Buck converter control method based on linear extended state observer and MPC

Abstract

The application discloses a control method of a step-down converter based on a linear extended state observer and MPC, which is used for improving the dynamic performance of output voltage and inductance current under time-varying characteristics of circuit parameters. The control system adopts a double closed-loop structure, the outer ring is a voltage loop, which is used for controlling the output voltage, the inner ring is a current loop, which is used for controlling the current flowing through the energy storage inductor, and the output of the voltage loop controller is used as the reference signal of the current loop controller. The voltage outer loop adopts linear active disturbance rejection control, the linear extended state observer is constructed to identify the parameter perturbation and load disturbance in real time, and a feedforward compensation mechanism is introduced to correct the trajectory of the output current reference signal. The current inner loop adopts model predictive control, and the optimal switching sequence is generated based on a two-step prediction algorithm. The current reference signal output by the voltage outer loop has strong inhibition ability to the load disturbance, and improves the tracking performance and anti-interference ability of the system.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of power electronic control, and relates to improvement of dynamic performance of a step-down converter under time-varying characteristics of circuit parameters, in particular to a step-down converter control method based on a linear extended state observer and MPC. BACKGROUND

[0002] The step-down converter (also known as a Buck converter) has the advantages of simple structure, high conversion efficiency, and large power density, and is widely used in daily life and industrial production. However, the step changes of the load resistance, the random fluctuations of the input voltage, and the time-varying characteristics of the circuit parameters are coupled with each other, which affects the dynamic performance and steady-state accuracy of the converter. Therefore, constructing a control mechanism with strong robustness to improve the dynamic performance and steady-state accuracy of the output voltage of the converter under parameter uncertainty has become a research content of the Buck converter.

[0003] Conventional Buck converters mostly use proportional-integral (PI) control, which has high steady-state accuracy of the output voltage and good anti-disturbance performance under small parameter perturbations. However, for nonlinear disturbances such as load step change, constant power load negative impedance effect, etc., the dynamic response is slow and the anti-disturbance ability is limited. For Buck converters with a wide input voltage range, the stability is limited by the operating point, and nonlinear oscillation is prone to occur. SUMMARY

[0004] The technical problem to be solved by the application is to provide a step-down converter control method based on a linear extended state observer and MPC, which is used to solve the problem of poor dynamic performance caused by time-varying characteristics of parameters of the Buck converter under nonlinear disturbance application occasions.

[0005] The technical solution of the application is as follows:

[0006] A step-down converter control method based on a linear extended state observer and MPC, the step-down converter adopts double-loop control, the outer loop is a voltage control loop, and a linear active disturbance rejection control LADRC is used; the inner loop is a current control loop, and a model predictive control algorithm (MPC) is used to generate an optimal switching sequence; the output signal of the outer loop controller is used as the current reference signal of the inner loop controller The linear extended state observer LESO of the linear active disturbance rejection controller LADRC is used to identify the capacitor parameter perturbation and the load disturbance in real time, and the derivative of the error between the observed value and the measured value of the output voltage is introduced in the linear extended state observer LESO to correct the trajectory of the current reference signal , so as to realize active suppression of the disturbance;

[0007] The implementation steps are as follows:

[0008] Step 1: Establishing the prediction model of the buck converter;

[0009] Step 2: Designing the current control loop of the buck converter's double closed-loop control system;

[0010] Step 2.1: Based on the current reference signal output by the voltage control loop Establishing the cost function representing the error of inductor current;

[0011] Step 2.2: Using a two-step prediction method with N=2 to reduce calculation delay.

[0012] Step 3: Designing the voltage control loop of the buck converter's double closed-loop control system;

[0013] Step 3.1: Designing the linear extended state observer LESO of the linear active disturbance rejection controller LADRC;

[0014] Step 3.2: Calculating the characteristic polynomial of the coefficient matrix of the observation error dynamic equation;

[0015] Step 3.3: Configuring the parameters β1, β2 and β of the linear extended state observer LESO 3 .

