Fractional order nonsingular terminal sliding mode control method for quasi-z-source rectifier

Abstract

This invention discloses a single-phase calibrator Z The fractional-order non-singular terminal sliding mode control method for the quasi-Z source rectifier includes employing voltage and current dual closed-loop PI control on the AC side of the quasi-Z source rectifier to obtain a sinusoidal modulation wave. On the DC side, a fractional-order term is introduced into the sliding surface to obtain the equivalent control law of the fractional-order non-singular terminal sliding mode controller. The global control law is combined with the sinusoidal modulation wave, and the generated drive signal controls the rectifier bridge and the quasi-Z source rectifier. Z The source network uses switching transistors to achieve the control objective. This invention's fractional-order non-singular terminal sliding mode control enables the system to converge in a finite time, and compared to single-phase quasi-singular... Z The integer-order non-singular terminal sliding mode control of the source rectifier reduces the distortion rate of the input AC current, reduces the fluctuation of the output DC voltage, improves the dynamic response speed of the output DC voltage, has higher control accuracy, and improves the dynamic and static performance of the system.

Description

Technical Field

[0001] This invention relates to the field of power electronics technology, and specifically discloses a fractional-order non-singular terminal sliding mode control method applicable to single-phase quasi-Z source rectifiers. Background Technology

[0002] With the development of power electronics technology, PWM rectifiers have been widely used in power systems, electric drives, and other fields. Among them, quasi-Z-source rectifiers, compared to traditional voltage-source or current-source rectifiers, have advantages such as simple topology, the ability to boost or buck voltage, shoot-through capability, and high reliability, showing broad application prospects and currently being used in on-board integrated chargers. For the DC side control of single-phase quasi-Z-source rectifiers, a dual-closed-loop PI control strategy with an outer voltage loop and an inner current loop is generally adopted. However, PI control suffers from drawbacks such as large overshoot, slow response speed, and poor dynamic performance, making it difficult to meet the control requirements of the rectifier. In recent years, sliding mode control has been widely used in PWM rectifiers. Sliding mode control features simple algorithms, fast response speed, good dynamic performance, and good robustness. However, the essence of sliding mode control is discontinuous control, which can cause chattering in the converter system output, and it still has shortcomings in terms of system dynamic performance and control accuracy.

[0003] With the development of fractional calculus theory, fractional modeling and control have been widely applied in the field of power electronics. Based on this, this invention discloses a fractional non-singular terminal sliding mode control method for a single-phase quasi-Z source rectifier, which introduces fractional calculus operators into traditional sliding mode control, enabling the system to have better dynamic performance and robustness. Summary of the Invention

[0004] To address the shortcomings of the aforementioned background technology, this invention provides a fractional-order non-singular terminal sliding mode control method suitable for quasi-Z source rectifiers. This method enables unity power factor operation on the AC side of a single-phase quasi-Z source rectifier, rapid convergence and tracking control of the DC voltage on the output side, and improves the dynamic performance of the rectifier and the system control accuracy.

[0005] To achieve the above-mentioned objectives, the present invention employs the following technical solution:

[0006] A fractional-order non-singular terminal sliding mode control method for a quasi-Z-source rectifier employs dual closed-loop PI control of voltage and current on the AC side and fractional-order non-singular terminal sliding mode control and sinusoidal pulse width modulation control on the DC side. The method includes the following steps:

[0007] Step 1: Establish a DC-side model of a single-phase quasi-Z-source controllable rectifier to obtain the state equations and the voltage state equations of the output capacitor.

[0008] Step 2: Select the state variables for sliding mode control, design the sliding surface, and obtain the equivalent control law of sliding mode control by making its derivative zero; design the reaching law, design the sliding controller using the exponential reaching law, and combine the reaching law with the equivalent control law to obtain the global control law of sliding mode control.

[0009] Step 3: Introduce fractional-order calculus operators and add fractional-order terms to the sliding surface to obtain a fractional-order non-singular terminal sliding surface; design a power-order reaching law and combine the control law with the reaching law to obtain the global control law for fractional-order non-singular terminal sliding control, i.e., the direct-through duty cycle D of the single-phase quasi-Z source rectifier.

[0010] Step 4: Based on the direct duty cycle D, use a sinusoidal pulse width modulation algorithm to output a drive signal to control the on / off state of the five switching transistors of the single-phase quasi-Z source rectifier.

[0011] Preferably, in step 1, the shoot-through and non-shoot-through states of the rectifier are analyzed, and the inductor current and capacitor voltage in the Z-source network are used as state variables to establish state equations and voltage state equations for the output capacitor. The switching function is introduced into the state equations. When the switching function is 0 or 1, the single-phase quasi-Z-source rectifier is in different circuit states.

[0012] As a preferred embodiment, the state equation of the single-phase quasi-Z source rectifier is expressed as:

[0013] X = A + Bu

[0014] in,

[0015] Where A and B are the coefficients of the state equation; L is the inductance of the quasi-Z source network, and C is the capacitance of the quasi-Z source network; i pn is the output current of the rectifier bridge; u is the switching function. When u = 1, the single-phase quasi-Z source rectifier is in the shoot-through state, and when u = 0, the single-phase quasi-Z source rectifier is in the non-shoot-through state.

[0016] The state equation for the output capacitor voltage is expressed as:

[0017]

[0018] Among them, C o For the output capacitor, R o For load.

