SIDO Buck-Boost converter control method based on improved fractional order linear extended state observer

Abstract

The invention discloses an SIDO Buck-Boost converter control method based on an improved fractional order linear expansion state observer, and the method specifically comprises the following steps: 1, building a state space averaging model of a write SIDO Buck-Boost converter according to a state space averaging method, and converting the model into a second-order active-disturbance-rejection normal form; 2, designing an improved fractional order linear expansion state observer; 3, designing a logarithmic convergence sliding mode controller; and step 4, designing a control rule of the SIDO Buck-Boost converter. According to the method, the problems that the external total disturbance estimation precision of the single-inductor dual-output converter is insufficient due to traditional active disturbance rejection control and cross influence exists between two output branches are solved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of electronic power, and relates to an SIDO Buck-Boost converter control method based on an improved fractional order linear extended state observer. BACKGROUND

[0002] The control strategy of the single-inductor dual-output Buck-Boost converter faces many unique challenges. The traditional method mainly adopts a time-multiplexed PWM control architecture to achieve dual-output by alternately allocating the inductor current, but this method has obvious limitations under dynamic conditions. Since the two outputs share the same energy storage element, when one of the loads suddenly changes, it will affect the stability of the other output through inductor current coupling, causing significant cross-regulation. Existing control strategies often need to compromise between response speed and regulation accuracy when dealing with this problem, making it difficult to meet the requirements of fast transient response and accurate voltage regulation. The Buck-Boost converter needs to smoothly switch between Buck, Boost, and transition modes, and traditional linear control methods perform poorly in handling this nonlinear characteristic. Although PI and other nonlinear control strategies can provide better robustness, their inherent chattering problem introduces additional harmonic interference. Although advanced algorithms such as predictive control developed in recent years can theoretically improve system performance, they face implementation challenges such as high computational complexity and difficult parameter tuning in practical applications. In addition, the time delay effect and sampling quantization error introduced by digital control also bring new factors to consider for control strategy design. These control-level difficulties jointly restrict the promotion and use of single-inductor dual-output Buck-Boost converters in high-end application fields.

[0003] In response to the control difficulties of the single-inductor dual-output Buck-Boost converter, the academic community has proposed various advanced nonlinear control strategies. Among them, sliding mode control exhibits superior performance under parameter perturbation conditions due to its strong robustness; differential flatness control effectively manages nonlinear dynamics through accurate description of system differential geometric characteristics; adaptive control significantly improves system stability under time-varying conditions by adjusting control parameters online. In particular, the anti-disturbance control technology is worth noting, which takes the extended state observer as the core component, estimates the system state in real time, and feeds the observation value back to the control loop, achieving excellent anti-interference ability without relying on accurate mathematical models. This control architecture significantly decouples the system, effectively suppressing cross-regulation; the algorithm structure is simple and efficient; it has fast dynamic response and high-precision tracking capability, and has shown excellent control effect in practical engineering applications. SUMMARY

[0004] The application aims to provide a SIDO Buck-Boost converter control method based on an improved fractional order linear extended state observer, solve the problem of insufficient estimation accuracy of external total disturbance of a traditional active disturbance rejection control for a single-inductor dual-output converter and cross influence between two output branches.

[0005] The technical scheme adopted by the application is that the SIDO Buck-Boost converter control method based on the improved fractional order linear extended state observer specifically comprises the following steps: Step 1: a state space average model of the SIDO Buck-Boost converter is established according to a state space average method, and the model is converted into a second-order active disturbance rejection paradigm; Step 2: an improved fractional order linear extended state observer is designed; Step 3: a logarithmic convergent sliding mode controller is designed; Step 4: a control law of the SIDO Buck-Boost converter is designed.

