A tracking control method for DC-DC power converter

Abstract

The present invention discloses a tracking control method for a DC-DC power converter, and belongs to the field of power electronics technology. The method comprises the following steps: first, a dynamic system for controlling a DC-DC power converter is established; second, a switching control strategy based on data-driven is developed by collecting the operating data of the system, driving the system trajectory to converge to a bounded local area, and realizing the global actual stability of the system; 2) In order to improve the limitations of the actual stability results, the system expected trajectory is characterized as a limit cycle, and the optimal tracking control of the state trajectory of the controlled system to the limit cycle under data-driven is realized. The power converter control scheme provided by the present invention can realize the power converter voltage output control problem when the device parameter information is inaccurate.

Description

Technical Field

[0001] The invention belongs to the technical field of power electronics, and in particular relates to a tracking control method for a DC-DC power converter. Background Art

[0002] As we all know, switching power supplies have the advantages of high efficiency, small size, and light weight, and are widely used in various fields such as aerospace, communications, and computers. The core of the switching power supply is the power converter, and one of the research hotspots is the DC-DC power converter, also known as the DC chopper. It controls the switch tube and then converts the input DC voltage into a DC voltage or current that meets the load requirements through energy storage and filtering elements such as capacitors and inductors. It is a typical switching affine system.

[0003] However, it is very difficult to study the above system. The existing pain points are manifested in two aspects. On the one hand, it is due to the existence of affine terms, which means that the existing results cannot be directly applied to the system. On the other hand, it is due to its inherent nonlinearity and dynamic switching between modes. These characteristics make the system behavior difficult to predict and control, especially when external conditions change rapidly. Therefore, traditional control strategies often cannot adapt to all operating modes, resulting in low efficiency or insufficient stability in practical applications. Summary of the invention

[0004] In order to solve the above technical problems, the present invention proposes a tracking control method for a DC-DC power converter to solve the above problems in the prior art.

[0005] To achieve the above object, the present invention provides a tracking control method for a DC-DC power converter, comprising the following steps:

[0006] Define the performance function and loss function of the tracking control method;

[0007] Defining a value function of a switching strategy based on the performance function, obtaining an optimal value function based on the value function, and designing an optimal switching control strategy based on the optimal value function;

[0008] Define a state action value function, and use the state action value function as the current moment selection mode, optimize the optimal switching control strategy based on the state action value function, and obtain the optimized optimal switching control strategy;

[0009] The state action value function in the optimized optimal switching control strategy is reconstructed through a neural network to obtain a reconstructed optimal switching control strategy;

[0010] The reconstructed optimal switching control strategy is subjected to stability analysis. When the reconstructed optimal switching control strategy is stable, the performance function, loss function, value function, optimal switching control strategy and state-action value function are optimized by characterizing the limit cycle to obtain the final switching control strategy.

[0011] Preferably, the performance function expression characterizing the optimized limit cycle is:

[0012]

[0013] In the formula, U represents the loss function, Indicates the system status of the circuit, represents the desired system state, Represents the mode of the circuit.

[0014] Preferably, the loss function expression after characterizing the limit cycle optimization is:

[0015]

[0016] In the formula, Indicates the current selection mode. represents a positive definite real matrix.

[0017] Preferably, the value function expression characterizing the optimized limit cycle is:

[0018]

[0019] In the formula, represents the switching control strategy, represents the generated system state trajectory, represents the decision sequence, Represents the target trajectory.

[0020] Preferably, the optimal switching control strategy expression after characterizing the limit cycle optimization is:

[0021]

[0022] In the formula, represents the loss function, represents the optimal value function.

[0023] Preferably, the state action value function expression characterizing the optimized limit cycle is:

[0024]

[0025] In the formula, Indicates the system status of the circuit, represents the desired system state, represents the mode of the circuit, represents the generated system state trajectory, represents the decision sequence, Represents the target trajectory.

[0026] Preferably, the connection relationship between the input layer and the hidden layer of the neural network is , the connection relationship between the hidden layer and the output layer is ;

[0027] The reconstructed state-action value function expression is: ;

[0028] In the formula, represents the hth hidden layer neuron, represents the number of data sets, represents the connection weight between the input layer and the hidden layer neurons, , represents the number of neurons in the hidden layer, Represents the weights between the neurons in the hidden layer and the output layer.

[0029] Preferably, the final switching control strategy expression is:

[0030] ;

[0031] In the formula, represents the weights between neurons in the hidden layer and the output layer, represents the hidden layer neurons, where , represents the threshold in the hidden layer, Represents the activation function.

