Design method of sliding mode decoupling controller for single-inductor dual-output Buck converter based on ESO

Abstract

The present invention discloses a design method of a sliding mode decoupling controller for a single-inductor dual-output Buck converter based on ESO. The main circuit ESO is used to estimate the load disturbance and compensate it to a backstepping sliding mode controller BSMC. ​​The improved reaching law is combined to optimize the chattering problem and anti-disturbance capability of the sliding mode, so as to reduce the influence of branch a on the load mutation between branches. Meanwhile, a sliding mode self-disturbance rejection controller SM-ADRC is used to independently control branch b, so as to eliminate the total disturbance composed of branch coupling terms and internal and external interferences in the branch b model, and further reduce the cross-influence of branch b disturbance on branch a.

Description

Technical Field

[0001] The invention belongs to the technical field of converters, and in particular relates to a design method of a sliding mode decoupling controller of a single-inductor dual-output Buck converter based on ESO. Background Art

[0002] With the development of portable devices, the miniaturization of internal devices and the high integration of functional modules have made people pay more and more attention to the solution of multi-channel module power supply. The single-inductor dual-output (SIDO) converter can convert one input voltage into two output voltages using only one inductor. Therefore, the use of SIDO converter power supply has the advantages of reducing size and improving efficiency. [1] Compared with the traditional single-inductor single-output converter, the main circuit and two branches of the SIDO converter have independent control switches and there is a more complex coupling relationship between the branches. When the output of one branch changes due to a load jump, the energy provided by the inductor to the other branch will also change, which will affect the stability of the system and produce serious cross-effects. Therefore, how to optimize the control strategy to further improve the dynamic performance of the SIDO converter and reduce the cross-effect has become a hot topic for researchers.

[0003] The SIDO converter is a time-varying nonlinear system. When working in the continuous conduction mode (CCM), the two branches are always in a coupled state. When the input voltage, temperature, load and other factors bring uncertain disturbances, it will have a serious impact on the system performance. For this strongly coupled nonlinear system, the use of nonlinear control methods can greatly improve the system dynamic performance and control accuracy. At present, many nonlinear controls are applied to single-input single-output converters, such as backstepping control, anti-disturbance control, sliding mode variable structure control, etc. However, there are few research reports on the nonlinear control of SIDO converters.

[0004] Sliding Mode Control (SMC), as a type of nonlinear control, has limited control effects due to jitter and output error problems. Extended State Observers (ESO), as a disturbance estimation technology, is used to observe the state variables and disturbances of the system, and use the observed values ​​to compensate in the feedforward channel, which can greatly improve the performance of the system. Since the jitter problem of sliding mode is also attributed to disturbances, the method of combining ESO with sliding mode can make up for the defects of sliding mode control and further improve the control performance. Literature Wang J, Li S, Yang J, et al. Extended state observer based sliding mode control for PWM-based DC-DCbuck power converter systems with mismatched disturbances [J]. IET Control Theory & Applications, 2015, 9(4): 579-586. It is proposed to apply the method of combining ESO and sliding mode control to the Buck converter, which improves the response speed and anti-interference ability of the system; Literature Wang Junxiao, Rong Jiayi, Yu Li. Design and implementation of reduced-order extended state observer and sliding mode control for DC buck converter. [J]. Control Theory and Applications. 2019, 36(9): 1486–1492. A control method combining reduced-order observer and sliding mode applied to Buck converter is proposed, which reduces the gain of extended state observer ESO and optimizes the noise problem; Literature Chen Qiang, Yang Chenbing, Nan Yurong. Anti-disturbance control of Buck converter based on variable speed reaching law [J]. Control and Decision, 2021, 36(4): 893-900. It is proposed to apply the variable speed reaching law sliding mode combined with disturbance observer to Buck converter, which reduces the control parameters and weakens the jitter. The above strategies can make the low-order single-input single-output system have good dynamic performance and anti-interference ability. However, when applied to high-order multi-output systems, it not only increases the order of the observer, but also the coupling of the system causes the control algorithm to be complex and the parameters to be difficult to adjust.

[0005] Active Disturbance Rejection Control (ADRC), as a control method based on ESO, does not require an accurate model of the controlled object and has certain advantages in complex high-order system control. Reference

[10]

[0006] Huangfu Y, Zhuo S, Chen F, et al. Robust Voltage Control of Floating Interleaved Boost Converter for Fuel Cell Systems[J]. IEEE Transactions on Industry Applications, 2018, 54(1): 665-674 proposed a dual closed-loop control output series boost converter composed of super-twisted sliding mode and ADRC. The unmodeled part and internal and external disturbances are regarded as total disturbances through ESO, and the outer loop PD controller is used for reverse compensation, thereby achieving overall reduction of the total disturbance; Literature Yang Liben, Wei Wenjun, et al. Improved ADRC attitude control algorithm for horizontal twin-rotor vector aircraft[J]. Systems Engineering and Electronics, 2021, 43(10): 2976-2983 proposed ADRC decoupling control based on transfer function for small pressurized water reactor, which solved the problem of pressurized water reactor pressure stabilization. Coupling problem between pressure and water level of the pressurizer; Literature Shi Bo, Li Daixing, Guo Wei, et al. Research on multivariable self-disturbance rejection decoupling control of small pressurized water reactor pressurizer [J]. Nuclear Power Engineering, 2021, 42(05): 143-148 Aiming at the serious coupling between attitudes and weak anti-disturbance ability of dual-rotor vector aircraft, a self-disturbance rejection decoupling controller design method is proposed. According to these two documents, for high-order multi-output systems, ADRC can correspond each input to output. After control parameter optimization, the cross-influence (coupling) between outputs is observed as the total disturbance of independent control loops and offset as a whole. Therefore, ADRC has natural decoupling. In summary, the control idea of ​​combining ESO with sliding mode control and introducing ADRC for decoupling is in line with the nonlinear and branch coupling characteristics of SIDO converter. Summary of the invention

[0007] The purpose of the present invention is to provide a design method for a sliding mode decoupling controller of a single-inductor dual-output Buck converter based on ESO, which solves the problem that the output branches of the single-inductor dual-output Buck converter have serious cross-influence and slow transient response when load disturbance occurs.