[0019] Preferably, in step 2, the error between the actual value and the reference value of the quasi-Z source network inductor current and the output DC voltage, and the integral of the sum of the two errors, are selected as the sliding mode control state variables, expressed as:

[0020]

[0021] In the formula, iL2 u Co These are the instantaneous current values ​​of the quasi-Z source network inductor L2 and the instantaneous output DC voltage values, respectively. L2ref u Coref These are the reference values ​​for the current and the output DC voltage of the quasi-Z source network inductor L2, respectively.

[0022] Preferably, in step 2, the linear combination function of the state variables is used as the sliding surface, expressed as:

[0023] s=α1x1+α2x2+α3x3=J T X

[0024] Where J = [α1, α2, α3] T The sliding mode coefficient vector;

[0025] Substituting the state equation containing the switching function into the time derivative of the sliding mode function, and setting the derivative to zero, yields the equivalent control law of sliding mode control. The time derivative of the sliding mode function is expressed as:

[0026]

[0027] The exponential law of convergence is expressed as:

[0028]

[0029] In the formula, β1 and β2 are adjustable control parameters, β1 is the coefficient of the exponential approach term, β2 is the coefficient of the switching function, and β1 and β2 > 0, and sign is the sign function.

[0030] As a preferred approach, combining the state equation, the time derivative of the sliding mode function, and the exponential reaching law, the global control law for sliding mode control is obtained, i.e., the direct-current duty cycle D of the single-phase quasi-Z source rectifier is:

[0031]

[0032] Where k1, k2, k3, and k4 are the fixed gain parameters of the sliding mode controller, and R0 is the output resistance. For output voltage, Let C1 be the instantaneous value of the voltage across capacitor C1 in the Z-source network. Let be the instantaneous value of the voltage across capacitor C2 in the Z-source network. For the current of the quasi-Z source network inductor L2,

[0033] Preferably, in step 3, the fractional-order non-singular terminal sliding surface is represented as:

[0034] s=α1x1+α2x2+α3x3+α4D α x3

[0035] The time derivative of the sliding mode function is expressed as:

[0036]

[0037] Where α⁴ is the sliding mode coefficient of the fractional calculus term, and D α For fractional calculus operators, use the caputo definition;

[0038] The power-to-approach law is expressed as:

[0039]

[0040] Wherein, sig(s) γ =|s γ sign(s)

[0041] As a preferred approach, combining the state equation, the time derivative of the sliding mode function, and the power-law approach, the global control law for fractional-order non-singular terminal sliding mode control is obtained, namely, the shoot-through duty cycle D of the single-phase quasi-Z-source rectifier is:

[0042]

[0043] Preferably, in step 4, for the AC side of the single-phase quasi-Z source rectifier, a dual closed-loop control of voltage outer loop and current inner loop is adopted to sample the output voltage of the rectifier bridge. The sampled value is compared with the reference value, and the error is obtained through the PI controller to obtain the amplitude reference value of the AC side input current. The amplitude reference value of the current is compared with the sampled value of the current, and the error is obtained through the PI controller to obtain the sinusoidal modulation wave SPWM of the rectifier bridge. The sinusoidal modulation wave is compared with the triangular wave, and a traditional SPWM wave is generated by unipolar frequency doubling sinusoidal pulse width modulation. Combined with the direct duty cycle D of the single-phase quasi-Z source rectifier, the direct zero vector signal is superimposed with the traditional SPWM wave to obtain the SPWM modulation wave with the direct zero vector added, which is the switching signal of the quasi-Z source rectifier, and the switching transistor in the control circuit is turned off.

[0044] Preferably, the reference value for the amplitude of the AC input current is expressed as follows:

[0045] I gmref =k p (u pnref -u pn )+k i ∫(u pnref -u pn )dt

[0046] In the formula, u pn This is the reference value for the rectifier bridge output voltage; the subscript ref indicates the reference value.

[0047] The sinusoidal modulation wave SPWM of the rectifier bridge is expressed by the formula:

[0048] u in =k p (i gmref -i g )+k i ∫(i gmref -i g )dt

[0049] In the formula, i g For the AC input current, k p k is the proportional coefficient in a PI controller. i This represents the integral coefficient in the PI controller.

[0050] The present invention, by adopting the above technical solution, has the following beneficial effects:

[0051] This invention proposes a fractional-order non-singular terminal sliding mode control method for a single-phase quasi-Z-source rectifier, which can achieve the control objective of stable DC output voltage while maintaining the rectifier's power factor. Compared with traditional integer-order non-singular terminal sliding mode control, the method disclosed in this invention offers higher control freedom and higher control precision. Under the same conditions, this invention reduces the distortion rate of the AC input current of the single-phase quasi-Z-source rectifier, improves power quality, results in a more stable DC output voltage, reduces voltage fluctuations, and enhances dynamic response. When the system receives external interference, the rectifier can quickly adjust to achieve stable DC output voltage, thus improving the rectifier's dynamic performance and robustness. Attached Figure Description

[0052] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings of the embodiments will be briefly described below.

