A control space-based control method for a DC-DC buck converter

Abstract

This invention discloses a control method for a DC-DC buck converter based on control space, belonging to the field of electrical automation equipment. The invention constructs the ideal state-space equations of the DC-DC buck converter using the state averaging method. Then, considering the parameter uncertainties of the converter, the state-space equations are modified to construct an error system with parameter uncertainties. Inspired by the dynamic window method, a performance index function for the converter system is defined for the error system. The optimal control quantity is selected in the discretized control space by solving an optimization problem. For the parameter uncertainties of the converter, a time-delayed observer is designed to estimate the uncertainties and compensate for the control quantity. This invention proposes an optimal control method for DC-DC buck converters with parameter uncertainties, which can improve converter accuracy and control efficiency.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of electrical automation equipment, and particularly relates to a DC-DC buck converter control method based on control space. BACKGROUND

[0002] Under the driving of the rapid development of power electronics technology and smart grid technology, a global energy clean-up boom has been triggered, and the energy structure mainly based on fossil energy is gradually transforming into an energy structure mainly based on renewable energy such as wind energy, solar energy, and water energy. Due to various uncertainties and disturbances in clean energy power systems, including circuit parameter disturbance, load change, and power supply voltage fluctuation, these factors will seriously reduce the voltage regulation accuracy of the DC-DC converter. Therefore, when facing inevitable system uncertainties and disturbances, how to improve the control performance of the DC-DC converter is a key problem.

[0003] Due to the advantages of low cost, high efficiency, and simple structure, the DC-DC converter has been widely used in industrial fields such as uninterruptible power supply, power system, DC motor, and telecommunication equipment. It is difficult to solve the control performance problem of the DC-DC converter system by using the traditional linear control method. In order to obtain better control performance, based on the inherent characteristics of the DC-DC converter, many advanced control methods are used to construct the DC-DC converter control algorithm, such as optimal control, LMI control, robust control, model predictive control, and sliding mode control. However, the above algorithms still have the problems of low regulation accuracy and insufficient anti-interference ability when dealing with the voltage regulation problem of the discrete DC-DC converter system with parameter uncertainty. SUMMARY

[0004] The purpose of the present application is to provide a DC-DC buck converter control method based on control space, to solve the problem that the current control algorithm still has low regulation accuracy and insufficient anti-interference ability when dealing with the voltage regulation of the discrete DC-DC converter system with parameter uncertainty.

[0005] To solve the above technical problems, the present application provides a DC-DC buck converter control method based on control space, comprising:

[0006] Step 1, constructing the state space equation of the DC-DC buck converter with parameter uncertainty;

[0007] Step 2, constructing a discretized error system;

[0008] Step 3, solving the optimal control quantity based on control space;

[0009] Step 4, delay estimation of system parameter uncertainty;

[0010] Step 5, realizing tracking control to the expected output voltage.

[0011] Optionally, the method for constructing the state space equation of the DC-DC buck converter with parameter uncertainty comprises:

[0012] The state average method is adopted to construct the ideal state space system as shown in equation (1):

[0013]

[0014] Wherein is the derivative of the average output voltage of the converter, is the derivative of the average inductor current value, v o , i L are the average output voltage and the average inductor current value, respectively, v in is the nominal input voltage value, R is the nominal load resistance value, L is the nominal inductance value, C is the nominal capacitance value, and the duty cycle u∈[0,1] is the control quantity of the system, which is used to drive the signal;

[0015] The system shown in equation (1) does not consider the uncertainty of the system parameters, and equation (1) is written in the following form:

[0016]

[0017] Wherein ΔC, ΔR, ΔL, Δv in are the capacitance uncertainty, the load resistance uncertainty, the inductance uncertainty and the input voltage uncertainty of the system, respectively;

[0018] In order to facilitate calculation, equation (2) is rewritten in the following form:

[0019]

[0020] Wherein d 11 , d 12 are the system comprehensive uncertainty, and are bounded, and the specific expressions are as follows:

[0021]

[0022]

[0023] Optionally, the method for constructing the discrete error system comprises:

[0024] The expected output voltage is represented by v r , and the output voltage tracking error is represented by e1=v o -v rTo facilitate calculation, a new error state variable is defined. It is the first derivative of the desired output voltage, and the error system is constructed as follows:

[0025]

[0026] in, It is the first derivative of the output voltage tracking error. It is the first derivative of the new error state quantity. It is the second derivative of the output voltage.