[0008] The technical solution adopted by the present invention is a design method of a sliding mode decoupling controller for a single-inductor dual-output Buck converter based on ESO, which uses the main ESO to estimate the load disturbance and compensate it to the backstepping sliding mode controller BSMC, and combines the improved reaching law to optimize the chattering problem and anti-disturbance ability of the sliding mode to reduce the impact of branch a on the load mutation between branches; at the same time, the sliding mode self-disturbance rejection controller SM-ADRC is used to independently control branch b, eliminating the total disturbance composed of branch coupling terms and internal and external interference in the branch b model, and further reducing the cross-influence of branch b disturbance on branch a, which specifically includes the following steps:

[0009] Step 1: CCM SIDO Buck converter modeling;

[0010] The SIDO Buck converter model includes a main circuit, which is connected to branch a and branch b. The main circuit includes a circuit connected to the input voltage V in The main power switch tubes VT connected in sequence i , the main circuit inductor L, the main circuit inductor L and the main circuit power switch tube VT i The connecting end is also connected to a freewheeling diode VD, and the branch a includes a branch a power switch tube VT which is connected in sequence with the main circuit inductor L. a , the load equivalent resistance R of branch a a , load equivalent resistance R a The actual output capacitance C of the upper parallel branch a a , branch b includes branch b power switch tube VT connected to the main circuit inductor L in sequence b , the load equivalent resistance R of branch b b , load equivalent resistance R b The actual output capacitance C of the upper parallel branch b b ;

[0011] Step 2: Main Switch Controller Design

[0012] Main switch tube VT i To control the voltage of branch a, the system model is first modeled by considering the load disturbance term. Based on the deviation state model, the backstepping sliding mode controller and the main ESO are designed respectively, as follows:

[0013] Step 2.1: State transition modeling;

[0014] Step 2.2: Backstepping sliding mode controller design;

[0015] Step 2.3: Main road ESO design;

[0016] Step 3: Branch switch controller design

[0017] Branch switch tube VT bIt is used to control the voltage of branch b. Since there is parameter coupling between branches, the idea of ​​the branch controller is to separate branch b from the system, complete the one-to-one correspondence between the input and output loops, and convert the obtained control law d b The overall control is completed by coordinating with the main controller. Therefore, according to the characteristics of ADRC that it does not rely on the object model, a fitting model is first established for branch b, and then the branch ESO is established based on the fitting model. Finally, the sliding mode active disturbance rejection controller is designed based on the branch ESO as the framework, as follows:

[0018] Step 3.1: Branch system fitting;

[0019] Step 3.2, branch ESO design;

[0020] Step 3.3: Sliding mode ADRC design.

[0021] The present invention is also characterized in that:

[0022] The state space average model of the CCM SIDO Buck converter model in step 1 is:

[0023]

[0024] In formula (1), i L is the inductor current, d i ,d a and d b They are respectively driving the power switch tube VT i VT a and VT b The duty cycle, v oa 、v ob They are the transient values ​​of the output voltages of branch a and branch b respectively. When the SIDO Buck converter works in CCM, the duty cycles of the two branches are complementary, which satisfies: a +d b =1;

[0025] The steady-state value of the output voltage of the two branches of the CCM SIDOBuck converter is v oa 、v ob The expression is:

[0026]

[0027] Step 2.1 is as follows:

[0028] Define the voltage deviations x1 and x3 of branches a and b as:

[0029]

[0030] In formula (3), v aref 、v brefThey are the reference voltages of branches a and b respectively;

[0031] For branch a, combining equation (1) and equation (3), we get:

[0032]

[0033] In formula (4), is the bounded disturbance caused by the load change of branch a, R 0a is the nominal value of the equivalent resistance of branch load a;

[0034] According to formula (1), x2 is defined as:

[0035]

[0036] According to equations (4) and (5), the deviation model of branch a is rewritten as:

[0037]

[0038] In formula (6),

[0039] According to the above method, the deviation model of branch b is rewritten as:

[0040]

[0041] In formula (7),

[0042] Step 2.2 is as follows:

[0043] The tracking error ξ1 of branch a is defined as:

[0044] ξ1=x1=v oa -v aref (8)

[0045] Define the Lyapunov function V1 as:

[0046]

[0047] Introducing the virtual control quantity ξ2, we get:

[0048]

[0049] In formula (10), α is a positive constant;

[0050] After taking the derivative of formula (9), substitute formula (10) to obtain:

[0051]

[0052] Equation (11) represents the first subsystem constructed by the backstepping method. In order to make it stable, it must satisfy Therefore, it is necessary to make ξ2 converge to 0;

[0053] Combined with sliding mode variable structure control, the sliding surface S = ξ2 is defined. Substituting equation (6) into equation (10), we get:

[0054] S=x2+f1(t)+αξ1 (12)

[0055] Define the Lyapunov function V i for:

[0056]

[0057] In formula (13), V2 = 0.5S 2 ;

[0058] Taking the derivative of formula (13) we get:

[0059]

[0060] The improved reaching law is selected as:

[0061]

[0062] In formula (15), 0<τ<1, k1>0, and the form of the adaptive function f(S) is:

[0063]

[0064] In formula (16), γ>1, ε>0, k2>0.

[0065] The form of the sigmoid (S) function in formula (15) is:

[0066]

[0067] In formula (17), κ>0.

[0068] Step 2.3 is as follows:

[0069] According to equations (6) and (7), the main road ESO is:

[0070]

[0071] In formula (19), z1 and z2 are the observed values ​​of the state variable x1 of the deviation model of branch a and the bounded load disturbance f1(t), z3 and z4 are the observed values ​​of the state variable x3 of the deviation model of branch b and the bounded load disturbance f3(t), β = [β1, β2, β3, β4] is the gain value of the observer, and β1 = β3 > 0, β2 = β4 > 0;

[0072] According to formula (19), the a-branch observer is rewritten as follows:

[0073]

[0074] In formula (20), z = [z1, z2] T , x=[x1,x2] T ;

[0075] According to equation (20), the two poles of the a-branch observer are configured to the left half plane, and we can obtain:

[0076] |sE0-A|=s 2 +β1s+β2=(s+ω0) 2 (twenty one)

[0077] In formula (21), E0 is the unit matrix, ω0 is the bandwidth of the main ESO;

[0078] According to equation (21), the observer gain β of branch a is configured as:

[0079]

[0080] According to equations (12)-(17) and equations (6) and (19), the main switch control law d is obtained i for:

[0081]

[0082] In formula (23), z5 is the observed value of x2;

[0083] At this point, the design of the main switch controller is completed.

[0084] Step 3.1 is as follows:

[0085] According to the self-disturbance rejection paradigm, the second-order system of branch b is defined as:

[0086]

[0087] In formula (40), is the total disturbance required; is the output voltage v of branch b ob , u is the driving signal d of branch b b , b is the exact value of the control gain, It is the comprehensive characteristics of the time-varying dynamics and external disturbances generated by the coupling between branches in the system. Since the value of b is not easy to obtain, the easily available estimated value b0 is used as the control gain.

