An accurate feedback linearization optimal control method based on three-level boost converter

Abstract

The application is a kind of accurate feedback linearization optimal control method based on three-level Boost converter, which can improve the dynamic performance and stability of three-level Boost converter.The method includes establishing three-level Boost converter model to obtain system state space equation; based on accurate feedback linearization technology, the mathematical model is converted into Bruneovsky standard type, which effectively reduces the design difficulty of subsequent controller; based on linear quadratic optimal control theory, the performance index is defined, the Riccati equation is solved to obtain the optimal feedback gain matrix, and the linear optimal control law is derived; the linear optimal control law is substituted into the feedback linearization control law and restored to the original state variable to obtain the final switch duty ratio optimal control law. The application can improve the response speed of the system, and has small voltage fluctuation, fast regulation time and good dynamic and static performance when the system is disturbed.

Description

Technical Field

[0001] This invention relates to the field of power electronic converter control technology, specifically to a precise feedback linearization optimal control method based on a three-level Boost converter, which is suitable for DC boost applications requiring high efficiency, high power density, and fast dynamic response. Background Technology

[0002] Compared to traditional two-level boost converters, three-level boost converters have advantages such as low voltage stress on switching devices, low inductor current ripple, and low electromagnetic interference, and are widely used in high-voltage and high-power applications.

[0003] However, the three-level boost converter is a strongly nonlinear, time-varying system with a more complex topology than the traditional two-level boost converter, placing increasingly higher demands on control strategies. Traditional linear control methods (such as PID control) are typically based on small-signal models, designing controllers with fixed parameters near the operating point. When the load changes abruptly or the input voltage fluctuates significantly, the system operating point shifts over a wide range, making it difficult for the PID controller to guarantee global dynamic response performance, easily leading to problems such as large overshoot, long settling time, or even instability.

[0004] While some nonlinear control methods (such as sliding mode control) exist in existing technologies, they often suffer from chattering problems, making it difficult to simultaneously achieve global linearization, optimal dynamics, midpoint equalization, and disturbance suppression. Furthermore, they exhibit poor stability under wide operating conditions. Therefore, there is an urgent need for a three-level Boost converter control scheme that can simultaneously achieve global stability, dynamic response speed, and optimal energy loss. Summary of the Invention

[0005] The purpose of this invention is to provide a precise feedback linearization optimal control method based on a three-level Boost converter, so as to achieve global optimal control of the converter and improve dynamic response, steady-state accuracy and disturbance rejection.

[0006] To achieve the above objectives, the precise feedback linearization optimal control method based on a three-level Boost converter includes the following steps: S1. Establish a three-level Boost converter model and obtain the system state-space equation; S2. Based on the system state-space equations, the mathematical model is transformed into the Brunovsky canonical form through precise feedback linearization techniques. S3. Based on the linear quadratic optimal control theory, define the performance index, solve the Riccati equation to obtain the optimal feedback gain matrix, and derive the linear optimal control law. S4. Substitute the linear optimal control law into the feedback linearized control law and restore it to the original state variables to obtain the final optimal control law for the switching duty cycle.

[0007] Preferably, step S1 specifically includes the following process: Take the inductor current of the three-level Boost converter i L and output voltage v o As a state variable, assuming the converter operates in continuous conduction mode, the system has two modes: switch off and switch on.

[0008] In these two modes, the state equations can be obtained using the KCL and KVL laws: in V in This is the power supply voltage. C For capacitors, L It's an inductor. R For load, Q For power switching transistors, the duty cycle of the switching transistor is... d ∈(0,1).

[0009] Preferably, step S2 specifically includes: According to the literature, the total stored energy and input power of the three-level boost converter are regarded as new system state variables: Take the first derivative of the above equation and use the exact feedback linearization technique to linearize the original system into the Brunovsky canonical form: In the formula, v Intermediate control rate; z This represents an unmeasurable constant disturbance. By setting up a nonlinear disturbance observer, the disturbance error will converge to zero as time approaches infinity. Its specific expression is: Simultaneously, the following can be introduced: Preferably, step S3 specifically includes: The core of the optimal control problem lies in the selection of the weighting matrix. This is achieved by rationally determining the state weighting matrix in the performance index function. Q and control weighting matrix R The optimal state feedback control law can be derived from this. The linear quadratic optimal control algorithm aims to achieve the best control effect of the system under certain performance indicators by minimizing the weighted combination of state error and control energy. According to the theory of linear quadratic regulators, the state equation and output equation for an infinite-time linear time-invariant system are as follows: In the formula, m ( t )yes e dimensional state vector, v ( t )for r An uncontrolled control vector. y 1 is n 3D output vector, A , B , C It is a constant matrix. The control objective is to find the optimal control function. v This minimizes the quadratic performance index functional defined below: In the formula, Q 1 is e×e A positive semi-definite constant matrix, Q 2 is r×r A positive definite constant matrix.

