A discrete-time robust current-limited voltage tracking control method and system for DC-DC step-down converter under multi-source disturbance

Abstract

This invention discloses a discrete-time robust current-constrained voltage tracking control method and system for a DC-DC buck converter under multi-source disturbances. The method includes: establishing a discrete-time model of the buck converter system based on its circuit topology and considering the multi-source disturbances present in the system; designing discrete-time disturbance observers for both matched and unmatched multi-source disturbances to estimate the disturbances respectively; designing a discrete-time current-constrained controller using control barrier function technology to ensure the stability of the buck converter system and strictly constrain the inductor current under multi-source disturbances; and performing robust stability analysis on the buck converter system to obtain the relationship between controller parameters and sampling time and the stability and current-constrained performance of the buck converter system. This invention can guarantee system stability, strictly constrain the inductor current under multi-source disturbances, and improve output voltage tracking performance.

Description

Technical Field

[0001] This invention relates to advanced control technology for power electronic systems, and in particular to a discrete-time robust current-constrained voltage tracking control method and system for DC-DC buck converters under multi-source disturbances. Background Technology

[0002] Thanks to its high efficiency, strong controllability and high reliability, Buck converters have been widely used in a variety of electrified vehicle systems, including spacecraft hybrid power systems, electric vehicles, photovoltaic power generation systems and wireless charging systems.

[0003] To improve output voltage tracking performance, recent research has explored various innovative controller design schemes based on a second-order structure integrating voltage and current loops. This structure exhibits significant advantages in parameter adjustment flexibility and direct control efficiency. Despite these advantages, the control structure still faces two key challenges that urgently need to be addressed. The primary challenge stems from multi-source disturbances, which severely affect the high-precision voltage regulation capability of Buck converters. For example, in photovoltaic power generation systems, the input voltage is directly determined by the light intensity, while the time-varying nature of cloud positions causes input voltage fluctuations; similarly, in DC drive motors, different operating conditions cause load variations in the Buck converter. Furthermore, the actual values ​​of inductors and capacitors may deviate from their nominal values. Among these disturbances, inductor parameter variations and input voltage fluctuations are considered matching disturbances, while capacitor parameter uncertainties and unknown loads are classified as non-matching disturbances—since they are on different channels from the control input, they cannot be directly compensated for. The second challenge lies in the fact that the reference value of the current loop in traditional voltage regulation architectures is determined by the voltage loop. To achieve overcurrent protection, a saturation function limit is typically imposed on this reference value. However, in a second-order control structure, the current, as a system state variable, cannot be constrained using the same method. As is well known, inductors have parameters such as rated current and saturation current. When the current exceeds a specified threshold, the inductance value decreases, thus affecting the inductor's performance and efficiency. In extreme cases, overcurrent can cause overheating, potentially damaging the inductor and posing safety hazards. Therefore, it is essential to strictly constrain the inductor current while achieving voltage tracking and steady-state accuracy control.

[0004] The following technical means are mainly used in the existing technology: (1) A controller with separate external voltage loop and internal current loop is used: the external loop is responsible for output voltage tracking, and the internal loop uses the barrier Lyapunov function to realize inductor current constraint. However, this method does not consider the disturbance of system resistance, capacitance and inductance parameters, and only relies on the inherent feedback mechanism of the controller to suppress the disturbance, which makes it difficult to obtain satisfactory voltage tracking accuracy and disturbance rejection performance. (2) An artificial neural network controller is constructed based on the approximate dynamic programming theory. Although it can simultaneously guarantee voltage tracking accuracy and current constraint, the integral link in its controller responds slowly and can only offset the disturbance through slow feedback adjustment, which leads to a significant deterioration of the dynamic performance of the system when facing a sharp disturbance. (3) A model predictive control method for DC-DC converter is designed. This method considers input and state constraints. However, its core problem is that the system's need for fast response and the heavy computational burden brought by online optimization are contradictory, which may be difficult to meet the requirements of real-time applications.

[0005] In recent years, the concept of safety-critical control has attracted widespread attention from scholars. Safety-critical control, as discussed here, refers to maintaining the system state within a safe range. The core technology for establishing safety constraints is the control barrier function (CBF), which ensures the control invariance of the set by limiting certain state-related control input constraints. A typical characteristic of CBF is that when the system state trajectory starts within a safe region, it will always be constrained within that region, thus ensuring the absolute safety of the system state. However, it should be noted that traditional CBF design, if ignoring multi-source disturbances, may lead to the failure of state constraints, and relying solely on CBF cannot guarantee the stability of the closed-loop system. Therefore, the key to achieving current-constrained voltage regulation in DC-DC converter systems lies in effectively integrating disturbance rejection control technology with CBF. Furthermore, a key challenge has emerged in digital applications: continuous-time CBF design is usually implemented through discretization, which cannot guarantee state constraints during the sampling interval, and this becomes particularly pronounced under large sampling period conditions. Summary of the Invention

[0006] Purpose of the invention: The purpose of this invention is to provide a discrete-time robust current-constrained voltage tracking control method and system for DC-DC buck converters under multi-source disturbances. This method can ensure system stability, strictly constrain the inductor current under multi-source disturbances, and improve the output voltage tracking performance.

