A robust switching control method for wide load range dc boost converter

Abstract

This invention discloses a robust switching control method for DC-DC boost converters with a wide load range, designed to improve the anti-interference performance of DC-DC boost converters under a wide load range. The system employs dual-loop control: the inner loop uses Lyapunov switching law control, and the outer loop uses PI control. First, a state-space model of the DC-DC boost converter is established, obtaining the state-space expressions of the switching system and its subsystems. Next, the maximum load average matrix and the minimum load average matrix are constructed, and the robust positive definite symmetric matrix is ​​solved using the constructed robust stability linear matrix inequality constraint equations. The dynamic reference state vector obtained from the outer-loop PI control is used to define the real-time state error vector, and the derivatives of the Lyapunov energy function under two operating modes are solved to determine the switching rule. Verification shows that this method exhibits excellent robustness and fast dynamic response capability under a wide range of load fluctuations.

Description

Technical Field

[0001] This invention belongs to the field of power electronic control technology, and particularly relates to a robust switching control method for DC-DC boost converters with uncertain linear matrix inequalities under wide load operating conditions. Background Technology

[0002] DC-DC boost converters, also known as Boost converters, are a typical type of DC-DC converter used to boost the input voltage to a certain output voltage. They are widely used in photovoltaic power generation, electric vehicles, portable electronic devices, and other fields. Due to their characteristics such as switching nonlinearity and time-varying parameters, designing high-performance controllers has always been a research hotspot for improving the output performance of DC-DC boost converters. Traditional control methods often employ PID control or pulse width modulation (PWM) techniques based on small-signal models. These methods typically involve linearization design near the steady-state operating point. When the system deviates from the operating point or the load undergoes large-scale abrupt changes, the dynamic performance of the controller will significantly degrade, and may even lead to system instability.

[0003] To overcome the limitations of traditional linear control, switching control methods based on Lyapunov stability theory have received widespread attention in recent years due to their excellent large-signal stability and fast dynamic response. Patent CN111934524A discloses a switching control method for a DC-DC converter. This invention utilizes a method that compares the derivative of the Lyapunov function with the stability threshold to determine the switching time. Its core idea is to calculate the desired output based on an ideal circuit model and construct an error signal, then recursively determine the duty cycle and switching sequence for each switching cycle. However, this method directly uses fixed circuit parameters when calculating the desired output (inductor current reference value). When the actual load changes abruptly, causing parameter drift, the desired output calculated based on fixed parameters will no longer be accurate, leading to steady-state errors in the system. Furthermore, obtaining a fixed positive definite matrix based on nominal parameters means that when the load resistance fluctuates within a large range, a single positive definite matrix cannot guarantee that the Lyapunov derivative is always less than zero, thus affecting the global stability of the system. Chinese invention patent publication number 111969848B discloses "A Control Method for a DC-DC Converter Based on Switching Control." This invention proposes a discrete switching control law based on data sampling, selecting the switching state by minimizing a cost function, and introducing a linear matrix inequality to solve the parameter matrix. The balance reference values ​​in both patents are calculated based on ideal model parameters. When the load is unknown or changing, this calculated value cannot be automatically corrected, leading to deviations in the control objective. This method relies on sampled discrete signals for switching decisions. Although the sampling interval is considered, its optimization strategy based on specific sampling points still has room for improvement in anti-interference capability when dealing with drastic parameter perturbations in the continuous domain. Invention patent publication number 114785121A (application number CN202210445724.1) discloses "A Switching Control Method for a Boost Converter Based on Output Feedback." This invention introduces a Luenberger observer to estimate the system state (such as inductor current), aiming to reduce the number of sensors, lower costs, and design a switching law based on the observed state. The performance of the Luenberger observer in this invention is highly dependent on the accuracy of the system model. When the load resistance or inductance in the actual circuit changes, the internal model parameters of the observer do not match the actual object, which can lead to large errors in the state estimation and affect the switching decision.

