An internal model control method based on bias current decoupling of dual-buck symmetrical half-bridge power amplifier

Abstract

The present invention discloses an internal model control method based on bias current decoupling of a dual-buck symmetrical half-bridge power amplifier, the method comprising the following steps: step one, design of a BCDIMC; step two, sensitivity analysis of the system to changes in BCDIMC parameters. Based on an in-depth analysis of the key factors affecting the degree of cross-coupling and output current error of a DBSHBA, the present invention designs a BCDIMC suitable for a DBSHBA that can significantly suppress the current error caused by cross-coupling. In addition, the present invention also conducts a detailed analysis of how control parameters affect the suppression effect of cross-coupling, and proves the effectiveness of the control method of the present invention through simulation, ensuring that the output current of the system can maintain high precision and high efficiency under complex dynamic conditions.

Description

Technical Field

[0001] The present invention belongs to the field of power supply and motor drive, and relates to an internal model control method based on dual-buck symmetrical half-bridge power amplifier (DBSHBA) bias current decoupling. Background Art

[0002] In the field of high-precision power supply and motor drive, DBSHBA plays a vital role. By injecting bias current, DBSHBA keeps the inductor operating in continuous conduction mode, reducing the total harmonic distortion (THD) of the output current and significantly improving the stability and dynamic response of the system. Figure 1 Figure 2 is a DBSHBA topology circuit model under non-ideal conditions. However, due to the dead-zone effect of the DBSHBA and the non-ideal characteristics of the circuit, the decoupling between the bias current and the output current is incomplete, resulting in an output current error.

[0003] Although dead-zone-free DBSHBAs have been proposed, these models fail to fully consider the impact of component nonidealities on current output quality in real applications. Furthermore, while increasing the system switching frequency can suppress current errors caused by cross-coupling, this approach changes the circuit's operating conditions. Therefore, DBSHBAs require a robust control method with a limited number of tuning parameters to suppress output current distortion caused by cross-coupling without changing the circuit's operating conditions. Summary of the Invention

[0004] This paper presents an internal model control method based on bias current decoupling for a dual-buck symmetrical half-bridge power amplifier (DBSHBA). This method aims to address the cross-coupling issue between the output current and bias current of a DBSHBA under non-ideal conditions. By designing a current-decoupling internal model controller (BCDIMC), this method effectively suppresses the current error caused by cross-coupling in the DBSHBA, improving the output accuracy and stability of the DBSHBA system. Simulations validate the effectiveness of this control method, which is applicable to power amplifiers in high-precision motion systems, enabling precise motion control with low harmonic content.

[0005] The purpose of the present invention is achieved through the following technical solutions:

[0006] An internal model control method based on bias current decoupling of a dual-buck symmetrical half-bridge power amplifier comprises the following steps:

[0007] Step 1: Design of BCDIMC:

[0008] Step 1: Equivalent the control structure of the DBSHBA system based on the internal model control principle to a simple feedback structure. The equivalent controller is G c (s), G c(s), system output I(s), and feedback signal d(s) are as follows:

[0009]

[0010] F(s)=[G(s)=G n (s)]U(s)+d(s)

[0011] Where C(s) is BCDIMC, G(s) is DBSHBA system, G n (s) is the mathematical model of the non-ideal DBSHBA system, F(s) is the feedback signal, I * (s) is the input reference value, I(s) is the system output, U(s) is the controller output, and d(s) is the external disturbance;

[0012] Steps 1 and 2: Under ideal conditions, that is, when the model is completely accurate and there is no external disturbance, the system output can completely replicate the reference input. The system mathematical model is decomposed into two parts: one containing delay and non-ideal characteristics, and the other containing minimum phase characteristics. BCDIMC is based on the inverse sum filter design of the minimum phase link and optimizes system performance by adjusting control parameters. The decomposition of the system mathematical model is shown below:

[0013] G n (s)=G n+ (s)·G n- (s)

[0014] Where G n+ (s) is the time delay of the system transfer function, the zero point of the right half plane and the unmodelable link under non-ideal conditions, G n- (s) is the transfer function of the system with minimum phase characteristics;

[0015] Step 13: Define BCDIMC as the inverse sum filter of the minimum phase link L(s) = 1 / (αs+1) n The product of is expressed as follows:

[0016]

