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

Abstract

The invention discloses a fractional order nonsingular terminal sliding mode control method for a single-phase quasi-Z-source rectifier, and the method comprises the steps: carrying out the voltage and current double-closed-loop PI control at an AC side of the quasi-Z-source rectifier, obtaining a sinusoidal modulation wave, introducing a fractional order item into a sliding mode surface at a DC side, and obtaining an equivalent control law of a fractional order nonsingular terminal sliding mode controller. And combining a global control law with sinusoidal modulation waves, and controlling a rectifier bridge and a switch tube in the quasi-Z-source network through the generated driving signal so as to realize a control target. The fractional order nonsingular terminal sliding mode control can enable the system to converge within finite time, and compared with integer order nonsingular terminal sliding mode control of a single-phase quasi-Z-source rectifier, the fractional order nonsingular terminal sliding mode control has the advantages that the input side alternating current distortion rate is reduced, the fluctuation of the output side direct current voltage is reduced, the dynamic response speed of the output side direct current voltage is increased, and the system reliability is improved. The control precision is higher, and the dynamic and static performance of the system is improved.

Description

Technical Field

[0001] The invention relates to the technical field of power electronics, and specifically discloses a fractional-order non-singular terminal sliding mode control method suitable for a single-phase quasi-Z-source rectifier. Background Art

[0002] With the development of power electronics technology, PWM rectifiers have been widely used in power systems, electric traction and other fields. Among them, compared with traditional voltage-type or current-type rectifiers, quasi-Z-source rectifiers have the advantages of simple topology, voltage boost or voltage reduction, direct pass and strong reliability. They have broad application prospects and are currently used in vehicle integrated chargers. For the control of the DC side of a single-phase quasi-Z-source rectifier, a double closed-loop PI control strategy with voltage outer loop and current inner loop is generally adopted. However, PI control has the disadvantages of large overshoot, slow response speed and poor dynamic performance, which makes 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 has the characteristics of simple algorithm, fast response speed, good dynamic performance and good robustness. However, the essence of sliding mode control is discontinuous control, and the output of the converter system will produce jitter problems. There are still deficiencies in system dynamic performance and control accuracy.

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

[0004] In view of the shortcomings of the above-mentioned background technology, the present invention provides a fractional-order non-singular terminal sliding mode control method suitable for a quasi-Z-source rectifier, which can achieve 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 improve the dynamic performance of the rectifier and the system control accuracy.

[0005] The present invention adopts the following technical solutions to achieve the above-mentioned invention object:

[0006] A fractional-order non-singular terminal sliding mode control method suitable for a quasi-Z-source rectifier adopts voltage and current double closed-loop PI control on the AC side of the single-phase quasi-Z-source controlled rectifier, and adopts fractional-order non-singular terminal sliding mode control and sinusoidal pulse width modulation control on the DC side, comprising the following steps:

[0007] Step 1, establishing a DC side model of a single-phase quasi-Z-source controlled rectifier, and obtaining a state equation and a voltage state equation of an output side capacitor;

[0008] Step 2: Select the state variable of the sliding mode control, design the sliding surface, and obtain the equivalent control law of the sliding mode control by making its derivative equal to 0; design the reaching law, use the exponential reaching law to design the sliding mode controller, and combine the reaching law with the equivalent control law to obtain the global control law of the sliding mode control;

[0009] Step 3, introducing a fractional-order calculus operator, adding a fractional-order term to the sliding surface, and obtaining a fractional-order non-singular terminal sliding surface; designing a power reaching law, combining the control law with the reaching law, and obtaining a global control law of the fractional-order non-singular terminal sliding mode control, that is, a through duty cycle D of the single-phase quasi-Z-source rectifier;

[0010] Step 4: Based on the direct duty cycle D, a sinusoidal pulse width modulation algorithm is used to output a driving signal to control the on and off of five switch tubes of the single-phase quasi-Z-source rectifier.

[0011] Preferably, in step 1, the direct-flow and non-direct-flow states of the rectifier are analyzed, the inductor current and capacitor voltage in the Z-source network are used as state variables, a state equation and a voltage state equation of the output side capacitor 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.

[0012] Preferably, 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 direct-flow state, when u=0, the single-phase quasi-Z source rectifier is in the non-direct-flow state;

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

[0017]

[0018] Among them, C o is the output side capacitance, R o For load.