[0007] Technical solution: The method described in this invention includes the following steps:

[0008] Based on the circuit topology of the DC-DC buck converter, and considering the multi-source disturbances existing in the buck converter system, a discrete-time model of the buck converter system is established using the forward Euler method. The multi-source disturbances include matched multi-source disturbances and unmatched multi-source disturbances. Matched multi-source disturbances include input voltage fluctuations and inductor parameter perturbations, while unmatched multi-source disturbances include load changes and capacitor parameter perturbations.

[0009] Based on the discrete-time model of the buck converter system, discrete-time disturbance observers for matched and unmatched multi-source disturbances are designed respectively to estimate matched and unmatched multi-source disturbances.

[0010] Based on the estimation of matched and unmatched multi-source disturbances by the discrete-time disturbance observer, a discrete-time state feedback controller is designed. Using the control barrier function technique, a discrete-time current constraint controller is designed to ensure the stability of the buck converter system and strictly constrain the inductor current under multi-source disturbances.

[0011] Based on a discrete-time current-constrained controller, a rigorous robust stability analysis is performed on the buck converter system to obtain the relationship between controller parameters and sampling time and the stability and current-constrained performance of the buck converter system.

[0012] Furthermore, methods for establishing discrete-time models of buck converter systems include:

[0013] (1) Based on the circuit topology of the DC-DC buck converter, a nominal average model of the buck converter system considering multi-source disturbances is established;

[0014] (2) Considering the multi-source disturbances in the buck converter system, the unmatched multi-source disturbances caused by capacitor parameter perturbation and load change, and the matched multi-source disturbances caused by inductor parameter perturbation and input voltage fluctuation are added to the nominal average model of the buck converter system.

[0015] (3) The forward Euler method is used to obtain the discrete-time model of the buck converter system.

[0016] Furthermore, the discrete-time model expression of the buck converter system is as follows:

[0017] ;

[0018] in, The sampling period of the buck converter system. For the first The output voltage of each sampling period For the first The output voltage of each sampling period For the first Inductor current per sampling period For the first Inductor current per sampling period For the first Mismatched multi-source disturbances in each sampling period For the first Matching multi-source disturbances for each sampling period, For the first The control input of the discrete-time current constraint controller for each sampling period. , , and These are the capacitor C, inductor L, load resistance R, and input voltage, respectively. Nominal parameters;

[0019] and The model is expressed as and , This is the upper bound for the variation of unmatched multi-source disturbances in adjacent sampling periods. To match the upper bound of multi-source disturbance changes between adjacent sampling periods, For the first Mismatched multi-source disturbances in each sampling period For the first Matching multi-source disturbances for each sampling period;

[0020] Set inductor current Subject to constant Restriction, i.e., satisfaction ;and Related security sets Defined as:

[0021] ;

[0022] in, For real numbers, The upper bound is set for the inductor current constraint. , This is the lower bound of the inductor current constraint. .

[0023] Furthermore, the discrete-time perturbation observer for unmatched multi-source perturbations is represented as:

[0024] ,

[0025] ,

[0026] in, As an intermediate variable, , The sampling period of the buck converter system. For the first Inductor current per sampling period For the first The output voltage of each sampling period , and These are the nominal parameters of capacitor C, inductor L, and load resistance R, respectively. and The first Individual and Internal state variables of a discrete-time disturbance observer with a sampling period of mismatched multi-source disturbance. For discrete-time perturbation observer gain parameters of unmatched multi-source perturbations, for The estimated value, For the first Unmatched multi-source disturbances in each sampling period;

[0027] The discrete-time perturbation observer that matches multi-source perturbations is represented as:

[0028] ,

[0029] ,

[0030] in, As an intermediate variable, , Input voltage The nominal parameters, For the first The control input of the discrete-time current constraint controller for each sampling period. for Estimated value For the first Matching multi-source disturbances for each sampling period, and The first The and the first An internal state variable employing a periodic perturbation observer, Gain parameters for discrete-time disturbance observers to match multi-source disturbances.

[0031] Furthermore, methods for designing discrete-time current-constrained controllers include:

[0032] (1) Based on the discrete-time model of the buck converter considering multi-source disturbances, and combined with the estimation of disturbances by the discrete-time disturbance observer, the tracking error of the output voltage and the state variables are selected to obtain the system equation of the buck converter.