[0006] The specific process of step 1 is as follows: The state space average model of the SIDO Buck-Boost converter is established according to the state space average method, as shown in the following formula (1):

[0007] In the formula, V in indicates a converter input voltage value; L 、 C a and C b indicate a converter energy storage inductance value and a branch filter capacitance value respectively; R a 、 R b is a load resistance; V a 、 V b is an output voltage; i L is an inductance current value; S i1 、 S i2 is a main switch tube, S a 、 S b indicate branch switch tubes of branch a and branch b respectively, d i is a main switch tube S il 、 Si2 duty cycle, d a , d b They are respectively S a , S b The duty cycle, and satisfying d a + d b =1, v a , v b These represent the transient output voltage values ​​of the two branches, respectively. As shown in equation (1), the SIDO Buck-Boost converter is a typical second-order system. Therefore, the state-space average model of the converter is fitted to a standard second-order system, as shown in equation (2) below:

[0008] In the formula, y o u is the system output, and u is the system input. This indicates external disturbances to the system. b Indicates the system input gain. a 1. a 2 represents system parameters; Separate the internal uncertainties of the system and include the internal and external disturbances into the total disturbance, and rewrite the system as shown in the following formula (3):

[0009] In the formula, b o This is an estimated value. This represents the total disturbance.

[0010] The specific process of step 2 is as follows: Take feedforward error signal e f = y - y ref , y ref Given the input values ​​to the system, and following the design principles of the extended state observer, the state variables are first defined. x 1= e f , x 2= , x 3= f Thus, the state-space expression of equation (4) is obtained:

[0011] The fractional order linear extended state observer for equation (4) is established as:

[0012] The bias of the alternative e1 is designed to adjust the derivatives of z2 and z3, as shown in equation (6):

[0013] The equation (6) is arranged as:

[0014] From equation (7), we have z 2 and x 2, the error between 3 and z 3 is x , and the improved fractional order linear extended state observer is constructed as:

[0015] In the formula, e 1 represents the observation error, e 1 is the difference between the observed value and the actual value; z 1 is the estimated value of x 1; z 2 is the estimated value of x 2, and z3 is the total disturbance of the coupling term, internal disturbance and unmodeled part f ; β 1, β 2 are the gains of the observer.

[0016] The specific process of step 3 is: according to the observed state variable x 1 of the observer z 1, the error between the system output value and the expected value e 1 is defined as:

[0017] The logarithmic convergent sliding mode surface is defined as:

[0018] In the formula, h 1, h 2, k 1 are the constants to be designed; The first-order derivative of the sliding mode surface is obtained as:

[0019] In the formula, is the first-order derivative of the sliding mode surface.​

[0020] Substitute equation (8) into equation (11) to get the equivalent control law of logarithmic convergent sliding mode u eq is:

[0021] For the switching control law, the double adaptive variable reaching law is introduced into the switching control law u sw Therefore, the controller switching control law is:

[0022] Simultaneous equations (12) and (13) to get the overall control law of the system u is:

[0023] In the formula, d>0, k2>0, c>0, ε>0, γ>1, -1<a<0, 0<b<1 are all design parameters.

[0024] The specific process of step 4 is: Step 4.1, the main road switch tube voltage single closed loop controller design; Step 4.2, the branch switch tube controller design.

[0025] The specific process of step 4.1 is: The main road is a voltage single closed loop control system, collecting b branch voltage control main switch tube, equation (1) is rewritten as:

[0026] In the formula, represents the unmodeled part of the system and external disturbance; In order to convert the controlled object into a second order active disturbance rejection paradigm, the second derivative is obtained:

[0027] Equation (16) is fitted into a second order active disturbance rejection paradigm:

[0028] In the formula, v b represents the output of b branch system, u iv is the voltage outer loop system control quantity, b 1 is the estimated value of the control quantity gain, F 1 represents the total disturbance of b branch, , , , , ; Define the b branch voltage loop improvement score of the fractional order linear extended state observer error e vb1 And the error of the logarithmic convergent sliding mode controller e vb Is:

[0029] Substitute equation (18) into equation (14) to obtain the overall control law of the main switch tube voltage loop:

[0030] The specific process of step 4.2 is: Step 4.2.1, design the voltage outer loop control law; Step 4.2.2, current inner loop control law.