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

[0020]

[0021] In the formula, iL2 、u Co They are the quasi-Z source network inductance L 2 The instantaneous value of the current and the instantaneous value of the output DC voltage, i L2ref 、u Coref They are the quasi-Z source network inductance L 2 The current reference value and the output DC voltage reference value.

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

[0023] s=α 1 x 1 +α 2 x 2 +α 3 x 3 =J T X

[0024] Where J = [α 1 ,α 2 ,α 3 ] T is the sliding mode coefficient vector;

[0025] Substitute the state equation containing the switching function into the time derivative of the sliding mode function, make the derivative equal to 0, and obtain the equivalent control law of the sliding mode control. The time derivative of the sliding mode function is expressed as:

[0026]

[0027] The exponential reaching law is expressed as:

[0028]

[0029] In the formula, β 1 , β 2 is an adjustable control parameter, β 1 is the coefficient of the exponential approach term, β 2 is the coefficient of the switching function, and β 1 , β 2 >0, sign is the sign function.

[0030] As a preferred method, the global control law of sliding mode control is obtained by combining the state equation, the time derivative of the sliding mode function, and the exponential reaching law, that is, the through duty cycle D of the single-phase quasi-Z source rectifier is:

[0031]

[0032] Among them, k 1 , k 2 , k 3 and k 4is the fixed gain parameter of the sliding mode controller, R0 is the output resistance, is the output voltage, is the capacitance C of the Z source network 1 The instantaneous value of the voltage, is the capacitance C of the Z source network 2 The instantaneous value of the voltage, The inductance L of the source network is 2 Current,

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

[0034] s=α 1 x 1 +α 2 x 2 +α 3 x 3 +α 4 D α x 3

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

[0036]

[0037] Among them, α 4 is the sliding mode coefficient of the fractional calculus term, D α is a fractional calculus operator, defined using Caputo;

[0038] The power reaching law is expressed as:

[0039]

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

[0041] As a preferred method, the global control law of fractional-order non-singular terminal sliding mode control is obtained by combining the state equation, the time derivative of the sliding mode function, and the power reaching law, that is, the 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 a voltage outer loop and a current inner loop is adopted to sample the output voltage of the rectifier bridge, and the sampled value is compared with the reference value. The error obtained is passed through a PI controller to obtain an amplitude reference value of the input current on the AC side; the amplitude reference value of the current is compared with the sampled value of the current, and the error obtained is passed through a PI controller to obtain a 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 a unipolar double-frequency sinusoidal pulse width modulation SPWM, and then combined with the direct-pass duty cycle D of the single-phase quasi-Z-source rectifier, the direct-pass zero vector signal is superimposed on the traditional SPWM wave to obtain an SPWM modulation wave with a direct-pass zero vector added, and a switching signal of the quasi-Z-source rectifier is obtained to control the shutdown of the switch tube in the circuit.

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

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

[0046] In the formula, u pn is the reference value of the rectifier bridge output voltage, and the subscript ref represents the reference value;

[0047] The sinusoidal modulation wave SPWM of the rectifier bridge is expressed as follows:

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

[0049] In the formula, i g is the input current on the AC side, k p is the proportional coefficient in the PI controller, k i Represents the integral coefficient in the PI controller.

[0050] The present invention adopts the above technical solution and has the following beneficial effects:

[0051] The present 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 goal of the rectifier operating at a power factor and outputting a stable DC voltage. Compared with the traditional integer-order non-singular terminal sliding mode control, the control freedom disclosed by the present invention is higher and the control accuracy is higher. Under the same conditions, the present invention reduces the distortion rate of the input current on the AC side of the single-phase quasi-Z-source rectifier, improves the power quality, makes the output DC voltage more stable, the voltage fluctuation is smaller, and the dynamic response is faster. When the system receives external interference, the rectifier can achieve rapid adjustment to achieve the stability of the output DC voltage, and the dynamic performance and robustness of the rectifier are improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] In order to more clearly illustrate the technical solution of the embodiment of the present invention, the drawings of the embodiment are briefly introduced below.

