A fractional order non-singular terminal sliding mode control method and device

Abstract

The application discloses a fractional order non-singular terminal sliding mode control method and device, and collects output voltage and inductance current signals of a DC-DC converter; the collected output voltage and inductance current signals are converted into digital signals through an ADC module; a fractional order non-singular terminal sliding mode control module establishes a mathematical model of the converter system according to the digital signals of the output voltage and the inductance current; a nonlinear disturbance observer is designed according to the mathematical model, and disturbance estimation is carried out by using the nonlinear disturbance observer; a fractional order non-singular terminal sliding mode surface and a control law of the DC-DC converter system are designed, and whether the system is stable is judged according to Lyapunov stability theory; the duty cycle of a DC-DC converter switching driving signal is obtained by solving the control law of the DC-DC converter system, and a driving signal is output to control the on-off of a switching tube of the DC-DC converter. The application effectively alleviates the chattering problem of the sliding mode control output, and reduces the number of sensors required by the converter system.

Description

Technical Field

[0001] This invention relates to the technical field of DC-DC converter applications, and in particular to a fractional-order non-singular terminal sliding mode control method and apparatus. Background Technology

[0002] Currently, DC-DC converters are widely used in DC microgrids, electric vehicles, and other fields. The commonly used control methods for these converters in industry are PI control and PID control. However, these control methods have poor robustness and suffer from slow dynamic response and large output voltage errors.

[0003] Sliding mode control is a robust nonlinear control method with advantages such as simple algorithms and insensitivity to system parameters and external disturbances. Therefore, its application in industrial control is becoming increasingly widespread. Traditional sliding mode control typically uses a linear sliding surface, which can only asymptotically converge the state variables of the converter system but cannot reach equilibrium within a finite time. Furthermore, due to the inherent characteristics of sliding mode control, chattering can occur in the converter system's output, degrading the control performance and potentially causing hardware damage. Summary of the Invention

[0004] The primary objective of this invention is to overcome the shortcomings and deficiencies of the prior art and provide a fractional-order non-singular terminal sliding mode control method that enables the state variables of the converter system to reach equilibrium within a finite time and alleviates the chattering problem of sliding mode control, thereby giving the converter system better dynamic performance and robustness under disturbances such as sudden changes in input voltage and load.

[0005] The second objective of this invention is to provide a fractional-order non-singular terminal sliding mode control device.

[0006] The first objective of this invention is achieved through the following technical solution: a fractional-order non-singular terminal sliding mode control method, applied to a DC-DC converter, requires the configuration of a voltage sampling module, a current sampling module, an ADC module, and a fractional-order non-singular terminal sliding mode control module. The voltage sampling module acquires the output voltage signal of the DC-DC converter, the current sampling module acquires the inductor current signal of the DC-DC converter, the ADC module converts the acquired output voltage and inductor current signals into digital signals, and the fractional-order non-singular terminal sliding mode control module is used to control the on / off state of the switching transistors of the DC-DC converter.

[0007] The specific implementation of the fractional-order non-singular terminal sliding mode control method includes the following steps:

[0008] Step 1: Acquire the output voltage and inductor current signals of the DC-DC converter through the voltage sampling module and the current sampling module respectively, and input the sampled signals into the ADC module;

[0009] Step 2: Convert the acquired output voltage and inductor current signals into digital signals using the ADC module, and input the digital signals into the fractional-order non-singular terminal sliding mode control module;

[0010] Step 3: The fractional-order non-singular terminal sliding mode control module establishes a mathematical model of the converter system based on the digital signals of the output voltage and inductor current;

[0011] Step 4: Design a nonlinear disturbance observer based on the mathematical model of the converter system, and use the nonlinear disturbance observer to estimate the disturbance.

[0012] Step 5: Design a fractional-order non-singular terminal sliding surface based on the disturbance estimate and the mathematical model of the converter system. Design the control law of the DC-DC converter system based on the fractional-order non-singular terminal sliding surface. Then, determine whether the system is stable based on Lyapunov stability theory.

[0013] Step 6: Obtain the duty cycle of the DC-DC converter switch drive signal by solving the control law of the DC-DC converter system, and output the drive signal to control the switching of the DC-DC converter.