[0033] (2) The discrete-time state feedback controller is designed as follows:

[0034] ;

[0035] in, The control output of the discrete-time state feedback controller. and For discrete-time state feedback controller gain, , and These are the capacitor C, inductor L, and input voltage, respectively. The nominal parameters, The sampling period of the buck converter system. For the tracking error of the output voltage, For state variables, For the first Unmatched multi-source disturbance estimates for each sampling period For the first Inductor current per sampling period For the first Matched multi-source disturbance estimates for each sampling period For the first The output voltage for each sampling period;

[0036] (3) Combining the estimation of disturbance by the discrete-time disturbance observer, and based on the control barrier function technique and safety set... Construct the control input inequality for the discrete-time current-constrained controller:

[0037] ;

[0038] in, For the first The control input of the discrete-time current constraint controller for each sampling period. For positive integers, For positive integers, , For parameters, , ; The upper bound is set for the inductor current constraint. This is the lower bound of the inductor current constraint. To match the gain parameters of the discrete-time disturbance observer for multi-source disturbances, For discrete-time disturbance observer gain parameters of unmatched multi-source disturbances;

[0039] Based on the control input inequality of the discrete-time current-constrained controller, the control input set is obtained. for:

[0040] As an intermediate variable, , It is the control input set.

[0041] (4) Integrate the control output of the discrete-time state feedback controller that ensures the stability of the buck converter system. With the control input set of a discrete-time state feedback controller that ensures current constraints A discrete-time current-constrained controller was constructed:

[0042] ;

[0043] in, For the first The control input of the discrete-time current constraint controller for each sampling period. for The limit, The optimal control input, which simultaneously guarantees the stability of the buck converter system and the current constraint, can be solved based on the quadratic programming algorithm. The control output of the discrete-time state feedback controller;

[0044] Using the control input set as constraints, the optimal control input that simultaneously guarantees the stability of the buck converter system and the current constraint can be solved based on the quadratic programming algorithm.

[0045] Furthermore, based on a discrete-time current-constrained controller, a rigorous robust stability analysis is performed on the buck converter system, specifically including:

[0046] Based on a discrete-time current-constrained controller, for initial conditions , Let be the initial value of the inductor current. For the control input set of a discrete-time state feedback controller, even with multi-source disturbances, the inductor current... It is also strictly constrained to a safe set Within this scope, the guarantee holds if the control parameters of the discrete-time current-constrained controller adhere to the following design principles:

[0047] Discrete-time perturbation observer gain and satisfy: and ;in, The sampling period of the buck converter system. To match the gain parameters of the discrete-time disturbance observer for multi-source disturbances, For discrete-time disturbance observer gain parameters of unmatched multi-source disturbances;

[0048] Discrete-time current-constrained controller gain , and satisfy:

[0049] ;

[0050] ;

[0051] ;

[0052] ;

[0053] in, , These are the capacitor C and the input voltage, respectively. The nominal parameters, For positive integers, For parameters.

[0054] The system corresponding to the method described in this invention includes:

[0055] The discrete-time model building unit is used to establish a discrete-time model of the buck converter system based on the circuit topology of the DC-DC buck converter, while considering the multi-source disturbances existing in the buck converter system. The forward Euler method is used to establish the discrete-time model of the buck converter system. The multi-source disturbances include matched multi-source disturbances and unmatched multi-source disturbances. Matched multi-source disturbances include input voltage fluctuations and inductor parameter perturbations, while unmatched multi-source disturbances include load changes and capacitor parameter perturbations.

[0056] The observer design unit is used to design discrete-time disturbance observers for matched and unmatched multi-source disturbances based on the discrete-time model of the buck converter system, and to estimate matched and unmatched multi-source disturbances respectively.

[0057] The controller design unit is used to design a discrete-time state feedback controller based on the estimation of matched and unmatched multi-source disturbances by the discrete-time disturbance observer, and to design a discrete-time current constraint controller using the control barrier function technique to ensure the stability of the buck converter system and strictly constrain the inductor current under multi-source disturbances.

[0058] The stability analysis unit is used to perform rigorous robust stability analysis on the buck converter system based on the discrete-time current-constrained controller, and to obtain the relationship between the controller parameters and sampling time and the stability and current-constrained performance of the buck converter system.

[0059] An electronic device for storing and executing the method includes:

[0060] Memory, used to store computer programs;

[0061] A processor for executing the computer program to implement the method.

[0062] A non-volatile storage medium for storing and executing the method, for storing a computer program, wherein the computer program implements the method when executed by a processor.

[0063] A computer program product for storing and executing the method includes a computer program / instructions that, when executed by a processor, implement the method.