[0053] Figure 1 This is a schematic diagram of the topology of a single-phase quasi-Z source rectifier in an embodiment of the present invention;

[0054] Figures 2(a)-(b) are equivalent circuit diagrams of the single-phase quasi-Z source rectifier in different states in the embodiments of the present invention;

[0055] Figure 3 This is a control block diagram of a single-phase quasi-Z source rectifier in an embodiment of the present invention;

[0056] Figure 4 This is a trend diagram showing the changes in the THD of the input AC current of the single-phase quasi-Z source rectifier under fractional-order non-singular terminal sliding mode control in an embodiment of the present invention, as well as the changes in the order of the fractional-order term and the switching frequency in the fractional-order non-singular terminal sliding mode control.

[0057] Figure 5(a) shows the voltage and current waveforms under integer-order non-singular terminal sliding mode control in an embodiment of the present invention.

[0058] Figure 5(b) shows the voltage and current waveforms under fractional-order non-singular terminal sliding mode control in an embodiment of the present invention.

[0059] Figure 5(c) is the THD diagram of the input-side AC circuit under sliding mode control of integer-order non-singular terminal in an embodiment of the present invention;

[0060] Figure 5(d) is the THD diagram of the input-side AC circuit under fractional-order non-singular terminal sliding mode control in an embodiment of the present invention;

[0061] Figure 6(a) shows the trend of THD with input voltage under integer-order non-singular terminal sliding mode control and fractional-order non-singular terminal sliding mode control in the embodiments of the present invention.

[0062] Figure 6(b) shows the trend of THD with output power under integer-order non-singular terminal sliding mode control and fractional-order non-singular terminal sliding mode control in the embodiments of the present invention.

[0063] Figure 7(a) is a comparison of the simulation waveforms of the output voltage change of a single-phase quasi-Z source rectifier under integer-order non-singular terminal sliding mode control in an embodiment of the present invention when the given output voltage changes.

[0064] Figure 7(b) is a waveform diagram of the output DC voltage under fractional-order non-singular terminal sliding mode control in an embodiment of the present invention.

[0065] Explanation of the labels in the figure: NTSMC is integer-order non-singular terminal sliding mode control, and FONTSMC is fractional-order non-singular terminal sliding mode control. Detailed Implementation

[0066] The technical solution of the present invention will now be described in detail with reference to the accompanying drawings.

[0067] This invention proposes a fractional-order non-singular terminal sliding mode control method for a single-phase quasi-Z-source rectifier, which includes using voltage and current dual closed-loop PI control on the AC side, fractional-order non-singular terminal sliding mode control on the DC side, and sinusoidal pulse width modulation to control the single-phase quasi-Z-source rectifier, thereby achieving unity power factor operation on the AC side and stable output and fast response of the DC voltage on the output side of the single-phase quasi-Z-source rectifier.

[0068] Specifically, it includes:

[0069] Step 1: Based on the topology of the single-phase quasi-Z-source rectifier, analyze the rectifier's two operating states: shoot-through and non-shoot-through. Select the inductor current and capacitor voltage in the quasi-Z-source network as state variables to obtain the state equations for different states, and write the voltage state equation for the output capacitor. Furthermore, introduce the switching function into the state equations; a switching function of 0 or 1 corresponds to different circuit states of the single-phase quasi-Z-source rectifier.

[0070] Reference Figure 1 This is a schematic diagram of the topology of a single-phase quasi-Z-source rectifier in an embodiment of the present invention, including an input-side AC power supply and filter inductor, a rectifier bridge, a quasi-Z-source network, and an output-side filter capacitor and load. Compared with traditional voltage source or current source rectifiers, the single-phase quasi-Z-source rectifier allows the bridge arm to shoot through for a short time, has high circuit reliability, and can realize voltage step-up and step-down transformations.

[0071] The single-phase quasi-Z-source controllable rectifier includes an AC power supply ug, an inductor Lg, a controllable rectifier H-bridge, a Z-source network circuit, an output capacitor C0, and an output resistor R0. The controllable rectifier H-bridge is composed of switching transistors S1, S2, S3, and S4, and diodes D1, D2, D3, and D4. The Z-source network circuit is composed of inductors L1 and L2, capacitors C1 and C2, and a switching transistor S5. One output terminal of the AC power supply is connected to one end of inductor Lg. The other end of inductor Lg is connected to the source of switching transistor S1, the drain of switching transistor S2, the anode of diode D1, and the cathode of diode D2. The other output terminal of the AC power supply is connected to the source of switching transistor S3, the drain of switching transistor S4, the anode of diode D3, and the cathode of diode D4. The drains of switching transistors S1 and S3, the cathodes of diodes D1 and D3 are connected to one end of capacitor C1 and one end of inductor L1. The other end of inductor L1 is connected to one end of capacitor C2 and the drain of switching transistor S5. The other end of capacitor C2 is connected to one end of output capacitor C0, one end of output resistor R0, the source of switching transistors S2 and S4, the anode of diode D2, and the anode of diode D4. The other end of capacitor C1 is connected to the source of switching transistor S7 and one end of inductor L2. The other end of inductor L2 is connected to the other end of output capacitor C0 and the other end of output resistor R0.

[0072] S5 is the power switch for the quasi-Z source, and S1-S4 are the four power switches for the controllable rectifier H-bridge. When S5 is off, the rectifier operates in a shoot-through state; when S5 is on, the rectifier operates in a non-shoot-through state.

[0073] Referring to Figures 2(a) and 2(b), the two states of the single-phase quasi-Z source rectifier in the embodiment of the present invention are: shoot-through state and non-shoot-through state. As shown in Figure 2(a), the circuit is in the shoot-through state, at which time the two switches on the same bridge arm of the rectifier bridge are simultaneously turned on, and switch S5 in the quasi-Z source network is turned off.

