] (2) Verification of resistance to circuit parameter perturbation

[0177] In actual operating conditions, converters are susceptible to factors such as temperature and component aging, which can cause deviations between the actual and nominal values ​​of the circuit's capacitors and inductors. Furthermore, the design of the DFBC relies on an accurate model of the system, inevitably leading to unmodeled components that affect system stability. Therefore, an FTSM is added to the controller's outer loop to reduce its sensitivity to circuit parameter perturbations.

[0178] The following three parameter perturbation scenarios were designed to verify the sensitivity of the TSMFC controller to circuit parameters: Case 1: L1 = L2 = 150μH, C = 100μF; Case 2: L1 = L2 = 150μH, C = 200μF; and Case 3: L1 = L2 = 300μH, C = 200μF. Comparing Case 1 with Case 2 reveals the impact of capacitance perturbation on the system output, while comparing Case 2 with Case 3 reveals the impact of inductance perturbation on the system output. Figure 3 shows the output voltage waveforms for Cases 1 to 3 when the output voltage drops from 100V to 60V at 0.02s. Figure 3(a) shows the effect of the TSMFC controller, and Figure 3(b) shows the effect of the CDFBC controller.

[0179] Analysis of Figure 3 shows that in all three cases, the controller system of the present invention returns to its new steady-state value within 0.6ms with virtually no overshoot. The CDFBC controller also returns to its new steady-state value within 1.2ms, but a comparison between Case 1 and Case 2 reveals a 20V difference in output overshoot, and a comparison between Case 2 and Case 3 reveals a 10V difference in output overshoot. Therefore, the nonlinear control method of the present invention reduces the system's sensitivity to circuit parameters, making perturbations of circuit parameters essentially ineffective.

[0180] (3) Steady-state characteristics verification

[0181] To verify the switching characteristics of the two-phase interleaved parallel Buck converter, Figure 4 This is the steady-state simulation waveform with a reference output voltage of 100V under the TSMFC control strategy. The sampling frequency is 40kHz and due to the staggered conduction of the corresponding switch tubes, active current sharing is achieved in each phase. L The sampling frequency is 80kHz, and the ripple of the inductor current is significantly reduced.

[0182] (4) Set the expected output voltage of the interleaved parallel Buck converter to 100V. Figure 5 The figure shows the output voltage startup process under different control strategies of CPI, CDFBC and TSMFC. Figure 5It can be seen that the output voltages of CPI control and CDFBC control transition to the desired value through overshoots of 14V and 8V respectively, while the output voltage of TSMFC control has no overshoot, and the adjustment time under TSMFC control is the shortest.

[0183] In real-world operating conditions, the load of a switching power supply can change suddenly at any time, altering the output characteristics of the power supply system. Therefore, to verify the TSMFC control strategy's ability to withstand load disturbances, simulations were conducted to compare it with the CPI and CDFBC control strategies under load disturbances. The load suddenly decreased from full load to 60% in 20ms; from 60% to 46% in 30ms; from 46% to 67% in 40ms; and from 67% to full load in 50ms.

[0184] Figure 6 shows the output voltage waveforms of the system under three different control strategies when subjected to a load disturbance. Figures 6(b) and 6(c) show magnified views of the disturbance at 20 ms and 40 ms, respectively. Table 3 lists the disturbance rejection performance parameters for different control strategies. Analysis of Figures 6 and Table 3 shows that the TSMFC control strategy minimizes the impact of load disturbances on the system and provides the shortest adjustment time, demonstrating excellent disturbance rejection performance.