[0053] Figure 1 Schematic diagram of the topological structure of a single-phase quasi-Z-source rectifier in an embodiment of the present invention;

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

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

[0056] Figure 4 It is a trend diagram of the THD of the input side AC current changing with the order of the fractional-order term and the switching frequency in the fractional-order non-singular terminal sliding mode control of the single-phase quasi-Z-source rectifier in the embodiment of the present invention under the fractional-order non-singular terminal sliding mode control;

[0057] FIG5( a ) is a waveform diagram of voltage and current under integer-order non-singular terminal sliding mode control according to an embodiment of the present invention;

[0058] FIG5( b ) is a waveform diagram of voltage and current under fractional-order non-singular terminal sliding mode control in an embodiment of the present invention;

[0059] FIG5( c ) is a THD diagram of the input-side AC circuit under integer-order non-singular terminal sliding mode control in an embodiment of the present invention;

[0060] FIG5( d ) is a 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] FIG6( a ) is a graph showing a trend of THD changing with input voltage under integer-order non-singular terminal sliding mode control and fractional-order non-singular terminal sliding mode control in an embodiment of the present invention;

[0062] FIG6( b ) is a graph showing the variation 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 an embodiment of the present invention;

[0063] FIG7( a ) is a comparison diagram of simulated waveforms of output voltage changes of a single-phase quasi-Z-source rectifier under integer-order non-singular terminal sliding mode control when a given output voltage changes in an embodiment of the present invention;

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

[0065] Explanation of the numbers 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 DESCRIPTION

[0066] The technical solution of the present invention is described in detail below with reference to the accompanying drawings.

[0067] The present invention proposes a fractional-order non-singular terminal sliding mode control method for a single-phase quasi-Z-source rectifier, comprising controlling the single-phase quasi-Z-source rectifier by adopting voltage and current dual closed-loop PI control on the AC side, adopting fractional-order non-singular terminal sliding mode control on the DC side, and sinusoidal pulse width modulation, so as to achieve unity power factor operation on the AC side of the single-phase quasi-Z-source rectifier and stable output and rapid response of the DC voltage on the output side.

[0068] Specifically include:

[0069] Step 1, based on the topological structure of the single-phase quasi-Z source rectifier, analyze the two working states of the rectifier, namely, direct and non-direct, select the inductor current and capacitor voltage in the quasi-Z source network as state variables, obtain the state equations at different states, and write the voltage state equation of the output side capacitor. Furthermore, the switch function is introduced into the state equation, and the switch function is 0 or 1 corresponding to different circuit states of the single-phase quasi-Z source rectifier.

[0070] Reference Figure 1 , is a schematic diagram of the topological structure of a single-phase quasi-Z-source rectifier in an embodiment of the present invention, including an input-side AC power supply and a filter inductor, a rectifier bridge, a quasi-Z-source network, and an output-side filter capacitor and a load. Compared with a traditional voltage source or current source rectifier, a single-phase quasi-Z-source rectifier allows the bridge arm to be directly connected in a short time, has high circuit reliability, and can achieve voltage up and down conversion.

[0071] The single-phase quasi-Z-source controlled rectifier includes an AC power supply ug, an inductor Lg, a controlled rectifier H-bridge, a Z-source network circuit, an output capacitor C0 and an output resistor R0. The controlled rectifier H-bridge is composed of a switch tube S1, a switch tube S2, a switch tube S3, a switch tube S4 and a diode D1, a diode D2, a diode D3, and a diode D4. The Z-source network circuit is composed of an inductor L1, an inductor L2, a capacitor C1, a capacitor C2 and a switch tube S5. One output end of the AC power supply is connected to one end of the inductor Lg, and the other end of the inductor Lg is connected to the source of the switch tube S1, the drain of the switch tube S2, the positive electrode of the diode D1 and the negative electrode of the diode D2; the other output end of the AC power supply is connected to the source of the switch tube S3, the drain of the switch tube S4, the positive electrode of the diode D3 and the negative electrode of the diode D4; the drain of the switch tube S1, the drain of the switch tube S3, the negative electrode of the diode D1 and the negative electrode of the diode D3 are connected to one end of the capacitor C1 and one end of the inductor L1, the other end of the inductor L1 is connected to one end of the capacitor C2 and the drain of the switch tube S5, the other end of the capacitor C2 is connected to one end of the output capacitor C0, one end of the output resistor R0, the source of the switch tube S2, the source of the switch tube S4, the positive electrode of the diode D2 and the positive electrode of the diode D4; the other end of the capacitor C1 is connected to the source of the switch tube S7 and one end of the inductor L2, and the other end of the inductor L2 is connected to the other end of the output capacitor C0 and the other end of the output resistor R.

[0072] S5 is the power switch of the quasi-Z source, and S1-S4 are the four power switches of the controllable rectifier H bridge. When S5 is turned off, the rectifier works in the direct-flow state, and when S5 is turned on, the rectifier works in the non-direct-flow state.