[0074] Choosing the inductor current and capacitor voltage of the quasi-Z source network as state variables, the state-space equations are as follows:

[0075]

[0076] Where L1 and L2 are the inductors in the quasi-Z source network, and C1 and C2 are the capacitors in the quasi-Z source network, C o This is the capacitor on the output side.

[0077] As shown in Figure 2(b), when the circuit is in a non-straight-through state, the two switches on the same arm of the rectifier bridge are not simultaneously turned on, and switch S5 is turned on. The state-space equation is:

[0078]

[0079] Among them, i pn This is the output current of the rectifier bridge.

[0080] Let L1 = L2 = L, C1 = C2 = C, and combining this with the above equation, we can obtain the state equation of the single-phase quasi-Z-source rectifier. Introducing the switching function u, the equation can be written in the following form:

[0081] X = A + Bu

[0082] in,

[0083] Where A and B are the coefficients of the state equation; L is the inductance of the quasi-Z source network, and C is the capacitance of the quasi-Z source network; i pn Let be the output current of the rectifier bridge; u is the switching function. When u = 1, the single-phase quasi-Z-source rectifier is in a shoot-through state, and switch S5 in the quasi-Z-source network is cut off. When u = 0, the single-phase quasi-Z-source rectifier is in a non-shoot-through state, and switch S5 in the quasi-Z-source network is closed. In addition, the state equation for the output capacitor voltage can be obtained as follows:

[0084]

[0085] Among them, R o For the output-side load, the above formula can be written as

[0086]

[0087] Among them, C o For the output capacitor, R oFor load.

[0088] Step 2: Design a sliding mode controller for the single-phase quasi-Z-source rectifier, including sliding surface design and reaching law design. The errors between the actual and reference values ​​of the quasi-Z-source network inductor current and output DC voltage, and the integral of the sum of these errors, are selected as the state variables for sliding mode control. The linear combination function of the state variables is used as the sliding surface. Substituting the state equation containing the switching function into the time derivative of the sliding function, making the derivative zero, yields the equivalent control law for sliding mode control. To ensure the system reaches the sliding surface from the initial state as expected, an exponential reaching law is introduced. Combining the reaching law with the equivalent control law yields the global control law for sliding mode control, i.e., the direct-load duty cycle D of the single-phase quasi-Z-source rectifier. Specifically,

[0089] When designing a sliding mode controller, the current i in the quasi-Z source network inductor L2 is... L2 and output DC voltage u Co The error between the actual value and the reference value, and the integral of the sum of their errors, are used as the state variables of the sliding mode control.

[0090]

[0091] Among them, i L2 u Co These are the instantaneous current values ​​of the quasi-Z source network inductor L2 and the instantaneous output DC voltage values, respectively. L2ref u Coref These are the reference values ​​for the current and the output DC voltage of the quasi-Z source network inductor L2, respectively.

[0092] The designed sliding surface is a linear combination function of the three state variables mentioned above:

[0093] s=α1x1+α2x2+α3x3=J T X

[0094] Where α1, α2, and α3 are the sliding mode coefficients, J = [α1, α2, α3] T The sliding mode coefficient vector;

[0095] When the system state variable is on the sliding surface, the actual value of the state variable under sliding mode control is the same as the reference value, satisfying the sliding mode function s = 0, and the derivative of the sliding mode function is 0. Based on the above equation, the derivative of the sliding mode function with respect to time can be obtained as follows:

[0096]

[0097] Substituting the previously obtained state equation into the above equation, we can obtain...

[0098]

[0099] Setting the derivative to zero, we can obtain the equivalent control law u of the sliding mode controller. eq for

[0100]

[0101] Where k1 and k2 are the fixed gain parameters of the sliding mode controller. u eq For the equivalent control law, satisfying 0 eq <0.5, u eq In fact, it is the direct duty cycle D of a single-phase quasi-Z source rectifier.

[0102] The sliding surface is reachable, as shown in the following process:

[0103] When s < 0 and u = 1, assuming the sliding surface is unreachable, the single-phase quasi-Z-source rectifier will always be in a shoot-through state with a shoot-through duty cycle D = 0.5. When the shoot-through duty cycle D approaches 0.5, the capacitor voltage and inductor current of the quasi-Z-source network approach infinity. This is in conjunction with the designed sliding surface.

[0104]

[0105] It can be seen that if the sliding mode coefficients satisfy α1>0, α2>0, and α3>0, then s>0 is guaranteed.

[0106] When s > 0 and u = 0, assuming the sliding surface is unreachable, the quasi-Z source network switch will always be in the on state, with a shoot-through duty cycle D = 0. The capacitor voltage of the quasi-Z source network equals the output voltage, and the inductor current equals the rectifier bridge output current. Based on the designed sliding surface, if the sliding coefficients satisfy α1 > 0, α2 > 0, and α3 > 0, then s < 0. Based on the above analysis, it can be seen that the designed sliding surface is reachable.

[0107] When the system moves to the sliding surface, its state trajectory must be confined to the sliding surface and move toward zero.

