Sampled output feedback voltage tracking control method for buck type dc-dc converter

Abstract

The application discloses a sampling output feedback voltage tracking control method of a BUCK type DC-DC converter. The method establishes a continuous time state equation of the converter based on an average voltage model, constructs a reference output voltage, introduces an external system to generate a reference signal, and converts the system into a linear time-invariant error system through variable replacement and coordinate transformation; on this basis, a sampling output feedback control law containing a dynamic compensator is designed, the output feedback signal is sampled and the control input is updated at the sampling time, a zero-order holder is used in the adjacent sampling interval to keep the control input unchanged, and the sampling interval is constrained by preset upper and lower bounds. Through Lyapunov stability analysis, it is proved that the output voltage tracking error of the closed-loop system asymptotically converges to zero. The control law is in the form of discrete signals, is suitable for digital controller implementation, and allows non-periodic sampling to reduce the sampling and updating frequency.

Description

Technical Field

[0001] This invention belongs to the field of power electronics and automatic control technology, specifically relating to a sampling output feedback voltage tracking control method for a BUCK DC-DC converter. Background Technology

[0002] BUCK-type DC-DC converters are widely used in automotive power supplies, communication power supplies, distributed power supply, and embedded system voltage regulation. However, due to the influence of non-ideal switching devices, the output voltage is prone to fluctuations, making it difficult to simultaneously achieve both tracking accuracy and dynamic response.

[0003] Existing voltage-mode control, current-mode control, and PI (proportional-integral) / feedforward compensation-based control methods often employ fixed sampling period updates. In scenarios with high switching frequencies or high performance requirements, this often leads to a high sampling and computational burden. Furthermore, when the sampling time is affected by processor scheduling, communication, or multitasking and unequal intervals occur, the stability and performance guarantees of the fixed period design may no longer hold.

[0004] Therefore, a control method is needed that is digitally oriented and can still ensure that the output voltage tracking error converges to zero under non-periodic sampling conditions. Summary of the Invention

[0005] To address the problems existing in the prior art, the purpose of this invention is to provide a sampling output feedback voltage tracking control method for a BUCK-type DC-DC converter. This invention addresses the precise output voltage regulation requirements of BUCK converters under digital controller implementation conditions. It employs variable substitution and coordinate transformation to convert the system into a linear time-invariant error system that is easier to analyze and design. Based on this, a sampling output feedback control law with dynamic compensation is designed. The control input is updated at the sampling time, and a zero-order hold is used within the sampling interval to achieve output voltage tracking control of the reference voltage, ensuring that the output voltage tracking error asymptotically converges to zero.

[0006] The present invention is achieved by at least one of the following technical solutions.

[0007] A sampling output feedback voltage tracking control method for a BUCK-type DC-DC converter includes the following steps:

[0008] Step 1: Establish a continuous-time state-space model of the BUCK-type DC-DC converter based on the average voltage; construct the load-side reference output voltage and establish an external system model for generating the reference output voltage;

[0009] Step 2: Perform variable substitution and coordinate transformation on the system from Step 1 and define the voltage tracking error to obtain the linear time-invariant system and the error system;

[0010] Step 3: Design a sampling output feedback control law that includes a dynamic compensator. At the sampling time, sample the output feedback signal and update the control input. Use a zero-order hold to keep the control input unchanged in adjacent sampling intervals.

[0011] Step 4: Select the control gain and compensator parameters to make the closed-loop system matrix satisfy the Hurwitz condition, ensuring that the output voltage tracking error asymptotically converges to zero.

[0012] Step 5: Verify the effectiveness of the proposed control strategy through MATLAB / Simulink simulation.

[0013] Step 6: The effectiveness of the proposed control strategy was verified through physical experiments.

[0014] Furthermore, the BUCK converter topology, based on a continuous-time model of the average voltage, can be expressed as follows:

[0015] (1)

[0016] in, , and These represent the capacitance, inductance, and load resistance of the circuit, respectively. A constant DC power supply voltage is used... This indicates that the converter input voltage is ,in It is the duty cycle of the switching transistor (determined by the PWM control signal).

[0017] Furthermore, define the reference output voltage across the load. At this time, the load reference output voltage Modeling can be done through external systems as follows:

[0018] (2)

[0019] in Indicates the status of the external system. This represents the coefficient between the reference output voltage and the external system state.