[0064] Beneficial effects: Compared with the prior art, the significant technical effects of the present invention are as follows:

[0065] (1) Compared with the existing buck converter current constraint controller, it can simultaneously achieve strict current constraint and closed-loop system stability, and is not affected by whether the equivalent initial current exceeds the limit range;

[0066] (2) The discrete-time CBF proposed in this invention effectively solves the problem of current constraint failure caused by ignoring the sampling period in the continuous-time CBF method in practical applications, and is more suitable for application scenarios of digital platforms;

[0067] (3) This invention provides the relationship between controller parameters and sampling time and the stability and current constraint performance of buck converter system, which facilitates engineering parameter adjustment. Attached Figure Description

[0068] Figure 1 This is a flowchart of the tracking and control method of the present invention;

[0069] Figure 2 This is a schematic diagram of the circuit topology and tracking control system of the DC-DC buck converter of the present invention. Detailed Implementation

[0070] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0071] To improve output voltage tracking performance, the second-order structure based on the fusion of voltage and current loops suffers from multi-source disturbances, severely impacting the high-precision voltage regulation capability of the Buck converter. Furthermore, the actual values ​​of the inductor and capacitor may deviate from their nominal values. In addition, under the second-order control structure, the current, as a system state variable, must be strictly constrained while achieving voltage tracking and steady-state accuracy control. Therefore, this invention provides a discrete-time robust current-constrained voltage tracking control method for a DC-DC buck converter under multi-source disturbances. Employing two discrete-time disturbance observers and a discrete-time current-constrained controller, system stability is guaranteed, and the control barrier function technique is used to strictly constrain the inductor current under multi-source disturbances. Moreover, the discrete-time form of the control strategy facilitates digital implementation.

[0072] like Figure 1 As shown, the specific steps include:

[0073] Step 1: Based on the circuit topology of the DC-DC buck converter, and considering the multi-source disturbances present in the buck converter system, a discrete-time model of the buck converter system is established using the forward Euler method. These multi-source disturbances include input voltage fluctuations, inductor parameter perturbations, load changes, and capacitor parameter perturbations. Input voltage fluctuations and inductor parameter perturbations are matched multi-source disturbances, while load changes and capacitor parameter perturbations are unmatched multi-source disturbances. Specifically, these include:

[0074] 1) Based on the circuit topology of the DC-DC buck converter, establish a nominal average model of the buck converter system considering multi-source disturbances:

[0075] ;

[0076] in, , and These represent the input voltage, output voltage, and inductor current, respectively. The derivative of the output voltage. The derivative of the inductor current. Indicates capacitance. Indicates the load resistance. This represents the inductance, and u is the control input of the discrete-time current constraint controller.

[0077] 2) Considering the multi-source disturbances present in the buck converter system, the nominal average model of the buck converter system can be further expressed as:

[0078] ;

[0079] in, , , and These are the capacitor C, inductor L, load resistance R, and input voltage, respectively. Nominal parameters; This represents the mismatched multi-source disturbance caused by capacitance parameter perturbation and load variation. ; This represents the matching multi-source disturbance caused by inductor parameter perturbation and input voltage fluctuation. .

[0080] 3) Using the forward Euler method, the discrete-time model of the buck converter system can be obtained as follows:

[0081] ;

[0082] in, The sampling period of the buck converter system. For the first The output voltage of each sampling period For the first The output voltage of each sampling period For the first Inductor current per sampling period For the first Inductor current per sampling period For the first Mismatched multi-source disturbances in each sampling period For the first Matching multi-source disturbances for each sampling period, For the first The control input of the discrete-time current constraint controller for each sampling period.

[0083] Disturbance and The model can be expressed as and , This is the upper bound for the variation of unmatched multi-source disturbances in adjacent sampling periods. To match the upper bound of multi-source disturbance changes between adjacent sampling periods, For the first Mismatched multi-source disturbances in each sampling period For the first Matching multi-source disturbances for each sampling period. Setting the inductor current. Subject to constant Restriction, i.e., satisfaction .and Related security sets Defined as:

[0084] ;

[0085] in, For real numbers, The upper bound is set for the inductor current constraint. , This is the lower bound of the inductor current constraint. .

[0086] Step 2: Based on the discrete-time model of the buck converter system in Step 1, design two discrete-time disturbance observers to estimate matched and unmatched multi-source disturbances. Matched multi-source disturbances include input voltage fluctuations and inductor parameter uncertainties, while unmatched multi-source disturbances include load variations and capacitor parameter uncertainties. Specifically, these include:

[0087] Based on the discrete-time model of the buck converter system in step 1, the two discrete-time disturbance observers are designed as follows:

[0088] The discrete-time perturbation observer for unmatched multi-source perturbations is represented as:

[0089] ,

[0090] ,

[0091] and

[0092] The discrete-time perturbation observer that matches multi-source perturbations is represented as:

[0093] ,

[0094] ,

[0095] in, and As an intermediate variable, , , and respectively and Estimated value and For the first An internal state variable employing two periodic perturbation observers. and These are the discrete-time disturbance observer gain parameters for unmatched multi-source disturbances and the discrete-time disturbance observer gain parameters for matched multi-source disturbances, respectively. and For the first Each uses two periodic disturbance observers with internal state variables.