[0108] Let the Lyapunov function of the system be

[0109]

[0110] Then its derivative is

[0111]

[0112] According to Lyapunov's stability theory, in order to guarantee the existence of sliding motion, that is, the system can reach the sliding surface from any initial state in a finite time, the following condition must be met:

[0113]

[0114] ​From the above formula, we can obtain that

[0115]

[0116] When s→0+ and s<0, u s→0+ =0,

[0117]

[0118] When s→0- and s>0, u s→0+ =0.5,

[0119]

[0120] When the sliding mode control parameters of a single-phase quasi-Z source rectifier satisfy the above two equations, sliding mode motion exists.

[0121] Using the equivalent control law u eq Instead of the switching function u, the discontinuous system can be transformed into a continuous sliding mode system, as shown in the following state equations:

[0122]

[0123] Substituting the equivalent control law into the above equation, we can obtain the ideal sliding dynamics of the sliding mode control of a single-phase quasi-Z source rectifier as follows:

[0124] By setting the derivative on the left side of the equation to zero, the steady-state operating point can be obtained as follows:

[0125]

[0126] Linearizing the ideal sliding mode dynamics around the equilibrium point, we get:

[0127]

[0128] Therefore, the characteristic equation of the linearized system can be obtained as follows:

[0129] s 2 -(a 11 +a 22 )s+a 11 a 22 -a 12 a 21 =0

[0130] Based on the stability requirements, we can obtain a. 11 +a 22 <0 and a 11 a 22 -a 12 a 21 When the value is greater than 0, the system is stable.

[0131] Since the initial state of the system is not on the sliding surface s=0, if the control law described above is still used to control the system at s=0, the system's state variables will not converge properly, and the sliding control will not function correctly. Therefore, it is necessary to first design a reaching law to make the system slide as expected, from the initial state to the sliding surface, controlling the sliding speed of the moving point and reducing jitter. After the system reaches the sliding surface, the control law described above is used to make the state variables move along the sliding surface, eventually converging to the equilibrium point.

[0132] To ensure the system slides from its initial state to the sliding surface as expected, an exponential reaching law is used to design the sliding mode controller for the single-phase quasi-Z-source rectifier. This controller controls the sliding speed of the moving point and reduces jitter. The exponential reaching law selected is:

[0133]

[0134] Where β1 and β2 are adjustable control parameters, β1 is the coefficient of the exponential approach term, β2 is the coefficient of the switching function, and β1 and β2 > 0, and sign is the sign function.

[0135] An exponential reaching law is used, with the reaching speed varying exponentially. The values ​​of the adjustable control parameters determine the control performance of the sliding mode controller. The adjustable parameter β1 affects the speed at which the system's motion point approaches s=0. The reaching speed increases with increasing β1 and decreases with decreasing β1, but excessively large values ​​of β1 can affect system convergence and increase jitter. -β2s ensures that when the sliding surface is large, the system state can approach the sliding mode at a relatively high speed. During the exponential reaching process, the speed gradually decreases to 0, reaching a relatively small speed at s=0. Generally, to enable the system's motion point to approach at a faster speed while suppressing jitter, the method of increasing the value of β2 while decreasing the value of β1 is adopted.

[0136] Combining the state equation, the time derivative of the sliding mode function, and the exponential reaching law, the global control law of sliding mode control can be obtained, i.e., the direct-current duty cycle D of the single-phase quasi-Z source rectifier is:

[0137]

[0138] Where k1, k2, k3, and k4 are the fixed gain parameters of the sliding mode controller.

[0139] Since the sliding surface *s* is a function of the system's state variables, the stability of the sliding mode control system of a single-phase quasi-Z-source rectifier can be analyzed by examining the Lyapunov function composed of the sliding surface *s*, based on the Lyapunov function stability theory. Substituting the exponential reaching law into the derivative of the Lyapunov function, we obtain:

[0140]

[0141] According to the stability theorem of Lyapunov functions, the sliding mode control system of a single-phase quasi-Z source rectifier is stable.

[0142] Step 3: In order to make the energy transfer speed of the system slower, reduce the chattering range, and increase the degree of freedom of the system sliding mode control, a fractional-order calculus operator is introduced to add a fractional-order term to the sliding surface to obtain a fractional-order non-singular terminal sliding surface. Combined with the selected power-law approaching law, the global control law of the fractional-order non-singular terminal sliding mode control is obtained, which is the direct duty cycle D of the single-phase quasi-Z source rectifier.

[0143] Fractional calculus theory extends traditional calculus to the fractional domain. Compared to traditional integer calculus theory, fractional calculus theory has more general significance. Introducing fractional calculus operators into sliding mode control yields fractional sliding mode control. Compared to integer sliding mode control, fractional sliding mode control transfers energy more slowly and has a smaller chattering range, thus improving system stability. This embodiment introduces the fractional calculus operator D based on the aforementioned sliding surface. α Add information about the current i of the quasi-Z source network inductor L2. L2 and output DC voltage u Co The fractional term of the integral of the sum of the errors between the actual value and the reference value is used to design the sliding surface expression as follows:

[0144] s=α1x1+α2x2+α3x3+α4D α x3

[0145] Similar to integer-order sliding mode control, when the system state variable is on the sliding surface, the actual value of the state variable in fractional-order sliding mode control is the same as the reference value, satisfying the sliding mode function s = 0, and the derivative of the sliding mode function is 0. Based on the above equation, the derivative of the sliding mode function with respect to time can be obtained as follows:

[0146]

[0147] Where α⁴ is the sliding mode coefficient of the fractional calculus term, and D α Defined using caputo.