[0004] Therefore, a DC-DC boost converter control method is needed that can maintain strong robust stability of the system under conditions of parameter uncertainty such as large load fluctuations, and can automatically eliminate steady-state errors. The robust switching control method of this invention, which combines wide-load-range uncertainty linear matrix inequalities with an outer-loop PI controller, is proposed precisely to solve the above-mentioned technical problems. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a robust switching control method for DC-DC boost converters with wide load range uncertainty linear matrix inequalities, which can be used to improve the anti-interference performance of DC-DC boost converters under load change conditions with wide load range.

[0006] A robust switching control method for a DC-Boost converter with a wide load range. The topology of the DC-DC boost converter is as follows: DC power supply The positive terminal of the energy storage inductor L One end, energy storage inductor L The other end is connected to a diode The positive electrode and the power MOSFET power switch Drain of the diode The negative terminal is connected to the load resistor. R one end and filter capacitor C One end, load resistor R The other end and the filter capacitor C The other end and the source of the power MOSFET are connected to a DC power supply. The negative terminal of the diode; negative terminal to DC power supply The voltage between the negative terminals is the output voltage. The current flowing through the energy storage inductor is , The positive direction is from the positive terminal of the DC power supply to the inductor; power MOSFET power switching transistor The gate of the power MOSFET receives the PWM signal, which controls the power MOSFET power switch. The on / off state controls the output voltage. Size; The DC-DC boost converter adopts dual closed-loop control. The outer loop is a voltage control loop, which uses PI control, and the inner loop is a current control loop, which uses switching control. The outer loop is given by a voltage reference signal. Output voltage As the voltage feedback signal, the output of the outer loop controller PI is , The current reference signal and voltage reference signal are for the inner loop controller. This is another input signal to the inner current loop switching controller; the feedback signal of the switching controller is the inductor current. and load voltage Switch the on / off state of the controller output. Used to control power switching transistors The switching on and off of the circuit achieves output voltage stability; The steps for establishing a control system for a DC-DC boost converter are as follows: Step 1: Establish the state-space expression of the DC-DC boost converter, i.e., the state-space expression of the switching system; When the power switch transistor When the circuit is on, according to Kirchhoff's voltage and current laws, we can obtain: (1) When the power switching transistor When the circuit is turned off, according to Kirchhoff's voltage and current laws, we can obtain: (2) For current and output voltage Perform sampling and set the state vector. The state-space model of the DC-DC boost converter is obtained as follows: (3) In the formula, the subscript Indicates the switching state as it changes over time. Take 0 and 1, when At that time, i.e., power switching transistor When At that time, i.e., power switching transistor Shutdown; Define equation (3) as the switching system, which has two subsystems, when At that time, power switching transistor The shutdown is called a subsystem. ,when At that time, power switching transistor When the circuit is turned on, it is called a subsystem. ; Set the state vector ; power switching transistors When shutting down, the corresponding switching system subsystem The state-space expression is: (4); make , ,say For switching system subsystems The coefficient matrix, For switching system subsystems The input matrix; power switching transistors When the switch is activated, the corresponding subsystem of the switching system... The state-space expression is: (5); , ,say For switching system subsystems The coefficient matrix, For switching system subsystems The input matrix; Step 2: Solve for the ideal duty cycle Construct the maximum load average matrix and minimum load average matrix ; Step 3: Construct robust stability linear matrix inequality constraints and solve for the robust positive definite symmetric matrix. ; Step 4: Based on the minimum Lyapunov energy function Based on the attenuation principle, a switching control strategy for the inner current loop is designed. Construct the dynamic reference state vector as follows Define the real-time state error vector Construct the Lyapunov energy function Based on the robust positive definite symmetric matrix obtained in step three and dynamic reference state vector Calculate the corresponding subsystems of the switching system respectively. and subsystem The derivative of the Lyapunov energy function and Choose the derivative of the Lyapunov energy function. The switch state with the smallest value is taken as the switch state at the current moment. Used to control power switching transistors Turn on or off; Step 5: Design the PI parameters for the voltage outer loop controller.

