A model predictive control method for BUCK converter based on load estimation

Abstract

The present invention discloses a model predictive control method for a BUCK converter based on load estimation, including: optimizing the average state space model of the BUCK converter; sampling the input voltage, output voltage and inductor current, and estimating the load current based on the optimized average state space model and the sampling result; considering the influence of sampling and calculation delay on system stability, and compensating through state estimation; and reducing the influence of environmental noise on state estimation through Kalman filtering; using a single closed-loop control structure, generating a current reference instruction according to the result of state estimation and voltage given, and calculating the optimal duty cycle according to the state space model of the system and the reference current. The present invention solves the problem of limited bandwidth of the traditional double closed-loop PI control structure, and at the same time realizes rapid tracking of the change of load current without a load current sensor, greatly improving the dynamic performance and anti-interference ability of the system.

Description

Technical Field

[0001] The present invention belongs to the technical field of switching power supplies of power electronics, and more specifically, relates to a model predictive control method of a BUCK converter with high dynamic response capability based on load estimation. Background Art

[0002] With the advancement of power electronics technology and the gradual popularization of third-generation semiconductor devices, the performance of DC-DC converters has been improved in terms of switching frequency, size, power density, etc. In the context of vigorously advocating green development, the demand for DC-DC converters in energy storage systems, aerospace, DC microgrids, renewable energy, new energy vehicles and other fields is also increasing. At the same time, higher requirements are also put forward for the performance indicators of DC-DC converters.

[0003] However, the traditional control strategy based on PI regulator has the characteristics of phase lag, which limits the bandwidth of the control loop and reduces the dynamic performance of the system. This shortcoming seriously restricts the application of the converter in situations such as wide input voltage and frequent load changes.

[0004] In view of the problem that the traditional PI control has poor dynamic performance, the present invention proposes a model predictive control method with high dynamic response capability based on load estimation for the BUCK converter. Summary of the invention

[0005] Aiming at the shortcomings of traditional PI control strategy in dynamic performance, the present invention proposes a model predictive control method without load current sensor for BUCK converter, which aims to improve the dynamic performance and anti-interference ability of BUCK converter and shorten the dynamic recovery time when input voltage and load change.

[0006] To achieve the above object, in a first aspect, the present invention provides a model predictive control method for a BUCK converter based on load estimation, comprising the following steps:

[0007] S1, discretize the continuous-time state equation of the BUCK converter by integrating in a single cycle to obtain the optimized average state space model;

[0008] S2, sampling and filtering the input voltage, output voltage and inductor current, substituting the filtering results into the optimized average state space model for solving, and obtaining the estimated value of the system state in the current switching cycle;

[0009] S3, adopting a single closed-loop control structure, generates an inductor current given value of the current switching cycle according to the system state estimation value of the current switching cycle and the voltage given;

[0010] S4, with the goal of minimizing the deviation between the given value of the inductor current of the current switching cycle and the actual value of the inductor current of the next switching cycle, solving to obtain the optimal duty cycle of the current switching cycle.

[0011] Furthermore, in S1, the optimized average state space model is expressed as:

[0012]

[0013] Among them, v o (k+1) represents the output voltage of the k+1th switching cycle, i L (k) represents the inductor current of the kth switching cycle, C represents the output filter capacitor, T s represents the switching cycle, L represents the inductance, R L represents the DC resistance of the inductor, i o (k) represents the load current in the kth switching cycle, v i (k) represents the input voltage of the kth switching cycle, and d(k) represents the duty cycle of the kth switching cycle.

[0014] Furthermore, in S3, the given value iL of the inductor current in the kth switching cycle is ref (k) is:

[0015]

[0016] i MIN ≤iL ref (k)≤iL MAX

[0017] V refadj (k) = V refadj (k-1)+K I (k)(V ref -v o (k))

[0018]

[0019] Among them, V refadj (k) represents the voltage reference correction value of the kth switching cycle, K D Indicates the dynamic current compensation coefficient, iL MIN and iL MAX Indicates V refadj (k) lower and upper limits; V ref Indicates voltage given, K I (k) represents the integral term coefficient used to correct the given voltage, σ represents the error range of the output voltage that allows the correction term to work, k e Represents the gain of the integral term coefficient corrected according to the output voltage error.