[0014] Furthermore, in step 3, the mathematical model of the converter system is established as follows:

[0015]

[0016] In the formula, i L and v C The inductor current and output voltage of the converter are represented by ; P represents the power value of the constant power load; A1, A2, B1, B2, C1, C2 are the converter system parameters respectively; L represents the inductance value, and C represents the converter capacitance value; the total energy x1 of the converter system is expressed as: Taking the derivative of x1 gives the derivative of x1. Then, state variable x2 and disturbance d1 are introduced; the derivative of x2 is obtained by taking the derivative of x2. By introducing the process control law v and the disturbance d2, the mathematical model of the converter system can be transformed into...

[0017] Furthermore, in step 4, the nonlinear disturbance observer is designed as follows: and In the formula, z1 and z2 represent the observer state variables. and k1 and k2 represent the derivatives of the observer's state variables, respectively, and the observer's gain coefficients. and This represents the observer's disturbance estimate; the disturbance estimation error is defined as... and Represented as

[0018] Furthermore, in step 5, the control law design for the fractional-order non-singular terminal sliding surface and the DC-DC converter is as follows:

[0019] Define the system error variable as Represented as the total energy reference value of the boost converter, virtual control law Represented as Where c1 is the error coefficient; design a fractional-order non-singular terminal sliding surface. in, It is the α-order fractional derivative of RL defined with initial time t0 and t as the time variable, 0 < α < 1; λ and ρ are control coefficients, λ = (g / h), where g and h represent positive odd numbers, 1 < λ < 2; sgn(x) is the sign function, and x is the independent variable of the sign function; sgn(x) is a function with x as the independent variable. λ It can be equivalent to |x| λ sgn(x); Based on the designed fractional-order nonsingular terminal sliding surface, the control law v is designed as follows: in, Total energy reference value The second derivative, For disturbance estimates The derivative of Let be the derivative of the error variable value e1, and m1 and m2 be the control parameters. The initial time is t0, and the fractional derivative of the α+1th order RL is defined with t as the time variable. Finally, the stability of the system is determined using Lyapunov stability theory. If the system is stable, the next step is performed; otherwise, an error is returned.

[0020] The second objective of this invention is achieved through the following technical solution: a fractional-order non-singular terminal sliding mode control device for implementing the aforementioned fractional-order non-singular terminal sliding mode control method. This device comprises a voltage sampling module, a current sampling module, an ADC module, and a fractional-order non-singular terminal sliding mode control module. The voltage sampling module is connected to both ends of the output capacitor of the DC-DC converter. The current sampling module is connected in series with the inductor of the DC-DC converter. The input terminal of the ADC module is connected to the output terminals of both the voltage sampling module and the current sampling module. The output terminal of the ADC module is connected to the fractional-order non-singular terminal sliding mode control module. The input terminal of the control module is connected; the other end of the fractional-order non-singular terminal sliding mode control module is connected to the switching transistor drive terminal of the DC-DC converter; the voltage sampling module and the current sampling module sample the output voltage and inductor current respectively, and input the sampled signals to the ADC module; the ADC module converts the input sampled signals into digital signals and inputs them to the fractional-order non-singular terminal sliding mode control module; the fractional-order non-singular terminal sliding mode control module solves the control law to obtain the switching duty cycle, thereby controlling the switching transistor of the DC-DC converter to turn off, thus realizing the control of the DC-DC converter.

[0021] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0022] 1. Traditional sliding mode control methods generally select linear sliding surfaces, while this invention selects a nonlinear fractional-order nonsingular terminal sliding surface, which enables the state variables of the converter system to reach equilibrium in a finite time.

[0023] 2. This invention utilizes a nonlinear disturbance observer to estimate the output power of the converter. Therefore, it only needs to detect the inductor current and output voltage of the DC-DC converter, reducing the number of sensors used, which is beneficial for reducing the size of the converter and lowering costs.

[0024] 3. This invention also utilizes fractional derivative theory to suppress chattering in sliding mode control, thereby giving the converter system better dynamic performance and robustness. Attached Figure Description

[0025] Figure 1 This is a schematic diagram of the circuit implementation of the present invention.

[0026] Figure 2 This is a flowchart of the implementation method of the present invention.

[0027] Figure 3 The circuit diagram shows a specific system device for implementing this invention.

[0028] Figure 4 This is a schematic diagram of the output voltage of the present invention when the input voltage changes.

[0029] Figure 5 This is a schematic diagram of the output voltage of the present invention when the constant power load changes.