[0016] The topology of the buck converter is as follows: the input DC power source , power switch tube , energy storage inductor and load resistor are connected in series to form a loop, the positive electrode of the DC power source is connected to the drain of the power switch tube , the source of the power switch tube is connected to one end of the energy storage inductor L, the other end of the energy storage inductor L is connected to one end of the load resistor R, the other end of the load resistor R is connected to the negative electrode of the power source ; the filter capacitor and the load are connected in parallel; the anode of the freewheeling diode is connected to the negative electrode of the input DC power source ; the cathode of the freewheeling diode is connected to the source of the power switch tube ; the power switch tube is an N-MOS tube.

[0017] In step 1, the prediction model of the buck converter is:

[0018] ;

[0019] where is the current flowing through the energy storage inductor L, is the voltage across the load resistor R, is the sampling period;

[0020] is the duty cycle of the pulse width modulation (PWM) signal controlling the power switch S, ; when the PWM signal is high 1, the power switch S is closed, and when the PWM signal is low 0, the power switch S is opened.

[0021] In step 2.1, the current control loop adopts a model predictive control algorithm (MPC) to improve the dynamic response of the current and minimize the error between the predicted value and the reference value of the inductor current, and the cost function is , which is used to characterize the tracking performance of the inductor current to the current reference signal :

[0022] ,

[0023] In the formula, N represents the prediction step;

[0024] represents the inductor current value corresponding to the duty cycle D(k) at time k. The duty cycle D(k) that minimizes the cost function is the optimal duty cycle

[0025] at time k. :

[0026] ;

[0027] In the formula, arg min[ ] represents the value of the independent variable that minimizes the function in [ ], which here refers to the D(k) corresponding to the minimum value.

[0028] Step 2.2: A two-step prediction method with N=2 is used to reduce the calculation delay.

[0029] In order to suppress the problem of phase lag of the inductor current reference trajectory caused by calculation delay, a two-step prediction method with N=2 is used, based on the state variables predicted at time k , and the duty cycle signal , the inductor current at time k+1 is further predicted, i.e.:

[0030] ;

[0031] ​​​​​​According to the predicted result inductive current value at the moment re-calculate the duty cycle that minimizes the cost function, i.e. the optimal duty cycle

[0032] Due to the existence of calculation delay, the duty cycle signal at k+1 moment is determined by the predicted current at k+2 moment, therefore, the cost function of two-step prediction is only represented by the second step error:

[0033]

[0034] According to gradient optimization, when , the optimal duty cycle is solved as .

[0035]

[0036] The linear extended state observer (LESO) model of the linear active disturbance rejection controller (LADRC) in step 3.1 is:

[0037] ,

[0038] In the formula, z1 is the observation value of the output voltage of the step-down converter , z2 is the observation value of the total disturbance y of the system, y represents the total disturbance of the system, k represents the k moment, β1, β2 and are the linear extended state observer parameters.

[0039] The observation error is defined as:

[0040]

[0041] Discretization obtains the observation error dynamic equation:

[0042] ,

[0043] The coefficient matrix of the observation error dynamic equation is:

[0044] .

[0045] The characteristic polynomial of the coefficient matrix A of the observation error dynamic equation is:

[0046] ,

[0047] In the formula, I represents the unit matrix of , represents​​​​ determinant of matrix A.

[0048] configuring linear extended state observer parameters β1, β2 and β 3 .

[0049] Critical damping configuration is adopted, i.e. the characteristic polynomial of matrix A must have two repeated roots, and the characteristic polynomial of the coefficient matrix A of the observation error dynamic equation must satisfy:

[0050] ;

[0051] In order to make the system have no overshoot and fast convergence speed in step response, and effectively suppress the risk of nonlinear oscillation, symmetric gain simplified parameter design is adopted, i.e. configuring ;

[0052] Therefore, according to the above formula, linear extended state observer parameters β1, β2 and β are configured:

[0053] ;

[0054] In the formula, is a bandwidth parameter; , is a sampling frequency, .