[0088] By using the state average method to model the converter for small signals, the control-output transfer function of branch b can be obtained as follows:

[0089]

[0090] In formula (41), a0 = R a -2d b R a +d b 2 R a +d b 2 R b

[0091] a1=L+C b R a R b -2C b d b R a R b +C a d b 2 R a R b +C b d b 2 R a R b

[0092] a2=C a LR a +C b LR b

[0093] a3=C a C b LR a R b

[0094] c0=(I L -d b )I L R a R b +d b R b (v oa -v ob )

[0095] c1=I L LR b +C a d b R a R b (v oa -v ob )

[0096] c2=C a I L LR a R b

[0097] According to the form of formula (40), formula (41) is rewritten as:

[0098]

[0099] In formula (42), according to formula (40), b0 = c1 / a3,

[0100] Step 3.2 is as follows:

[0101] Define the state variable of branch b as:

[0102]

[0103] The b-branch fitting system model is written as:

[0104]

[0105] In formula (44), C = [1 0 0];

[0106] According to formula (44), the designed branch ESO is:

[0107]

[0108] In formula (45), θ=[θ1,θ2,θ3]T; θ1, θ2, θ3 are the outputs of branch b respectively. Derivative of the output and the observed value of the total disturbance ω; is the observation error of branch ESO; L=[l1,l2,l3] T is the gain of the observer;

[0109] The characteristic polynomial of the branch ESO is obtained by Laplace transforming equation (45), and then configured with the branch ESO bandwidth to obtain:

[0110] s 3 +l1s 2 +l2s+l3=(s+ω1) 3 (46)

[0111] In formula (46), ω1 is the bandwidth of the branch ESO, and the corresponding configuration of the branch ESO gain is l1 = 3ω1, l2 = 3ω1 2 , l3=ω1 3 ;

[0112] If the observer gain is adjusted based on the switching frequency of the branch control system, the observed value can maintain a good tracking effect on the output and the total disturbance, that is, θ1→η1, θ2→η2, θ3→η3.

[0113] Step 3.3 is as follows:

[0114] The output tracking error of branch b is defined as:

[0115] e0=θ1-v bref (47)

[0116] Taking the first and second order derivatives of equation (47) respectively, we get:

[0117]

[0118] Select the sliding surface S1 as:

[0119]

[0120] The sliding mode reaching law is chosen as:

[0121]

[0122] In formula (50), w1>0, w2>0;

[0123] According to equations (47)-(50), the branch switch control law is:

[0124]

[0125] According to formula (45), the state variable η3, i.e., ω, representing the disturbance is expanded in the fitting system model of branch b and tracked by the state variable θ3 of branch ESO. Substituting formula (51) into formula (44) to reduce the total disturbance η3 (i.e., θ3), the original object is simplified to an integral series system, i.e.:

[0126]

[0127] In formula (52), u0 = -w1S1 - w2sign(S1) - cθ2

[0128] At this point, the branch switch controller design is completed.

[0129] The beneficial effects of the present invention are:

[0130] 1) The present invention proposes a design method for a sliding mode decoupling controller of a single-inductor dual-output Buck converter based on ESO, and uses a coordinated control strategy of main ESO-BSMC and branch SM-ADRC to control the voltages of the two branches. The main ESO observes and compensates for load disturbances, and the branch ESO observes and compensates for coupling and internal and external disturbances, respectively, thereby realizing anti-disturbance decoupling control of the output voltage.

[0131] 2) Compared with the CMV-DMV control strategy, by analyzing the overshoot and transient response time under disturbance, it can be seen that the present invention improves the anti-disturbance capability and transient response speed of the system and reduces the cross-effect between branches.

[0132] 3) The present invention introduces ESO for feedforward compensation of control, which not only eliminates the steady-state error existing in the sliding mode and improves the voltage tracking capability, but also enhances the robustness of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0133] Figure 1 This is the circuit topology diagram of the SIDO Buck converter model;

[0134] Figure 2 This is the sliding mode decoupling control block diagram of the CCM SIDO Buck converter based on ESO;

[0135] Figure 3 is a comparison of the images of two groups of functions, where Figure 3(a) is the function (|S|+1) -ε|S| With the function e -ε|S| 3(b) is a comparison diagram of the image of the continuous function sigmoid(S) and the symbol function sign(S);

[0136] Figure 4 is the sliding mode motion characteristic diagram;

[0137] Figure 5 This is the main road ESO+BSMC control block diagram;

[0138] Figure 6 This is the branch SM-ADRC control block diagram;

[0139] FIG7 is a simulation comparison diagram of two control strategies when the load of branch a is disturbed, wherein FIG7(a) is a waveform diagram of the output voltage of CMV-DMV control when the load of branch a is disturbed, and FIG7(b) is a waveform diagram of the output voltage of the controller of the present invention when the load of branch a is disturbed;

[0140] FIG8 is a simulation comparison diagram of two control strategies when the b branch load is disturbed, wherein FIG8(a) is a waveform diagram of the output voltage of the CMV-DMV control when the b branch load is disturbed, and FIG8(b) is a waveform diagram of the output voltage of the controller of the present invention when the b branch load is disturbed;

[0141] FIG. 9 is a simulation output waveform diagram of two control strategies of a SIDO Buck converter, wherein FIG. 9( a ) is a simulation output waveform diagram of a SIDO Buck converter controlled by CMV-DMV, and FIG. 9( b ) is a simulation output waveform diagram of a SIDO Buck converter controlled by a controller of the present invention;

[0142] FIG10 is a simulation comparison diagram of ESO-BSMC and BSMC for branch a, wherein FIG10(a) is a control comparison diagram of ESO+BSMC and BSMC for branch a, FIG10(b) is an enlarged diagram of range A in FIG10(a), and FIG10(c) is an enlarged diagram of range B in FIG10(a);

[0143] Fig.11 This is the simulation comparison diagram of SM-ADRC and traditional SMC of branch a;

[0144] FIG12 is a comparison diagram of the simulation results of the ESO observation values ​​and the actual values ​​of the two branches, where FIG12(a) is the comparison diagram of the output voltage observation, FIG12(b) is the comparison diagram of the disturbance observation of branch a, and FIG12(c) is the comparison diagram of the disturbance observation of branch b. DETAILED DESCRIPTION

[0145] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0146] The present invention discloses a design method for a sliding mode decoupling controller of a single-inductor dual-output Buck converter based on ESO. The main ESO is used to estimate the load disturbance and compensate it to the backstepping sliding mode controller BSMC. ​​The improved reaching law is combined to optimize the chattering problem and anti-disturbance capability of the sliding mode, so as to reduce the influence of the load mutation between branches on branch a. Meanwhile, the sliding mode anti-disturbance controller SM-ADRC is used to independently control branch b, so as to eliminate the total disturbance composed of branch coupling terms and internal and external interferences in the branch b model, and further reduce the cross-influence of the branch b disturbance on branch a. The method specifically includes the following steps:

[0147] Step 1: CCM SIDO Buck converter modeling;

[0148] The SIDO Buck converter model circuit topology is as follows Figure 1 As shown, it includes a main circuit, the main circuit is connected to branch a and branch b respectively, and the main circuit includes a circuit with input voltage V in The main power switch tubes VT connected in sequence i , the main circuit inductor L, the main circuit inductor L and the main circuit power switch tube VT i The connecting end is also connected to a freewheeling diode VD, and the branch a includes a branch a power switch tube VT which is connected in sequence with the main circuit inductor L. a , the load equivalent resistance R of branch a a , load equivalent resistance Ra The actual output capacitance C of the upper parallel branch a a , branch b includes branch b power switch tube VT connected to the main circuit inductor L in sequence b , the load equivalent resistance R of branch b b , load equivalent resistance R b The actual output capacitance C of the upper parallel branch b b ;

[0149] The state space average model of the CCM SIDO Buck converter model in step 1 is:

[0150]

[0151] In formula (1), i L is the inductor current, d i ,d a and d b They are respectively driving the power switch tube VT i VT a and VT b The duty cycle, v oa 、v ob They are the transient values ​​of the output voltages of branch a and branch b respectively. When the SIDO Buck converter works in CCM, the duty cycles of the two branches are complementary, which satisfies: a +d b =1;

[0152] The steady-state value of the output voltage of the two branches of the CCM SIDOBuck converter is v oa 、v ob The expression is:

[0153]

[0154] The sliding mode decoupling control block diagram of the CCM SIDO Buck converter based on ESO is shown in the figure. Figure 2 As shown in FIG. 1 , since the converter has multiple switch tubes, the control is complicated. Therefore, the controllers for the main switch tube and the branch switch tube are designed separately.

[0155] Step 2: Main Switch Controller Design

[0156] Main switch tube VT i To control the voltage of branch a, the system model is first modeled by considering the load disturbance term. Based on the deviation state model, the backstepping sliding mode controller and the main ESO are designed respectively, as follows:

[0157] Step 2.1: State transition modeling;

[0158] Define the voltage deviations x1 and x3 of branches a and b as:

[0159]

[0160] In formula (3), v aref 、v bref They are the reference voltages of branches a and b respectively;

[0161] For branch a, combining equation (1) and equation (3), we get:

[0162]

[0163] In formula (4), is the bounded disturbance caused by the load change of branch a, R 0a is the nominal value of the equivalent resistance of branch load a;

[0164] According to formula (1), x2 is defined as:

[0165]

[0166] According to equations (4) and (5), the deviation model of branch a is rewritten as:

[0167]

[0168] In formula (6),

[0169] According to the above method, the deviation model of branch b is rewritten as:

[0170]

[0171] In formula (7),

[0172] Step 2.2: Backstepping sliding mode controller design;

[0173] The a branch adopts backstepping sliding mode control. The idea is to divide the controller into two subsystems, design virtual control quantities as subsystems and introduce static compensation, so that the subsystems can be recursively controlled and stabilized, and finally form the main switch tube VT. i The control law d i The specific design can be divided into two steps:

[0174] Step 1: Define the tracking error ξ1 of branch a as:

[0175] ξ1=x1=v oa -v aref (8)

[0176] Define the Lyapunov function V1 as:

[0177]

[0178] Introducing the virtual control quantity ξ2, we get:

[0179]

[0180] In formula (10), α is a positive constant;

[0181] After taking the derivative of formula (9), substitute formula (10) to obtain:

[0182]

[0183] Equation (11) represents the first subsystem constructed by the backstepping method. In order to make it stable, it must satisfy Therefore, it is necessary to make ξ2 converge to 0;

[0184] Step 2: Define the sliding surface S = ξ2 in combination with sliding mode variable structure control. Substitute equation (6) into equation (10) to obtain:

[0185] S=x2+f1(t)+αξ1 (12)

[0186] Define the Lyapunov function V i for:

[0187]

[0188] In formula (13), V2 = 0.5S 2 ;

[0189] Taking the derivative of formula (13) we get:

[0190]

[0191] The improved reaching law is selected as:

[0192]

[0193] In formula (15), 0<τ<1, k1>0, and the form of the adaptive function f(S) is:

[0194]

[0195] In formula (16), γ>1, ε>0, k2>0.

[0196] The form of the sigmoid (S) function in formula (15) is:

[0197]

[0198] In formula (17), κ>0.

[0199] Figure 3 shows the image comparison of two groups of functions, where Figure 3(a) shows the function (|S|+1) -ε|S| With the function e -ε|S| Figure 3(b) shows the image comparison of the continuous function sigmoid(S) and the symbol function sign(S). Analyzing equation (16) and Figure 3(a), we can see that the function (|S|+1) -ε|S| As |S| increases, it approaches 0, and as |S| decreases, it approaches 1. This is similar to the function e in

[15] . -ε|S| In comparison, when ε takes the same value, |S| increases, and the convergence characteristics of the two functions are similar, both of which can make f(S) quickly approach γk2, making the state quantity approach faster. When the system state approaches the sliding surface, that is, |S| is approaching 0, the function (|S|+1) -ε|S| The trend close to 1 is gentler and the state quantity approaches more slowly, which makes the function f(S) have better adjustment performance.

[0200] From the analysis of formula (17) and Figure 3(b), we can see that changing the value of κ can change the slope of the function sigmoid(S). When the value of κ is larger, the image is closer to the sign function sign(S). When S is 0, the function sigmoid(S) will not be unable to take a value, which improves the discontinuity of the original switching control and suppresses chattering.

[0201] Comparison of the motion characteristics of the sliding mode under the action of the improved reaching law and the exponential reaching law Figure 4 As shown, the exponential reaching law expression is:

[0202]

[0203] Analytical formula (18) and Figure 4 It can be seen that when the system state is far from the sliding surface, the exponential term k1S plays a dominant role. When the system state is close to the sliding surface, since the switching function sign(S) always has a gain k2, the exponential reaching law will eventually form chattering near the origin. The improved reaching law is f(S)|S| when approaching the sliding surface. τ Sigmoid(S) plays a leading role, and the approach trajectory is a smooth and continuous curve. As the sliding mode motion approaches the origin, the approach speed becomes slower, and the gain of the switching function sigmoid(S) eventually approaches 0 as x1 decreases.