[0031] The specific process of step 4.2.1 is: the branch switch tube collects the a branch voltage as the outer loop control signal, which is the same as the main switch tube voltage loop control, and the mathematical model of the a branch is fitted into a second-order system:

[0032] In the formula, v a The a branch voltage outer loop system output is represented by, b 2 is the estimated value of the control gain, u av The voltage loop system control quantity is, F 2 represents the total disturbance of the a branch voltage outer loop; Define the a branch voltage outer loop observation error e va1 And the error of the logarithmic convergent sliding mode controller e va Is:

[0033] Substitute equation (21) into equation (14) to obtain the overall control law of the branch switch tube voltage outer loop:

[0034] The specific process of step 4.2.2 is: The branch switch tube collects the inductor current i L As the inner loop control signal, first fit the mathematical model of the a branch inner loop inductor current into a second-order system:

[0035] In the formula, i Lrepresents the a branch current inner loop system output quantity, b 3 is a control quantity gain, u ai is a current loop system control quantity, F 3 represents the a branch current inner loop total disturbance; define the a branch current inner loop observation error e ia1 and the logarithmic convergent sliding mode controller error e ia is:

[0036] Substitute formula (24) into formula (14), the whole control law of the branch switch tube current inner loop is:

[0037] The beneficial effects of the present application are: the present application first models SIDO Buck-Boost and converts it into a second-order active disturbance rejection paradigm, improves the system, and designs a fractional linear extended state observer and a controller, and the specific effects are as follows: (1) the fractional linear extended state observer is improved by introducing a fractional calculus link to the basic framework of the traditional linear extended state observer, and the derivative of the update error e (t) is designed to adjust z 2 and the derivative of z 3, so that z 2, z 3 more accurately and quickly approximate x 2, x3. In this way, the performance of the observer is improved, and the observation ability of the disturbance is improved. (2) The traditional SMC usually adopts a linear sliding surface, and the convergence speed is limited by a fixed gain, and the convergence time is slow. The logarithmic convergence sliding mode provides stronger convergence drive when the error is large, and accelerates the response speed in the initial stage. Through the smooth transition of the nonlinear sliding surface, the mutation of the control input is reduced, thereby reducing the chattering amplitude. When the error is large, the logarithmic term enhances the control effect and accelerates the convergence. When the error is small, the logarithmic term weakens the control effect and avoids excessive regulation. Through the natural nonlinear convergence mechanism, stability can be achieved at a lower gain, and high-frequency excitation of the system is reduced. (3) The double adaptive variable speed approach law is designed, different approach laws can be represented at different positions according to the boundary layer adaptive variable speed approach law. This method can make the system retain the exponential term when far away from the boundary layer, to a certain extent, avoid the interference of the constant speed term, and reach the sliding surface with faster convergence speed, and reduce the convergence speed when close to the sliding surface, and play the stable convergence characteristics of the constant speed term, and reduce the inertia. Finally, the variable speed effect is realized, the chattering is suppressed, and the convergence speed is improved. And it can better adapt to the influence of various uncertain factors on the system, such as parameter change, load disturbance and the like, so as to ensure the control performance of the system, and has strong robustness. BRIEF DESCRIPTION OF DRAWINGS