[0032] Compared with the prior art, the present invention has the following advantages and technical effects:

[0033] The present invention discloses a tracking control method for a DC-DC power converter, and belongs to the field of power electronics technology. The method comprises the following steps: first, a dynamic system for controlling a DC-DC power converter is established; second, a switching control strategy based on data drive is developed by collecting the operating data of the system, driving the system trajectory to converge to a bounded local area, and realizing the global actual stability of the system; 2) to improve the limitations of the actual stability results, the system expected trajectory is characterized as a limit cycle, and the state trajectory of the controlled system under data drive is optimally tracked to the limit cycle. The power converter control scheme provided by the present invention can realize the power converter voltage output control problem when the device parameter information is inaccurate.

[0034] The present invention can design an effective limit cycle tracking control strategy by utilizing existing data without in-depth complex dynamic modeling of the system itself. This method can reduce the complexity and cost of model establishment and system identification while improving the control effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] The drawings constituting a part of the present application are used to provide a further understanding of the present application. The illustrative embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0036] Figure 1 The following is a flow chart of a tracking control method for a DC-DC power converter according to an embodiment of the present invention. DETAILED DESCRIPTION

[0037] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0038] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0039] Embodiment 1

[0040] like Figure 1 As shown, in this embodiment, a tracking control method for a DC-DC power converter is provided, including two parts: data-driven control of a switching affine system based on actual stability dependence of a convergence domain and limit cycle tracking control of a switching affine system based on a data-driven method. The specific method is as follows:

[0041] (1) Data-driven control of switched affine systems with actual stability dependence in the convergence domain:

[0042] Achieving practical stability of switched affine systems through a data-driven approach involves a series of technical steps that aim to comprehensively utilize advanced technologies in data acquisition, analysis, and control strategy design. The specific technical route is as follows:

[0043] 1) Define performance function and loss function: Clearly switch the affine system to achieve the goal of minimizing the error between the equilibrium point and improving stability. The performance function is described as:

[0044]

[0045] in represents the positive definite loss function, which is used to describe the deviation between the actual system state and the expected equilibrium point. Indicates the system status of the circuit, Represent the mode of the circuit. Determine the constraints that affect the design of the performance function and loss function. Based on the goals and constraints, select key indicators to measure the performance of the model or system. This embodiment considers the following quadratic loss function:

[0046]

[0047] in represents the expected equilibrium point, yes The positive definite real matrix of yes It can be seen that the loss function is consistent with the target It is directly related to the CNN and reflects its affine characteristics and multi-modal dynamic switching characteristics.

[0048] 2) Design the value function and control strategy of the switching strategy: select and define the value criteria based on performance objectives such as time cost function, energy consumption, and the sum of squares of state deviations. represents the switching control strategy. According to the performance function (1), the switching strategy is defined The value function of is defined as:

[0049]

[0050] in The switching control strategy Generated, Represents the generated system state trajectory. It is not difficult to see that the value function represents the sum of the cumulative loss functions corresponding to the execution of a given strategy from the current moment. Thus, the optimal switching strategy can be defined as The corresponding optimal value function is:

[0051]

[0052] in represents the optimal decision sequence, and the sequence Denotes the corresponding optimal state trajectory. Further, according to the Bellman optimality principle, equation (4) can be rewritten into the following recursive form:

[0053]

[0054] The optimal switching control strategy can be designed as:

[0055]

[0056] The value function should reflect the expected cost or benefit of taking the optimal control strategy to reach the target state from the current state. Use the value function to determine the optimal control strategy for each state or condition. Design switching logic or rules to determine when and how to switch between different control strategies or system modes to adapt to system dynamics.

[0057] 3) Control strategy optimization: According to formula (6), the selection of the optimal mode at the current moment requires the knowledge of the system state at the next moment. Therefore, the system state equation is required to be known. In order to eliminate the switching strategy's requirements on the system dynamic equation, this embodiment defines the strategy Q function Select the modality for the current moment , and the switching strategy will be executed from the next moment The sum of the loss functions corresponding to the generated system trajectory is expressed as:

[0058]

[0059] Similar to the derivation in the previous section, we can obtain the optimal Bellman equation for the Q function:

[0060]

[0061] The optimal switching control strategy can be expressed as:

[0062]

[0063] At this step, due to It is also one of the independent variables of the Q function. It is only necessary to know the current state to determine the mode that needs to be activated. At this point, the model of the system is no longer a necessary condition for finding a solution.