[0017] Where α is the time constant used to adjust the filter, i.e., the control parameter, s is the complex frequency variable in the Laplace transform, and n is the filter order;

[0018] Step 14: Substitute the expression of BCDIMC to obtain the closed-loop output and error expression of the system:

[0019]

[0020] Where f(s) is the transfer function of the feedback filter, e m(s)=[G(s)-G n (s)] / G n (s) is used to indicate the degree of mismatch between the model and the actual system;

[0021] Step 15: When the model and the actual system are completely matched and external interference is ignored, e m (s) = d(s) = 0, the expression in step 14 is simplified to:

[0022] I(s)=G n+ (s)f(s)I * (s)

[0023] e(s)=[1-G n+ (s)f(s)]I * (s)

[0024] Step 2: Analysis of the system's sensitivity to changes in BCDIMC parameters:

[0025] Step 2.1: Introduce the perturbation model to analyze the robust stability of the system:

[0026] G(s)=G * (s)+Δ(s)ω(s)

[0027] Where G * (s) is the transfer function of the ideal system, Δ(s) represents the mismatch between the system perturbation and the model, and ω(s) is the weight function;

[0028] Step 2. In order to measure the influence of BCDIMC parameters on the output I(s) of the perturbed DBSHBA system, the sensitivity function of the closed-loop transfer function of the system to the change of C(s) when the external disturbance d(s) is ignored is calculated. As shown below:

[0029]

[0030] Where, It is the performance indicator of the system.

[0031] Compared with the prior art, the present invention has the following advantages:

[0032] Based on an in-depth analysis of the key factors affecting cross-coupling and output current error in DBSHBAs, this paper designs a BCDIMC suitable for DBSHBAs that significantly suppresses current errors caused by cross-coupling. Furthermore, this paper provides a detailed analysis of how control parameters influence cross-coupling suppression. Simulations demonstrate the effectiveness of this control method, ensuring high output current accuracy and efficiency under complex dynamic conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 This is the DBSHBA topology circuit model under non-ideal conditions;

[0034] Figure 2 This is the internal model control principle diagram of the DBSHBA system. In the figure, i * ref is the reference input current, i * bias is the desired bias current, C(s) is BCDIMC, α is the control parameter, U(s) is the output of the controller, G(s) is the transfer function of DBSHBA, d(s) is the external disturbance, I(s) is the actual output current of the system, I n (s) is the current error caused by non-ideal factors, F(s) is the feedback signal, G n (s) is the transfer function of the non-ideal DBSHBA, P 11 (s), P 12 (s), P 21 (s), P 22 (s) is the transfer function of the cross-coupling effect inside DBSHBA;

[0035] Figure 3 This is the equivalent structure diagram of the internal model control of the DBSHBA system;

[0036] Figure 4 It is the equivalent structure of BCDIMC. In the figure, PWM modulation is the pulse width modulation module, which is used to generate PWM1 and PWM2 signals to control the switching action of DBSHBA topology. G(s) is the transfer function of DBSHBA topology. DBSHBAtopology is the dual-buck symmetrical half-bridge converter topology. out is the output current, i L1 、i L2 is the inductor current, i cf is the capacitor current, K cf For gain, Controlle G c (s) is the transfer function of the equivalent controller, i ref is the reference current, i bias is the bias current, u out is the input voltage, u bias is the bias voltage, u1 * , u2 * Indicates the desired PWM signal;

[0037] Figure 5 Comparison of current harmonics under different control methods. DETAILED DESCRIPTION

[0038] The technical solution of the present invention is further described below with reference to the accompanying drawings, but is not limited thereto. Any modification or equivalent replacement of the technical solution of the present invention that does not depart from the spirit and scope of the technical solution of the present invention should be included in the scope of protection of the present invention.

[0039] The present invention provides an internal model control method based on bias current decoupling of a dual-buck symmetrical half-bridge power amplifier. The method aims to suppress the impact of cross-coupling on the output current in a DBSHBA by designing a BCDIMC. This method utilizes the principles of internal model control and combines current decoupling technology to effectively separate the coupling relationship between the bias current and the output current, thereby reducing the THD of the output current. At the same time, by introducing a perturbation model and sensitivity analysis, the present invention explores the system's sensitivity to changes in the BCDIMC parameters. Therefore, the present invention can be divided into two parts: the design of the BCDIMC and the analysis of the system's sensitivity to changes in the BCDIMC parameters.