[0007] In step two: (6); In the formula, ; load Can be in the range Internal regulation, and These represent the maximum and minimum allowable loads for normal operation of the boost DC-DC converter, respectively; due to the coefficient matrix and Contains Therefore, the system exhibits time-varying characteristics; when the load is At that time, the corresponding subsystem coefficient matrix The corresponding subsystem coefficient matrix Maximum load average matrix When the load is At that time, the corresponding subsystem coefficient matrix The corresponding subsystem coefficient matrix Minimum load average matrix .

[0008] Step 3: Solve for the robust positive definite symmetric matrix The linear matrix inequality constraints are: (7); in, Represents a 2×2 identity matrix. It is a positive semi-definite weighting matrix used to adjust the convergence speed. , This is the current error weighting coefficient. This is the voltage error weighting coefficient, and and The values ​​of are positively correlated with the reciprocal of the square of the nominal inductor current and the reciprocal of the square of the desired output voltage, respectively, to eliminate the influence of the difference in the dimensions of the state variables. .

[0009] The specific implementation method of the inner loop switching law in step four is as follows: The general expression: (8); Real-time state error vector derivative : (9); (8) can be simplified to: (10); Substituting into equation (10), we obtain the derivative of the Lyapunov energy function corresponding to the subsystem. : (11); Will Substituting into equation (10), we obtain the subsystem. The derivative of the corresponding Lyapunov energy function : (12); if , Switching transistor Conductive; if , Switching transistor Turn off.

[0010] The mathematical expression is: (13).

[0011] This law guarantees that the system always follows the Lyapunov energy function. The direction with the fastest attenuation is switched.

[0012] Step 5: Design the PI parameters for the voltage outer loop controller.

[0013] In step five: Outer loop voltage error signal For voltage error signals Perform PI control, and the output signal of the PI controller, , Represents the proportionality coefficient. Indicates the integral coefficient; proportionality coefficient and integral coefficient Determine using the following formula: (20) in, The cutoff frequency of the outer voltage loop is denoted as . For the ideal duty cycle.

[0014] The design process for the PI parameters of the voltage outer loop controller is as follows: (1) Establish the small-signal model of the voltage outer loop: Since the dynamic response speed of the inner-loop Lyapunov controller is much faster than that of the outer-loop voltage PI controller, the current inner loop can be regarded as an ideal current tracking element when designing the outer loop, that is, assuming that the actual inductor current is always equal to the reference current: .

[0015] According to the charge balance equation of the capacitor node of the DC-DC boost converter, in steady state we have: (14) By modeling the small-signal perturbation and performing a Laplace transform, the open-loop transfer function from the inductor current to the output voltage can be obtained. for: (15) (2) Construct a PI controller and perform zero-pole configuration: The transfer function of the outer loop PI controller is (16) The open-loop transfer function of the voltage outer loop is To simplify system order reduction and improve system stability under wide loads, this invention employs a zero-pole cancellation method, where the zeros of the PI controller cancel out the low-frequency poles of the system transfer function. A nominal load resistance is selected. To conduct the design, let: (17) At this point, the open-loop transfer function of the outer voltage loop simplifies to that of a typical first-order system: (18) (3) Determine the proportionality coefficient and integral coefficient : Set the cutoff frequency (crossover frequency) of the outer voltage loop as follows: To ensure the separation of time scales between the inner and outer loops and avoid control coupling interference, It should be much smaller than the equivalent switching frequency of the inner loop.