[0204] Note 1: The convergence law parameters mainly include k1, τ, k2, γ, and ε. When the system state is far away from the sliding surface, appropriately increasing the value of the exponential term coefficient k1 according to the dynamic performance of the system can improve the rapidity of the system. The power term parameter is selected as 0<τ<1, which can ensure that when the system state is close to the sliding surface, there is a smaller control gain to reduce the vibration. Increasing k2 and γ can increase the convergence speed, but at the same time it will increase the generation of vibration, so the value should not be too large. Adjustment of the size of ε (|S|+1) -ε|S| The speed approaching 0 determines the adjustment range of f(S). Considering the specific working conditions of the converter, the value of ε should not be too small.

[0205] Since equation (14) contains unknown disturbance terms and model parameter deviations, it is necessary to establish a main road ESO to observe the variables in the equation and compensate them into the control law, thereby improving system performance.

[0206] Step 2.3: Main road ESO design;

[0207] According to equations (6) and (7), the main road ESO is:

[0208]

[0209] In formula (19), z1 and z2 are the observed values ​​of the state variable x1 of the deviation model of branch a and the bounded load disturbance f1(t), z3 and z4 are the observed values ​​of the state variable x3 of the deviation model of branch b and the bounded load disturbance f3(t), β = [β1, β2, β3, β4] is the gain value of the observer, and β1 = β3 > 0, β2 = β4 > 0;

[0210] The size of the observer gain β will affect the anti-interference ability of the system. Therefore, selecting a suitable gain combination can ensure that the value of β is within the feasible range. According to formula (19), taking the a branch observer in the main road ESO as an example, the a branch observer is rewritten as follows:

[0211]

[0212] In formula (20), z = [z1, z2] T , x=[x1,x2] T ;

[0213] According to equation (20), the two poles of the a-branch observer are configured to the left half plane, and we can obtain:

[0214] |sE0-A|=s 2 +β1s+β2=(s+ω0) 2 (twenty one)

[0215] In formula (21), E0 is the unit matrix, ω0 is the bandwidth of the main ESO;

[0216] According to formula (21), the observer gain β is configured as:

[0217]

[0218] If the observer gain is adjusted based on the system switching frequency, the observed value can maintain a good tracking effect on the state variables and disturbances, that is, z1→x1, z2→f1(t), z3→x3, z4→f3(t). The error analysis method of the main ESO is the same as that of Wang J, Li S, Yang J, et al. Extended state observer based sliding mode control for PWM-based DC-DC buck power converter systems with mismatched disturbances [J]. IET Control Theory & Applications, 2015, 9 (4): 579-586., and will not be repeated here.

[0219] According to equations (12)-(17) and equations (6) and (19), the main switch control law d is obtained i for:

[0220]

[0221] In formula (23), z5 is the observed value of x2;

[0222] At this point, the design of the main switch controller is completed.

[0223] In summary, the control block diagram of the main ESO+BSMC of the CCMSIDO Buck converter is as follows: Figure 5 shown.

[0224] Main road control system stability analysis

[0225] Lemma 1: For the following continuous and smooth hyperbolic tangent function:

[0226]

[0227] In formula (24), The size of the value determines how fast the inflection point of the hyperbolic tangent function changes.

[0228] According to the properties of the hyperbolic tangent function, for any x∈R, there exists a constant So that the following inequality holds

[16] :

[0229]

[0230] In formula (25), μ=0.2785.

[0231] Lemma 2: For any real number x i , if there exists h∈(0,1), then the following inequality holds:

[0232] (|x1|+…+|x n |) h ≤|x1| h +…+|x n | h (26)

[0233] Lemma 3: The finite-time Lyapunov stability theorem holds for For such a nonlinear system, and f(0) = 0, assume that there exists a continuously differentiable positive definite function V(x), scalar λ>0, 0<υ<1 and 0<ζ<∞, such that V(x)≤-λV υ (x)+ζ holds, then we can say that the system It is practical finite-time stable (PFS) and converges in time T reach for

[18] :

[0234]

[0235] In formula (27), 0≤θ0≤1, V(x0) is the initial value of V(x).

[0236] Note 2: For a DC-DC converter system, the estimation errors of the ESO for both the state variables and disturbance terms of the system are bounded.

[0237] Theorem 1: For the CCM SIDO Buck converter of equation (1), under the action of the improved reaching law of equation (15), the extended state observer of equation (19), and the backstepping sliding mode controller of equation (23), the main control system of the converter is practically finite-time stable, and the output voltage of branch a eventually converges to the expected value.

[0238] Proof: Substitute equation (6) into equation (14) and replace Then, substitute formula (23) into formula (14) to obtain:

[0239]

[0240] In formula (28), e1, e2, e3, e4, e5 are x1, x3, f1(t), x2, The estimated error between its observed value;

[0241] According to formula (17), the expression of sigmoid (S) function is:

[0242]

[0243] According to formula (24), the expression of tanh(S) function is:

[0244]

[0245] According to Lemma 1 and combined with Equation (29) and Equation (30), the following inequality holds for the sigmoid(S) function:

[0246]

[0247] Substituting formula (31) into formula (28), the following inequality holds:

[0248]

[0249] According to the basic inequality theorem, equation (32) can be transformed into:

[0250]

[0251] In formula (33), are the upper bounds of the estimation errors e1 to e5; α>1 / (R 0a C a ), k1>0.5, σ1>0, σ1>0, ψ>0 and

[0252] According to Lemma 2, we can get:

[0253]

[0254] In equation (34), σ3=min(σ1, σ2).

[0255] According to Lemma 3 and Eq. (34), the system is practically finite-time stable and converges within T reach for:

[0256]

[0257] The state variables of the system will converge to the following stable domain Θ in a finite time:

[0258]

[0259] That is, there exists a neighborhood Δ of the sliding surface that satisfies:

[0260]

[0261] Let S≤Δ, according to equations (6), (8) and (37), we can obtain:

[0262]

[0263] Solving equation (38) yields:

[0264]

[0265] According to equation (39), if the value of α is large enough, then when t→∞, x1(t)→0, that is, the output voltage v of branch a is oa Finally, it can converge to the reference voltage v of branch a aref nearby.

[0266] Step 3: Branch switch controller design

[0267] Branch switch tube VT b It is used to control the voltage of branch b. Since there is parameter coupling between branches, the idea of ​​the branch controller is to separate branch b from the system, complete the one-to-one correspondence between the input and output loops, and convert the obtained control law d b Coordinate with the main controller to complete the overall control. Therefore, according to the characteristics of ADRC that it does not rely on the object model, first establish a fitting model for branch b, then establish the branch ESO based on the fitting model, and finally design a sliding mode active disturbance rejection controller based on the branch ESO as the framework, as follows:

[0268] Step 3.1: Branch system fitting;

[0269] According to the self-disturbance rejection paradigm, the second-order system of branch b is defined as:

[0270]

[0271] In formula (40), is the total disturbance required; is the output voltage v of branch b ob , u is the driving signal d of branch b b , b is the exact value of the control gain, It is the comprehensive characteristics of the time-varying dynamics and external disturbances generated by the coupling between branches in the system. Since the value of b is not easy to obtain, the easily available estimated value b0 is used as the control gain.