[0038] Figure 1 It is the overall control block diagram of the SIDO Buck-Boost converter control method based on the improved fractional order linear extended state observer of the application; Figure 2 It is the observer control block diagram in the SIDO Buck-Boost converter control method based on the improved fractional order linear extended state observer of the application; Figure 3 It is the logarithmic convergence sliding mode controller block diagram in the SIDO Buck-Boost converter control method based on the improved fractional order linear extended state observer of the application; Figure 4 (a) is a control result diagram when the load disturbance of branch a is from 1A to 2A by using the PI control strategy; i a Figure 4 (b) is a control result diagram when the load disturbance of branch a is from 1A to 2A by using the PI control strategy; Figure 4 (b) is a control result diagram when the load disturbance of branch a is from 1A to 2A by using the PI control strategy; i a Figure 4 (b) is a control result diagram when the load disturbance of branch a is from 1A to 2A by using the PI control strategy; Figure 4 (c) is a control result diagram when the load disturbance of branch a is from 1A to 2A by using the PI control strategy; i a Figure 4 (b) is a control result diagram when the load disturbance of branch a is from 1A to 2A by using the PI control strategy; Figure 4 (b) is a control result diagram when the load disturbance of branch a is from 1A to 2A by using the PI control strategy; ia The control result diagram of the SIDO Buck-Boost converter control method based on the improved fractional-order linear extended state observer of the present invention when the voltage drops abruptly from 2A to 1A; Figure 5(a) shows the load disturbance of branch b when i a The result of using a PI control strategy when A suddenly increases from 1A to 2A; Figure 5(b) shows the load disturbance of branch b when i a The result of using a PI control strategy when the A value suddenly drops from 2A to 1A; Figure 5(c) Branch b under load disturbance i a The control result diagram of the SIDO Buck-Boost converter control method based on the improved fractional-order linear extended state observer of the present invention when the converter suddenly increases from 1A to 2A; Figure 5(d) Branch b under load disturbance when i a The control result diagram of the SIDO Buck-Boost converter control method based on the improved fractional-order linear extended state observer of the present invention when the voltage drops abruptly from 2A to 1A; Figure 6(a) shows when u in The result of using a PI control strategy when the voltage suddenly increases from 20V to 30V; Figure 6(b) shows when u in The result of using a PI control strategy when the voltage drops suddenly from 30V to 20V; Figure 6(c) is when u in The control result diagram of the SIDO Buck-Boost converter control method based on the improved fractional-order linear extended state observer of the present invention when the voltage suddenly increases from 20V to 30V is shown in the figure. Figure 6(d) shows when u in The control result diagram of the SIDO Buck-Boost converter control method based on the improved fractional-order linear extended state observer of this invention when the voltage suddenly drops from 30V to 20V is shown. Detailed Implementation

[0039] The following detailed description is provided in conjunction with specific implementation methods.

[0040] Example 1 This invention relates to a SIDO Buck-Boost converter control method based on an improved fractional-order linear extended state observer, which specifically includes the following steps: Step 1, state space average model of SIDO Buck-Boost converter is listed according to state space average method, and is converted into second order active disturbance rejection paradigm; step 1 is specifically: Figure 1 In the present application, V in represents the input voltage value of the converter; L 、 C a and C b respectively represent the energy storage inductance value and branch filter capacitance value of the converter; R a 、 R b is the load resistance; V a 、 V b is the output voltage; i L is the inductance current value; S i1 、 S i2 is the main switch tube, S a 、 S b respectively represent the branch switch tube of branch a and branch b, d i is the duty cycle of the main switch tube S il 、 S i2 d a 、 d b respectively are S a 、 S b the duty cycle of d a + d b =1.

[0041] In the present application, branch a is a leading branch, and the state space average model of SIDO Buck-Boost converter is listed according to state space average method: Figure 1 (1) In the formula, v a 、 v b respectively represent the transient output voltage value of the two branches.

[0042] ​​From equation (1), SIDO Buck-Boost converter is a typical second-order system, so the state-space average model of the converter needs to be fitted into a standard second-order system: (2) In the formula, y o is the system output, u is the system input, represents the external disturbance of the system, b represents the system input gain, a 1, a 2 is the system parameter.

[0043] Separate the internal uncertainty disturbance of the system, and put the internal and external disturbances into the total disturbance, the system can be rewritten as: (3) In the formula, b o is the estimated value, is the total disturbance.

[0044] Step 2, improve the design of fractional order linear extended state observer; for the above second-order system, take the feedforward error signal e f = y - y ref , y ref is the given value of the system input. According to the design principle of extended state observer, first define the state variable x 1= e f , , x 3= f , get the state space expression of equation (4): (4) The fractional order linear extended state observer is established for equation (4): (5) In the formula, e 1 represents the observation error, e 1 is the difference between the observed value and the actual value; z 1 is the estimated value of x 1; z 2 is the estimated value of x 2, z3 is the estimated value of the total disturbance of coupling term, internal disturbance and unmodeled part, etc. f ; β 1, β 2 are the gains of the observer.

[0045] In the design of ESO, the priority of the observed variables is crucial, first make z1 quickly approach x1, second make z2 approach x2, once the order is wrong, the adjustment of the system will fail. Of course, the control of the system to z1, z2 is carried out at the same time. Under this adjustment mechanism, it is meaningless to control z2 to track x2 before z1 tracks x1 to the steady state; When the tracking adjustment of z1 to x1 is completed, the adjustment of z2 and z3 becomes difficult, because the error e1 is very small at this time. The derivative of z1 adjusted by e1 in the traditional ESO conforms to the error control principle, and the derivative of z2 adjusted by error e1 is not suitable. Therefore, the deviation instead of e1 is designed to adjust the derivative of z2 and z3.