[0016] Based on amplitude-frequency characteristics The parameter design formula for the outer loop PI controller can be derived: (19) (20) Using the above formula, the system can determine the hardware parameters ( ) and nominal load ( ), calculate the optimal and parameter. Beneficial effects

[0017] This invention discloses a robust switching control method for a DC-DC boost converter with wide load range uncertainty linear matrix inequalities. The method utilizes a robust positive definite symmetric matrix obtained by solving linear matrix inequalities. Mathematically, this guarantees that the converter can operate under load changes. arrive Under drastic changes, the closed-loop system remains within the Lyapunov stability region, resolving the instability problem caused by parameter mismatch in traditional methods and significantly improving the robustness of the converter. Furthermore, the introduction of the outer-loop PI controller enables the system to automatically compensate for voltage drops caused by load changes, achieving precise tracking of the desired voltage.

[0018] In addition, patent application CN111934524A discloses a switching control method for a DC-DC converter. The method involves subtracting the output signal of the circuit from the expected value to obtain an error signal, comparing the derivative of the Lyapunov function of the error signal with the stability threshold to determine the switching time, and limiting the switching to only once per switching cycle. This switching rule ensures that the switching must be performed in each switching cycle, thereby determining the duty cycle in each cycle. The method features low switching frequency, good stability, and high accuracy, effectively reducing the number of switching operations and determining the duty cycle of the DC-DC converter in each cycle.

[0019] This application makes significant improvements based on the existing patent, as detailed below: 1. Control Architecture: Compared to the single-loop control structure used in patent (CN111934524A), which directly subtracts the circuit output from the calculated desired output to obtain an error signal, and then calculates the derivative of the Lyapunov function based on this error signal to determine the switching time, the "A Robust Switching Control Method for a Wide Load Range DC-DC Boost Converter" adopts a dual closed-loop control system. The outer loop is a voltage control loop using PI control, and the inner loop is a current control loop using Lyapunov switching law control.

[0020] 2. Method for Obtaining the Expected Value (Reference Signal): Compared to patent (CN111934524A), which relies on a fixed ideal mathematical model and calculates the system's switching equilibrium point as the expected output by solving equations in an open loop, this method is prone to steady-state errors when parameters drift. In the paper "A Robust Switching Control Method for a Wide Load Range DC-DC Boost Converter," the voltage outer-loop PI controller dynamically calculates and outputs a current reference signal based on the voltage error signal, thereby constructing a dynamic reference state vector. Introducing outer-loop PI control can automatically compensate for voltage drops caused by load changes, achieving zero steady-state error tracking.

[0021] 3. Methods to Combat Load Parameter Variation: Compared to patent (CN111934524A), which solves the Lyapunov equations using a single fixed-parameter model to obtain a fixed positive definite symmetric matrix P, the method described in "A Robust Switching Control Method for DC-DC Boost Converters with a Wide Load Range" introduces an uncertainty model under a wide load range. It constructs maximum and minimum load average matrices based on the boundaries of load variations. By constructing robust stability linear matrix inequality (LMI) constraint equations, a common robust positive definite symmetric matrix P that simultaneously satisfies the extreme load conditions is obtained. This mathematically guarantees the global stability of the system under large and drastic load variations.

[0022] 4. Switching Decision Mechanism: Compared to patent (CN111934524A), which sets a stable operating neighborhood and integrates forced switching signals, uses recursive equations to calculate the duty cycle, obtaining the switching time sequence and switching signal sequence, and limits switching to only once per switching cycle, the "A Robust Switching Control Method for a Wide Load Range DC-DC Boost Converter" makes instantaneous decisions based on the principle of minimizing Lyapunov energy function decay. The system calculates the derivative of the Lyapunov energy function in real time under two operating modes (on and off) and directly selects the switching state that minimizes the derivative value as the control state at the current moment. This ensures that the system always switches along the direction of fastest energy decay.