[0148] Substituting the previously obtained state equation into the above equation, we can obtain...

[0149]

[0150] Setting the derivative to zero, we can obtain the equivalent control law u of the fractional-order sliding mode controller. eq for

[0151]

[0152] Where k5 is the fixed gain parameter of the fractional-order sliding mode controller.

[0153] Similar to integer-order sliding mode control, in order to ensure that the state vector of the fractional-order sliding mode control of a single-phase quasi-Z source rectifier can smoothly enter the sliding surface and optimize the approach process, sig(s) is used. γ Instead of sign(s), the power-sum approach law is designed as follows:

[0154]

[0155] Wherein, sig(s) γ =|s γ sign(s).

[0156] Combining the state equation, the time derivative of the sliding mode function, and the power-law approach, the global control law for fractional-order non-singular terminal sliding mode control can be obtained, i.e., the shoot-through duty cycle D of the single-phase quasi-Z-source rectifier is:

[0157]

[0158] Step 4: The reference value and sampled value of the rectifier bridge output voltage are sent to the outer voltage loop. The output of the outer voltage loop obtained through PI control is multiplied by the phase of the input AC voltage to obtain the reference value of the input AC voltage. Combined with the sampled current value, a sinusoidal modulation wave is obtained through PI control of the inner current loop. Using the shoot-through duty cycle D obtained through fractional-order non-singular terminal sliding mode control, the drive signals for the five switches in the circuit are obtained using a sinusoidal pulse width modulation (SPWM) algorithm, thereby controlling the voltage and current of the single-phase quasi-Z-source rectifier. Specifically,

[0159] For the AC side of the single-phase quasi-Z source rectifier, a dual closed-loop control strategy of voltage outer loop and current inner loop is adopted. The output voltage of the rectifier bridge is sampled, and the sampled value is compared with the reference value. The resulting error is passed through a PI controller and expressed by the formula:

[0160] I gmref =k p (u pnref -u pn )+k i ∫(u pnref -u pn )dt

[0161] Among them, I gmref u is the reference value for the amplitude of the AC input current. pn This is the reference value for the rectifier bridge output voltage.

[0162] The AC input voltage is sampled, and the output of the outer voltage loop is multiplied by the phase of the AC input voltage to obtain a reference value for the AC input current. This reference value is compared with the sampled current value, and the modulation wave of the rectifier bridge is obtained through PI control, expressed by the formula:

[0163] u in =k p (i gmref -i g )+k i ∫(i gmref -i g )dt

[0164] The sinusoidal modulated wave is compared with the triangular wave, and a traditional SPWM wave is generated by unipolar frequency-doubled sinusoidal pulse width modulation (SPWM). Then, combined with the direct duty cycle D of the single-phase quasi-Z source rectifier, the direct zero vector signal is superimposed with the traditional SPWM wave to obtain an SPWM modulated wave with the direct zero vector added, which is the five-way switching signal, thereby controlling the turn-off of the five switching transistors in the circuit.

[0165] Reference Figure 3 This is a block diagram of fractional-order non-singular terminal sliding mode control for a single-phase quasi-Z source rectifier in an embodiment of the present invention. pnref i gref i L2ref and u C2ref These are the reference values ​​for the rectifier bridge output voltage, AC side input current, current in the quasi-Z source network inductor L2, and voltage across the quasi-Z source network capacitor C2, respectively; pn i g i L2 and u C2 These represent the instantaneous values ​​of the rectifier bridge output voltage, AC side input current, quasi-Z source network inductor L2 current, and quasi-Z source network capacitor C2 voltage, respectively; D is the shoot-through duty cycle of the single-phase quasi-Z source rectifier. As shown in the figure, the reference value of the AC side input current is obtained by multiplying the output of the rectifier bridge output voltage under PI control of the outer loop by the phase of the AC side input voltage, while the sinusoidal modulation wave is obtained by the output of the AC side input current under PI control of the inner loop. Based on the sampled and calculated values, the required shoot-through duty cycle D of the single-phase quasi-Z source rectifier is obtained through the proposed fractional-order non-singular terminal sliding mode control. Combined with the sinusoidal modulation wave, a switching drive signal is obtained through sinusoidal pulse width modulation (SPWM), thereby controlling the conduction and cutoff of the five switching transistors in the circuit.

[0166] like Figure 4The figure shows the trend of the percentage of harmonic distortion (THD) of the input AC current to the fundamental current under fractional-order non-singular terminal sliding mode control in the single-phase quasi-Z source rectifier of this embodiment of the invention, as a function of the order of the fractional-order term in the fractional-order non-singular terminal sliding mode control and the switching frequency. It can be seen from the figure that THD decreases with increasing switching frequency, reaching its minimum at approximately α = 0.68, providing a basis for determining the switching frequency and the magnitude of the fractional-order term.