[0064] 4) Reconstructing the state-action value function: state-action value function The role of is to provide a quantitative benchmark for the expected benefits of taking different actions in a specific state, thereby guiding the decision-making process to optimize system behavior. Next, we will use a fully connected neural network to reconstruct the state action value function The fully connected layer plays the role of feature mapping and nonlinear transformation in the neural network, thereby increasing the model's expressiveness and learning ability. The connection relationship between the input layer and the hidden layer is:

[0065]

[0066] in represents the hidden layer neurons, represents the number of data sets, represents the connection weight between the input layer and the hidden layer neurons, , Represents the number of neurons in the hidden layer. The connection relationship between the hidden layer and the output layer is:

[0067]

[0068] in represents the network output, represents the connection weights between neurons in the hidden layer and the output layer, , is the number of neurons in the output layer. The reconstructed state action value function can be expressed as .

[0069] 5) Stability analysis of control strategy: Analyze the influence of approximate error and termination condition on the convergence of Q function and the stability of the optimal strategy. The derivation process refers to the convergence proof of the approximate value iteration algorithm based on the model. Since there are affine terms in the system, it is necessary to characterize a convergence domain that converges to the expected equilibrium point.

[0070] The convergence analysis is as follows:

[0071] For any initial state x 0 , there exists at least one exchange sequence {σ k} = 0, the corresponding performance function has a finite value, as shown below:

[0072]

[0073] in, Indicates the system status of the target, Indicates that the state is x k+1 The switching strategy when (m) (x,σ)} = 0 represents the Q function sequence iteratively generated by the Q learning algorithm, where Q （0） (x,σ)=0,∀σ∈I. If the assumption holds, then {Q (m) (x,σ)} =0 is a monotone non-decreasing sequence, and there exists a finite upper bound function, which optimally converges to the optimal solution of the Bellma equation, and there exists an upper bound function Y, namely:

[0074]

[0075]

[0076]

[0077] In the formula, represents the optimal Q function.

[0078] According to equations (13) and (14), {Q (m) (x,σ)} = 0 there exists a finite number of monotone non-decreasing bounds. Therefore, there exists a function Q ∞ (x, σ) iteratively generates the q function sequence, namely:

[0079] .

[0080] Let σ′ denote an arbitrary switching strategy. There exists:

[0081]

[0082] Then, let m→∞ on the right side of the inequality, and we can get from equation (13):

[0083]

[0084] Furthermore, if we set the left-hand side of equation (17) to m→∞, we can get:

[0085]

[0086] Since σ′ can be any switching strategy, its expression is:

[0087]

[0088] From formula (12), we can get:

[0089]

[0090] Due to formula (13), it exists:

[0091]

[0092] When m→∞, it can be deduced that:

[0093]

[0094] Combining equation (20) and equation (23), we can get:

[0095]

[0096] Comparing (24) and (12), it is easy to see that Q (∞) (x,σ) is the solution to the Bellman optimal equation. This completes the convergence proof.

[0097] Through such a technical route, this embodiment can directly use the data-driven method to design an effective controller or switching signal, providing a stable and efficient control solution for the switching affine system.

[0098] (2) Limit cycle tracking control of switched affine systems based on data-driven methods:

[0099] To achieve limit cycle tracking control of switched affine systems through a data-driven approach, the technical route will focus on extracting control strategies directly from data. This approach focuses on using existing operating data to guide the design and optimization of controllers. The following is the technical route:

[0100] 1) Characterizing limit cycles: Characterizing limit cycles, i.e., the process of identifying and describing stable periodic solutions in a dynamic system, is a core task in the theory of nonlinear dynamic systems. The limit cycle in this embodiment can be characterized as , which is crucial to the system's long-term behavior, stability, and the way it responds to external stimuli.

[0101] 2) Define performance function and loss function: The goal of optimal tracking control is to design a stable controller that minimizes the following performance function:

[0102]

[0103] Based on the objectives and constraints, key indicators for measuring model or system performance are selected. This embodiment considers the following quadratic loss function:

[0104]

[0105] It can be seen that the loss function is consistent with the target trajectory. directly related to the dynamic switching characteristics of the multi-mode.

[0106] 3) Design the value function and control strategy of the switching strategy: select and define the value criteria based on performance objectives such as time cost function, energy consumption, and the sum of squares of state deviations. represents the switching control strategy. According to the performance function (25), the switching strategy is defined The value function of is defined as:

[0107]

[0108] in Represent the target trajectory respectively. Thus, the optimal switching strategy can be defined The corresponding optimal value function is:

[0109]

[0110] Furthermore, according to the Bellman optimality principle, equation (28) can be rewritten into the following recursive form:

[0111]

[0112] The optimal switching control strategy can be designed as:

[0113]

[0114] The value function should reflect the expected cost or benefit of taking the optimal control strategy to reach the target state from the current state. The value function is used to design switching logic or rules to decide when and how to switch between different control strategies or system modes to adapt to system dynamic changes.