[0046] (6) The formula (6) can be obtained: (7) From formula (7), we can get z The error between 2 and x 2 is , z The error between 3 and x 3 is . Using it as a control variable can speed up the convergence speed of the system, and thus the improved fractional order linear extended state observer is constructed as: (8) Step 3: Design of logarithmic convergence sliding mode controller; According to the observed state variable x 1 observed by the observer z 1, the error between the system output value and the expected value e is defined as: (9) The logarithmic convergence sliding surface is defined as: (10) In the formula, h 1, h 2, k 1 is a constant to be designed.

[0047] The first order derivative of the sliding surface is: (11) In the formula, is the first order derivative of the sliding surface.

[0048] Substituting formula (8) into formula (11) can get the equivalent control law of logarithmic convergence sliding mode u eq : (12) For the switching control law, in order to further reduce the system chattering, a double adaptive variable reaching law is introduced into the switching control law u sw , so the controller switching control law is as follows: (13) In the formula, d>0, k2>0, c>0, ε>0, γ>1, -1<a<0, 0<b<1, are all parameters to be designed.

[0049] Combining formula (12) and formula (13), the overall control law of the system can be obtained as follows: (14) Step 4, control system design; Combining the design of the logarithmic convergence sliding mode active disturbance rejection control strategy, the proposed control strategy is applied to the SIDO Buck-Boost converter in this invention. In order to suppress the influence of non-minimum phase, the leading conduction branch adopts a double closed-loop control structure, and the trailing conduction branch adopts a single closed-loop structure. That is, the branch adopts a double closed-loop control of current and voltage, and the main circuit adopts a single closed-loop control of voltage.

[0050] Embodiment 2 The specific process of Step 4 is as follows: Step 4.1, design of the single closed-loop controller for the voltage of the main circuit switch tube; The main circuit is a single closed-loop control system for voltage. The voltage of the b branch is collected to control the main switch tube, and formula (1) is rewritten as: (15) In the formula, represents the unmodeled part of the system and external disturbances.

[0051] To transform the controlled object into the second-order active disturbance rejection normal form, its second derivative is obtained as follows: (16) Fitting formula (16) into the second-order active disturbance rejection normal form, we get: (17) In the formula, v b represents the output of the b-branch system, u iv is the control quantity of the voltage outer-loop system, b 1 is the estimated value of the control quantity gain, F 1 represents the total disturbance of the b branch, , , , , .

[0052] Define the b branch voltage loop improvement fractional order linear extended state observer error e vb1 And the error of the logarithmic convergent sliding mode controller e vb Is: (18) Substitute equation (18) into equation (14), the main road switch tube voltage loop overall control law is: (19) Step 4.2, branch switch tube controller design; Step 4.2.1, voltage outer loop control; The branch switch tube collects a branch voltage as an outer loop control signal, which is the same as the main switch tube voltage loop control. The mathematical model of a branch is fitted into a second-order system as: (20) In the formula, v a The a branch voltage outer loop system output is represented by b 2 is the estimated value of the control gain, u av The voltage loop system control quantity is F 2 represents the total disturbance of the a branch voltage outer loop.

[0053] Define the a branch voltage outer loop observation error e va1 And the error of the logarithmic convergent sliding mode controller e va Is: (21) Substitute equation (21) into equation (14), the branch switch tube voltage outer loop overall control law is: (22) Step 4.2.2, current inner loop control The branch switch tube collects the inductor current i L As an inner loop control signal, first fit the mathematical model of the a branch inner loop inductor current into a second-order system: (23) In the formula, i L The a branch current inner loop system output is represented by b 3 is the control gain, u ai The current loop system control quantity is F 3 represents the total disturbance of the a branch current inner loop.