[0167] like Figures 5(a) to 5(d) As shown, this is a comparison of the simulated voltage and current waveforms and the THD of the input AC current of a single-phase quasi-Z source rectifier under fractional-order non-singular terminal sliding mode control and integer-order non-singular terminal sliding mode control in this embodiment of the invention. In the figure, V g For AC input voltage, I g For AC input current, V Co The figure shows the DC-side output voltage. As can be seen from the figures, both integer-order and fractional-order non-singular terminal sliding mode control can achieve in-phase AC-side voltage and current, allowing the rectifier to operate at unity power factor and stabilizing the DC-side output voltage at the target of 320V. Figures 5(a) and 5(c) show that with integer-order non-singular terminal sliding mode control, the THD of the AC-side current is 1.55%, and the DC-side output voltage fluctuation is 0.4V. Figures 5(b) and 5(d) show that with fractional-order non-singular terminal sliding mode control, the THD of the AC-side current is 1.39%, and the DC-side output voltage fluctuation is 0.25V. It can be seen that the proposed fractional-order non-singular terminal sliding mode control can reduce the THD of the AC-side current, decrease the fluctuation of the DC-side output voltage, and improve the steady-state performance of the system.

[0168] Figures 6(a) and 6(b) show a comparison of the total harmonic distortion (THD) of the AC side current of a single-phase quasi-Z-source rectifier under different input voltages and output power using fractional-order non-singular-terminal sliding mode control (NTSMC) and integer-order non-singular-terminal sliding mode control (FONTSMC) in this embodiment of the invention. In the figures, NTSMC represents integer-order non-singular-terminal sliding mode control, and FONTSMC represents fractional-order non-singular-terminal sliding mode control. It can be seen from the figures that the THD of the AC side current increases with increasing input voltage and decreases with increasing output power. Furthermore, it can be seen that the THD using fractional-order non-singular-terminal sliding mode control is lower than that using integer-order control. Therefore, fractional-order non-singular-terminal sliding mode control is more effective in harmonic compensation, reducing more harmonic pollution on the AC side and achieving better power quality.

[0169] Figures 7(a) and 7(b) show a comparison of the simulated waveforms of the output voltage change of a single-phase quasi-Z-source rectifier when the given output voltage changes, under fractional-order non-singular terminal sliding mode control and integer-order non-singular terminal sliding mode control in this embodiment of the invention. Figure 7(a) shows that under integer-order non-singular terminal sliding mode control, the DC-side output voltage requires 0.0075s to achieve stable tracking of the reference value. Figure 7(b) shows that under fractional-order non-singular terminal sliding mode control, the DC-side output voltage requires 0.005s to achieve stable tracking of the reference value, and the voltage overshoot is smaller. Therefore, by adopting the improved fractional-order non-singular terminal sliding mode control, the system has a faster dynamic response, and the output-side DC voltage can reach steady state in the shortest possible time.

[0170] This invention discloses a fractional-order nonsingular terminal sliding mode control method suitable for quasi-Z-source rectifiers. In terms of modeling, compared to traditional integer-order modeling, fractional-order state equations can better describe the actual operating state of the rectifier. In terms of control, compared to traditional control, fractional-order control adds an adjustable parameter of fractional order, resulting in higher control freedom and accuracy. Therefore, by introducing fractional-order calculus operators into traditional sliding mode control, designing fractional-order sliding surfaces, and designing system control laws based on these surfaces, fractional-order sliding mode control is achieved, giving the system better dynamic performance and robustness.

[0171] It should be noted that in existing fractional-mode sliding mode control methods for converters, the control law obtained through the fractional-mode sliding mode control strategy is either the direct duty cycle of a certain switch, the given signal of a certain state variable in the closed-loop control, or the sinusoidal modulation wave required for a certain pulse width modulation, used to participate in the control and operation of the converter. However, in this application, the control law obtained by fractional-mode sliding mode control is the duty cycle of the bridge arm in direct operation, which, combined with the modulation wave, jointly controls the conduction and turn-off of the bridge arm switch. Simultaneously, it is also closely related to the switching state of the switch in the quasi-Z source network on the rectifier side. The control law participates in both the sinusoidal pulse width modulation strategy of the AC side voltage and current dual closed loop and the turn-on and turn-off of the DC side switch. Applying the control law obtained through fractional-mode sliding mode control to the entire converter results in higher control freedom, higher control accuracy, reduced distortion rate of the AC side input current, and improved power quality, exhibiting significant advantages.

[0172] 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 other changes, modifications, substitutions, combinations, or simplifications made without departing from the purpose of the present invention should be considered equivalent substitutions and are all included within the protection scope of the present invention.

Claims

1. A fractional order non-singular terminal sliding mode control method suitable for quasi-Z-source rectifier, characterized in that, The voltage and current double closed loop PI control is adopted for the AC side of the single-phase quasi-Z-source controllable rectifier, the fractional order non-singular terminal sliding mode control and the sinusoidal pulse width modulation control are adopted for the DC side, including the following steps. Step 1, a DC side model of the single-phase quasi-Z-source controllable rectifier is established, state equations and voltage state equations of the capacitor on the output side are obtained; Step 2, state variables of the sliding mode control are selected, a sliding surface is designed, equivalent control law of the sliding mode control is obtained by making the derivative of the sliding surface as 0, an approaching law is designed, the sliding mode controller is designed by adopting the exponential approaching law, the global control law of the sliding mode control is obtained by combining the approaching law with the equivalent control law, that is, the shoot-through duty cycle D of the single-phase quasi-Z-source rectifier; Step 3, a fractional order calculus operator is introduced, a fractional order term is added in the sliding surface, a fractional order non-singular terminal sliding surface is obtained, the global control law of the fractional order non-singular terminal sliding mode control is obtained by combining the control law with the approaching law, that is, the shoot-through duty cycle D of the single-phase quasi-Z-source rectifier; Step 4, based on the shoot-through duty cycle D, the driving signal is output by using the sinusoidal pulse width modulation algorithm to control the on-off of the switch tube of the single-phase quasi-Z-source rectifier.