[0096] Step 3: Based on the multi-source disturbance estimation using the discrete-time disturbance observer designed in Step 2, design a discrete-time state feedback controller. Using the control barrier function technique, design a discrete-time current constraint controller to ensure the stability of the buck converter system under disturbances and strictly constrain the inductor current. Specifically, this includes:

[0097] 1) Based on the discrete-time model of the buck converter considering multi-source disturbances established in step 1, and combined with the disturbance estimation in step 2, the tracking error of the output voltage is selected as... and state variables , For the first Using a reference voltage with a given cycle, we can obtain:

[0098] ;

[0099] in, For the first Tracking error per sampling period, For the first The state variables for each sampling period For the first Unmatched multi-source disturbance estimates for each sampling period For the first The mismatch perturbation estimation error for each sampling period .

[0100] 2) To effectively eliminate the influence of matched and unmatched multi-source disturbances, a discrete-time state feedback controller is designed as follows:

[0101] ;

[0102] in, The control output of the discrete-time state feedback controller. and This represents the gain of the discrete-time state feedback controller.

[0103] However, this discrete-time state feedback controller can only achieve control over the inductor current by selecting a conservative gain. The constraints will inevitably sacrifice the dynamic and steady-state performance of the buck converter system.

[0104] 3) To strictly limit inductor current Within the constraints, combining the estimation of matched multi-source disturbances from step 2, and based on the control barrier function technique and safety set... Construct the control input inequality for the discrete-time current-constrained controller:

[0105] ;

[0106] in, For the first The control input of the discrete-time current constraint controller for each sampling period. For positive integers, For positive integers, , For parameters, , .

[0107] Based on the control input inequality of the discrete-time current-constrained controller, the control input set is obtained. for:

[0108] As an intermediate variable, . It is the control input set.

[0109] 4) Integrate the control output of the discrete-time state feedback controller that ensures the stability of the buck converter system. With the control input set of a discrete-time state feedback controller that ensures current constraints A discrete-time current-constrained controller was constructed:

[0110] ;

[0111] in, For the first The control input of the discrete-time current constraint controller for each sampling period. for The limit, The optimal control input, which simultaneously guarantees the stability of the buck converter system and the current constraint, can be solved based on the quadratic programming algorithm. This is the control output of the discrete-time state feedback controller.

[0112] Constraints:

[0113] .

[0114] Step 4: Based on the discrete-time current-constrained controller designed in Step 3, a rigorous robust stability analysis is performed on the buck converter system to obtain the relationship between the controller parameters and sampling time and the stability and current-constrained performance of the buck converter system; specifically including:

[0115] Based on the discrete-time current constraint controller designed in step 3, for the initial conditions , Given the initial value of the inductor current, even with multi-source disturbances, the inductor current... It is also strictly constrained to a safe set Within. This guarantee holds true if the control parameters of the discrete-time current-constrained controller adhere to the following design principles:

[0116] Discrete-time perturbation observer gain and satisfy: and ;

[0117] Discrete-time current-constrained controller gain , and satisfy:

[0118] ;

[0119] ;

[0120] ;

[0121] .

[0122] The above method first designs two discrete-time disturbance observers to estimate matched and mismatched multi-source disturbances, including input voltage fluctuations, load changes, and parameter perturbations of inductors and capacitors in the converter system. Then, combining the disturbance estimates, a discrete-time current-constrained controller is proposed. This controller employs a composite feedback structure to ensure system stability and utilizes control barrier function techniques to strictly constrain the inductor current under disturbances. Furthermore, the discrete-time form of the controller facilitates digital implementation. This invention performs rigorous robust stability analysis on the closed-loop system, obtaining the relationship between controller parameters and system stability and current constraints.

[0123] like Figure 2 As shown, in the PWM timer interrupt, the inductor current is first collected by the current sensor and the voltage sensor respectively. and output voltage Then, based on the collected inductor current and output voltage Matching multi-source disturbances are estimated using a discrete-time disturbance observer. Unmatched multi-source disturbance Secondly, based on and The set of discrete-time state feedback controller and control quantities that guarantee current constraints are calculated by matching multi-source disturbance estimates and unmatching multi-source disturbance estimates. Finally, the control signal u(k) is solved by quadratic programming.

[0124] The method is proven to consist of the following three steps.

[0125] 1) First, it is proven that the designed discrete-time perturbation observer can accurately estimate multi-source perturbations.

[0126] Define the disturbance estimation error as and , For the first The estimation error of mismatched multi-source disturbances per sampling period For the first The matching multi-source disturbance estimation error for each sampling period, The estimation error system can be expressed as:

[0127] ;

[0128] in, For the first The estimation error of mismatched multi-source disturbances per sampling period For the first Mismatched multi-source disturbances in each sampling period For the first Unmatched multi-source disturbance estimates for each sampling period This is the upper bound for the variation of unmatched multi-source disturbances in adjacent sampling periods.

[0129] Similarly, The estimation error system can be expressed as:

[0130] ;

[0131] in, For the first The matching multi-source disturbance estimation error for each sampling period, The upper bound of the multi-source disturbance variation is matched between adjacent sampling periods.