[0055] In the control framework of extended state observer (ESO), in order to realize accurate regulation of system state and disturbance compensation, the state feedback control rate is designed:

[0056] ,

[0057] In the formula, represents a voltage reference signal;

[0058] Controller parameters and bandwidth parameter satisfy:

[0059] .

[0060] Beneficial effects: the application discloses a voltage reduction converter control method based on a linear extended state observer and MPC, and is especially used for improving the output voltage and inductance current dynamic performance under the time-varying characteristic of circuit parameters. The control system adopts a double closed loop structure, the outer ring is a voltage ring used for controlling the output voltage, the inner ring is a current ring used for controlling the current flowing through the energy storage inductance, and the output of the voltage ring controller is used as the reference signal of the current ring controller. The voltage outer ring adopts a linear active disturbance rejection control, the parameter perturbation and load disturbance are identified in real time through the construction of a linear extended state observer, and a feedforward compensation mechanism is introduced to correct the trajectory of the current reference signal. The current inner ring adopts a model predictive control, and the optimal switching sequence is generated based on a two-step prediction algorithm. The dynamic current reference signal output by the voltage outer ring has strong inhibition ability to the load disturbance, eliminates the demand of traditional PI parameter setting, and improves the tracking performance and anti-interference ability of the system. BRIEF DESCRIPTION OF DRAWINGS

[0061] Figure 1 It is a voltage reduction converter schematic diagram.

[0062] Figure 2 It is a control block diagram of the voltage reduction converter based on the linear extended state observer and the model prediction of the application.

[0063] Figure 3 It is a current inner ring control block diagram provided by the application.

[0064] Figure 4 It is an inductance current actual value and theoretical value deviation comparison diagram provided by the application.

[0065] Figure 5 It is a linear active disturbance rejection control LADRC structure diagram provided by the application.

[0066] Figure 6 It is an output voltage and inductance current waveform diagram in the system starting process, wherein (a) adopts the LADRC+PI control method, and (b) adopts the control method provided by the application.

[0067] Figure 7 It is an inductance current and output voltage waveform diagram of the load step change (the load resistance is changed from to ), wherein (a) adopts the LADRC+PI control method, and (b) adopts the control method provided by the application. DETAILED DESCRIPTION

[0068] The application will be further described in detail below in combination with the drawings and specific embodiments. However, it should not be understood that the above-mentioned subject matter of the application is limited to the following embodiments only, and all the technologies realized based on the content of the application belong to the range of the application.

[0069] The voltage reduction converter schematic diagram is as followsFigure 1 As shown in the figure is an input DC power supply voltage, S is a power switch tube MOSFET, a diode is connected in antiparallel between the source and the drain of S, VD is a freewheeling diode, L is an energy storage inductor, C is a filter capacitor, R is a load, and the voltage across R is an output voltage, and the current flowing through the inductor L is By controlling the on and off time of the power switch tube S, the desired output voltage can be obtained.

[0070] The control structure of the system is shown in the figure Figure 2 , and the system adopts double closed-loop control. The outer loop is a voltage control loop, the voltage reference signal of the voltage control loop is , and the output voltage of the step-down converter serves as a feedback signal. Through voltage closed-loop control, the dynamic response speed of the output voltage tracking the given voltage control signal is improved, and stable and static error-free control and active suppression of load disturbance are realized. The inner loop is a current control loop, and the inductor current tracks the current reference value quickly and without error. The output signal of the voltage controller serves as the current reference signal of the current inner loop , and the inductor current serves as a feedback signal, and the output signal of the current controller is used to control the power switch tube S of the step-down converter. The voltage outer loop adopts linear active disturbance rejection control (LADRC). In order to realize linear active disturbance rejection control, a linear extended state observer (LESO) is constructed to identify the inductor and capacitor parameter perturbation and load disturbance in real time, and the derivative of the error between the observed value and the measured value of the output voltage is introduced into the LESO to correct the trajectory of the current reference signal , so that the current inner loop MPC acts in advance, and active disturbance suppression is realized. The current inner loop adopts model predictive control (MPC) to generate an optimal switching sequence, and realize fast and error-free tracking of the inductor current. The model predictive control of the current uses a cost function characterizing the inductor current error to solve the optimal duty cycle , reduces the inductor current tracking error, improves the response speed, reduces the time delay of sampling, and does not need to be parameterized.