[0010] According to the LQR theorem, when { A , B When it is fully controllable, its optimal control v It exists and is unique, and its value is determined by the following formula: v =- Q 2 -1 BFm In the formula, F express s×s A symmetric positive definite constant matrix of dimension 1, which satisfies the following Riccati matrix algebraic equation: A T F+FA-FBS -1 B T F+Q =0 From the above analysis, it can be seen that the three-level Boost converter has been completely linearized into a purely integral linear system. Now, we design a linear quadratic optimal state regulator for the three-level Boost converter system. Therefore, we take the aforementioned new state variables... m =[ m 1, m 2] T ,in, m 1= x 1- x 1ref , m 2=x 2- x 2ref .so m The first derivative can be expressed as: The above formula can be written in the following form: in, A = , B = First, we need to verify the controllability of the system: rank [ B AB ] = rank =2 Obviously { A , B The condition of complete controllability is satisfied, therefore the corresponding optimal control law is... v It exists and is unique.

[0011] Since this system is a single-input single-output system, therefore it is assumed that... Q 1= , Q 2 = ( q 2), put A , B , Q 1, Q Substituting 2, we get: Summarized as follows: because P It is a 2×2 symmetric positive definite constant matrix, so let p 12 = p 21 Seeking P for: Simplifying the above equation, we get: make k 1= q 1 1 / 2 q 2 -1 / 2 , k 2= q 1 1 / 4 q 2 -1 / 4 ,sok 1 = 1 / 2 k 2 2 ,so: Preferably, step S4 specifically includes the following process: Because, for a three-level Boost converter, we have: Substituting the values, we can obtain the optimal control as follows: Compared with the prior art, the present invention has the following advantages and beneficial effects: By combining precise feedback linearization technology with optimal control theory and introducing it into the three-level Boost converter, on the one hand, the nonlinear mathematical model is transformed into the Brunofsky canonical form based on precise feedback linearization technology, which effectively reduces the design difficulty of the subsequent controller; on the other hand, combined with the optimal controller, the dynamic adjustment time of the output voltage is shortened from 80ms~150ms to ≤30ms when the system is disturbed, the output voltage overshoot is suppressed from 10%~20% to ≤5%, the midpoint potential balance deviation is controlled at ≤2%, the output voltage steady-state error is controlled at ≤1%, the overall conversion efficiency is not less than 93%, and the output voltage ripple is controlled at ≤1%, which has good dynamic and static characteristics and strong robustness.

[0012] The control method proposed in this invention is applicable to three-level and any multi-level Boost converter topologies derived therefrom. Attached Figure Description

[0013] Figure 1 This is a topology diagram of a three-level Boost converter; Figure 2 This is a system control block diagram of a three-level Boost converter; Figure 3 This is a simulation model of a three-level Boost converter; Figure 4 The output voltage reference value of the three-level Boost converter v oref Simulated waveform during the change.

[0014] Figure 5 For the load of a three-level Boost converter R Simulated waveform during the change.

[0015] Figure 6 The input voltage of the three-level Boost converter V in Simulated waveform during the change. Detailed Implementation

[0016] The embodiments of the present invention will be described in further detail and clearly below with reference to the accompanying drawings and specific implementation methods.

[0017] The specific implementation scheme of the present invention to solve the above-mentioned technical problems is as follows: The first step is to establish the state-space average model of the three-level Boost converter; Figure 1 This is a topology diagram of a three-level Boost converter, where... V in This is the power supply voltage. C 1 is a flying capacitor. C 2. C 3 and L These are the filter capacitor and the inductor. Q For power switching transistors, the duty cycle of the switching transistor is... d ∈(0,1), D 1. D 2. D All three are diodes.

[0018] Take the inductor current of the three-level Boost converter i L and output voltage v o As a state variable, assuming the converter operates in continuous conduction mode, according to Figure 1 It can be seen that the system has two modes: switch off and switch on.