[0132] To analyze the stability of the estimation error system for mismatched multi-source perturbations, a Lyapunov function is selected. for Then we have:

[0133] ;

[0134] in, For the first The Lyapunov function of the estimation error system for unmatched multi-source disturbances over a sampling period. For the first The Lyapunov function of the estimation error system for unmatched multi-source disturbances over a sampling period. As an intermediate variable, If the observer gain satisfy ,Right now Then the disturbance estimation error It converges to a bounded region. Similarly, define... , can be obtained ,in, For the first Lyapunov function matching multi-source perturbations for each sampling period, For the first Lyapunov function matching multi-source perturbations for each sampling period, For parameters, For parameters, , Under the condition At that time, the estimation error It can converge to a bounded region.

[0135] 2) Secondly, it is proven that the proposed discrete-time current constraint controller can ensure the current constraint is satisfied under the above-mentioned disturbance.

[0136] definition and ,in, This is the upper bound of the inductor current constraint, which includes the disturbance estimation error. For parameters, If we define a lower bound for the inductor current constraint that includes the perturbation estimation error, then a new set can be constructed. :

[0137] ;

[0138] in, This is a safety set that includes the perturbation estimation error.

[0139] According to the set and As can be seen from the definition, yes A subset of.

[0140] Firstly based on Further analysis reveals:

[0141]

[0142] in, For the first The upper bound of the inductor current constraint for each sampling period;

[0143] Under the condition At that time, it can be obtained , For the first The upper bound of the inductor current constraint for each sampling period, which includes the estimation error of the matched multi-source disturbance. Similarly, we can obtain... , For the first The lower bound of the inductor current constraint, including the perturbation estimation error, for each sampling period. Because yes A subset of, therefore for all moments All meet and This essentially indicates that the inductor current... It is strictly constrained within its preset upper and lower bounds at all times.

[0144] 3) Finally, it is proven that the discrete-time current-constrained controller can guarantee the global stability of the buck converter system.

[0145] Based on the Karush-Kuhn-Tucker (KKT) conditions, the first The control input of the discrete-time current constraint controller for each sampling period The specific expression is:

[0146] ;

[0147] in, To calculate the upper bound of the control input based on the KKT conditions, , To calculate the lower bound of the control input based on the KKT conditions, , Calculate the range of values ​​for the upper bound of the control input for the KKT conditions. Calculate the range of values ​​for the lower bound of the control input for the KKT conditions;

[0148] ;

[0149] ;

[0150] First, let's analyze... and Control behavior under certain conditions, at this time .Will Substituting this into the buck converter system, we can obtain the following: The function of the buck converter system:

[0151] ;

[0152] Choose the Lyapunov function: , For the reason The Lyapunov function of the buck converter system;

[0153] Using the discrete-time Lyapunov method, we can obtain:

[0154] ;

[0155] in, For the first Lyapunov function for each sampling period, and As an intermediate variable; , ,in, and As an intermediate variable; , ;

[0156] because and There is a boundary, so Bounded. If the control gain , satisfy Then the output voltage Trackable reference signal To the bounded area.

[0157] Next, we will analyze the control behavior under other conditions. It should be noted that during voltage regulation, At any given time, it can only reach either the upper or lower boundary. (Regarding reaching the upper boundary...) For example, the control expression is:

[0158] ;

[0159] Choosing Lyapunov functions Combining the buck converter system established in step 1 with the upper bound of the control input calculated based on the KKT conditions We can obtain:

[0160] ;

[0161] in, For the first Each sampling period is composed of The Lyapunov function of the buck converter system. For the first Each sampling period is composed of The Lyapunov function of the buck converter system. As an intermediate variable, , and As an intermediate variable, , and As an intermediate variable;

[0162] ;

[0163] ;

[0164] ;

[0165] Only parameters satisfy The inductor current continues to converge during the current constraint period, meaning the voltage tracking error decreases. Two scenarios then emerge:

[0166] when hour, The equivalent value of the inductor current under the reference voltage; as the voltage tracking error decreases, Detach from upper constraint boundary, control input Restore to ;when hour, By remaining within the constraint boundaries, the voltage tracking error always lies within the bounded region. The analysis for the current reaching the lower boundary is similar and is omitted here. Proof complete.

[0167] The system corresponding to the method described in this invention includes:

[0168] The discrete-time model building unit is used to establish a discrete-time model of the buck converter system based on the circuit topology of the DC-DC buck converter, while considering the multi-source disturbances existing in the buck converter system. The forward Euler method is used to establish the discrete-time model of the buck converter system. The multi-source disturbances include matched multi-source disturbances and unmatched multi-source disturbances. Matched multi-source disturbances include input voltage fluctuations and inductor parameter perturbations, while unmatched multi-source disturbances include load changes and capacitor parameter perturbations.