[0020] make This verifies that the reference output voltage is generated by the external system (2). To convert model (1) into a standard linear time-invariant (LTI) system, we perform the following transformation:

[0021] (3)

[0022] Furthermore, it is then defined as follows:

[0023] (4)

[0024] Then, by combining the external system (2), the following LTI system can be obtained.

[0025] (5)

[0026] in Indicates the system status. Indicates control input, This represents the voltage tracking error. For simplicity, when there is no risk of confusion, we use... replace ,in .

[0027] Furthermore, we consider the following control law to ensure the voltage tracking error of the BUCK-type DC-DC converter. It converges to zero.

[0028] (6)

[0029] in, and For all , Indicates the sampling interval. Indicates the first Each sampling time, Represents the set of non-negative integers. Boundary. and It is to satisfy . a normal number. These represent three dynamic compensator systems. These represent the coefficients of the corresponding error sampling signals. The parameters in the above equations are defined as follows:

[0030] (7)

[0031] Furthermore, we now introduce the closed-loop regulator equation to determine the steady-state state and steady-state input. They are respectively used This indicates that for system (5), there exists a unique solution. Satisfy the following regulator equation

[0032] (8)

[0033] We ordered Through calculation, the solution to the following regulator equation was obtained.

[0034] (9)

[0035] Next, we performed the following transformations.

[0036] (10)

[0037] And define

[0038] (11)

[0039] Because for all , Therefore, for all , This means for all , Substituting control law (6) into (5), we can obtain...

[0040] (12)

[0041] in

[0042] (13)

[0043] choose Make the matrix It's Hurwitz, and I chose... Make the matrix It's by Hurwitz. So, regarding... There exists a positive definite matrix. Make Established, among which .

[0044] Choosing Lyapunov functions

[0045] (14)

[0046] Then we can get

[0047] (15)

[0048] in , , According to (12), (14) and We can get The time derivative along the trajectory of system (12) satisfies

[0049] (16)

[0050] According to (12) and (15), for any have

[0051] (17)

[0052] in , According to (12), (15) and (17), for any have

[0053] (18)

[0054] in , , According to (12), (15) and (18), for any have

[0055] (19)

[0056] Based on (15), (16), and (19), we can obtain

[0057] (20)

[0058] in , , , , , .

[0059] Next, prove .if If this is not true, then there exists a moment... , making According to (16), for any , , , and , Therefore, there exists another moment. , making

[0060] (twenty one)

[0061] According to the third inequality in (20) and (21), we let Established, we have This contradicts the second inequality in (21), therefore we can obtain Establishment and

[0062] (twenty two)

[0063] let ,in

[0064] (twenty three)

[0065] because , and Then (23) can be further obtained

[0066] (twenty four)

[0067] definition .because It is a continuous function, and further... This means .because and We can get Therefore when Approaching infinity Approaching zero, that is .therefore, Furthermore, the stable output voltage tracking error of the BUCK-type DC-DC system can asymptotically converge to zero.

[0068] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0069] This invention addresses the digital implementation requirements of BUCK-type DC-DC converters. Based on average voltage modeling, a reference signal external system generation mechanism, and the construction of a linear time-invariant error system, a sampling output feedback voltage tracking control law is designed that can be directly executed on a digital platform. Under the condition that the sampling interval meets preset upper and lower bound constraints, the output voltage tracking error is guaranteed to converge asymptotically to zero, achieving high-precision voltage tracking. Simultaneously, the proposed control law employs a sampling update and zero-order hold execution method, which does not rely on continuous update of the control input and allows non-periodic sampling, thereby reducing the number of sampling and control update operations, significantly reducing processor computational resource consumption, and improving engineering feasibility and system operating efficiency. Attached Figure Description

[0070] Figure 1 This is a topology diagram of the BUCK-type DC-DC converter in an embodiment of the present invention;

[0071] Figure 2 This is a flowchart of the sampling output feedback voltage tracking control method for a BUCK-type DC-DC converter in an embodiment of the present invention;

[0072] Figure 3 This is a graph showing the system state and reference voltage curves in the MATLAB numerical simulation of an embodiment of the present invention;

[0073] Figure 4This is a state curve diagram of the dynamic compensator in the MATLAB numerical simulation of an embodiment of the present invention;

[0074] Figure 5 This is a voltage tracking error curve in the MATLAB numerical simulation of an embodiment of the present invention;