[0027] To facilitate the construction of the predictive controller, the system is first discretized. Through Euler discretization, the system of equation (6) is transformed into a discretized system as shown in equation (7):

[0028]

[0029] Where h is the sampling period and k is time k.

[0030] Optionally, the solution for the optimal control quantity based on the control space includes:

[0031] Inspired by the dynamic window method, it is assumed that the control quantity u(k) of the system (7) remains unchanged within N sampling periods after time k. Multiple sets of control quantities are sampled in the space of control quantity u(k), and the state quantity changes of the system (7) under the action of these control quantities are simulated. After obtaining multiple sets of state quantity changes, the optimal control quantity is selected by solving the optimization problem to drive the converter to work for one sampling period. At time k+1 of the next sampling period, the state quantity of the system is updated, and the above steps are repeated.

[0032] To reduce the computational load of the algorithm and find the optimal control quantity in the control space more quickly, the range of values ​​for the system control quantity u(k) is discretized into n parts, resulting in the control space U as follows:

[0033] U={u i i = 0, 1, 2, 3, ..., n-1 | u i =i / n-1} (8)

[0034] The optimal control quantity is obtained in the control space U by solving the following optimization problem:

[0035]

[0036] The performance index function J(u(k)) is defined as follows:

[0037]

[0038] Where c is the weighting coefficient, e1(k+i) and e2(k+i) represent the predicted state quantities at time k+i under the action of the control quantity u(k); the first term of the performance index, |e1(k+i)|, is used to penalize the cumulative output voltage tracking error within a time period, and the second term, c|e2(k+i)|, is used to penalize the change in the cumulative output voltage tracking error.

[0039] Optionally, the delay estimation of the system parameter uncertainty includes:

[0040] The above control algorithm involves unmeasurable system-wide uncertainties d1 and d2 in the process of solving for the optimal control quantity, making it impossible to directly solve for the optimal control quantity. Therefore, the following time-delayed disturbance observer is constructed. To estimate the overall uncertainty of the system:

[0041]

[0042]

[0043] Optionally, the implementation of tracking control of the desired output voltage includes: at time k, substituting the system comprehensive uncertainty calculated by equations (11) and (12) into equation (7); and then combining equations (9) and (10) to find a control quantity u(k) in the control space that minimizes the performance index function J(u(k)), thereby realizing tracking control of the desired output voltage.

[0044] The control space-based DC-DC buck converter control method provided in this invention combines a dynamic window method with a time-delayed observer for DC-DC buck converter systems with mismatched disturbances. The time-delayed observer is used to observe the comprehensive uncertainty caused by factors such as system model mismatch, distortion, and disturbances. The dynamic window method selects the optimal control quantity in the control space online according to the performance index function and implements it for one control cycle. The system state is updated in the next control cycle, and the optimization calculation is performed continuously. Compared with other DC-DC buck converter control algorithms, the method of this invention can not only timely compensate for the comprehensive uncertainty caused by model mismatch, distortion, and disturbances, but also has better dynamic performance. It can also timely compensate for the comprehensive uncertainty of the system, has low requirements for system accuracy, is easy to model, and the control algorithm is easier to implement. It is easy to extend to constrained, time-delayed DC-DC buck converter models and can effectively handle multi-variable and multi-constraint optimization problems. Attached Figure Description

[0045] Figure 1 This is a schematic diagram of the DC-DC buck converter circuit structure;

[0046] Figure 2 This is a framework diagram of the DC-DC buck converter control method based on control space provided by the present invention. Detailed Implementation

[0047] The following detailed description, in conjunction with the accompanying drawings and specific embodiments, provides a control method for a DC-DC buck converter based on control space proposed in this invention. The advantages and features of this invention will become clearer from the following description and claims. It should be noted that the drawings are all in a very simplified form and use non-precise scales, and are only used to facilitate and clarify the illustration of the embodiments of this invention.