[0019] In these two modes, the state equations can be obtained using the KCL and KVL laws: The second step is to perform precise feedback linearization on the nonlinear model of the three-level Boost converter. According to the literature, the total stored energy and input power of the three-level boost converter are regarded as new system state variables: Take the first derivative of the above equation and use the exact feedback linearization technique to linearize the original system into the Brunovsky canonical form: In the formula, v Intermediate control rate; z This represents an unmeasurable constant disturbance. By setting up a nonlinear disturbance observer, the disturbance error will converge to zero as time approaches infinity. Its specific expression is: Simultaneously, the following can be introduced: The third step is to derive the linear optimal control law based on the linear quadratic optimal control theory. The core of the optimal control problem lies in the selection of the weighting matrix. This is achieved by rationally determining the state weighting matrix in the performance index function. Q and control weighting matrix R The optimal state feedback control law can be derived from this. The linear quadratic optimal control algorithm aims to achieve the best control effect of the system under certain performance indicators by minimizing the weighted combination of state error and control energy. According to the theory of linear quadratic regulators, the state equation and output equation for an infinite-time linear time-invariant system are as follows: In the formula, m ( t )yes e dimensional state vector, v ( t )for r An uncontrolled control vector. y 1 is n 3D output vector, A , B , C It is a constant matrix. The control objective is to find the optimal control function. v This minimizes the quadratic performance index functional defined below: In the formula, Q 1 is e×e A positive semi-definite constant matrix, Q 2 is r×r A positive definite constant matrix.

[0020] According to the LQR theorem, when { A , B When it is fully controllable, its optimal control v It exists and is unique, and its value is determined by the following formula: v =- Q 2 -1 BFm In the formula, F express s×s A symmetric positive definite constant matrix of dimension 1, which satisfies the following Riccati matrix algebraic equation: A T F+FA-FBS -1B T F+Q =0 From the above analysis, it can be seen that the three-level Boost converter has been completely linearized into a purely integral linear system. Now, we design a linear quadratic optimal state regulator for the three-level Boost converter system. Therefore, we take the aforementioned new state variables... m =[ m 1, m 2] T ,in, m 1= x 1- x 1ref , m 2= x 2- x 2ref .so m The first derivative can be expressed as: The above formula can be written in the following form: in, A = , B = First, we need to verify the controllability of the system: rank [ B AB ] = rank =2 Obviously { A , B The condition of complete controllability is satisfied, therefore the corresponding optimal control law is... v It exists and is unique.

[0021] Since this system is a single-input single-output system, therefore it is assumed that... Q 1= , Q 2 = ( q 2), , put A , B , Q 1, Q Substituting 2, we get: Summarized as follows: because P It is a 2×2 symmetric positive definite constant matrix, so let p 12 = p21 Seeking P for: Simplifying the above equation, we get: make k 1= q 1 1 / 2 q 2 -1 / 2 , k 2= q 1 1 / 4 q 2 -1 / 4 ,so k 1 = 1 / 2 k 2 2 ,so: Step 4: Substitute the linear optimal control law into the feedback linearized control law and restore it to the original state variables to obtain the final optimal control law for the switching duty cycle. Because, for a three-level Boost converter, we have: Substituting the values, we can obtain the optimal control as follows: Achieving optimal control v Afterwards, optimal control of the linear system of the three-level Boost converter can be achieved, and its control block diagram is as follows: Figure 2 As shown.

[0022] To verify the effectiveness of the precise feedback linearization optimal control method proposed in this invention, this embodiment uses the Matlab / Simulink numerical simulation platform to construct a simulation model of a three-level Boost converter for research. The specific circuit is as follows: Figure 3 As shown in the table below. The parameters of the three-level Boost converter used in this embodiment are as follows: Figure 4 Given v oref Simulated waveforms of the system when the V increases abruptly from 15V to 20V at 0.1s and 0.15s, and when the V changes back to 15V. v oref During a transition, the optimal control strategy can make v o Stable at 15V, which is the reference value. v orefFurthermore, the optimal control strategy can smoothly stabilize during both transitions without significant fluctuations, demonstrating excellent dynamic and static adjustment characteristics.

[0023] Figure 5 Given R Simulated waveforms of the system when the ohmmeter jumps from 100Ω to 150Ω at 0.3s and 0.35s, and when it drops back to 100Ω. R When a disturbance occurs, the output current i o Capable of rapid tracking R Transformation, while the optimal control strategy can make v o Stable at 15V, which is the reference value. v oref Simulation data show that the proposed optimal control strategy can maintain excellent control performance under load disturbance conditions, and the overshoot is almost negligible.

[0024] Figure 6 Given V in Simulated waveforms of the system when the voltage jumps from 5V to 7V at 0.4s and 0.45s, respectively, and when the voltage jumps back from 7V to 5V. V in During a transition, the optimal control strategy can make v o It is stabilized at 15V, achieving fast and accurate tracking of the output voltage to the reference value. It has better dynamic and static regulation characteristics in suppressing disturbances and exhibits stronger robustness. In summary, this invention proposes an optimal control strategy based on precise feedback linearization theory for a three-level Boost converter. First, a mathematical model of the system is established using the state-space averaging method. Then, precise feedback linearization technology is applied to linearize the original nonlinear system. An optimal controller is designed, taking full account of external disturbances. Finally, simulation experiments verify that the proposed control method has advantages in resisting disturbances and improving dynamic and static performance, demonstrating good engineering application value.