[0272] By using the state average method to model the converter for small signals, the control-output transfer function of branch b can be obtained as follows:

[0273]

[0274] In formula (41), a0 = R a -2d b R a +d b 2 R a +d b 2 R b

[0275] a1=L+C b R a R b -2C b d b R a R b +C a d b 2 R a R b +C b d b 2 R a R b

[0276] a2=C a LR a +C b LR b

[0277] a3=C a C b LR a R b

[0278] c0=(I L -d b )I L R a R b +d b R b (v oa -v ob )

[0279] c1=I L LR b +C a d b R a R b (v oa -v ob )

[0280] c2=C a I L LR a R b

[0281] According to the form of formula (40), formula (41) is rewritten as:

[0282]

[0283] In formula (42), according to formula (40), b0 = c1 / a3,

[0284] Step 3.2, branch ESO design;

[0285] Different from the design of the main ESO in step 2.3, the branch ESO must observe the output term and the total disturbance term, and define the state variable of branch b as:

[0286]

[0287] The b-branch fitting system model is written as:

[0288]

[0289] In formula (44), C = [1 0 0];

[0290] According to formula (44), the designed branch ESO is:

[0291]

[0292] In formula (45), θ=[θ1,θ2,θ3]T; θ1, θ2, θ3 are the outputs of branch b respectively. Derivative of the output and the observed value of the total disturbance ω; is the observation error of branch ESO; L=[l1,l2,l3] T is the gain of the observer;

[0293] The characteristic polynomial of the branch ESO is obtained by Laplace transforming equation (45), and then configured with the branch ESO bandwidth to obtain:

[0294] s 3 +l1s 2 +l2s+l3=(s+ω1) 3 (46)

[0295] In formula (46), ω1 is the bandwidth of the branch ESO, and the corresponding configuration of the branch ESO gain is l1 = 3ω1, l2 = 3ω12 , l3=ω1 3 ;

[0296] If the observer gain is adjusted based on the switching frequency of the branch control system, the observed value can maintain a good tracking effect on the output and the total disturbance, that is, θ1→η1, θ2→η2, θ3→η3.

[0297] Note 3: ESO usually uses 3 to 5 times the system crossover frequency to configure the observer bandwidth, so that the observation rate of ESO is much higher than the system operation rate. Then, feedforward compensation can be performed on the estimation of interference and state quantities, which can eliminate steady-state errors and reduce the impact of disturbances in control.

[0298] Step 3.3: Sliding mode ADRC design;

[0299] The output tracking error of branch b is defined as:

[0300] e0=θ1-v bref (47)

[0301] Taking the first and second order derivatives of equation (47) respectively, we get:

[0302]

[0303] Select the sliding surface S1 as:

[0304]

[0305] The sliding mode reaching law is chosen as:

[0306]

[0307] In formula (50), w1>0, w2>0;

[0308] According to equations (47)-(50), the branch switch control law is:

[0309]

[0310] Note 4: b0 is the disturbance compensation factor of the observer. If the value is too large or too small, it will affect the compensation effect and dynamic performance. Therefore, after the circuit parameters are initially determined according to formula (42), they are gradually adjusted based on the response speed of the system.

[0311] According to formula (45), the state variable η3, i.e., ω, representing the disturbance is expanded in the fitting system model of branch b and tracked by the state variable θ3 of branch ESO. Substituting formula (51) into formula (44) to reduce the total disturbance η3 (i.e., θ3), the original object is simplified to an integral series system, i.e.:

[0312]

[0313] In formula (52), u0 = -w1S1 - w2sign(S1) - cθ2

[0314] At this point, the branch switch controller design is completed.

[0315] In summary, the CCMSIDO Buck converter branch SM-ADRC control block diagram is as follows: Figure 6 shown.

[0316] Branch control system and branch ESO stability analysis

[0317] Define the Lyapunov function V3 as:

[0318]

[0319] Taking the derivative of formula (53) we can get:

[0320]

[0321] From formula (54), we can see that The designed controller satisfies the Lyapunov stability criterion, and the branch control system can quickly converge to the sliding surface within a finite time. The analysis method is the same as branch a and will not be repeated here.

[0322] The branch ESO tracking error is defined as:

[0323]

[0324] In formula (55), e a 、e b 、e c is the error between the observed value and the actual value;

[0325] By Laplace transforming equation (55), the characteristic equation of the branch ESO error system can be obtained as:

[0326] s 3 +3ω1s 2 +3ω1 2 s+ω1 3 =0 (56)

[0327] Analyzing equation (56), we can see that the characteristic roots of the characteristic equation are all located in the left half plane of the s plane. Therefore, the branch ESO error system is stable. According to the terminal value theorem of Laplace transform, when t→∞, the observation error in equation (56) tends to 0.

[0328] Simulation Analysis

[0329] In order to verify the effectiveness of the control algorithm, the controller control strategy designed by the present invention and the common mode voltage and differential mode voltage (CMV-DMV) control simulation circuits were built for the CCM SIDO Buck converter in the PSIM simulation software. The simulated circuit parameters are: V in =30V, R 0a =10Ω, R 0b =20Ω,v aref =10V,v bref =20V, f s =100kHz, L = 50μH, C a =C b =300μF; the controller parameters are shown in Table 1.

[0330] Table 1 Control strategy parameters of this paper

[0331]

[0332] (I) Comparison between the proposed control strategy and CMV-DMV control simulation

[0333] 1) Load disturbance comparison

[0334] In order to compare the cross-effects between the two types of control under load disturbance, the output voltage waveforms under the disturbance of branches a and b are selected as shown in Figures 7 and 8 respectively.

[0335] Analysis of Figure 7 shows that at 0.04s, the load of branch a increases, and the output current changes from 1A to 2A; at 0.05s, the load of branch a decreases, and the output current of branch a changes from 2A to 1A. The maximum overshoot caused by the self-disturbance of branch a of the converter under CMV-DMV control is 2.2V, and the voltage of branch b is v ob The maximum overshoot caused by the load change of branch a is 1.6V. The maximum overshoot caused by the disturbance of branch a itself under the control strategy of this paper is 0.035V, and the voltage of branch b is v ob The maximum overshoot caused by the load change of branch a is 0.06V. It can be seen that the main ESO+BSMC significantly improves the anti-interference ability of branch a.