[0073] Referring to FIG. 2(a) and FIG. 2(b), two states of the single-phase quasi-Z-source rectifier in the embodiment of the present invention are shown: the direct-through state and the non-direct-through state. As shown in FIG. 2(a), the circuit is in the direct-through state, at which time the upper and lower switches of the same arm of the rectifier bridge are turned on at the same time, and the switch S in the quasi-Z-source network is turned on. 5 Deadline.

[0074] Selecting the inductor current and capacitor voltage of the quasi-Z source network as state variables, the state space equation is:

[0075]

[0076] Among them, L 1 and L 2 is the inductance in the quasi-Z source network, C 1 and C 2 is the capacitance in the quasi-Z source network, C o is the capacitance on the output side.

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

[0078]

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

[0080] Make L 1 =L 2 =L, C 1 =C 2 =C, combined with the above formula, the state equation of the single-phase quasi-Z source rectifier can be obtained. By 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 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 direct-on state, and the switch tube S in the quasi-Z source network 5 When u=0, the single-phase quasi-Z source rectifier is in a non-straight-through state, and the switch tube S in the quasi-Z source network 5 In addition, the state equation of the output capacitor voltage can be obtained as:

[0084]

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

[0086]

[0087] Among them, C o is the output side capacitance, R o For load.

[0088] Step 2, design a sliding mode controller for a single-phase quasi-Z-source rectifier, including sliding surface design and reaching law design. The error between the actual value of the inductor current and output DC voltage of the quasi-Z-source network and the reference value and the integral of the sum of the errors are selected as the state variables of the sliding mode control, and the linear combination function of the state variables is used as the sliding surface. Substitute the state equation containing the switching function into the derivative of the sliding mode function with respect to time, make the derivative equal to 0, and obtain the equivalent control law of the sliding mode control. In order to make the system reach the sliding surface from the initial state as expected, the exponential reaching law is introduced. By combining the reaching law with the equivalent control law, the global control law of the sliding mode control, that is, the through duty cycle D of the single-phase quasi-Z-source rectifier, can be obtained. Specifically,

[0089] When designing a sliding mode controller, the quasi-Z source network inductor L 2 Current i L2 And output DC voltage u Co The error between the actual value and the reference value and the integral of the sum of the errors are used as the state variables of the sliding mode control, that is,

[0090]

[0091] Among them, i L2 、u Co They are the quasi-Z source network inductance L 2 The instantaneous value of the current and the instantaneous value of the output DC voltage, i L2ref 、u Coref They are the quasi-Z source network inductance L 2 The current reference value and the output DC voltage reference value.

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

[0093] s=α 1 x 1 +α 2 x 2 +α 3 x 3 =J T X

[0094] Among them, α 1 , α 2 and α 3 is the sliding mode coefficient, J = [α 1 ,α 2 ,α 3 ] T is the sliding mode coefficient vector;

[0095] When the system state variable is on the sliding surface, the actual value of the state variable of the 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 formula, the derivative of the sliding mode function with respect to time is:

[0096]

[0097] Substituting the previously obtained state equation into the above formula, we can get

[0098]

[0099] Setting the derivative to 0, we can obtain the equivalent control law u of the sliding mode controller eq for

[0100]

[0101] Among them, k 1 , k 2 is the fixed gain parameter of the sliding mode controller, u eq is the equivalent control law, satisfying 0 eq <0.5,u eq In fact, it is the through duty cycle D of the single-phase quasi-Z source rectifier.

[0102] The proof by contradiction proves that the sliding surface is reachable. The process is as follows:

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

[0104]

[0105] It can be seen that if the sliding mode coefficient satisfies α 1 >0,α 2 >0,α 3 >0, then s>0.

[0106] When s>0, u=0, assuming that the sliding mode surface is unreachable, the quasi-Z source network switch tube will always be in the on state, the direct duty cycle D=0, the capacitor voltage of the quasi-Z source network is equal to the output voltage, and the inductor current is equal to the output current of the rectifier bridge. Combined with the designed sliding mode surface, it can be seen that if the sliding mode coefficient satisfies α 1 >0,α 2 >0,α 3 >0, then s<0. Based on the above analysis, it can be seen that the designed sliding surface is reachable.

[0107] When moving to the sliding surface, the state trajectory of the system must be restricted to the sliding surface and move toward the zero point.