[0169] The observer design unit is used to design discrete-time disturbance observers for matched and unmatched multi-source disturbances based on the discrete-time model of the buck converter system, and to estimate matched and unmatched multi-source disturbances respectively.

[0170] The controller design unit is used to design a discrete-time state feedback controller based on the estimation of matched and unmatched multi-source disturbances by the discrete-time disturbance observer, and to design a discrete-time current constraint controller using the control barrier function technique to ensure the stability of the buck converter system and strictly constrain the inductor current under multi-source disturbances.

[0171] The stability analysis unit is used to perform rigorous robust stability analysis on the buck converter system based on the discrete-time current-constrained controller, and to obtain the relationship between the controller parameters and sampling time and the stability and current-constrained performance of the buck converter system.

[0172] An electronic device for storing and executing the method includes:

[0173] Memory, used to store computer programs;

[0174] A processor for executing the computer program to implement the method.

[0175] A non-volatile storage medium for storing and executing the method, for storing a computer program, wherein the computer program implements the method when executed by a processor.

[0176] A computer program product for storing and executing the method includes a computer program / instructions that, when executed by a processor, implement the method.

Claims

1. A discrete-time robust current-limited voltage-tracking control method for DC-DC buck converters under multiple-source perturbations, characterized in that, Includes the following steps: Based on the circuit topology of the DC-DC buck converter, and considering the multi-source disturbances existing in the buck converter system, a discrete-time model of the buck converter system is established using the forward Euler method. The multi-source disturbances include matched multi-source disturbances and unmatched multi-source disturbances. Matched multi-source disturbances include input voltage fluctuations and inductor parameter perturbations, while unmatched multi-source disturbances include load changes and capacitor parameter perturbations. Based on the discrete-time model of the buck converter system, discrete-time disturbance observers for matched and unmatched multi-source disturbances are designed respectively to estimate matched and unmatched multi-source disturbances. Based on the estimation of matched and unmatched multi-source disturbances by the discrete-time disturbance observer, a discrete-time state feedback controller is designed. Using the control barrier function technique, a discrete-time current constraint controller is designed to ensure the stability of the buck converter system and strictly constrain the inductor current under multi-source disturbances. Based on a discrete-time current-constrained controller, a rigorous robust stability analysis is performed on the buck converter system to obtain the relationship between controller parameters and sampling time and the stability and current-constrained performance of the buck converter system.

2. The method of claim 1, wherein, Methods for establishing discrete-time models of buck converter systems include: (1) Based on the circuit topology of the DC-DC buck converter, a nominal average model of the buck converter system considering multi-source disturbances is established; (2) Considering the multi-source disturbances in the buck converter system, the unmatched multi-source disturbances caused by capacitor parameter perturbation and load change, and the matched multi-source disturbances caused by inductor parameter perturbation and input voltage fluctuation are added to the nominal average model of the buck converter system. (3) The forward Euler method is used to obtain the discrete-time model of the buck converter system.

3. The method of claim 2, wherein, The discrete-time model expression for the buck converter system is: ； wherein, is the output voltage for the buck converter system sampling period, is the output voltage for the first sampling period, is the output voltage for the first sampling period, is the inductor current for the first sampling period, is the inductor current for the first sampling period, is the unmatched multi-source disturbance for the first sampling period, is the matched multi-source disturbance for the first sampling period, is the control input of the discrete-time current-constrained controller for the first sampling period, , , and are the nominal parameters of the capacitor C, inductor L, load resistance R and input voltage , respectively; and The model is expressed as and , This is the upper bound for the variation of unmatched multi-source disturbances in adjacent sampling periods. To match the upper bound of multi-source disturbance changes between adjacent sampling periods, For the first Mismatched multi-source disturbances in each sampling period For the first Matching multi-source disturbances for each sampling period; Set inductor current Subject to constant Restriction, i.e., satisfaction ;and Related security sets Defined as: ； in, For real numbers, The upper bound is set for the inductor current constraint. , This is the lower bound of the inductor current constraint. .

4. The method according to claim 1, characterized in that, The discrete-time perturbation observer for unmatched multi-source perturbations is represented as: ， ， in, As an intermediate variable, , The sampling period of the buck converter system. For the first Inductor current per sampling period For the first The output voltage of each sampling period , and These are the nominal parameters of capacitor C, inductor L, and load resistance R, respectively. and The first Individual and Internal state variables of a discrete-time disturbance observer with a sampling period of mismatched multi-source disturbance. For discrete-time perturbation observer gain parameters of unmatched multi-source perturbations, for The estimated value, For the first Unmatched multi-source disturbances in each sampling period; The discrete-time perturbation observer that matches multi-source perturbations is represented as: ， ， in, As an intermediate variable, , Input voltage The nominal parameters, For the first The control input of the discrete-time current constraint controller for each sampling period. for Estimated value For the first Matching multi-source disturbances for each sampling period, and The first The and the first An internal state variable employing a periodic perturbation observer, Gain parameters for discrete-time disturbance observers to match multi-source disturbances.