[0048] This invention provides a control method for a DC-DC buck converter based on control space to address the voltage regulation problem of discrete DC-DC converter systems with parameter uncertainties. The method specifically includes the following steps:

[0049] Step 1: Construct the state-space equations of the DC-DC buck converter with parameter uncertainties.

[0050] For example Figure 1 The DC-DC buck converter shown can be used to construct an ideal state-space system as shown in the following equation using the state averaging method:

[0051]

[0052] in It is the derivative of the average output voltage of the converter. It is the derivative of the average inductor current, v o i L These are the average output voltage and average inductor current values, respectively. in R is the nominal input voltage value, L is the nominal load resistance value, L is the nominal inductance value, C is the nominal capacitance value, and the duty cycle u∈[0,1] is the control quantity of the system, used to drive the signal.

[0053] The system shown in equation (1) does not consider the uncertainty of system parameters. For a more accurate description, equation (1) can be written in the following form:

[0054]

[0055] Where ΔC, ΔR, ΔL, Δv in These represent the system's capacitance uncertainty, load resistance uncertainty, inductance uncertainty, and input voltage uncertainty, respectively.

[0056] For ease of calculation, equation (2) is rewritten in the following form:

[0057]

[0058] Where d 11 d 12 The system encompasses all uncertainties, all of which are bounded. The specific expression is as follows:

[0059]

[0060]

[0061] Step 2: Construct a discretized error system.

[0062] Desired output voltage in V r Therefore, the output voltage tracking error can be expressed as e1 = v o -v r To facilitate calculation, a new error state variable is defined. This is the first derivative of the expected output voltage, from which the error system can be constructed as follows:

[0063]

[0064] in, It is the first derivative of the output voltage tracking error. It is the first derivative of the new error state quantity. It is the second derivative of the output voltage.

[0065] To facilitate the construction of the predictive controller, the system needs to be discretized first. Through Euler discretization, the system in equation (6) can be transformed into the following discretized system:

[0066]

[0067] Where h is the sampling period and k is time k.

[0068] Step 3: Solve for the optimal control quantity based on the control space.

[0069] Inspired by the dynamic window method, it is assumed that the control quantity u(k) of system (7) remains unchanged for N sampling periods after time k. Multiple sets of control quantities are sampled in the space of control quantity u(k), and the state changes of system (7) under the action of these control quantities are simulated. After obtaining multiple sets of state changes, the optimal control quantity is selected to drive the converter to work for one sampling period by solving the optimization problem. At the next sampling period k+1, the state of the system is updated, and the above steps are repeated (i.e., multiple sets of control quantities are sampled in the space of control quantity u(k), and the state changes of system (7) under the action of these control quantities are simulated. After obtaining multiple sets of state changes, the optimal control quantity is selected to drive the converter to work for one sampling period by solving the optimization problem).

[0070] To reduce the computational cost of the algorithm and more quickly find the optimal control variable in the control space, the range of values ​​for the system control variable u(k) needs to be discretized. The control variable is discretized into n parts, resulting in the control space U as follows:

[0071] U={u i i = 0, 1, 2, 3, ..., n-1 | u i =i / n-1} (8)

[0072] The optimal control quantity can be obtained in the control space U by solving the following optimization problem.

[0073]

[0074] The performance index function J(u(k)) is defined as follows:

[0075]

[0076] Where c is the weighting coefficient, and e1(k+i) and e2(k+i) represent the predicted state quantities at time k+i under the action of the control quantity u(k). The first term of the performance index (i.e., |e1(k+i)|) is used to penalize the cumulative output voltage tracking error over a time period, and the second term (i.e., c|e2(k+i)|) is used to penalize the magnitude of the change in the cumulative output voltage tracking error.

[0077] Step 4: Delay estimation of system parameter uncertainty.

[0078] The aforementioned control algorithm, in solving for the optimal control quantity, involves unmeasurable system-wide uncertainties d1 and d2, making it impossible to directly solve for the optimal control quantity. Therefore, the following time-delayed disturbance observer is constructed. To estimate the overall uncertainty of the system:

[0079]

[0080]

[0081] At time k, the system comprehensive uncertainty calculated by equations (11) and (12) is substituted into equation (7). Combined with equations (9) and (10), a control variable u(k) can be found in the control space that minimizes the performance index function J(u(k)), thus achieving tracking control of the desired output voltage. The overall algorithm framework diagram is shown below. Figure 2 .