[0040] (1) Design of BCDIMC

[0041] Figure 2 It is the control structure of DBSHBA system based on internal model control principle. * (s)=[I * out (s), I * bias (s)] T is the input reference value, I * out (s) and I * bias (s) are the two components of the desired current, I * out (s) is the desired output current, I * bias (s) is the desired bias current, I(s)=[I out (s), I bias (s)] T is the system output, I out (s) and I bias (s) are the two components of the actual current, I out (s) is the actual output current, I bias (s) is the actual bias current, G(s) is the DBSHBA system, G n (s) is the mathematical model of the non-ideal DBSHBA system, C(s) is the BCDIMC, and F(s) is the feedback signal.

[0042] Will Figure 2 The structure shown is equivalent to Figure 3 The simple feedback structure shown in the figure, the equivalent controller is G c(s), G c (s), system output I(s), and feedback signal d(s) are as follows:

[0043]

[0044] F(s)=[G(s)=G n (s)]U(s)+d(s) (3)

[0045] It can be seen that the internal model control method uses the difference between the actual system and the mathematical model as a feedback signal to control the system. In an ideal situation, that is, when the model is completely accurate and there are no external disturbances, the system output can completely replicate the reference input. The system mathematical model is decomposed into two parts: one containing delay and non-ideal characteristics, and the other containing the minimum phase characteristics. BCDIMC is based on the inverse sum filter design of the minimum phase link and optimizes system performance by adjusting control parameters. The decomposed system mathematical model is shown below:

[0046] G n (s)=G n+ (s)·G n- (s) (4)

[0047] Where G n+ (s) is the time delay of the system transfer function, the zero point of the right half plane and the unmodelable link under non-ideal conditions, G n- (s) is the transfer function of the system with minimum phase characteristics.

[0048] BCDIMC is defined as the inverse sum filter of the minimum phase link L(s) = 1 / (αs+1) n The product of is expressed as follows:

[0049]

[0050] Where α is the time constant used to adjust the filter, that is, the control parameter.

[0051] By substituting the expression of BCDIMC, the closed-loop output and error expressions of the system are as follows:

[0052]

[0053] Where, e m (s)=[G(s)-G n (s)] / G n (s) is used to indicate the degree of mismatch between the model and the actual system. When the model and the actual system are completely matched and external interference is ignored, e m (s) = d(s) = 0, equations (6) and (7) can be simplified to:

[0054] I(s)=G n+ (s)f(s)I * (s) (8)

[0055] e(s)=[1-G n+ (s)f(s)]I * (s) (9)

[0056] It can be seen that except for G n+ (s) needs to include all the unmodelable and time-delayed links of the system and the order of the filter f(s) needs to ensure that the controller is feasible. The control parameter α is the only adjustable parameter.

[0057] The structure of the equivalent controller finally designed is as follows Figure 4 As shown in FIG, the coupling effect between the output current and the bias current is suppressed by adjusting the control parameter α.

[0058] (2) Analysis of the system's sensitivity to changes in BCDIMC parameters

[0059] In the internal model control method, uncertainty mainly comes from model mismatch. Therefore, when designing BCDIMC, it is necessary to introduce a perturbation model to analyze the robust stability of the system.

[0060] G(s)=G * (s)+Δ(s)ω(s) (10)

[0061] Where G * (s) is the transfer function of the ideal system, Δ(s) represents the mismatch between the system perturbation and the model, and should satisfy ||Δ(S)|| ∞ ≤1, ω(s) is the weight function, which can be obtained through the frequency response characteristics of the system.

[0062] In order to measure the influence of BCDIMC parameters on the output I(s) of the perturbed DBSHBA system, the sensitivity function of the closed-loop transfer function of the system to the change of C(s) when the external disturbance d(s) is ignored is calculated. As shown below:

[0063]

[0064] Where, It is the performance indicator of the system.

[0065] It can be concluded that when the perturbation acts on the forward channel surrounded by the feedback loop, the sensitivity of the closed-loop system to the link characteristics or parameter changes caused by the perturbation is reduced by 1+C(s)Δ(s)ω(s) times. The smaller S is, the stronger the system's ability to track the input signal.