[0336] Analysis of Figure 8 shows that at 0.07s, the load of branch b increases, and the output current changes from 1A to 2A; at 0.08s, the load of branch b decreases, and the output current of branch b changes from 2A to 1A. The maximum overshoot caused by the self-disturbance of branch b of the converter under CMV-DMV control is 1.6V, and the voltage of branch a is v oaThe maximum overshoot caused by the load change of branch b is 1.3V. However, the maximum overshoot caused by the disturbance of branch b itself under the control strategy of this paper is 0.025V, and the voltage of branch a v oa The maximum overshoot caused by the load change of branch b is 0.015V. It can be seen that the SM-ADRC control of branch b makes branch a have almost no cross-effect, and only the voltage ripple changes.

[0337] 2) Input voltage disturbance comparison

[0338] In order to compare the dynamic performance of the two controls under input voltage disturbance, the simulated output waveforms of the two controls are shown in FIG9 .

[0339] From the analysis of Figure 9, it can be seen that the converter is subjected to -5V and +10V input voltage disturbances at 0.06s and 0.08s respectively. The maximum overshoot of the voltage of the two branches of the converter under CMV-DMV control caused by the input voltage disturbance is 2.4V, and the adjustment range is significantly larger when the input voltage increases from 25V to 35V at 0.08s. However, the maximum overshoot of the output voltage of the two branches of the converter under the control strategy of this paper is 0.01V caused by the input voltage disturbance, and the overshoot and adjustment time caused by the two disturbances at 0.06s and 0.08s are similar. Therefore, the control strategy of this paper controls the CCM SIDO Buck converter with better robustness and dynamic performance.

[0340] (II) Comparison of ESO’s control effects

[0341] 1) Comparison of branch a control methods

[0342] In order to verify the compensation effect of ESO on control, branch a selects ESO+BSMC and conventional BSMC output for comparison, and the control method of branch b remains unchanged. The simulation results are shown in Figure 10.

[0343] From the analysis of Figure 10, it can be seen that when the output voltage of branch a is disturbed by the input voltage of -5V and +5V at 0.03s and 0.04s, and by the load current jump of 1A-2A and 2A-1A at 0.05s and 0.06s, if branch a only uses BSMC, there will be steady-state errors of varying degrees after the disturbance. If branch a uses ESO+BSMC, after compensating for the disturbance, the steady-state error is eliminated, the output voltage of branch a is stabilized at the reference value, and the voltage ripple is significantly reduced.

[0344] 2) Comparison of branch b control methods

[0345] The SM-ADRC is selected for branch b to compare with the traditional SMC output. The control method of branch a remains unchanged. The simulation results are shown in Fig.11 shown.

[0346] analyze Fig.11 It can be seen that when branch b is subjected to input voltage disturbances of -5V and +5V at 0.055s and 0.065s, and load current jumps of 1A-2A and 2A-1A at 0.07s and 0.08s, if only the traditional SMC is used to control branch b, since the fitting system of branch b is not an accurate model, the traditional SMC fails to eliminate the total disturbance caused by the deviation of the modeling and the disturbance effect, and the output steady-state error of branch b is up to 0.4V, and it cannot return to the reference voltage v bref If SM-ADRC is used in branch b, the unknown total disturbance can be estimated and compensated in real time according to the operation of the converter, which can not only follow the reference voltage v of branch b well, but also bref , combined with the advantages of sliding mode control, good anti-disturbance performance and transient response speed are obtained.

[0347] 3) Comparison between ESO observations and actual values

[0348] In order to verify the observation effect of ESO on state variables and disturbances, the ESO observation values ​​of two branches are selected for comparison with the actual values. The simulation results are shown in Figure 12.

[0349] In Figure 12, branch a experiences a load current jump of 1A-2A and 2A-1A at 0.04s and 0.05s, and branch b experiences a load current jump of 1A-2A and 2A-1A at 0.07s and 0.08s. Analysis of the actual output voltage values ​​and observed value magnifications of the two branches in Figure 12(a) shows that the observed value can follow the output voltage well. Taking branch a as an example, the overshoot and adjustment time when subjected to load disturbance at 0.04s are also significantly smaller than the real-time output value. Analysis of Figures 12(b) and 12(c) shows that the main ESO can follow the load disturbance of branch a well, and when the load of branch b is disturbed, the output voltage of branch a is less affected, and the disturbance only changes slightly. The branch ESO is used to observe the total disturbance of the branch b model, and the influence of the load disturbance on the two branches can be accurately estimated, thereby ensuring the stability of the output of branch b.