[0071] Figure 3 The current inner loop control block diagram provided by the present application is shown in the figure, and the cost function is a function representing the error between the model prediction value and the current reference value, and the goal is to optimize the model parameters by minimizing this function. The model predictive controller (MPC) of the current inner loop predicts the system variables at each cycle, optimizes the duty cycle signal D(k), controls the switching sequence composed of the conduction and turn-off of the power switch S, and makes the inductor current actual value track the inductor current reference value .

[0072] As shown in Figure 4 , assuming that the given reference current signal of the current inner loop is constant, the inductor current is sampled at time , and the optimal switching state is calculated according to the current sampling value. The on-off state of the power switch S is controlled according to the obtained optimal switching state. In the ideal state of ignoring the calculation time, the current starts to decrease from the point at time , and approaches the given signal . However, due to the delay time caused by online prediction calculation, the calculated optimal switching state can only actually act on the power switch S at time . During this period of time , the switching state remains unchanged, causing the inductor current to continue to rise from the point to the point, and the actual current deviates from the ideal state point to point at time . Figure 4 The solid line in the middle represents the actual inductor current, and the dashed line represents the ideal inductor current without delay.

[0073] In order to improve the control accuracy of the system and eliminate the influence of the delay caused by prediction calculation on the inductor current, a two-step prediction method with N=2 is adopted to reduce the amplitude of the inductor current deviating from the reference signal due to calculation delay. Based on the state variables predicted at time , and the duty cycle signal , the inductor current at time is further predicted, so that the controller actively tracks the dynamic changes of the reference signal.

[0074] As can be seen from the linear active disturbance rejection control LADRC block diagram Figure 5 , the output voltage of the Buck converter is fed back to LADRC as an input signal of LESO inside LADRC, and the other input signal of LESO is , the output of LESO is and Two signals.

[0075] Due to the influence of the output voltage (i.e., the voltage across the load resistor R), the load resistance, and the filter capacitor, in order to ensure that the observer's disturbance observation speed is much faster than the control loop response speed, the disturbance signal is observed in real time and actively compensated. At the same time, a voltage tracking error is set to ensure the dynamic performance of the system. Example 1

[0076] The given buck converter parameters are shown in Table 1;

[0077] .

[0078] The prediction model for step-down transformers is as follows:

[0079] (1)

[0080] In the formula This is the sampling period; the sampling period is set here. for s. Where D is the duty cycle of the pulse width modulation (PWM) signal controlling the power switch S, and When the PWM signal is high level 1, the power switch transistor... When the circuit is closed and the PWM signal is low (0), the power switch transistor... disconnect.

[0081] Depend on Figure 1 The average equation for the output voltage of the Buck converter can be obtained as follows:

[0082] (2)

[0083] make , It is the total system disturbance.