[0108] Let the Lyapunov function of the system be

[0109]

[0110] Then its derivative is

[0111]

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

[0113]

[0114] ​From the above formula, we can get:

[0115]

[0116] When s→0+, s<0, u s→0+ =0,

[0117]

[0118] When s→0-, s>0, u s→0+ =0.5,

[0119]

[0120] When the sliding mode control parameters of the 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, and the state equation is as follows:

[0122]

[0123] Substituting the equivalent control law into the above formula, the ideal sliding dynamics of the sliding mode control of the single-phase quasi-Z-source rectifier can be obtained as:

[0124] By making the derivative on the left side of the equation equal to 0, the steady-state operating point is obtained as follows:

[0125]

[0126] Linearizing the ideal sliding mode dynamics near the equilibrium point yields:

[0127]

[0128] The characteristic equation of the linearized system is:

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

[0130] According to the stability requirements, a 11 +a 22 <0 and a 11 a 22 -a 12 a 21 When >0, the system is stable.

[0131] Since the initial state of the system is not on the sliding surface s=0, if the above control law is still used to control the system at this time, that is, s=0, s=0, the state variables of the system cannot converge normally, and the sliding mode control cannot work normally. Therefore, it is necessary to design a reaching law first to make the system slide as expected, reach the sliding surface from the initial state, control the sliding speed of the moving point, and reduce the jitter. After the system reaches the sliding surface, the above control law is used to make the state variables move along the sliding surface and finally converge to the equilibrium point.

[0132] In order to make the system slide from the initial state to the sliding mode surface as expected, the exponential reaching law is used to design the sliding mode controller of the single-phase quasi-Z source rectifier to control the sliding speed of the moving point and reduce the jitter. The exponential reaching law is selected as:

[0133]

[0134] Among them, β 1 , β 2 is an adjustable control parameter, β 1 is the coefficient of the exponential approach term, β 2 is the coefficient of the switching function, and β 1 , β 2 >0, sign is the sign function.

[0135] The exponential approach law is selected, and the approach speed changes exponentially. The value of the adjustable control parameter determines the control performance of the sliding mode controller. The adjustable parameter β 1 It affects the speed at which the moving point of the system approaches s = 0. The approach speed increases with β 1 As β increases, 1 The decrease of β 1 If the value is too large, it will affect the convergence of the system and increase the jitter. 2 s ensures that when the sliding surface is large, the system state can approach the sliding mode at a faster speed. In the process of exponential approach, the speed gradually decreases to 0, and the speed is still small when s = 0. In general, in order to make the moving point of the system approach at a faster speed and suppress the jitter, it is usually necessary to increase β 2 While taking the value of 1 The method of obtaining the value of .

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

[0137]

[0138] Among them, k 1 , k 2, k 3 and k 4 is the fixed gain parameter of the sliding mode controller,

[0139] The sliding surface s is a function of the system state variables. Therefore, according to the Lyapunov function stability theory, the stability of the sliding mode control system of the single-phase quasi-Z source rectifier can be analyzed by analyzing the Lyapunov function composed of the sliding surface s. Substituting the exponential reaching law into the derivative of the Lyapunov function, we can get:

[0140]

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

[0142] Step 3: In order to make the system transfer energy more slowly, reduce the jitter range, and increase the degree of freedom of the system sliding mode control, a fractional-order calculus operator is introduced, and fractional-order terms are added to the sliding surface to obtain a fractional-order non-singular terminal sliding surface. Combined with the selected power reaching law, the global control law of the fractional-order non-singular terminal sliding mode control is obtained, that is, the through duty cycle D of the single-phase quasi-Z-source rectifier.

[0143] Fractional calculus theory extends traditional calculus theory to the fractional order field. Compared with traditional integer calculus theory, fractional calculus theory has more universal significance. By introducing fractional calculus operators into sliding mode control, fractional sliding mode control can be obtained. Compared with integer sliding mode control, fractional sliding mode control transfers energy more slowly and has a smaller range of jitter, thus improving the stability of the system. This embodiment introduces the fractional calculus operator D on the basis of the above sliding surface. α , add about the quasi-Z source network inductor L 2 Current i L2 And the output DC voltage u Co The fractional-order term of the integral of the sum of the errors between the actual value and the reference value, the sliding surface expression of the design is as follows:

[0144] s=α 1 x 1 +α 2 x 2 +α 3 x 3 +α 4 D α x 3

[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 of the 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 formula, the derivative of the sliding mode function with respect to time is obtained as follows:

[0146]

[0147] Among them, α 4 is the sliding mode coefficient of the fractional calculus term, D α Use caputo definition.