Claims

1. A sliding mode decoupling controller design method for a single-inductor dual-output Buck converter based on ESO, characterized in that: The main line ESO is used to estimate the load disturbance and compensate it to the backstepping sliding mode controller BSMC, and the improved reaching law is combined to optimize the chattering problem and anti-disturbance ability of the sliding mode to reduce the impact of the load mutation between branches on branch a; at the same time, the sliding mode self-disturbance rejection controller SM-ADRC is used to independently control branch b, eliminating the total disturbance composed of branch coupling terms and internal and external interference in the branch b model, and further reducing the cross-effect of branch b disturbance on branch a. The specific steps include: Step 1: CCM SIDO Buck converter modeling; The SIDO Buck converter model includes a main circuit, which is connected to branch a and branch b. The main circuit includes a circuit connected to the input voltage V in The main power switch tubes VT connected in sequence i , the main circuit inductor L, the main circuit inductor L and the main circuit power switch tube VT i The connecting end is also connected to a freewheeling diode VD, and the branch a includes a branch a power switch tube VT which is connected in sequence with the main circuit inductor L. a , the load equivalent resistance R of branch a a , load equivalent resistance R a The actual output capacitance C of the upper parallel branch a a , branch b includes branch b power switch tube VT connected to the main circuit inductor L in sequence b , the load equivalent resistance R of branch b b , load equivalent resistance R b The actual output capacitance C of the upper parallel branch b b ; The state space average model of the CCM SIDO Buck converter model in step 1 is: In formula (1), i L is the inductor current, d i d a and d b They are respectively driving the power switch tube VT i VT a and VT b The duty cycle, v oa 、v ob They are the transient values ​​of the output voltages of branch a and branch b respectively. When the SIDO Buck converter works in CCM, the duty cycles of the two branches are complementary, which satisfies: a +d b =1; The steady-state value of the output voltage of the two branches of the CCM SIDOBuck converter is v oa 、v ob The expression is: Step 2: Main Switch Controller Design Main switch tube VT i To control the voltage of branch a, the system model is first modeled by considering the load disturbance term. Based on the deviation state model, the backstepping sliding mode controller and the main ESO are designed respectively, as follows: Step 2.1: Modeling state transitions; Step 2.1 is as follows: Define the voltage deviations x1 and x3 of branches a and b as: In formula (3), v aref 、v bref They are the reference voltages of branches a and b respectively; For branch a, combining equation (1) and equation (3), we get: In formula (4), is the bounded disturbance caused by the load change of branch a, R 0a is the nominal value of the equivalent resistance of branch a load; According to formula (1), x2 is defined as: According to equations (4) and (5), the deviation model of branch a is rewritten as: In formula (6), According to the above method, the deviation model of branch b is rewritten as: In formula (7), Step 2.2: Backstepping sliding mode controller design; Step 2.3: Main road ESO design; Step 3: Branch switch controller design Branch switch tube VT b It is used to control the voltage of branch b. Since there is parameter coupling between branches, the idea of ​​the branch controller is to separate branch b from the system, complete the one-to-one correspondence between the input and output loops, and convert the obtained control law d b The overall control is completed by coordinating with the main controller. Therefore, according to the characteristics of ADRC that it does not rely on the object model, a fitting model is first established for branch b, and then the branch ESO is established based on the fitting model. Finally, the sliding mode active disturbance rejection controller is designed based on the branch ESO as the framework, as follows: Step 3.1: Branch system fitting; Step 3.1 is as follows: According to the self-disturbance rejection paradigm, the second-order system of branch b is defined as: In formula (40), is the total disturbance required; is the output voltage v of branch b ob , u is the driving signal d of branch b b , b is the exact value of the control gain, It is the comprehensive characteristics of the time-varying dynamics and external disturbances generated by the coupling between branches in the system. Since the value of b is not easy to obtain, the easily available estimated value b0 is used as the control quantity gain. The converter is modeled with small signals using the state averaging method, and the control-output transfer function of branch b is obtained as follows: In formula (41), a0 = R a -2d b R a +d b2 R a +d b2 R b a1=L+C b R a R b -2C b d b R a R b +C a d b 2 R a R b +C b d b 2 R a R b a2=C a LR a +C b LR b a3=C a C b LR a R b c0=(I L -d b )I L R a R b +d b R b (v oa -v ob ) c1=I L LR b +C a d b R a R b (v oa -v ob ) c2=C a I L LR a R b According to the form of formula (40), formula (41) is rewritten as: In formula (42), according to formula (40), b0 = c1 / a3, Step 3.2, branch ESO design; Step 3.3: Sliding mode ADRC design.

2. The design method of sliding mode decoupling controller of single inductor dual output Buck converter based on ESO according to claim 1 is characterized in that: Step 2.2 is as follows: The tracking error ξ1 of branch a is defined as: ξ1=x1=v oa -v are f (8) Define the Lyapunov function V1 as: Introducing the virtual control quantity ξ2, we get: In formula (10), α is a positive constant; After taking the derivative of formula (9), substitute formula (10) to obtain: Equation (11) represents the first subsystem constructed by the backstepping method. In order to make it stable, it must satisfy Therefore, it is necessary to make ξ2 converge to 0; Combined with sliding mode variable structure control, the sliding surface S = ξ2 is defined. Substituting equation (6) into equation (10), we get: S=x2+f1(t)+αξ1 (12) Define the Lyapunov function V i for: In formula (13), V2 = 0.5S 2 ; Taking the derivative of formula (13) we get: The improved reaching law is selected as: In formula (15), 0<τ<1, k1>0, the form of the adaptive function f(S) is: In formula (16), γ>1, ε>0, k2>0; The form of the sigmoid (S) function in formula (15) is: In formula (17), κ>0.

3. The design method of sliding mode decoupling controller of single inductor dual output Buck converter based on ESO according to claim 2 is characterized in that: Step 2.3 is as follows: According to equations (6) and (7), the main road ESO is: In formula (19), z1 and z2 are the observed values ​​of the state variable x1 of the deviation model of branch a and the bounded load disturbance f1(t), z3 and z4 are the observed values ​​of the state variable x3 of the deviation model of branch b and the bounded load disturbance f3(t), β = [β1, β2, β3, β4] is the gain value of the observer, and β1 = β3 > 0, β2 = β4 > 0; According to formula (19), the a-branch observer is rewritten as follows: In formula (20), z = [z1, z2] T , x=[x1,x2] T ; According to formula (20), the two poles of the a-branch observer are configured to the left half plane: |sE0-A|=s 2 +β1s+β2=(s+ω0) 2 (21)In formula (21), E0 is the unit matrix, ω0 is the bandwidth of the main ESO; According to formula (21), the observer gain β is configured as: According to equations (12)-(17) and equations (6) and (19), the main switch control law d is obtained i for: In formula (23), z5 is the observed value of x2; At this point, the design of the main switch controller is completed.

4. The design method of sliding mode decoupling controller of single inductor dual output Buck converter based on ESO according to claim 1 is characterized in that: Step 3.2 is as follows: Define the state variable of branch b as: The b-branch fitting system model is written as: In formula (44), C = [1 0 0]; According to formula (44), the designed branch ESO is: In formula (45), θ = [θ1, θ2, θ3] T θ1, θ2, θ3 are the outputs of branch b system respectively Derivative of the output and the observed value of the total disturbance ω; is the observation error of branch ESO; L=[l1,l2,l3] T is the gain of the observer; The characteristic polynomial of the branch ESO is obtained by Laplace transforming equation (45), and then configured with the branch ESO bandwidth to obtain: s 3 +l1s 2 +l2s+l3=(s+ω1) 3 (46) In formula (46), ω1 is the bandwidth of the branch ESO, and the corresponding configuration of the branch ESO gain is l1 = 3ω1, l2 = 3ω1 2 , l3=ω1 3 ; If the observer gain is adjusted based on the switching frequency of the branch control system, the observed value will maintain a good tracking effect on the output and the total disturbance, that is, θ1→η1, θ2→η2, θ3→η3.

5. The design method of sliding mode decoupling controller of single inductor dual output Buck converter based on ESO according to claim 4 is characterized in that: Step 3.3 is as follows: The output tracking error of branch b is defined as: e0=θ1-v bref (47) Taking the first and second order derivatives of equation (47) respectively, we get: Select the sliding surface S1 as: The sliding mode reaching law is chosen as: In formula (50), w1>0, w2>0; According to equations (47)-(50), the branch switch control law is: According to formula (45), the state variable η3, i.e., ω, representing the disturbance is expanded in the fitting system model of branch b and tracked by the state variable θ3 of branch ESO. Substituting formula (51) into formula (44) eliminates the total disturbance η3, i.e., θ3, and the original object is simplified to an integral series system, i.e.: In formula (52), u0 = -w1S1 - w2sign(S1) - cθ2 At this point, the branch switch controller design is completed.

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