[0023] 5. Optimization of the Error Weighting Matrix (Q Matrix): Compared to patent (CN111934524A), which directly uses a negative identity matrix for solving, without mentioning special handling for the numerical differences of different state variables (current and voltage), the "A Robust Switching Control Method for a Wide Load Range DC-DC Boost Converter" specifically designs a positive semi-definite weighting matrix Q in the LMI constraints. The values ​​of its current error weighting coefficient and voltage error weighting coefficient are positively correlated with the reciprocal of the square of the nominal inductor current and the reciprocal of the square of the desired output voltage, respectively. This design effectively eliminates the influence of dimensional differences between state variables. Attached Figure Description

[0025] Figure 1 This is a schematic diagram of a DC-DC boost converter. Figure 2 This is a block diagram of the robust switching control proposed in this invention; Figure 3 The output voltage and inductor current waveforms of the converter under a wide load range of the system are shown. Detailed Implementation

[0027] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0028] Figure 1 This is the schematic diagram of a DC-DC boost converter. The parameters in the schematic diagram are shown in Table 1. The input DC voltage of the converter is... The desired output DC voltage is 12V. It is 24 V. Figure 2 This is a block diagram of the robust switching control proposed in this invention.

[0029] Table 1 Parameters of DC-DC boost converter examples parameter symbol nominal value Input voltage Vin 12 V Reference voltage Vref 24 V inductance L 10 mH capacitance C 1000 uF resistance R 15~50 Ω Solving for the ideal duty cycle Construct the maximum load average matrix and minimum load average matrix .

[0030] When the load resistance is taken When, the corresponding coefficient matrix , Maximum load average matrix When the load resistance is taken When, the corresponding coefficient matrix is , Minimum load average matrix .

[0031] Take the weight matrix for Solving for the robust positive definite symmetric matrix based on constraints .

[0032] Based on the specific embodiments of the present invention, the ideal duty cycle Filter capacitor nominal load resistance Set the outer loop cutoff frequency. Substituting into the above formulas (19) and (20), we can obtain the following: , In actual engineering implementation, the finely adjusted parameters are used. , That is, the value of the outer loop PI controller is... , .

[0033] Figure 3 The output voltage of the method of the present invention and inductor current The waveform diagram. During system startup, the load resistance... With a load resistance of 30 Ω, the system is stable and outputs 24 V. At t=0.1 s, the load resistance is changed. With a resistance of 15 Ω, the inductor current rises to approximately 3.2 A, and the voltage quickly stabilizes at 24 V, demonstrating the zero steady-state error capability of the outer-loop PI control. At t=0.3 s, the load resistance is changed... With an inductance of 50 Ω, the inductor current decreases, and the overshoot is within a suitable range, demonstrating that the Boost converter controlled by this method has strong robustness and can effectively suppress oscillations.

Claims

1. A robust switching control method for a DC-DC boost converter with a wide load range, characterized in that, The topology of the DC-DC boost converter is as follows: DC power supply The positive terminal is connected to one end of the energy storage inductor L, and the other end of the energy storage inductor L is connected to the diode. The positive electrode and the power MOSFET power switch Drain of the diode The negative terminal is connected to one end of the load resistor R and one end of the filter capacitor C, while the other end of the load resistor R, the other end of the filter capacitor C, and the source of the power MOSFET are connected to the DC power supply. The negative terminal of the diode; negative terminal to DC power supply The voltage between the negative terminals is the output voltage. The current flowing through the energy storage inductor is , The positive direction is from the positive terminal of the DC power supply to the inductor; power MOSFET power switching transistor The gate of the power MOSFET receives the PWM signal, which controls the power MOSFET power switch. The on / off state controls the output voltage. Size; The DC-DC boost converter adopts dual closed-loop control. The outer loop is a voltage control loop, which uses PI control, and the inner loop is a current control loop, which uses switching control. The outer loop is given by a voltage reference signal. Output voltage As the voltage feedback signal, the output of the outer loop controller PI is , The current reference signal and voltage reference signal are for the inner loop controller. This is another input signal to the inner current loop switching controller; the feedback signal of the switching controller is the inductor current. and load voltage Switch the on / off state of the controller output. Used to control power switching transistors The switching on and off of the circuit achieves stable output voltage.