[0030] Figure 6 This is a schematic diagram comparing the chattering amplitude of the sliding mold surface under different control methods according to the present invention. Detailed Implementation

[0031] The present invention will be further described in detail below with reference to the embodiments and accompanying drawings, but the embodiments of the present invention are not limited thereto.

[0032] like Figure 1 The diagram shown is a simplified illustration of the fractional-order non-singular terminal sliding mode control device provided in this embodiment. The device consists of a voltage sampling module, a current sampling module, an ADC module, and a fractional-order non-singular terminal sliding mode control module. Figure 3 A detailed circuit diagram of the device is provided. The boost converter circuit with a fractional-order non-singular terminal sliding mode control device includes an input DC power supply, an energy storage inductor L, an N-channel MOSFET, a diode D, an output capacitor C, and loads including a constant power load CPL and a resistive load R. The control circuit consists of a sampling module, an ADC module, and a fractional-order non-singular terminal sliding mode control module. The main circuit is specifically constructed as follows: the positive terminal of the input power supply is connected to one end of the energy storage inductor L, and the other end of the inductor L is connected to the anode of the power diode and the drain of the N-channel MOSFET. The cathode of the power diode is connected to the positive terminal of the output capacitor C and one end of the output load. The other end of the output load is connected to the negative terminal of the output capacitor, the source of the N-channel MOSFET, and the negative terminal of the input power supply. The voltage sampling module is connected to both ends of the output capacitor C. The current sampling module is connected in series with the energy storage inductor L. The input terminal of the ADC module is connected to the output terminals of the voltage sampling module and the current sampling module, respectively. The output terminal of the ADC module is connected to the input terminal of the fractional-order non-singular terminal sliding mode control module. The other end of the fractional-order non-singular terminal sliding mode control module is connected to the switching transistor drive terminal of the boost converter. The voltage sampling module and the current sampling module sample the output voltage and inductor current of the boost converter, respectively, and input the sampled signals to the ADC module. The ADC module converts the input sampled analog signals into digital signals and inputs them to the fractional-order non-singular terminal sliding mode control module. The fractional-order non-singular terminal sliding mode control module solves the control law to obtain the duty cycle of the boost converter's switching drive signal and generates a drive signal to control the switching transistors of the DC-DC converter.

[0033] like Figure 2 As shown, this embodiment provides a fractional-order nonsingular terminal sliding mode control method, implemented based on the above device, and the specific implementation is as follows:

[0034] Step 1: Collect the output voltage and inductor current signals of the boost converter through the voltage sampling module and the current sampling module respectively, and input the sampled signals into the ADC module.

[0035] Step 2: The acquired output voltage and inductor current signals are converted into digital signals by the ADC module and then input into the fractional-order non-singular terminal sliding mode control module.

[0036] Step 3: Establish the mathematical model of the converter system based on the output voltage and inductor current signals, as follows:

[0037]

[0038] Among them, i L and v C This represents the inductor current and output voltage of the converter; P represents the power value of the constant power load; V in This is the input voltage. q is the duty cycle of the switch drive signal, L represents the inductance value, C represents the converter capacitance value, and R represents the resistance value. The total energy of the converter system can be expressed as:

[0039]

[0040] Differentiating the above equation, we get:

[0041]

[0042] Introducing the state variable x2 and the uncertain disturbance d1, the original equation becomes:

[0043]

[0044]

[0045] R0 represents the nominal resistance value. Taking the derivative with respect to the state variable x2, we get:

[0046]

[0047] The process control law v and the uncertain disturbance d2 can be rewritten as:

[0048]

[0049]

[0050] Therefore, the mathematical model of the boost converter system is transformed as follows:

[0051]

[0052] Step 4: Design a nonlinear disturbance observer based on the mathematical model of the converter system, and use the nonlinear disturbance observer to estimate the disturbance.

[0053] The nonlinear disturbance observer is designed as follows:

[0054] and

[0055] Where z1 and z2 represent the observer state variables, and k1 and k2 represent the observer's state variable derivatives, and k1 and k2 represent the observer's gain coefficients. and This represents the disturbance estimate output by the observer.

[0056] Define the system error variable as:

[0057]

[0058] in, Represented as the total energy reference value of the boost converter, virtual control law Represented as:

[0059]

[0060]

[0061] Where c1 is the error coefficient, V ref The desired output voltage value of the converter system. Total energy reference value The derivative of This represents the disturbance estimate output by the observer.