[0075] Figure 6 This is a control input curve graph from the MATLAB numerical simulation of an embodiment of the present invention;

[0076] Figure 7 This is a waveform diagram of reference voltage, inductor current, and load voltage in the hardware experiment of this invention embodiment;

[0077] Figure 8 This is a state curve diagram of the dynamic compensator in the hardware experiment of this invention embodiment;

[0078] Figure 9 This is a control input curve diagram from the hardware experiment of this invention embodiment;

[0079] Figure 10 This is a waveform diagram of the output voltage tracking error in the hardware experiment of this invention embodiment. Detailed Implementation

[0080] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0081] A sampling output feedback voltage tracking control method for a BUCK (step-down) DC-DC converter includes the following steps:

[0082] Step 1: Establish a continuous-time state-space model of the BUCK DC-DC converter based on the average voltage, and clarify the dynamic relationship between inductance, capacitance, load resistance, input DC voltage and duty cycle.

[0083] Step 2: Construct an output voltage reference signal and establish an external system to generate the reference signal, forming a mapping relationship between the reference output voltage and the external system state;

[0084] Step 3: Perform variable substitution and coordinate transformation on the system described in Step 1, define the output voltage tracking error, and obtain the linear time-invariant error system and its equivalent expression, providing a unified modeling basis for control law design;

[0085] Step 4: Design a sampling output feedback control law with a dynamic compensator: sample the output feedback signal at the sampling time and update the control input. Use a zero-order hold to keep the control input unchanged in adjacent sampling intervals, and satisfy the preset upper and lower bound constraints of the sampling interval.

[0086] Step 5: Prove the stability of the closed-loop system based on the Hurwitz condition and the Lyapunov method, ensuring that the output voltage tracking error asymptotically converges to zero;

[0087] Step 6: Verify the effectiveness of the proposed sampling output feedback control strategy through MATLAB / Simulink simulation.

[0088] Step 7: Verify the effectiveness of the proposed sampling output feedback control strategy through physical experiments.

[0089] As one embodiment, step 1, the BUCK converter topology, can be represented by a continuous-time model based on the average voltage as follows:

[0090] (1)

[0091] in, , and These represent the capacitance, inductance, and load resistance of the circuit, respectively. A constant DC power supply voltage is used... This indicates that the converter input voltage is ,in It is the duty cycle of the switching transistor (determined by the PWM control signal).

[0092] Step 2: Define the reference output voltage across the load. At this time, the load reference output voltage Modeling can be done through external systems as follows:

[0093] (2)

[0094] in Indicates the status of the external system. This represents the coefficient between the reference output voltage and the external system state.

[0095] make This verifies that the reference output voltage is generated by the external system (2). To convert model (1) into a standard linear time-invariant (LTI) system, we perform the following transformation:

[0096] (3)

[0097] Step 3, then define as follows:

[0098] (4)

[0099] Then, by combining the external system (2), the following LTI system can be obtained.

[0100] (5)

[0101] in Indicates the system status. Indicates control input, This represents the voltage tracking error. For simplicity, when there is no risk of confusion, we use... replace ,in .

[0102] Step 4: We consider the following control law to ensure the voltage tracking error of the BUCK-type DC-DC converter. It converges to zero.

[0103] (6)

[0104] in, and For all , Indicates the sampling interval. Indicates the first Each sampling time, Represents the set of non-negative integers. Boundary. and It is to satisfy . a normal number. These represent three dynamic compensator systems. These represent the coefficients of the corresponding error sampling signals. The parameters in the above equations are defined as follows:

[0105] (7)

[0106] Step 5: Now we introduce the closed-loop regulator equation to determine the steady-state state and steady-state input. They are respectively used This indicates that for system (5), there exists a unique solution. Satisfy the following regulator equation

[0107] (8)

[0108] We ordered Through calculation, the solution to the following regulator equation was obtained.

[0109] (9)

[0110] Next, we performed the following transformations.

[0111] (10)

[0112] And define

[0113] (11)

[0114] Because for all , Therefore, for all , This means for all , Substituting control law (6) into (5), we can obtain...

[0115] (12)

[0116] in

[0117] (13)

[0118] choose Make the matrix It's Hurwitz, and I chose... Make the matrix It's by Hurwitz. So, regarding... There exists a positive definite matrix. Make Established, among which .