Claims

1. A nonlinear control method for interleaved parallel Buck converters based on an extended state observer, characterized in that: The inner current loop uses differential flat control, and the switching control law is derived from the system's state equation. The outer voltage loop employs global fast terminal sliding mode control, which determines the reference value of each phase inductor current based on the sliding mode. The sliding mode control law does not contain a switching function, which simplifies parameter adjustment. To further reduce chattering caused by sliding mode control, an extended state observer is used to estimate and compensate for the total disturbance. This involves the following steps: Step 1: Model the interleaved parallel Buck converter. Step 2: Construct a dual closed-loop nonlinear controller system for interleaved parallel Buck converter control, including a capacitor voltage outer-loop controller based on global fast sliding mode control (FTSM), an inductor current inner-loop controller based on differential flat control (DFBC), and an extended state observer (ESO). Step 3: Design the extended state observer ESO to observe and compensate the total disturbance term. Step 4: The capacitor voltage outer loop adopts global fast sliding mode control to make the system state converge to the equilibrium state; The step 4 is specifically as follows: Based on ESO, the external disturbance of the system is compensated to eliminate the influence of external disturbance on the system. The global fast terminal sliding surface is selected as (10) In formula (10): Output voltage deviation , , α 、 β are greater than 0, q 、 p are all positive odd numbers and satisfy q < p <2 q ; In order for the system to reach and maintain the sliding surface s Above, you need to meet s =0, then the terminal sliding mode attractor The origin of the phase plane , Substituting formula (5) into formula (10), we have (11) In formula (11), is the load side current, 、 is the inductance of the interleaved parallel Buck converter 、 The current signal, C is the capacitor C connected to the interleaved parallel Buck converter; Substituting the output voltage deviation estimate in the extended state observer ESO designed in step 3 into equation (11), the inductor current reference value after the observer model can be obtained: (12) In formula (12), z 1 is the state variable of the third-order observer model x Observation value of 1; Assume any initial state If it is not at the origin, then the initial state will always converge to the equilibrium state in a finite time on the sliding mode, and the required time is expressed as (13) Therefore, by adjusting the control parameters α , β , p , q Make the system state converge to the equilibrium state; Step 5: The inner loop of the inductor current uses differential flat control to calculate the current sharing control law for each phase, so that the inner loop current accurately follows the reference value, achieving nonlinear control of the interleaved parallel Buck converter. The step 5 is specifically as follows: When the interleaved parallel Buck converter is in steady-state current sharing, the inductor currents of each phase have the following relationship: (16) In formula (16): They are Reference value of Select the inductor current as the flat output and state variables ,Right now (17) In formula (17): for about The mapping function of According to equations (1) and (17), the flat output The input variables are composed of The expression is (18) In formula (18): ( y c , )for about The mapping function Equations (17) and (18) meet the flatness requirements of the system, and the flat output Get the reference value of flat output ; when Accurately follow the reference trajectory hour, and The deviation between, and the derivative and integral terms of the deviation have the following relationship: (19) In formula (19): 、 is the feedback gain matrix; The control object is equivalent to a second-order system to eliminate the steady-state error, and the closed-loop transfer function of the system is: (20) Combining equations (19) and (20), we get (21) In formula (21): ; Therefore, from formula (21) we can get (22) In formula (22): is the damping ratio of the second-order system, is the oscillation frequency; Combining equations (19) and (22), the differential term of the flat output variable is (23) Substituting Equation (23) into Equation (17) we can obtain the current sharing control law for each phase.

2. The nonlinear control method for interleaved parallel Buck converters based on extended state observer according to claim 1, characterized in that: The step 1 is specifically as follows: The interleaved parallel Buck converter is connected to an input voltage, a parallel capacitor C With resistive load R , the input voltage signal is , the voltage signal across the capacitor is The interleaved parallel Buck converter includes diodes ,diode , power switch , power switch and inductors ,inductance , 、 The phase difference is 180 degrees, and the current flows through the inductor respectively. 、 Current signal 、 The superposition of ; According to the structural characteristics of the interleaved parallel Buck converter, its state space average model is derived as follows: (1) In formula (1): is the load side current, and , 、 Power switch 、 The on-duty cycle, and .

3. The nonlinear control method of an interleaved parallel Buck converter based on an extended state observer according to claim 2, characterized in that: The step 3 is specifically as follows: For a nonlinear time-varying system with disturbances, the expression is (2) In formula (2): are the system state variables, w ( t ) is the disturbance term, u ( t ) is the control quantity, and b is the coefficient of the control quantity; In formula (2) , and the system expansion term a ( t ) Select the unknown total disturbance , therefore, formula (2) is expressed as: (3) The state observation model of the system is obtained from formula (3): (4) In formula (4), is the observer gain, , ,…… is a nonlinear function, the observed value will exactly follow the state variables ; For a two-phase interleaved parallel Buck converter, there exists (5) Output voltage deviation ,in, is the expected value of the output voltage. By combining equations (1) and (5) and taking their derivatives, the nonlinear system can be transformed into a series linear system, that is, (6) After formula (6) is expanded, it is expressed as: (7) In formula (7): ; ; ; ; ； is the expected value of output voltage; The load disturbance term in the above formula is a ( t ) expansion estimation, the third-order observer model is obtained as (8) In formula (8): is a state variable The observed value of is the total disturbance a ( t ) estimates; Selecting the observer gain based on the bandwidth configuration method , and in order to reduce the estimation bias of the observer system, the nonlinear function is designed as follows: (9)。 4. The nonlinear control method for interleaved parallel Buck converters based on extended state observer according to claim 1, characterized in that: In step 5, the damping ratio of the second-order system and oscillation frequency The selection of determines the transient characteristics of the inner loop controller system. When fixed, The larger the value, the faster the system responds, but It cannot be increased infinitely, the oscillation frequency is required for system stability Much smaller than the current loop system bandwidth , that is, satisfying the following relationship (24) In formula (24), is the system switching frequency.

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