[0062] Step 5: Design a fractional-order non-singular terminal sliding surface based on the disturbance estimate and the mathematical model of the converter system. Design the control law of the DC-DC converter system based on the fractional-order non-singular terminal sliding surface. Then, determine whether the system is stable based on Lyapunov stability theory.

[0063] A fractional-order nonsingular terminal sliding surface can be designed as follows:

[0064]

[0065] in, It is the α-order fractional derivative of RL defined with initial time t0 and t as the time variable, 0 < α < 1; λ and ρ are control coefficients, λ = (g / h), where g and h represent positive odd numbers, 1 < λ < 2; sgn(x) is the sign function, and x is the independent variable of the sign function; sgn(x) is a function with x as the independent variable. λ It can be equivalent to |x| λsgn(x); Based on the designed fractional-order nonsingular terminal sliding surface, the control law v can be designed as:

[0066]

[0067] in, Total energy reference value The second derivative, For disturbance estimates The derivative of Let be the derivative of the error variable value e1, and m1 and m2 be the control parameters. It is the fractional derivative of RL of order α+1 with initial time t0 and time variable t; the Lyapunov function is chosen:

[0068]

[0069]

[0070] Differentiating the Lyapunov function and substituting it into the above equation, we get:

[0071]

[0072] in, Estimating the error for the observer It has an upper bound. When m1≥0, When, because 1 < λ < 2, It can be concluded that Based on Lyapunov stability theory, it is proved that the proposed fractional-order nonsingular terminal sliding mode control module is stable.

[0073] Step 6, using the control law v and formula designed above. The duty cycle q of the switch drive signal is obtained by solving, and the output drive signal controls the on / off state of the boost converter switch.

[0074] To verify the effectiveness of the proposed method, a simulation experiment was conducted on the application of fractional-order non-singular terminal sliding mode control in a boost converter. The initial simulation conditions were L = 1mH, C = 1000uF, and V... in =12V, V ref =25V, while the constant power load power is 7.8W. Control module parameters m1=4500, m2=1000, ρ=2000, λ=1.66, order α=0.5. Observer coefficients k1=500, k2=300.

[0075] Figure 4 It is when the input voltage is at 0.2 seconds that V in =12V suddenly increases to V in =18V, from V in 0.3 secondsin =18V suddenly dropped to V in The schematic diagram of the 9V output voltage shows that the output voltage of the boost converter under both the backstepping sliding mode control module and the fractional-order non-singular terminal sliding mode control module quickly stabilizes and reaches the desired value after the input voltage increases or decreases. Compared with existing backstepping sliding mode control technology, the fractional-order non-singular terminal sliding mode control method has the advantages of small overshoot, short recovery time, and small steady-state error.

[0076] Figure 5 This diagram illustrates the output voltage when a constant power load suddenly increases from 7.8W to 14.7W in 0.5 seconds, and then decreases from 14.7W to 10.8W in 0.6 seconds. Simulation results show that the converter system output voltage under both control methods can quickly stabilize and reach the desired value after a constant power load change. It is evident that the control method of this invention has smaller overshoot, shorter recovery time, and smaller steady-state error compared to the backstepping sliding mode control method.

[0077] Figure 6 This diagram illustrates the chattering on the sliding mode surface of the converter system under two control methods during steady-state operation. It is readily apparent that the chattering amplitude of the fractional-order non-singular terminal sliding mode control method proposed in this invention is significantly smaller than that of the existing backstepping sliding mode control method. This demonstrates that fractional-order calculus theory can effectively alleviate the chattering problem in sliding mode control, further improving the robustness of the converter system. The control method designed in this invention exhibits good control performance for DC-DC converter systems, ensuring that the output voltage remains stable at the desired value under input voltage or load disturbances.