[0025] The embodiments described above should be understood only as specific illustrations of this invention and are not intended to limit the specific scope of protection of this invention. After reading the description of this invention, those skilled in the art will understand that this invention can have various changes and modifications. Any changes, modifications, substitutions, combinations, simplifications, improvements, etc., made within the spirit and principles of this application should be considered equivalent substitutions and are included within the scope of protection of this invention.

Claims

1. A precise feedback linearization optimal control method based on a three-level Boost converter, characterized in that: Includes the following steps: S1. Establish a mathematical model of the three-level Boost converter using the state-space averaging method; S2. The mathematical model is transformed into the Brunofsky canonical form using the exact feedback linearization method. S3. Derive the linear optimal control law based on the linear quadratic optimal control theory; S4. Restore the state variables to obtain the optimal control law for the switch duty cycle.

2. The precise feedback linearization optimal control method for a three-level Boost converter according to claim 1, characterized in that: The specific process of step S1 includes: Take the inductor current of the three-level Boost converter i L and output voltage v o Assuming the converter operates in continuous conduction mode as a state variable, the system has two modes: switch off and switch on. Under these two modes, the state-space average equation can be obtained using the KCL and KVL laws: in, V in This is the power supply voltage. C For capacitors, L It's an inductor. R For load, Q For power switching transistors, the duty cycle of the switching transistor is... d ∈(0,1).

3. The precise feedback linearization optimal control method for a three-level Boost converter according to claim 2, characterized in that: The specific process of step S2 includes: According to the literature, the total stored energy and input power of the three-level boost converter are regarded as new system state variables: Take the first derivative of the above equation and use the exact feedback linearization technique to linearize the original system into the Brunovsky canonical form: In the formula, v Intermediate control rate; z This represents an unmeasurable constant disturbance. By setting up a nonlinear disturbance observer, the disturbance error will converge to zero as time approaches infinity. Its specific expression is: Simultaneously, the following can be introduced:

4. The precise feedback linearization optimal control method for a three-level Boost converter according to claim 3, characterized in that: The specific process of step S3 includes: According to the theory of linear quadratic regulators, the state equation and output equation for an infinite-time linear time-invariant system are as follows: In the formula, m ( t )yes e dimensional state vector, v ( t )for r An uncontrolled control vector. y 1 is n 3D output vector, A , B , C It is a constant matrix. The control objective is to find the optimal control function. v This makes the quadratic performance index functional reach its minimum value as defined below: In the formula, Q 1 is e×e A positive semi-definite constant matrix, Q 2 is r×r A positive definite constant matrix. According to the LQR theorem, when { A , B When it is fully controllable, its optimal control v It exists and is unique, and its value is determined by the following formula: v =- Q 2 -1 BFm In the formula, F express s×s A symmetric positive definite constant matrix of dimension 1, which satisfies the following Riccati matrix algebraic equation: A T F + FA - FBS -1 B T F + Q =0 From the above analysis, it can be seen that the three-level Boost converter has been completely linearized into a purely integral linear system. Now, we design a linear quadratic optimal state regulator for the three-level Boost converter system. Therefore, we take the aforementioned new state variables... m =[ m 1, m 2] T ,in, m 1= x 1- x 1ref , m 2= x 2- x 2ref .so m The first derivative can be expressed as: The above formula can be written in the following form: in, A = , B = First, we need to verify the controllability of the system: rank [ B AB ] = rank =2 Obviously { A , B The condition of complete controllability is satisfied, therefore the corresponding optimal control law is... v It exists and is unique. Since this system is a single-input single-output system, therefore it is assumed that... Q 1= , Q 2 = ( q 2), put A , B , Q 1, Q Substituting 2, we get: Summarized as follows: because P It is a 2×2 symmetric positive definite constant matrix, so let p 12 = p 21 Seeking P for: P= Simplifying the above equation, we get: make k 1= q 1 1 / 2 q 2 -1 / 2 , k 2= q 1 1 / 4 q 2 -1 / 4 ,so k 1 = 1 / 2 k 2 2 ,so:

5. The precise feedback linearization optimal control method for a three-level Boost converter according to claim 4, characterized in that: The specific process of step S4 includes: Because, for a three-level Boost converter, we have: Substituting the values, we can obtain the optimal control as follows:

6. The precise feedback linearization optimal control method for a three-level Boost converter according to claim 1, characterized in that, This precise feedback linearization optimal control method is also applicable to any multilevel Boost converter topology derived from the three-level extension.

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