2. The fractional order non-singular terminal sliding mode control method according to claim 1, characterized in that, In step 1, the shoot-through and non-shoot-through states of the rectifier are analyzed, the inductor current and the capacitor voltage in the Z-source network are taken as state variables, state equations and voltage state equations of the capacitor on the output side are established, and the switching function is introduced into the state equation, when the switching function is 0 or 1, the single-phase quasi-Z-source rectifier is in different circuit states.

3. The fractional order non-singular terminal sliding mode control method according to claim 2, characterized in that, The state equation of the single-phase quasi-Z-source rectifier is represented as: , wherein , , , , Wherein, A and B are the coefficients of the state equation; L is the inductance of the quasi-Z-source network, C is the capacitance of the quasi-Z-source network; i pn is the output current of the rectifier bridge; u is the switching function, when u = 1, the single-phase quasi-Z-source rectifier is in the through state, when u = 0, the single-phase quasi-Z-source rectifier is in the non-through state; The state equation of the capacitor voltage on the output side is represented as: , where C o is an output-side capacitor, R o is a load.

4. The fractional order non-singular terminal sliding mode control method according to claim 1, characterized in that, In step 2, the error between the actual value and the reference value of the inductor current and the output DC voltage of the quasi-Z-source network and the integral of the sum of the two errors are selected as the state variables of the sliding mode control, which is represented as: , where i L2 , u Co are the instantaneous values of the inductor current and the output DC voltage of the quasi-Z-source network, respectively, i L2ref , u Coref are the reference values of the inductor current and the output DC voltage of the quasi-Z-source network, respectively.

5. The fractional order non-singular terminal sliding mode control method according to claim 4, wherein, In step 2, the linear combination function of the state variables is taken as the sliding surface, which is represented as: , where J = [α1, α2, α3] T is the sliding mode coefficient vector; The state equation containing the switching function is substituted into the derivative of the sliding function with respect to time, the derivative is made to be 0, and the equivalent control law of the sliding mode control is obtained, the derivative of the sliding function with respect to time is represented as: ； The exponential approaching law is represented as: , In the formula, β1 and β2 are adjustable control parameters, β1 is the coefficient of the exponential approaching term, β2 is the coefficient of the switching function, and β1 and β2>0, and sign is the sign function.

6. The fractional order non-singular terminal sliding mode control method according to claim 5, wherein, The global control law of the sliding mode control is obtained by combining the state equation, the derivative of the sliding function with respect to time, and the exponential approaching law, that is, the shoot-through duty cycle D of the single-phase quasi-Z-source rectifier is: , where k1, k2, k3 and k4 are fixed gain parameters of the sliding mode controller, R0 is the output resistance, is the output voltage, is the instantaneous value of the Z-source network capacitor C1 voltage, is the instantaneous value of the Z-source network capacitor C2 voltage, is the quasi-Z-source network inductor L2 current, , , , .

7. The fractional order non-singular terminal sliding mode control method according to claim 6, characterized in that, In step 3, the fractional order non-singular terminal sliding surface is represented as: , The derivative of the sliding function with respect to time is represented as: where a4is the sliding mode coefficient of the fractional calculus term, D α is the fractional calculus operator, using the caputo definition; The power approaching law is represented as: , wherein .

8. The fractional order non-singular terminal sliding mode control method according to claim 7, wherein, The global control law of the fractional order non-singular terminal sliding mode control is obtained by combining the state equation, the derivative of the sliding function with respect to time, and the power approaching law, that is, the shoot-through duty cycle D of the single-phase quasi-Z-source rectifier is 。 9. The fractional order non-singular terminal sliding mode control method according to any one of claims 1-8, characterized in that, In step 4, for the AC side of the single-phase quasi-Z-source rectifier, the double-loop control of the voltage outer loop and the current inner loop is adopted, the output voltage of the rectifier bridge is sampled, the sampling value is compared with the reference value, the error obtained is input into a PI controller to obtain the amplitude reference value of the AC side input current; the amplitude reference value of the current is compared with the sampling value of the current, the error obtained is input into a PI controller to obtain the sine modulation wave SPWM of the rectifier bridge; the sine modulation wave is compared with a triangular wave, the traditional SPWM wave is generated through unipolar frequency multiplication SPWM, and then the shoot-through duty cycle D of the single-phase quasi-Z-source rectifier is combined to superimpose the shoot-through zero vector signal and the traditional SPWM wave, so as to obtain the SPWM modulation wave with the shoot-through zero vector added, and the switching signal of the quasi-Z-source rectifier is obtained to control the turn-off of the switch tube in the control circuit.

10. The fractional order non-singular terminal sliding mode control method according to claim 9, wherein, The amplitude reference value of the AC side input current is represented as: , In the formula, u pn is the reference value of the rectifier bridge output voltage, and the subscript ref represents the reference value. The sine modulation wave SPWM of the rectifier bridge is represented by a formula as: , In the formula, is the alternating current input current, the subscript ref represents a reference value, is a proportional coefficient in the PI controller, is an integral coefficient in the PI controller.

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