5. The method according to claim 1, characterized in that, Methods for designing discrete-time current-constrained controllers include: (1) Based on the discrete-time model of the buck converter considering multi-source disturbances, and combined with the estimation of disturbances by the discrete-time disturbance observer, the tracking error of the output voltage and the state variables are selected to obtain the system equation of the buck converter. (2) The discrete-time state feedback controller is designed as follows: ； in, The control output of the discrete-time state feedback controller. and For discrete-time state feedback controller gain, , and These are the capacitor C, inductor L, and input voltage, respectively. The nominal parameters, The sampling period of the buck converter system. For the tracking error of the output voltage, For state variables, For the first Unmatched multi-source disturbance estimates for each sampling period For the first Inductor current per sampling period For the first Matched multi-source disturbance estimates for each sampling period For the first The output voltage for each sampling period; (3) Combining the estimation of disturbance by the discrete-time disturbance observer, and based on the control barrier function technique and safety set... Construct the control input set: ； in, For the first The control input of the discrete-time current constraint controller for each sampling period. For positive integers, For positive integers, , For parameters, , ; The upper bound is set for the inductor current constraint. This is the lower bound of the inductor current constraint. To match the gain parameters of the discrete-time disturbance observer for multi-source disturbances, For discrete-time disturbance observer gain parameters of unmatched multi-source disturbances; Based on the control input inequality of the discrete-time current-constrained controller, the control input set is obtained. for: As an intermediate variable, , It is the control input set; (4) Integrate the control output of the discrete-time state feedback controller that ensures the stability of the buck converter system. With the control input set of a discrete-time state feedback controller that ensures current constraints A discrete-time current-constrained controller was constructed: ； in, For the first The control input of the discrete-time current constraint controller for each sampling period. for The limit, The optimal control input, which simultaneously guarantees the stability of the buck converter system and the current constraint, can be solved based on the quadratic programming algorithm. The control output of the discrete-time state feedback controller; Using the control input set as constraints, the optimal control input that simultaneously guarantees the stability of the buck converter system and the current constraint can be solved based on the quadratic programming algorithm.

6. The method according to claim 1, characterized in that, Based on a discrete-time current-constrained controller, a rigorous robust stability analysis is performed on the buck converter system, specifically including: Based on a discrete-time current-constrained controller, for initial conditions , Let be the initial value of the inductor current. For the control input set of a discrete-time state feedback controller, even with multi-source disturbances, the inductor current... It is also strictly constrained to a safe set Within this scope, the guarantee holds if the control parameters of the discrete-time current-constrained controller adhere to the following design principles: Discrete-time perturbation observer gain and satisfy: and ;in, The sampling period of the buck converter system. To match the gain parameters of the discrete-time disturbance observer for multi-source disturbances, For discrete-time disturbance observer gain parameters of unmatched multi-source disturbances; Discrete-time current-constrained controller gain , and satisfy: ； ； ； ； in, , These are the capacitor C and the input voltage, respectively. The nominal parameters, For positive integers, For parameters.

7. A discrete-time robust current-constrained voltage tracking control system for a DC-DC buck converter under multi-source disturbances, characterized in that, include: The discrete-time model building unit is used to establish a discrete-time model of the buck converter system based on the circuit topology of the DC-DC buck converter, while considering the multi-source disturbances existing in the buck converter system. The forward Euler method is used to establish the discrete-time model of the buck converter system. The multi-source disturbances include matched multi-source disturbances and unmatched multi-source disturbances. Matched multi-source disturbances include input voltage fluctuations and inductor parameter perturbations, while unmatched multi-source disturbances include load changes and capacitor parameter perturbations. The observer design unit is used to design discrete-time disturbance observers for matched and unmatched multi-source disturbances based on the discrete-time model of the buck converter system, and to estimate matched and unmatched multi-source disturbances respectively. The controller design unit is used to design a discrete-time state feedback controller based on the estimation of matched and unmatched multi-source disturbances by the discrete-time disturbance observer, and to design a discrete-time current constraint controller using the control barrier function technique to ensure the stability of the buck converter system and strictly constrain the inductor current under multi-source disturbances. The stability analysis unit is used to perform rigorous robust stability analysis on the buck converter system based on the discrete-time current-constrained controller, and to obtain the relationship between the controller parameters and sampling time and the stability and current-constrained performance of the buck converter system.

8. An electronic device, characterized in that, include: Memory, used to store computer programs; A processor for executing the computer program to implement the method as described in any one of claims 1-6.

9. A non-volatile storage medium, characterized in that, Used to store a computer program, wherein the computer program, when executed by a processor, implements the method as described in any one of claims 1-6.

10. A computer program product comprising a computer program / instructions, characterized in that, When the computer program / instructions are executed by the processor, they implement the method described in any one of claims 1-6.

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