[0054] Definition of a branch current inner loop observation error e ia1 And logarithmic convergent sliding mode controller error e ia Is: (24) Substitute equation (24) into equation (14) to obtain the overall control law of the branch switch tube current inner loop as: (25) Embodiment 3 To verify the correctness of the above theory, a semi-physical experiment platform is built based on a hardware-in-the-loop system to experimentally verify the PI control strategy and the control strategy of the present application. Anti-load disturbance and anti-input voltage disturbance experiments are respectively carried out. The simulation parameter settings are shown in Table 1.

[0055] Table 1 SIDO Buck-Boost converter circuit parameters

[0056] Embodiment 4 The anti-disturbance experimental results of branch a are shown in Figs. 4(a)-4(d). The anti-load disturbance experimental results of branch b are shown in Figs. 5(a)-5(d). The anti-input voltage disturbance experimental results are shown in Figs. 6(a)-6(d).

[0057] As can be seen from Fig. 4(a), under the PI control strategy, when the load current i a increases from 1A to 2A, the load disturbance causes the voltage of branch a to drop to 1.62V, and the transition process time is 8.7ms; due to cross-influence, the voltage of branch b overshoots by 1.12V, and the transition process time is 7.5ms. u a As can be seen from Fig. 4(b), when the load current u b decreases from 2A to 1A, the load disturbance causes the voltage of branch a to rise by 1.45V, and the transition process time is 9.1ms; due to cross-influence, the voltage of branch b overshoots by 1.31V, and the transition process time is 8.2ms. i a As can be seen from Fig. 4(c), when the load current u a increases from 1A to 2A, the load disturbance causes the voltage of branch a to drop to 1.62V, and the transition process time is 8.7ms; due to cross-influence, the voltage of branch b overshoots by 1.12V, and the transition process time is 7.5ms. u b As can be seen from Fig. 4(d), when the load current

[0058] As can be seen from Fig. 4(c), when the load current i a increases from 1A to 2A. Under the converter control strategy in this paper, the load disturbance causes the voltage of branch a to drop to 1.62V, and the transition process time is 8.7ms; due to cross-influence, the voltage of branch b overshoots by 1.12V, and the transition process time is 7.5ms. u aThe voltage drop is 0.11V, and the transition time is 2.6ms; the voltage of branch b is affected by cross-influence. u b The overshoot is 0.10V, and the transition time is 2.7ms; analysis of Figure 4(d) shows that when i a The voltage drops abruptly from 2A to 1A. Under the control strategy in this chapter, the voltage in branch a is affected by load disturbances in the converter. u a The voltage rises to 0.12V with a transition time of 2.7ms; the voltage in branch b is affected by cross-influence. u b The overshoot is 0.11V and the transition time is 2.9ms.

[0059] Example 5 Analysis of Figure 5(a) shows that under the PI control strategy, when... i b The voltage in branch b suddenly increases from 1A to 2A due to the load disturbance. u b The voltage drop is 1.76V, and the transition time is 8.4ms; the voltage of branch a is affected by cross-influence. u a The overshoot is 1.35V, and the transition time is 8.5ms. Analysis of Figure 5(b) shows that when... i b The voltage of branch b drops suddenly from 2A to 1A due to load disturbance. u b The voltage rises to 1.73V with a transition time of 8.5ms; the voltage in branch a decreases due to cross-influence. u a The overshoot is 1.31V and the transition time is 8.1ms.

[0060] Analysis of Figure 5(c) shows that when i b The voltage suddenly increases from 1A to 2A. Under the control strategy described in this paper, the voltage in branch b is affected by the load disturbance. u b The voltage drop is 0.13V, and the transition time is 3.0ms; the voltage of branch a is affected by cross-influence. u a The overshoot is 0.11V, and the transition time is 2.9ms; analysis of Figure 5(d) shows that when i b The voltage drops abruptly from 2A to 1A. Under the control strategy in this chapter, the voltage in branch b is affected by load disturbances in the converter. u b The voltage rises to 0.12V with a transition time of 2.8ms; the voltage in branch a decreases due to cross-influence.u a The overshoot is 1.72V and the transient time is 9.2ms; the voltage of branch b overshoots 1.61V and the transient time is 8.1ms.