[0066] Figure 5The effects of different control methods on the harmonic content of the DBSHBA output current are demonstrated. When non-ideal resistor mismatch conditions are present, the BCDIMC significantly improves the output current harmonic distortion compared to a traditional proportional-integral controller. BCDIMC excels in suppressing the increase in harmonic content caused by resistor mismatch, especially at even-order harmonic frequencies, achieving an effect nearly equivalent to that of a proportional-integral controller under ideal conditions. This finding demonstrates that BCDIMC not only effectively reduces THD but also improves system robustness, enabling it to maintain stable performance despite variations in circuit component parameters.

Claims

1. An internal model control method based on bias current decoupling of a dual-buck symmetrical half-bridge power amplifier, characterized in that The method comprises the following steps: Step 1: Design of BCDIMC: Step 1: Equivalent the control structure of the DBSHBA system based on the internal model control principle to a simple feedback structure. The equivalent controller is G c (s), G c (s), system output I(s), and feedback signal d(s) are as follows: F(s)=[G(s)=G n (s)]U(s)+d(s) Where C(s) is BCDIMC, G(s) is DBSHBA system, G n (s) is the mathematical model of the non-ideal DBSHBA system, F(s) is the feedback signal, I * (s) is the input reference value, I(s) is the system output, U(s) is the controller output, and d(s) is the external disturbance; Steps 1 and 2: Under ideal conditions, that is, when the model is completely accurate and there is no external disturbance, the system output can completely replicate the reference input. The system mathematical model is decomposed into two parts: one containing delay and non-ideal characteristics, and the other containing minimum phase characteristics. BCDIMC is based on the inverse sum filter design of the minimum phase link and optimizes system performance by adjusting control parameters. The decomposition of the system mathematical model is shown below: G n (s)=G n+ (s)·G n- (s) Where G n+ (s) is the time delay of the system transfer function, the zero point of the right half plane and the unmodelable link under non-ideal conditions, G n- (s) is the transfer function of the system with minimum phase characteristics; Step 13: Define BCDIMC as the inverse sum filter of the minimum phase link L(s) = 1 / (αs+1) n The product of is expressed as follows: Where α is the time constant used to adjust the filter, i.e., the control parameter, s is the complex frequency variable in the Laplace transform, and n is the filter order; Step 14: Substitute the expression of BCDIMC to obtain the closed-loop output and error expression of the system: Where f(s) is the transfer function of the feedback filter, e m (s) is used to indicate the degree of mismatch between the model and the actual system; Step 15: When the model and the actual system are completely matched and external interference is ignored, e m (s) = d(s) = 0, the expression in step 14 is simplified to: I(s)=G n+ (s)f(s)I * (s) e(s)=[1-G n+ (s)f(s)]I * (s) Step 2: Analysis of the system's sensitivity to changes in BCDIMC parameters: Step 2.1: Introduce the perturbation model to analyze the robust stability of the system: G(s)=G * (s)+Δ(s)ω(s) Where G * (s) is the transfer function of the ideal system, Δ(s) represents the mismatch between the system perturbation and the model, and ω(s) is the weight function; Step 2. In order to measure the influence of BCDIMC parameters on the output I(s) of the perturbed DBSHBA system, the sensitivity function of the closed-loop transfer function of the system to the change of C(s) when the external disturbance d(s) is ignored is calculated. As shown below: Where, It is the performance indicator of the system.

2. The internal model control method based on bias current decoupling of a dual-buck symmetrical half-bridge power amplifier according to claim 1, characterized in that In the steps one by one, I * (s)=[I * out (s), I * bias (s)] T is the input reference value, I * out (s) is the desired output current, I * bias (s) is the desired bias current, I(s)=[I out (s), I bias (s)] T Output of the system.

3. The internal model control method based on bias current decoupling of a dual-buck symmetrical half-bridge power amplifier according to claim 1, characterized in that In the above steps, I(s)=[I out (s), I bias (s)] T is the system output, I out (s) is the actual output current, I bias (s) is the actual bias current.

4. The internal model control method based on bias current decoupling of a dual-buck symmetrical half-bridge power amplifier according to claim 1, characterized in that In the step 15, e m (s)=[G(s)-G n (s)] / G n (s).

5. The internal model control method based on bias current decoupling of a dual-buck symmetrical half-bridge power amplifier according to claim 1, characterized in that In the step 21, ||Δ(S)|| ∞ ≤1.

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