[0084] The inner current loop employs model predictive control, using a cost function. Characterizing the tracking performance of the inductor current to the current reference signal:

[0085] (3)

[0086] In the formula, N represents the prediction step size;

[0087] Indicates the prediction at time k. The inductor current value at any given time is based on the duty cycle D(k);

[0088] Equation (3) calculates online the duty cycle D(k) that minimizes the cost function, which is... Optimal duty cycle at time k+1 ,

[0089] (4)

[0090] Two-step prediction method with N=2 is adopted to reduce the amplitude of inductance current deviating from current reference signal caused by calculation delay, and based on state variable at time k+1 predicted by two-step prediction method , 、 and duty cycle signal at time k+1 , further prediction is made to obtain inductance current at time k+1 , that is:

[0091] (5)

[0092] According to formula (5), inductance current value at time k+1 predicted by prediction is obtained , re-calculate the duty cycle with minimum cost function, that is, optimal duty cycle ;

[0093] Due to the existence of calculation delay, the duty cycle signal at time k+1 is determined by the predicted current at time k+2, therefore, the cost function of two-step prediction is only represented by the second step error:

[0094] (6)

[0095] According to gradient optimization, when , the optimal duty cycle is solved as :

[0096] (7)

[0097] The optimal duty cycle calculated by formula (7) is applied to the power switch tube.

[0098] As can be seen from the linear active disturbance rejection control LADRC structure diagram, the output voltage of Buck converter Figure 5 is fed back to LADRC as an input signal of LESO in LADRC, and the other input signal of LESO is , LESO outputs two signals of and , and the extended state space equation of LESO is:

[0099] (8)

[0100] In the formula, is the observation value of , and ​​For the observed value, , and are linear extended state observer parameters.

[0101] where, From equation (2) and equation (8), we have:

[0102] (9)

[0103] Discretize equation (8) by combining equation (2) and equation (9), we have:

[0104] (10)

[0106] Define the observation error :

[0107] (11)

[0108] Take the derivative of the observation error , combine equation (2) and equation (10), and ignore , we have the observation error dynamic equation:

[0109] (12)

[0110] The coefficient matrix of the observation error dynamic equation is:

[0111] (13)

[0112] The characteristic polynomial of the coefficient matrix A of the observation error dynamic equation is:

[0113] (14)

[0114] Configure the linear extended state observer parameters , and :

[0115] (15)

[0116] Design the state feedback control rate as:

[0117] (16)

[0118] The controller parameters need to satisfy:

[0119] (17)

[0120] This embodiment takes ,

[0121] Ensure that the disturbance observation speed of the observer is much faster than the response speed of the control loop, the disturbance y is observed in real time, and active compensation is performed.

[0122] Experimental verification

[0123] In order to verify the effectiveness of the control method proposed in the application, a physical platform is built, and the control method proposed in the application and the LADRC-PI control method are used on the platform respectively, the experimental circuit parameters of the two control methods are consistent, , The system startup performance and load disturbance performance are tested respectively, Figure 6 The inductor current and output voltage waveforms in the startup process are shown in Figures 6 and 7, Figure 7 The inductor current and output voltage waveforms under load step change are shown in Figures 8 and 9.

[0124] Analysis Figure 6 It can be seen that the control method proposed in the application and the LADRC+PI method respectively take 8ms and 23ms to reach the stable working point, and the response speed of the control method proposed in the application from startup to reach the stable working point is greatly improved compared with the LADRC+PI.

[0125] Analysis Figure 7 It can be obtained that when the load changes from to , the output voltage change of the LADRC-PI control method is 1.2V, and the adjustment time is 8.1ms. The output voltage change of the control method proposed in the application is 0.6V, and the adjustment time is 3.2ms. For specific data comparison, see Table 2.

[0126] .

[0127] As can be seen from Table 2, compared with the LADRC+PI control method, the control method proposed in the application has better transient performance, rapidity and anti-interference performance, and the rapidity and anti-interference performance are improved.