[0148] Substituting the previously obtained state equation into the above formula, we can get

[0149]

[0150] Setting the derivative to 0, we can obtain the equivalent control law u of the fractional-order sliding mode controller eq for

[0151]

[0152] Among them, k 5 is the fixed gain parameter of the fractional-order sliding mode controller,

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

[0154]

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

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

[0157]

[0158] Step 4, send the reference value and sampled value of the rectifier bridge output voltage to the voltage outer loop, multiply the voltage outer loop output obtained by PI control by the phase of the input side AC voltage, so as to obtain the reference value of the input side AC, and combine it with the sampled value of the current, and obtain a sinusoidal modulated wave through the PI control of the current inner loop. Combined with the direct duty cycle D obtained by the fractional-order non-singular terminal sliding mode control, the sinusoidal pulse width modulation (SPWM) algorithm is used to obtain the drive signals of the five switching tubes in the circuit, so as to control 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 to sample the output voltage of the rectifier bridge, compare the sampled value with the reference value, and the error obtained is passed through the 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 is the reference value of the input current amplitude on the AC side, u pn It is the reference value of the rectifier bridge output voltage.

[0162] The input voltage on the AC side is sampled, and the output of the voltage outer loop is multiplied by the phase of the input voltage on the AC side to obtain the reference value of the input current on the AC side, which is compared with the current sampling value, and the modulation wave of the rectifier bridge is obtained through PI control, which can be expressed as follows:

[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 the traditional SPWM wave is generated by unipolar frequency-doubled sinusoidal pulse width modulation (SPWM). Combined with the direct-pass duty cycle D of the single-phase quasi-Z-source rectifier, the direct-pass zero vector signal is superimposed on the traditional SPWM wave to obtain the SPWM modulated wave with the direct-pass zero vector added, that is, a five-way switching signal is obtained, thereby controlling the shutdown of the five switching tubes in the circuit.

[0165] Reference Figure 3 , is a block diagram of a fractional-order non-singular terminal sliding mode control for a single-phase quasi-Z-source rectifier in an embodiment of the present invention. pnref 、igref 、i L2ref and u C2ref They are the output voltage of the rectifier bridge, the input current on the AC side, and the inductance L of the quasi-Z source network. 2 The current and the quasi-Z source network capacitance C 2 The reference value of the voltage; u pn 、i g 、i L2 and u C2 They are the output voltage of the rectifier bridge, the input current on the AC side, and the inductance L of the quasi-Z source network. 2 Current and quasi-Z source network capacitance C 2 The instantaneous value of the voltage; D is the through duty cycle of the single-phase quasi-Z-source rectifier. As can be seen from the figure, the reference value of the input current on the AC side is obtained by multiplying the output of the PI control of the outer loop of the rectifier bridge output voltage by the phase of the input voltage on the AC side, and the sinusoidal modulation wave is obtained by the output of the PI control of the inner loop of the input current on the AC side. According to the sampling values ​​and the calculated values, the through duty cycle D required by the single-phase quasi-Z-source rectifier is obtained by the proposed fractional-order non-singular terminal sliding mode control. Combined with the sinusoidal modulation wave, the switch drive signal is obtained by sinusoidal pulse width modulation (SPWM), thereby controlling the conduction and cutoff of the five switch tubes in the circuit.

[0166] like Figure 4 As shown, the current harmonic content of the input side AC current as a percentage of the fundamental current content (THD) under the fractional-order non-singular terminal sliding mode control of the single-phase quasi-Z source rectifier in the embodiment of the present invention changes with 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 the increase of the switching frequency and is the smallest when α=0.68, which provides a basis for determining the size of the switching frequency and the fractional order.

[0167] like Figure 5(a) to Figure 5(d) As shown in FIG. 1 , the voltage and current simulation waveforms of the single-phase quasi-Z-source rectifier in steady state and the THD comparison diagram of the input side AC current under the fractional-order non-singular terminal sliding mode control and the integer-order non-singular terminal sliding mode control in the embodiment of the present invention are shown. In the figure, V g is the AC input voltage, I g is the input current on the AC side, V Cois the DC side output voltage. As can be seen from the figure, both integer-order and fractional-order non-singular terminal sliding mode control can achieve the same phase of the AC side voltage and current, the rectifier operates at unity power factor, and the DC side output voltage is stabilized at the control target of 320V. As can be seen from Figure 5(a) and Figure 5(c), with integer-order non-singular terminal sliding mode control, the THD of the AC side current is 1.55%, and the fluctuation of the DC side output voltage is 0.4V. As can be seen from Figure 5(b) and Figure 5(d), with fractional-order non-singular terminal sliding mode control, the THD of the AC side current is 1.39%, and the fluctuation of the DC side output voltage 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, reduce the fluctuation of the DC side output voltage, and improve the steady-state performance of the system.