[0020] Furthermore, K D The value range is [0.1,0.5].

[0021] Furthermore, in S4, let the inductor current i of the k+1th switching cycle be L (k+1) is equal to the inductor current set value iL of the kth switching cycle ref (k), and substitute it into the optimized average state space model to obtain the optimal duty cycle d of k switching cycles opt (k) is:

[0022]

[0023] Furthermore, in S2, a Kalman filter is used for filtering.

[0024] In a second aspect, the present invention provides a model predictive control system for a BUCK converter based on load estimation, comprising: a computer-readable storage medium and a processor; the computer-readable storage medium is used to store executable instructions; the processor is used to read the executable instructions stored in the computer-readable storage medium, and execute the model predictive control method for the BUCK converter based on load estimation as described in the first aspect.

[0025] In general, the control method proposed in the present invention has the following advantages:

[0026] (1) Compared with the existing discretized average state space modeling, which assumes that the output voltage is constant within a single cycle and uses the backward difference method for the differential equation of the inductor current, which amplifies the sampling noise, the present invention uses the integration method within a single cycle for discretization, which can reduce the sampling noise. The present invention optimizes the average state space model of the BUCK converter, reduces the error of state estimation, and improves the control accuracy.

[0027] (2) The model predictive control method proposed in the present invention samples a single closed-loop control structure, which overcomes the limitation of the traditional double closed-loop control structure on the system bandwidth and improves the system's anti-interference ability and dynamic response speed.

[0028] (3) The present invention estimates the load current through the optimized average state space model and state feedback, has a certain model adaptability, and at the same time improves the system's ability to resist load changes; in addition, it saves the load current sampling circuit and reduces the hardware cost.

[0029] (4) The present invention takes into account the control delay and sampling noise problems existing in actual digital control systems, and processes them through state estimation and Kalman filtering, thereby improving the stability of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 This is the block diagram of the model predictive control structure of the BUCK converter.

[0031] Figure 2 is the PWM switching signal of the BUCK converter in a single cycle, and the inductor current i L (t), output voltage v o (t), load current i o (t) Waveform diagram.

[0032] Figure 3 Schematic diagram of system delay in digital control.

[0033] Figure 4 is the output voltage v o (t) Kalman filtering effect diagram.

[0034] Figure 5 is the inductor current i L (t) Kalman filtering effect diagram.

[0035] Figure 6 is the load current i o (t) Comparison between the actual waveform and the estimated waveform.

[0036] Figure 7 The output voltage v when the system starts o (t), inductor current i L (t) and load current i o (t) waveform diagram.

[0037] Figure 8 The output voltage is 50% load test. o (t), inductor current i L (t) and load current i o (t) waveform diagram.

[0038] Fig. 9 The output voltage v is 50% load reduction test o (t), inductor current i L (t) and load current i o (t) waveform diagram. DETAILED DESCRIPTION

[0039] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0040] In the present invention, the terms "first", "second", etc. (if any) in the present invention and the accompanying drawings are used to distinguish similar objects but not necessarily to describe a specific order or sequence.

[0041] The present invention provides a model predictive control method for a BUCK converter based on load estimation, comprising operations S1 to S4.

[0042] Operation S1 discretizes the continuous-time state equation of the BUCK converter by using a single-cycle integration method to obtain an optimized average state space model.

[0043] Researchers in this field are familiar with the working principle of the BUCK converter, so this invention will not go into details. Only the optimized average state space model is introduced. The topology of the BUCK converter is as follows: Figure 1 As shown. When the ESR of the capacitor is ignored, the state equation in the continuous time domain is expressed as:

[0044]

[0045]

[0046]

[0047] Where L represents inductance, C represents output filter capacitor, R L Indicates the DC resistance of the inductor, T s represents the switching cycle, i L (t) represents the inductor current, v o (t) represents the output voltage, R o represents the load resistance, and d(k) represents the duty cycle of the kth switching cycle.