[0119] Choosing Lyapunov functions

[0120] (14)

[0121] Then we can get

[0122] (15)

[0123] in , , According to (12), (14) and We can get The time derivative along the trajectory of system (12) satisfies

[0124] (16)

[0125] According to (12) and (15), for any have

[0126] (17)

[0127] in , According to (12), (15) and (17), for any have

[0128] (18)

[0129] in , , According to (12), (15) and (18), for any have

[0130] (19)

[0131] Based on (15), (16), and (19), we can obtain

[0132] (20)

[0133] in , , , , , .

[0134] Next, prove .if If this is not true, then there exists a moment... , making According to (16), for any , , , and , Therefore, there exists another moment. , making

[0135] (twenty one)

[0136] According to the third inequality in (20) and (21), we let Established, we have This contradicts the second inequality in (21), therefore we can obtain Establishment and

[0137] (twenty two)

[0138] let ,in

[0139] (twenty three)

[0140] because , and Then (23) can be further obtained

[0141] (twenty four)

[0142] definition .because It is a continuous function, and further... This means .because and We can get Therefore when Approaching infinity Approaching zero, that is .therefore, Furthermore, the stable output voltage tracking error of the BUCK-type DC-DC system can asymptotically converge to zero.

[0143] Furthermore, under the constraints of the sampling output feedback control law and the upper and lower bounds of the sampling interval, the closed-loop system of the BUCK-type DC-DC converter is stable, and the output voltage tracking error asymptotically converges to zero.

[0144] Furthermore, as can be seen from (6), the proposed sampling output feedback control law is in the form of discrete update: the output feedback signal is sampled and the control input is updated at the sampling time, and a zero-order hold is used in adjacent sampling intervals to keep the control input unchanged, so it can be directly executed on the digital controller platform.

[0145] Step 6: We will demonstrate an example through simulation and experimentation to verify the effectiveness of the proposed control scheme. The simulation and experimentation will be conducted based on the following parameters: , , , Next, we select the control law parameters as follows: , , , , The selection of the sampling interval by the digital controller enables For all k ∈ N, where .

[0146] Initial conditions are set as follows and The simulation was performed in MATLAB / Simulink using a fixed-step solver, where the step size equals the sampling period. For example... Figure 5 As shown, the output voltage error The voltage approaches zero over time, confirming that the proposed sampled-data state feedback law achieves asymptotic voltage tracking. This demonstrates that the proposed controller is well-suited for implementation on low-cost digital platforms without introducing unnecessary switching stress into the power stage.

[0147] like Figure 3 As shown, the state trajectories of the system (inductor current and load voltage) all converge to steady-state values. Figure 4 As shown, the dynamic compensator state All exhibit good convergence characteristics and tend to stabilize as constants under closed-loop regulation. For example... Figure 6 As shown, the corresponding control input The change trajectory varies within a reasonable range and eventually reaches a steady state without high-frequency oscillation, thus meeting the modulation requirements of practical switching devices.

[0148] Step 7: To further verify the feasibility and effectiveness of the proposed algorithm in actual engineering, the designed control law is deployed to the digital controller to control the actual BUCK converter hardware circuit.

[0149] In the hardware implementation, the digital controller uses an STM32F407ZGT6 microcontroller with a system clock configured at 128MHz. The PWM control signal is generated by an internal hardware advanced timer configured to achieve a minimum duty cycle of 0.01 (approximately 6.6-bit effective resolution). The output current is detected by an INA210 current sensing amplifier. The voltage and current measurement signals are sampled at high frequency by a 12-bit ADC configured in dual-channel scan mode and supporting continuous DMA (direct memory access) transfer. During each control update cycle, the system calculates the duty cycle instruction for the next cycle using the latest ADC sample value and the discrete control law; this instruction is written to the PWM compare register and remains constant using the inherent zero-order hold mechanism of the PWM hardware peripheral until the next update time.

[0150] like Figure 10 As shown, the system voltage tracking error converges to the zero reference line over time. Figure 7 It can be seen that the system state (inductor current and load voltage) converges to the steady-state value.

[0151] Figure 8 and Figure 9 The internal state and control variable operation data of the dynamic compensator during the experiment are exported through a microcontroller. Figure 8 This indicates that the dynamic compensator states converge after a limited period of oscillation adjustment. Figure 9The experimental results show that the control variable u tends to stabilize after initial dynamic adjustment. These experimental results are consistent with the numerical results in the numerical simulation, confirming that the proposed sampled data feedforward state feedback controller can be implemented on a low-cost digital platform and achieves satisfactory steady-state performance in a practical buck converter prototype.