[0115] 4) Control strategy optimization: According to equation (30), the selection of the optimal mode at the current moment requires knowing the system state at the next moment. Therefore, in order to eliminate the switching strategy's requirements on the system dynamic equations, this section defines the strategy Q function Select the modality for the current moment , and the switching strategy will be executed from the next moment The sum of the loss functions corresponding to the generated system trajectory is expressed as:

[0116]

[0117] Similar to the derivation in the previous section, we can obtain the optimal Bellman equation for the Q function:

[0118]

[0119] The optimal switching control strategy can be expressed as At this step, due to It is also one of the independent variables of the Q function. It is only necessary to know the current state to determine the mode that needs to be activated. At this point, the model of the system is no longer a necessary condition for finding a solution.

[0120] 5) Reconstructing the state action value function: state action value function The role of is to provide a quantitative benchmark for the expected benefits of taking different actions in a specific state, thereby guiding the decision-making process to optimize system behavior. Next, we will use a fully connected neural network to reconstruct the state action value function The fully connected layer plays the role of feature mapping and nonlinear transformation in the neural network, thereby increasing the model's expressiveness and learning ability. The connection relationship between the input layer and the hidden layer is , the connection relationship between the hidden layer and the output layer is , the reconstructed state action value function can be expressed as .

[0121] The final switching control strategy expression is:

[0122] ;

[0123] In the formula, represents the weights between neurons in the hidden layer and the output layer, represents the hidden layer neurons, where , represents the threshold in the hidden layer, Represents the activation function.

[0124] 6) Stability analysis of switching strategy: Analyze the influence of approximation error and termination condition on the convergence of Q function and the stability of the obtained optimal strategy. The derivation process refers to the convergence proof of the model-based approximate value iteration algorithm.

[0125] The above are only preferred specific implementations of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

1. A tracking control method for a DC-DC power converter, characterized in that: The following steps are involved: Define the performance function and loss function of the tracking control method; Defining a value function of a switching strategy based on the performance function, obtaining an optimal value function based on the value function, and designing an optimal switching control strategy based on the optimal value function; Define a state action value function, and use the state action value function as the current moment selection mode, optimize the optimal switching control strategy based on the state action value function, and obtain the optimized optimal switching control strategy; The state action value function in the optimized optimal switching control strategy is reconstructed through a neural network to obtain a reconstructed optimal switching control strategy; The reconstructed optimal switching control strategy is subjected to stability analysis. When the reconstructed optimal switching control strategy is stable, the performance function, loss function, value function, optimal switching control strategy and state-action value function are optimized by characterizing the limit cycle to obtain the final switching control strategy.

2. The tracking control method of a DC-DC power converter according to claim 1, characterized in that: The performance function expression after the limit cycle optimization is: In the formula, U represents the loss function, Indicates the system status of the circuit, represents the desired system state, Represents the mode of the circuit.

3. The tracking control method of the DC-DC power converter according to claim 2, characterized in that: The loss function expression after characterizing the limit cycle optimization is: In the formula, Indicates the current selection mode. represents a positive definite real matrix.

4. The tracking control method of the DC-DC power converter according to claim 3, characterized in that: The value function expression after characterizing the limit cycle optimization is: In the formula, represents the switching control strategy, represents the generated system state trajectory, represents the decision sequence, Represents the target trajectory.

5. The tracking control method of the DC-DC power converter according to claim 4, characterized in that: The expression of the optimal switching control strategy after characterizing the limit cycle optimization is: In the formula, represents the loss function, represents the optimal value function.

6. The tracking control method of the DC-DC power converter according to claim 5, characterized in that: The state action value function expression after the limit cycle optimization is: In the formula, Indicates the system status of the circuit, represents the desired system state, represents the mode of the circuit, represents the generated system state trajectory, represents the decision sequence, Represents the target trajectory.

7. The tracking control method of a DC-DC power converter according to claim 1, characterized in that: The connection relationship between the input layer and the hidden layer of the neural network is , the connection relationship between the hidden layer and the output layer is ; The reconstructed state-action value function expression is: ; In the formula, represents the hth hidden layer neuron, represents the number of data sets, represents the connection weight between the input layer and the hidden layer neurons, , represents the number of neurons in the hidden layer, Represents the weights between the neurons in the hidden layer and the output layer.

8. The tracking control method of a DC-DC power converter according to claim 7, characterized in that: The final switching control strategy expression is: ； In the formula, represents the weights between neurons in the hidden layer and the output layer, represents the hidden layer neurons, where , represents the threshold in the hidden layer, Represents the activation function.

Images