[0048] Conventional discretized average state space modeling assumes that the output voltage remains constant within a single cycle, and uses the backward difference method for the differential equation of the inductor current. The present invention uses the method of integration within a single cycle for discretization, and obtains the discretized state equation shown below:

[0049]

[0050] Assume that the load is normally stable and the load switching is instantaneous; the output voltage v o (t) changes linearly within a single cycle and the change is relatively small. Its waveform is as follows Figure 2 As shown. We can get:

[0051]

[0052] Therefore, the average state space model obtained by single-cycle integration can be expressed as:

[0053]

[0054] Assume that the state variable of the system is x(k)=[v o (k),i L (k),i o (k)] T , the control variable is u(k)=d(k), and the output is y(k)=[v o (k) i L (k)] T The above formula can be expressed as:

[0055]

[0056] In the above state-space model:

[0057]

[0058]

[0059]

[0060]

[0061] The reciprocal of the load resistance is G. o (k) It should be noted that there may be v o (k) = 0, then G o (k) = 0 to avoid system divergence problems.

[0062] Operation S2: sampling and filtering the input voltage, the output voltage and the inductor current, substituting the filtering result into the optimized average state space model for solving, and obtaining the estimated value of the system state of the current switching cycle.

[0063] The present invention requires that the input voltage v i (t), output voltage v o (t) and the inductor current i L (t) is sampled. Its sampling period is consistent with the control period, which is equal to the switching period. Considering the influence of control delay, the sampling result of the kth control period is recorded as:

[0064] x m (k-1)=[v i (k-1) v o (k-1) i L (k-1)] T

[0065] The sampling unit in the physical system will inevitably introduce sampling noise, which is Gaussian noise and is evenly distributed in the whole frequency domain. In order to reduce the influence of sampling noise on state estimation and steady-state performance, it is necessary to introduce a digital filtering algorithm. Conventional filtering algorithms designed based on frequency domain, such as low-pass filtering, high-pass filtering, band-pass filtering, and band-stop filtering, can only eliminate noise in a specific frequency band. Filtering algorithms designed based on time domain, such as sliding average filtering, weighted average filtering, etc., will cause sampling lag, which may cause output oscillation for control systems with high real-time performance, reducing the stability of the system. In order to avoid the above problems, the present invention adopts Kalman filtering.

[0066] As mentioned in the modeling section above, the system matrix is ​​a third-order matrix, and the third-order Kalman filter design is difficult. It is easy to know that the system matrix is ​​a singular matrix, and the system can be reduced in order to reduce the difficulty of filter design.

[0067] The state variable of the system after order reduction is x(k)=[v o (k) i L (k)], the system can be expressed as:

[0068]

[0069]

[0070]

[0071]

[0072] Ideally, data sampling, digital filtering, control quantity calculation and PWM signal generation are all completed instantaneously, and there is no delay in the closed-loop control system. However, in actual digital control, the sampling and calculation links will take up a certain amount of time resources, such as Figure 3 As shown. Assuming that sampling and calculation are completed within 1 switching cycle, the control signal generated by the sampling result at time k will be output at time k+1, and the control delay of the system is 1 switching cycle. Kalman filtering includes two stages: prediction and measurement update. The control method provided by the present invention adopts state estimation to eliminate control delay. The state estimation value of the k-1 control cycle can be used instead of the prediction value of the k control cycle to save computing resources. The state estimation value obtained in the k-1 control cycle is x e (k-1).

[0073] As shown in the following expression, the measurement update includes the update of the covariance matrix, the update of the Kalman gain matrix, and the update of the system state.

[0074] P - (k-1) = AP(k-2)AT +Q

[0075]

[0076] P(k-1)=(IK m H)P - (k-1)

[0077] x(k-1)=x e (k-1)+K m (x m (k-1)-Hx e (k-1))

[0078]

[0079] In the above expression, the Q matrix represents the observation noise of the system, and the R matrix represents the sampling noise of the system. Q and R are both second-order constant matrices, which determine the filtering effect of the Kalman filter and require engineers to adjust them according to actual working conditions. In addition, it should be noted that the initialization covariance matrix P(0) should be reasonably selected, which affects the convergence speed of the Kalman filter state variables.