[0168] As shown in Figure 6 (a) and Figure 6 (b), it is a comparison diagram of the THD of the AC side current of the single-phase quasi-Z-source rectifier under the fractional-order non-singular terminal sliding mode control and the integer-order non-singular terminal sliding mode control in the embodiment of the present invention at different input voltages and output powers. In the figure, NTSMC is the integer-order non-singular terminal sliding mode control, and FONTSMC is the fractional-order non-singular terminal sliding mode control. It can be seen from the figure that the THD of the AC side current increases with the increase of input voltage and decreases with the increase of output power. In addition, it can be seen that the THD when using fractional-order non-singular terminal sliding mode control is lower than that when using integer-order control. Therefore, the use of fractional-order non-singular terminal sliding mode control is more effective in harmonic compensation, reduces more harmonic pollution on the AC side, and can obtain better power quality.

[0169] As shown in Figure 7(a) and Figure 7(b), it is a comparison diagram of the simulated waveforms of the output voltage change of the single-phase quasi-Z-source rectifier when the given output voltage changes under the fractional-order non-singular terminal sliding mode control and the integer-order non-singular terminal sliding mode control in the embodiment of the present invention. It can be seen from Figure 7(a) that under the integer-order non-singular terminal sliding mode control, the DC side output voltage takes 0.0075s to achieve stable tracking of the reference value. It can be seen from Figure 7(b) that under the fractional-order non-singular terminal sliding mode control, the DC side output voltage takes 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 dynamic response is faster, and the output side DC voltage can reach a steady state in the shortest time.

[0170] The fractional-order non-singular terminal sliding mode control method for quasi-Z-source rectifier disclosed in the present invention has a modeling aspect, and compared with the traditional integer-order modeling, the fractional-order state equation can better describe the actual operating state of the rectifier. In terms of control, compared with the traditional control, the fractional-order control adds the adjustable parameter of the fractional order, which has a higher control freedom and a higher control accuracy. Therefore, the fractional-order calculus operator is introduced into the traditional sliding mode control, the fractional-order sliding mode surface is designed, and the system control law is designed based on the fractional-order sliding mode surface to realize the fractional-order sliding mode control, so that the system has better dynamic performance and robustness.

[0171] It should be noted that in the fractional-order sliding mode control method used in the prior art on the converter, the control law obtained by the fractional-order sliding mode control strategy is either the direct duty cycle of a certain switch tube, or a given signal of a certain state quantity in the closed-loop control, or a sinusoidal modulation wave required for a pulse width modulation, which is used to participate in the control and operation of the converter. However, in the present application, the control law obtained by the fractional-order sliding mode control is the duty cycle of the bridge arm directly passed, which is combined with the modulation wave to jointly control the conduction and shutdown of the bridge arm switch tube. At the same time, it is also closely related to the switching state of the switch tube in the quasi-Z source network on the rectifier side. The control law participates in both the sinusoidal pulse width modulation strategy of the voltage and current double closed loop on the AC side and the opening and closing of the DC side switch tube. The control law obtained by the fractional-order sliding mode control is applied to the entire converter, with higher control freedom and higher control accuracy, and the distortion rate of the input current on the AC side is reduced, and the power quality is improved, which has significant advantages.

[0172] The above embodiments are preferred implementation modes of the present invention, but the implementation modes of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications that do not deviate from the purpose of the present invention should be equivalent replacement methods and are included in the protection scope of the present invention.