Claims

1. A buck converter control method based on a linear extended state observer and MPC, characterized in that, The buck converter employs dual closed-loop control. The outer loop is a voltage control loop using a linear active disturbance rejection controller (LADRC); the inner loop is a current control loop using a model predictive control algorithm to generate the optimal switching sequence. The output signal of the outer loop controller serves as the current reference signal for the inner loop controller. ; The Linear Extended State Observer (LESO) of the Linear Active Disturbance Rejection Controller (LADRC) is used to identify capacitor parameter perturbations and load disturbances in real time. The LESO introduces the derivative of the error between the observed and measured output voltage values ​​to correct the current reference signal. The trajectory is used to actively suppress disturbances; The implementation steps are as follows: Step 1: Establish a predictive model for the buck converter; Step 2: Design the current control loop of the dual closed-loop control system for the buck converter; Step 2.1: Current reference signal based on voltage control loop output Establish a cost function characterizing the inductor current error; Step 2.2: Use a two-step prediction method with N=2 to reduce computational delay; Step 3: Design the voltage control loop of the dual closed-loop control system for the buck converter; Step 3.1: Design the linear extended state observer LESO for the linear active disturbance rejection controller LADRC; Step 3.2: Calculate the characteristic polynomial of the coefficient matrix of the dynamic equation of the observation error; Step 3.3: Configure the parameters β1, β2, and β3 of the Linear Extended State Observer (LESO). ; The model of the linear extended state observer (LESO) for the linear active disturbance rejection controller (LADRC) is as follows: ， In the formula, z1 is the output voltage of the buck converter. The observed value is z1, and the observed value of the total system disturbance y is z2. y represents the total system disturbance signal, and k represents the values ​​of β1, β2, and β3 at time k. These are the parameters for the linearly extended state observer; R is the load resistance. For filter capacitors The sampling period; Define observation error : ； Discretization The dynamic equation for the observation error is: ， Observation error dynamic equation coefficient matrix ; The characteristic polynomial of the coefficient matrix A of the dynamic equation of the observation error must satisfy: ； Based on the above formula, configure the linear extended state observer parameters β1, β2, and : ， In the formula For bandwidth parameters; , Sampling frequency, ; The output signal of the voltage control loop, i.e., the reference current signal of the current controller. : ； In the formula Indicates the voltage reference signal; parameter With bandwidth parameters Must meet: 。 2. The buck converter control method based on linear extended state observer and MPC according to claim 1, characterized in that: The topology of the buck converter is as follows: it consists of an input DC power supply. Power switching transistors Energy storage inductor and load resistance A DC power supply is connected in series to form a loop. The positive terminal is connected to the power switching transistor. The drain of the power switch transistor The source is connected to one end of the energy storage inductor L, and the other end of the energy storage inductor L is connected to one end of the load resistor R. The other end of the load resistor R is connected to the power supply. Negative terminal connection; filter capacitor and load Parallel connection; freewheeling diode The anode is connected to the input DC power supply. The negative terminal; freewheeling diode Cathode connected to power switching transistor The source of the power switch. It is an N-MOS transistor; The prediction model for the buck converter is as follows: ； In the formula, The current flowing through the energy storage inductor L, The voltage across the load resistor R is... The sampling period; It controls the duty cycle of the pulse width modulation signal for the power switch S. When the PWM signal is high level 1, the power switch transistor... When the circuit is closed and the PWM signal is low (0), the power switch transistor... disconnect.

3. The buck converter control method based on linear extended state observer and MPC according to claim 2, characterized in that: In step 2.1, the cost function is: Using cost function Characterizing the inductor current relative to the current reference signal Tracking performance; ； In the formula, N represents the prediction step size; Indicates the prediction at time k. The inductor current value at any given time is based on the duty cycle D(k); The duty cycle D(k) that minimizes the cost function is... Optimal duty cycle at time : ； In the formula, arg min[ ] represents the value of the independent variable that makes the function in [ ] take the minimum value.

4. The buck converter control method based on linear extended state observer and MPC according to claim 3, characterized in that: In step 2.2, a two-step prediction method with N=2 is used to suppress the phase lag of the inductor current reference signal trajectory caused by the calculation delay, based on... The state variables predicted at each time step , and duty cycle Further predictions have been made. Inductor current at time ,Right now: ； When the reference current signal equals the predicted inductor current, the optimal duty cycle is... for: 。

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