[0061] Example 6 As shown in Fig. 6(a), under the PI control strategy, when the input voltage is suddenly increased from 20V to 30V, the voltage of branch a overshoots 0.12V and the transient time is 2.7ms; the voltage of branch b overshoots 0.11V and the transient time is 2.8ms. u in The overshoot is 1.72V and the transient time is 9.2ms; the voltage of branch b overshoots 1.61V and the transient time is 8.1ms. u a The overshoot is 1.72V and the transient time is 9.2ms; the voltage of branch b overshoots 1.61V and the transient time is 8.1ms. u b The overshoot is 1.72V and the transient time is 9.2ms; the voltage of branch b overshoots 1.61V and the transient time is 8.1ms. u in The overshoot is 1.72V and the transient time is 9.2ms; the voltage of branch b overshoots 1.61V and the transient time is 8.1ms. u a The overshoot is 1.72V and the transient time is 9.2ms; the voltage of branch b overshoots 1.61V and the transient time is 8.1ms. u b The overshoot is 1.72V and the transient time is 9.2ms; the voltage of branch b overshoots 1.61V and the transient time is 8.1ms.

[0062] As shown in Fig. 6(c), u in The overshoot is 1.72V and the transient time is 9.2ms; the voltage of branch b overshoots 1.61V and the transient time is 8.1ms. u in The overshoot is 1.72V and the transient time is 9.2ms; the voltage of branch b overshoots 1.61V and the transient time is 8.1ms.

Claims

1. A SIDO Buck-Boost converter control method based on an improved fractional-order linear extended state observer, characterized in that: Specifically, it includes the following steps: Step 1: Establish the state-space average model of the SIDO Buck-Boost converter according to the state-space averaging method, and transform this model into a second-order active disturbance rejection normal form; Step 2: Design an improved fractional-order linear extended state observer; Step 3: Design a logarithmic convergence sliding mode controller; Step 4: Design the control law of the SIDO Buck-Boost converter.

2. The SIDO Buck-Boost converter control method based on an improved fractional-order linear extended state observer according to claim 1, characterized in that: The specific process of Step 1 is as follows: Establish the state-space average model of the SIDO Buck-Boost converter according to the state-space averaging method, as shown in the following formula (1): （1） In the formula, V in This indicates the input voltage value of the converter; L , C a and C b These represent the converter's energy storage inductance value and the branch filter capacitor value, respectively. R a , R b For load resistance; V a , V b This refers to the output voltage. i L This is the inductor current value; S i1 , S i2 Main switch transistor, S a , S b These represent the branch switch transistors for branch a and branch b, respectively. d i Main switch transistor S il , S i2 duty cycle, d a , d b They are respectively S a , S b The duty cycle, and satisfying d a + d b =1, v a , v b These represent the transient output voltage values ​​of the two branches, respectively. As known from formula (1), the SIDO Buck-Boost converter is a typical second-order system. Therefore, the state-space average model of the converter is fitted into a standard second-order system, as shown in the following formula (2): （2） In the formula, y o u is the system output, and u is the system input. This indicates external disturbances to the system. b Indicates the system input gain. a 1. a 2 represents the system parameters; the internal uncertainties of the system are separated, and the internal and external disturbances are included in the total disturbance, and the system is rewritten as shown in the following formula (3): （3） In the formula, b o This is an estimated value. This represents the total disturbance.

3. The SIDO Buck-Boost converter control method based on an improved fractional-order linear extended state observer according to claim 2, characterized in that: The specific process of step 2 is as follows: Define state variables. x 1= e f , , x 3= f Thus, the state-space expression of equation (4) is obtained: （4） Establish a fractional-order linear extended state observer for formula (4) as: （5） Design the deviation to replace e1 to adjust the derivatives of z2 and z3, as shown in the following formula (6): （6） After arranging formula (6), we get: （7） From equation (7), we get z 2 and x The error between 2 is , z 3 and x The error between 3 is The improved fractional-order linearly extended state observer is constructed as follows: （8） In the formula, e 1 represents the observation error. e 1 represents the difference between the observed value and the actual value.