Claims

1. A fractional-order non-singular terminal sliding mode control method for a 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 controlled rectifier, and the fractional-order non-singular terminal sliding mode control and sinusoidal pulse width modulation control are adopted for the DC side, including the following steps: Step 1, establishing a DC side model of a single-phase quasi-Z-source controlled rectifier, and obtaining a state equation and a voltage state equation of an output side capacitor; Step 2: Select the state variable of the sliding mode control, design the sliding surface, and obtain the equivalent control law of the sliding mode control by making its derivative equal to 0; design the reaching law, use the exponential reaching law to design the sliding mode controller, and combine the reaching law with the equivalent control law to obtain the global control law of the sliding mode control; Step 3, introducing a fractional-order calculus operator, adding a fractional-order term to the sliding surface, and obtaining a fractional-order non-singular terminal sliding surface; designing a power reaching law, combining the control law with the reaching law, and obtaining a global control law of the fractional-order non-singular terminal sliding mode control, that is, a through duty cycle D of the single-phase quasi-Z-source rectifier; Step 4: Based on the direct duty cycle D, a sinusoidal pulse width modulation algorithm is used to output a drive signal to control the on and 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 direct-flow and non-direct-flow states of the rectifier are analyzed, the inductor current and capacitor voltage in the Z source network are taken as state variables, the state equation and the voltage state equation of the output side capacitor 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 expressed as: X=A+Bu in, 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 direct-flow state, when u=0, the single-phase quasi-Z source rectifier is in the non-direct-flow state; The state equation of the output capacitor voltage is expressed as: Among them, C o is the output side capacitance, R o For 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 of the inductor current and the output DC voltage of the quasi-Z source network and the reference value and the integral of the sum of the errors are selected as sliding mode control state variables, which are expressed as: In the formula, i L2 、u Co are the instantaneous value of the current of the quasi-Z source network inductor L2 and the instantaneous value of the output DC voltage, i L2ref 、u Coref They are respectively the current reference value of the quasi-Z source network inductor L2 and the reference value of the output DC voltage.

5. The fractional-order non-singular terminal sliding mode control method according to claim 4, characterized in that: In step 2, the linear combination function of the state variables is used as the sliding surface, which is expressed as: s=α1x1+α2x2+α3x3=J T X Where J = [α1, α2, α3] T is the sliding mode coefficient vector; Substitute the state equation containing the switching function into the time derivative of the sliding mode function, make the derivative equal to 0, and obtain the equivalent control law of the sliding mode control. The time derivative of the sliding mode function is expressed as: The exponential reaching law is expressed as: 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, sign is the sign function.

6. The fractional-order non-singular terminal sliding mode control method according to claim 5, characterized in that: Combining the state equation, the time derivative of the sliding mode function, and the exponential reaching law, the global control law of the sliding mode control is obtained, that is, the through duty cycle D of the single-phase quasi-Z source rectifier is: Among them, k1, k2, k3 and k4 are the fixed gain parameters of the sliding mode controller, R0 is the output resistance, is the output voltage, is the instantaneous value of the voltage of capacitor C1 of the Z source network, is the instantaneous value of the voltage of capacitor C2 of the Z source network, is the current of the inductor L2 of the quasi-Z source network, 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 mode surface is expressed as: s=α1x1+α2x2+α3x3+α4D α x3 The time derivative of the sliding mode function is expressed as: Among them, α4 is the sliding mode coefficient of the fractional calculus term, D α is a fractional calculus operator, defined using Caputo; The power reaching law is expressed as: Among them, sig(s) γ =|s| γ sign(s).

8. The fractional-order non-singular terminal sliding mode control method according to claim 7, characterized in that: Combining the state equation, the time derivative of the sliding mode function, and the power reaching law, the global control law of the fractional-order non-singular terminal sliding mode control is obtained, that is, the 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 to 8, characterized in that: In step 4, for the AC side of the single-phase quasi-Z-source rectifier, a dual closed-loop control of a voltage outer loop and a current inner loop is adopted to sample the output voltage of the rectifier bridge, and the sampled value is compared with the reference value. The error obtained is passed through a PI controller to obtain the amplitude reference value of the input current on the AC side; the amplitude reference value of the current is compared with the sampled value of the current, and the error obtained is passed through a 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 a unipolar double-frequency sinusoidal pulse width modulation SPWM, and then combined with the direct-pass duty cycle D of the single-phase quasi-Z-source rectifier, the direct-pass zero vector signal is superimposed on the traditional SPWM wave to obtain an SPWM modulation wave with a direct-pass zero vector added, and a switching signal of the quasi-Z-source rectifier is obtained to control the shutdown of the switch tube in the circuit.

10. The fractional-order non-singular terminal sliding mode control method according to claim 9, characterized in that: The amplitude reference value of the AC side input current is expressed as: AND gmref =k p (in pnref -in pn )+k i ∫(in pnref -in pn )dt In the formula, u pn is the reference value of the rectifier bridge output voltage, and the subscript ref represents the reference value; The sinusoidal modulation wave SPWM of the rectifier bridge is expressed as follows: u in =k p (i gmref -i g )+k i ∫(i gmref -i g )dt In the formula, i g is the input current on the AC side, k p is the proportional coefficient in the PI controller, k i Represents the integral coefficient in the PI controller.

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