2. The robust switching control method for a DC-DC boost converter with a wide load range according to claim 1, characterized in that, The steps for establishing a control system for a DC-DC boost converter are as follows: Step 1: Establish the state-space expression of the DC-DC boost converter, i.e., the state-space expression of the switching system; Set the state vector ; power switching transistors When shutting down, the corresponding switching system subsystem The state-space expression is: （4）； make , ,say For switching system subsystems The coefficient matrix, For switching system subsystems The input matrix; power switching transistors When the switch is activated, the corresponding subsystem of the switching system... The state-space expression is: （5）； make , ,say For switching system subsystems The coefficient matrix, For switching system subsystems The input matrix; Step 2: Solve for the ideal duty cycle Construct the maximum load average matrix and minimum load average matrix ; Step 3: Construct robust stability linear matrix inequality constraints and solve for the robust positive definite symmetric matrix. ; Step 4: Based on the minimum Lyapunov energy function Based on the attenuation principle, a switching control strategy for the inner current loop is designed. Construct the dynamic reference state vector as follows Define the real-time state error vector Construct the Lyapunov energy function Based on the robust positive definite symmetric matrix obtained in step three and dynamic reference state vector Calculate the corresponding subsystems of the switching system respectively. and subsystem The derivative of the Lyapunov energy function and Choose the derivative of the Lyapunov energy function. The switch state with the smallest value is taken as the switch state at the current moment. Used to control power switching transistors To turn on or off; Step 5: Design the PI parameters for the voltage outer loop controller.

3. The robust switching control method for a DC-DC boost converter with a wide load range according to claim 1, characterized in that, In step two: （6）； In the formula, ; load Can be in the range Internal regulation, and These represent the maximum and minimum allowable loads for normal operation of the boost DC-DC converter, respectively; due to the coefficient matrix and Contains Therefore, the system exhibits time-varying characteristics; when the load is At that time, the corresponding subsystem coefficient matrix The corresponding subsystem coefficient matrix Maximum load average matrix When the load is At that time, the corresponding subsystem coefficient matrix The corresponding subsystem coefficient matrix Minimum load average matrix .

4. The robust switching control method for a DC-DC boost converter with a wide load range according to claim 1, characterized in that, Step 3: Solve for the robust positive definite symmetric matrix The linear matrix inequality constraints are: （7）； in, Represents a 2×2 identity matrix. It is a positive semi-definite weighting matrix used to adjust the convergence speed. , This is the current error weighting coefficient. This is the voltage error weighting coefficient, and and The values ​​of are positively correlated with the reciprocal of the square of the nominal inductor current and the reciprocal of the square of the desired output voltage, respectively, to eliminate the influence of the difference in the dimensions of the state variables. .

5. A robust switching control method for a DC-DC boost converter with a wide load range according to claim 1, characterized in that, The specific implementation method of the inner loop switching law in step four is as follows: The general expression: （8）； Real-time state error vector derivative : （9）； (8) can be simplified to: （10）； Will Substituting into equation (10), we obtain the subsystem. The derivative of the corresponding Lyapunov energy function : （11）； Will Substituting into equation (10), we obtain the subsystem. The derivative of the corresponding Lyapunov energy function : （12）； if , Switching transistor Conductive; if , Switching transistor Turn off. The mathematical expression is: （13）。 6. A robust switching control method for a DC-DC boost converter with a wide load range according to any one of claims 1-5, characterized in that, In step five: Outer loop voltage error signal For voltage error signals Perform PI control, and the output signal of the PI controller , , Represents the proportionality coefficient. Indicates the integral coefficient; proportionality coefficient and integral coefficient Determine using the following formula: ； （20） in, The cutoff frequency of the outer voltage loop is denoted as . For the ideal duty cycle.

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