4. The SIDO Buck-Boost converter control method based on an improved fractional-order linear extended state observer according to claim 3, characterized in that: The specific process of step 3 is as follows: based on the state variables observed by the observer... x 1 observation value z 1. Define the error between the system output value and the expected value. e for: （9） Define the logarithmic convergence sliding mode surface as: （10） In the formula, h 1. h 2. k 1 represents the constant to be designed; Take the first derivative of the sliding mode surface to get: （11） Substitute formula (8) into formula (11) to obtain the equivalent control law of the logarithmic convergence sliding mode as: （12） For switching control laws, the approach law of two adaptive variables is introduced. u sw Therefore, the controller switching control law is: （13） Combining equations (12) and (13), we obtain the overall control law of the system. u for: （14） In the formula, d>0, k2>0, c>0, ε>0, γ>1, -1 < a < 0, 0 < b < 1 are all parameters to be designed.

5. The SIDO Buck-Boost converter control method based on an improved fractional-order linear extended state observer according to claim 4, characterized in that: The specific process of Step 4 is as follows: Step 4.1: Design the single closed-loop voltage controller for the main circuit switch tube; Step 4.2: Design the controller for the branch circuit switch tube.

6. The SIDO Buck-Boost converter control method based on an improved fractional-order linear extended state observer according to claim 5, characterized in that: The specific process of Step 4.1 is as follows: The main circuit is a single closed-loop voltage control system. Collect the voltage of branch b to control the main switch tube, and rewrite formula (1) as: （15） In the formula, This represents the unmodeled parts of the system and external disturbances; to transform the controlled object into a second-order active disturbance rejection paradigm, the second derivative is obtained: （16） Fit formula (16) into a second-order active disturbance rejection normal form to get: （17） In the formula, v b This represents the output of branch b of the system. u iv This is the control quantity for the outer loop voltage system. b 1 represents the estimated value of the control gain. F 1 represents the total disturbance of branch b. , , , , ; Define the error e of the improved fractional-order linear extended state observer for the b-branch voltage loop. vb1 and the error of the logarithmically convergent sliding mode controller e vb : （18） Substitute formula (18) into formula (14) to obtain the overall control law of the voltage loop of the main circuit switch tube as: （19） in, e vb The error of the logarithmic convergent sliding mode controller for branch b.

7. The SIDO Buck-Boost converter control method based on an improved fractional-order linear extended state observer according to claim 6, characterized in that: The specific process of Step 4.2 is as follows: Step 4.2.1: Design the voltage outer-loop control law; Step 4.2.2: Design the current inner-loop control law.

8. The SIDO Buck-Boost converter control method based on an improved fractional-order linear extended state observer according to claim 7, characterized in that: The specific process of Step 4.2.1 is as follows: The branch circuit switch tube collects the voltage of branch a as the outer-loop control signal. Similar to the voltage loop control of the main switch tube, the mathematical model of branch a is fitted into a second-order system as: （20） In the formula, v a This represents the output of the outer loop system voltage of branch a. b 2 represents the estimated value of the control gain. u av For voltage loop system control variables, F 2 represents the total disturbance in the outer loop of the voltage of branch a; Define the outer loop observation error of branch a voltage. e va1 and logarithmically convergent sliding mode controller error e va for: （21） Substitute formula (21) into formula (14) to obtain the overall control law of the voltage outer-loop of the branch circuit switch tube as: （22） in, e va The error of the logarithmic convergence sliding mode controller for branch a.

9. The SIDO Buck-Boost converter control method based on an improved fractional-order linear extended state observer according to claim 8, characterized in that: The specific process of Step 4.2.2 is as follows: Branch switch transistors collect inductor current i L As the inner loop control signal, the mathematical model of the inner loop inductor current of branch a is first fitted to a second-order system: （23） In the formula, i L This represents the output of the inner loop system current in branch a. b 3 represents the control gain. u ai For control variables of the current loop system, F 3 represents the total disturbance in the inner loop of the current in branch a; Define the inner loop observation error of branch current. e ia1 and logarithmically convergent sliding mode controller error e ia for: （24） Substitute formula (24) into formula (14) to obtain the overall control law of the current inner-loop of the branch circuit switch tube as: （25） in, e ia This is the error of the logarithmically convergent sliding mode controller.

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