[0152] Based on comprehensive theoretical analysis, simulation, and experimental results, it is fully demonstrated that the sampling output feedback control method based on zero-order hold proposed in this invention not only theoretically guarantees that the tracking error asymptotically converges to zero, but also has excellent tracking performance in practical engineering applications, and successfully overcomes the stability challenge brought about by the non-periodic sampling of digital controllers.

[0153] The above is the content of this invention. Any changes made to the technical solution of this invention that do not exceed the scope of the technical solution of this invention shall fall within the protection scope of this invention.

Claims

1. A sampling output feedback voltage tracking control method for a BUCK-type DC-DC converter, characterized in that, Includes the following steps: Step 1: Establish a continuous-time state-space model of the BUCK-type DC-DC converter based on the average voltage; construct the load-side reference output voltage and establish an external system model for generating the reference output voltage; Step 2: Perform variable substitution and coordinate transformation on the state-space model and the external system model obtained in Step 1, and define the voltage tracking error to obtain the linear time-invariant system and the error system; Step 3: Based on the linear time-invariant system obtained in Step 2, design a sampling output feedback control law including a dynamic compensator. At the sampling time, sample the output feedback signal and update the control input. Use a zero-order hold to keep the control input unchanged in adjacent sampling intervals. After the control law is applied to the error system, a closed-loop system with a system matrix is ​​formed. Step 4: For the closed-loop system obtained in Step 3, select the control gain and compensator parameters so that the system matrix of the closed-loop system satisfies the Hurwitz condition. Based on this, prove that the output voltage tracking error asymptotically converges to zero using the Lyapunov method.

2. The method according to claim 1, characterized in that, The average voltage continuous-time model of the BUCK-type DC-DC converter is described as follows: (1) in , and These represent the capacitance, inductance, and load resistance of the circuit, respectively, and the constant DC power supply voltage is represented by... This indicates that the converter input voltage is ,in It is the duty cycle of the switching transistor.

3. The method according to claim 2, characterized in that, Reference output voltage is The external system is a linear autonomous system, and the reference output voltage is obtained by mapping the external system state through the output. (2) in Indicates the status of the external system. This represents the coefficient between the reference output voltage and the external system state.

4. The method according to claim 3, characterized in that, Variable substitution and coordinate transformation include combining the states of the BUCK-type DC-DC converter and the external system states, and defining variables to obtain a standard linear time-invariant system. The transformation relationship and variable definition are shown below. (3) Then define as follows: (4) Combining the external system, we obtain the following linear time-invariant system: (5) in Indicates the system status. Indicates control input, This indicates the voltage tracking error.

5. The method according to claim 4, characterized in that, The sampling output feedback control law is: (6) in, and For all , Indicates the sampling interval. Indicates the first Each sampling time, Represents the set of non-negative integers, and its boundary. and It is to satisfy positive numbers, These represent three dynamic compensator systems. These represent the coefficients of the corresponding error sampling signals; the parameters in the above equations are defined as follows: (7)。 6. The method according to claim 5, characterized in that, The steady-state state and steady-state input signal are determined by introducing closed-loop regulator equations. They are respectively used This indicates that for system (5), there exists a unique solution. Satisfy the following regulator equation (8)。 7. The method according to claim 6, characterized in that, Selecting the state feedback gain Make the matrix It's Hurwitz, and I chose... This makes the extended closed-loop system matrix It's by Hurwitz; in (9)。 8. The method according to claim 7, characterized in that, Constructing quadratic Lyapunov functions , where the extended state vector Positive definite matrix satisfy Choosing appropriate sampling intervals and control parameter boundaries ensures that the Lyapunov function of the closed-loop system satisfies... This ensures that the output voltage tracking error asymptotically converges to zero.

9. The method according to claim 8, characterized in that, The control input remains unchanged within adjacent sampling intervals using a zero-order hold mechanism to achieve discrete updates and continuous execution of the digital controller.

10. The method according to claim 9, characterized in that, The method allows for non-periodic sampling, which reduces the number of sampling and controller updates while ensuring that the sampling interval meets the upper and lower bound constraints, thereby reducing the consumption of computing resources and meeting the voltage regulation tracking performance requirements.

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