[0080] The state after Kalman filtering is the input variable that actually participates in delay compensation. Substituting it into the average state space model proposed in the previous article for solution can obtain the estimated value of the actual system state in the current control cycle. This solution result will be used as the feedback of the MPC controller and the state prediction value of the Kalman filter in the next control cycle.

[0081]

[0082] Operation S3 adopts a single closed-loop control structure to generate an inductor current reference value of the current switching cycle according to the system state estimation value of the current switching cycle and the voltage reference.

[0083] In this embodiment, in order to eliminate the limitation of the dual-loop structure on the system bandwidth and speed up the dynamic performance of the system, the model predictive control method proposed in the present invention adopts a single closed-loop control structure and only controls the inductor current. The inductor current given value is divided into a steady-state current given part and a dynamic current given part, and the current given is updated in each control cycle.

[0084] For a given portion of the steady-state current, assuming that the load resistance remains unchanged under steady-state conditions, then

[0085]

[0086] For a given part of the dynamic current, the capacitor model shows that:

[0087]

[0088] The change in the capacitance across a single control cycle depends on the magnitude of the current flowing through the capacitor during the control cycle. Similarly, the magnitude of the current flowing through the capacitor can also be determined by the desired output voltage increment. That is, the dynamic current setting can be expressed as:

[0089]

[0090] In the dynamic current given part, the dynamic current compensation coefficient K D Determines the dynamic response speed of the system. When K D If it is too large, it may cause output oscillation and affect the stability of the system. D If the value is too small, the dynamic adjustment time will be too long, which will reduce the dynamic response speed of the system. D The value range is [0.1,0.5].

[0091] The total inductor current setting can be expressed as the sum of the dynamic current setting and the steady-state current setting. Considering the limitations of the physical system and the safety of the system, the inductor current needs to be limited, that is:

[0092]

[0093] i MIN ≤iL ref (k)≤iL MAX

[0094] In the given expression for current, V refadj (k) represents the voltage reference correction amount. Considering that steady-state errors may be introduced due to sampling errors and parameter mismatch, it is considered to adjust the voltage reference by adding an error integral term to the voltage reference to eliminate the steady-state error. When the deviation between the reference and output voltage feedback is too large, the integral term is cancelled; when the output voltage feedback enters the steady-state range, the integral action is added to improve the steady-state accuracy.

[0095] V refadj (k) = V refadj (k-1)+K I (k)(V ref -v o (k))

[0096]

[0097] Operation S4 is to solve and obtain an optimal duty cycle of the current switching cycle with the goal of minimizing the deviation between the given value of the inductor current of the current switching cycle and the actual value of the inductor current of the next switching cycle.

[0098] The MPC controller designed in the present invention only controls the inductor current, and it is expected that the deviation between the given and feedback of the inductor current is minimized, and an implicit objective function is designed.

[0099] J=(iL ref (k)-i L (k+1)) 2

[0100] When the objective function is minimized, it satisfies: iL ref (k) = i L (k+1).

[0101] Substituting the above formula into the average state space model proposed above, we can obtain:

[0102]

[0103] Solving the above equations together can get the optimal duty cycle:

[0104]

[0105] In the physical system, the optimal duty cycle d opt (t) Limiting, that is:

[0106] 0≤d opt (k)≤d max

[0107] Based on the control scheme proposed above, simulation analysis is performed in Matlab / Simulink. The simulation conditions are: switching frequency 200KHz, input voltage 30V, output voltage 20V, rated load resistance 6Ω, inductance 33uH, output filter capacitor 100uF, inductor current limit 10A. The simulation results are shown below.

[0108] Figure 4 The Kalman filter effect diagram of the output voltage. It is easy to see that the sampling noise is significantly reduced in the steady state. In the transient process, the maximum deviation between the filter value and the actual value is about 0.16V, and the deviation rate relative to the rated output voltage is about 0.8%.