[0082] The above description is merely a description of preferred embodiments of the present invention and is not intended to limit the scope of the present invention in any way. Any changes or modifications made by those skilled in the art based on the above disclosure shall fall within the protection scope of the claims.

Claims

1. A control space-based DC-DC buck converter control method, characterized by, The application relates to a method for tracking control of a DC-DC buck converter with parameter uncertainty. Step 1, constructing a state space equation of a DC-DC buck converter with parameter uncertainty; Step 2, constructing a discretized error system; Step 3, solving an optimal control quantity based on a control space; Step 4, delay estimation of system parameter uncertainty; Step 5, realizing tracking control of a desired output voltage; The step of constructing a state space equation of a DC-DC buck converter with parameter uncertainty comprises the following steps: An ideal state space system shown in equation (1) is constructed by using a state average method: （1） wherein is the derivative of the transformer average output voltage, is the derivative of the average inductor current, , are the average output voltage and average inductor current values, respectively, is the nominal input voltage value, is the nominal load resistance value, is the nominal inductance value, is the nominal capacitance value, and is the control quantity of the system, which drives the signal. The system shown in equation (1) does not consider the uncertainty of system parameters, and equation (1) is written in the following form: （2） wherein , , , are the capacitance uncertainty, the load resistance uncertainty, the inductance uncertainty and the input voltage uncertainty of the system, respectively; In order to facilitate calculation, equation (2) is rewritten in the following form: （3） where , are system comprehensive uncertainties, and are bounded, and the specific expressions are as follows: （4） （5）； The step of constructing a discretized error system comprises the following steps: The desired output voltage is denoted as The output voltage tracking error is denoted as ; for the convenience of calculation, a new error state variable is defined as , The first derivative of the desired output voltage is denoted as （6） wherein is the first derivative of the output voltage tracking error, is the first derivative of the new error state quantity, is the second derivative of the desired output voltage, ; In order to facilitate construction of a prediction controller, system discretization is carried out, equation (6) is converted into a discretized system shown in equation (7) by using Euler discretization, wherein h is a sampling period, and k is a k time; ， The step of solving an optimal control quantity based on a control space comprises the following steps: Inspired by a dynamic window method, it is assumed that a control quantity u(k) of equation (7) remains unchanged in N sampling periods after a k time, a plurality of control quantities are sampled in a control space of the control quantity u(k), and state quantity changes of equation (7) under the action of the control quantities are simulated, after a plurality of state quantity changes are obtained, an optimal control quantity is selected by solving an optimization problem to drive the converter to work for one sampling period, the state quantity of the system is updated at a k+1 time, and the above steps are repeated; In order to reduce the calculation amount of the algorithm and more quickly search for the optimal control quantity in the control space, the value range of the system control quantity u(k) is discretized, the control quantity is discretized into n parts, and a control space U is obtained as follows: The optimal control quantity is obtained in the control space U by solving the following optimization problem: （8） The step of delay estimation of system parameter uncertainty comprises the following steps: （9） Performance indicator function is defined as: （10） where c is a weighting factor, represents the predicted state quantity at the k+i time instant under the action of the control quantity ; the first term of the performance index is used to penalize the accumulated output voltage tracking error over a time period, and the second term is used to penalize the variation amplitude of the accumulated output voltage tracking error. ​ In the process of solving the optimal control, the system comprehensive uncertainty which contains unmeasurable , cannot be directly solved to obtain the optimal control, so the time-delay disturbance observer is constructed as follows 、 to estimate the system comprehensive uncertainty: （11） （12）； The implementation of the tracking control of the desired output voltage comprises: at k time, the system comprehensive uncertainty calculated by equation (11) and equation (12) is brought into equation (7); and then combined with equation (9) and equation (10), a control amount u(k) making the performance index function The control amount u(k) making the performance index function reaches the minimum value is obtained, and the tracking control of the desired output voltage is implemented.

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