[0078] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A fractional-order non-singular terminal sliding mode control method, applied to a DC-DC converter, characterized in that, It needs to be configured with a voltage sampling module, a current sampling module, an ADC module, and a fractional-order non-singular terminal sliding mode control module. The voltage sampling module collects the output voltage signal of the DC-DC converter, the current sampling module collects the inductor current signal of the DC-DC converter, the ADC module converts the collected output voltage and inductor current signals into digital signals, and the fractional-order non-singular terminal sliding mode control module is used to control the on / off state of the DC-DC converter's switching transistors. The specific implementation of the fractional-order non-singular terminal sliding mode control method includes the following steps: Step 1: Acquire the output voltage and inductor current signals of the DC-DC converter through the voltage sampling module and the current sampling module respectively, and input the sampled signals into the ADC module; Step 2: Convert the acquired output voltage and inductor current signals into digital signals using the ADC module, and input the digital signals into the fractional-order non-singular terminal sliding mode control module; Step 3: The fractional-order non-singular terminal sliding mode control module establishes a mathematical model of the converter system based on the digital signals of the output voltage and inductor current; Step 4: Design a nonlinear disturbance observer based on the mathematical model of the converter system, and use the nonlinear disturbance observer to estimate the disturbance. Step 5: Design a fractional-order non-singular terminal sliding surface based on the disturbance estimate and the mathematical model of the converter system. Design the control law of the DC-DC converter system based on the fractional-order non-singular terminal sliding surface. Then, determine whether the system is stable based on Lyapunov stability theory. The control law design for the fractional-order nonsingular terminal sliding mode surface and the DC-DC converter is as follows: Define the system error variable as x1 is the total energy of the converter system, and x2 is the state variable. Represented as the total energy reference value of the boost converter, virtual control law Represented as Where c1 is the error coefficient; design fractional-order nonsingular terminal sliding surfaces. ;in, The initial time is , with t as the time variable The fractional derivative is defined by the order RL. ; , For control coefficients, g and h represent positive odd numbers. ; It is a sign function, where x is the independent variable of the sign function; a function with x as its independent variable. Equivalent to Based on the designed fractional-order nonsingular terminal sliding mode surface, the control law... Designed for ;in, This represents the observer's perturbation estimate. Total energy reference value The second derivative, For disturbance estimates The derivative, For error variable values The derivative of , where m1 and m2 are control parameters. The initial time is , with t as the time variable The fractional derivative is defined using the RL order. Finally, Lyapunov stability theory is used to determine whether the system is stable. If the system is stable, the process proceeds to the next step; otherwise, an error is returned. Step 6: Obtain the duty cycle of the DC-DC converter switch drive signal by solving the control law of the DC-DC converter system, and output the drive signal to control the switching transistors of the DC-DC converter to turn on and off.

2. The fractional-order nonsingular terminal sliding mode control method according to claim 1, characterized in that, In step 3, the mathematical model of the converter system is established as follows: ； In the formula, i L and v C The inductor current and output voltage of the converter are represented by ; P represents the power value of the constant power load; A1, A2, B1, B2, C1, C2 are the converter system parameters respectively; L represents the inductance value, and C represents the converter capacitance value; the total energy x1 of the converter system is expressed as: Taking the derivative of x1, we get the derivative of x1. Then, state variable x2 and disturbance d1 are introduced; the derivative of x2 is obtained by taking the derivative of x2. By introducing the process control law v and the disturbance d2, the mathematical model of the converter system can be transformed into... .

3. The fractional-order nonsingular terminal sliding mode control method according to claim 2, characterized in that, In step 4, the nonlinear disturbance observer is designed as follows: and In the formula, z1 and z2 represent the observer state variables. and k1 and k2 represent the observer's state variable derivatives, and k1 and k2 represent the observer's gain coefficients. and This represents the observer's disturbance estimate; the disturbance estimation error is defined as... and , represented as and .

4. A fractional-order nonsingular terminal sliding mode control device, characterized in that: To implement the fractional-order non-singular terminal sliding mode control method according to any one of claims 1-3, the device comprises a voltage sampling module, a current sampling module, an ADC module, and a fractional-order non-singular terminal sliding mode control module; the voltage sampling module is connected to both ends of the output capacitor of the DC-DC converter; the current sampling module is connected in series with the inductor of the DC-DC converter; the input terminal of the ADC module is connected to the output terminals of the voltage sampling module and the current sampling module respectively; the output terminal of the ADC module is connected to the input terminal of the fractional-order non-singular terminal sliding mode control module; the other end of the fractional-order non-singular terminal sliding mode control module is connected to the switching transistor driving terminal of the DC-DC converter; the voltage sampling module and the current sampling module sample the output voltage and the inductor current respectively, and input the sampled signals to the ADC module; the ADC module converts the input sampled signals into digital signals and inputs them to the fractional-order non-singular terminal sliding mode control module. The fractional-order non-singular terminal sliding mode control module solves the control law to obtain the switch duty cycle, thereby controlling the switching transistors of the DC-DC converter to turn off, thus realizing the control of the DC-DC converter.

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