[0109] Figure 5 The Kalman filter effect diagram of the inductor current. In the transient process, there is no sampling lag caused by filtering, but due to sampling noise and estimation error, there is a certain deviation between the filtered value and the average value of the inductor current.

[0110] Figure 6The waveforms are the comparison between the estimated load current and the actual load current. During the transient process, the load current changes can be tracked quickly, and the steady state is re-entered in about 16 switching cycles. During the steady state process, there is a static error of about 0.15A in the steady state due to the estimated deviation of the inductor current and the output voltage. The estimated load current noise caused by sampling noise is about 0.3A, which is about 4.5% of the rated current.

[0111] Figure 7 The waveforms of output voltage, inductor current and load current during startup are shown in Figure 1. During startup, the inductor current is always maintained near the current limit value. When the output voltage approaches steady state, the inductor current quickly exits saturation in 5 switching cycles. The startup process lasts about 300us, and the output voltage has no overshoot.

[0112] Figure 8 The output voltage, inductor current and load current waveforms during loading are shown in Figure 1. The output voltage drops by about 0.6V, the overshoot is 3%, and the adjustment time is about 100us.

[0113] Fig. 9 The waveforms of output voltage, inductor current and load current in the process of load reduction are shown in Figure 1. Its dynamic performance is basically the same as that in the process of load reduction.

[0114] It will be easily understood by those skilled in the art that the above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A model predictive control method for a BUCK converter based on load estimation, characterized in that: The following steps are involved: S1, discretize the continuous-time state equation of the BUCK converter by integrating in a single cycle to obtain the optimized average state space model; S2, sampling and filtering the input voltage, output voltage and inductor current, substituting the filtering results into the optimized average state space model for solving, and obtaining the estimated value of the system state in the current switching cycle; S3, adopting a single closed-loop control structure, generates an inductor current given value of the current switching cycle according to the system state estimation value of the current switching cycle and the voltage given; S4, taking the deviation between the given value of the inductor current of the current switching cycle and the actual value of the inductor current of the next switching cycle as the minimum, solving to obtain the optimal duty cycle of the current switching cycle; In S1, the optimized average state space model is expressed as: Among them, v o (k+1) represents the output voltage of the k+1th switching cycle, i L (k) represents the inductor current of the kth switching cycle, C represents the output filter capacitor, T s represents the switching cycle, L represents the inductance, R L represents the DC resistance of the inductor, i o (k) represents the load current in the kth switching cycle, v i (k) represents the input voltage of the kth switching cycle, d(k) represents the duty cycle of the kth switching cycle; In S3, the inductor current set value iL of the kth switching cycle ref (k) is: V refadj (k)=V refadj (k-1)+K I (k)(V ref -v o (k)) V refadj (k) represents the voltage reference correction value of the kth switching cycle, K D Indicates the dynamic current compensation coefficient, iL MIN and iL MAX Indicates V refadj (k) lower and upper limits; V ref Indicates voltage given, K I (k) represents the integral term coefficient used to correct the given voltage, σ represents the error range of the output voltage that allows the correction term to work, k e Represents the gain of the integral term coefficient corrected according to the output voltage error; In S4, let the inductor current i of the k+1th switching cycle be L (k+1) is equal to the inductor current set value iL of the kth switching cycle ref (k), and substitute it into the optimized average state space model to obtain the optimal duty cycle d of k switching cycles opt (k) is:

2. The model predictive control method for BUCK converter based on load estimation according to claim 1, characterized in that: K D The value range is [0.1,0.5].

3. The model predictive control method for BUCK converter based on load estimation according to claim 1, characterized in that: In S2, a Kalman filter is used for filtering.

4. A model predictive control system for a BUCK converter based on load estimation, characterized in that: include: A computer readable storage medium and a processor; The computer-readable storage medium is used to store executable instructions; The processor is used to read the executable instructions stored in the computer-readable storage medium to execute the model predictive control method for the BUCK converter based on load estimation as described in any one of claims 1 to 3.

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