Four-switch three-phase inverter based on Cuk converter and integral sliding mode controller
阅读说明：本技术 基于Cuk变换器的四开关三相逆变器及积分滑模控制器 (Four-switch three-phase inverter based on Cuk converter and integral sliding mode controller ) 是由 岳舟 成蒙 于 2021-01-13 设计创作，主要内容包括：针对现有FSTP逆变器的缺点,本发明提出了一种基于Cuk变换器的四开关三相逆变器及积分滑模控制器,其拓扑结构包括两个双向Cuk变换器,能够提供纯正弦输出电压,且无需输出滤波器。与传统的FSTP逆变器相比,本发明提供的逆变器提高了输入直流电源的电压利用率,提供了更高的输出线电压,可以扩展到直流输入电压的全值。此外,无需在同一桥臂开关之间插入死区,因此可以显著降低输出波形的失真以及非线性。而其对应的积分滑模控制器,能够通过优化系统的动态特性,保证系统在不同工况下的鲁棒性。(Aiming at the defects of the existing FSTP inverter, the invention provides a four-switch three-phase inverter based on Cuk converters and an integral sliding mode controller, wherein the topological structure of the four-switch three-phase inverter comprises two bidirectional Cuk converters, so that pure sine output voltage can be provided, and an output filter is not needed. Compared with the traditional FSTP inverter, the inverter provided by the invention improves the voltage utilization rate of an input direct-current power supply, provides higher output line voltage, and can be expanded to the full value of direct-current input voltage. In addition, since a dead zone does not need to be inserted between the switches of the same bridge arm, distortion and nonlinearity of an output waveform can be significantly reduced. And the corresponding integral sliding mode controller can ensure the robustness of the system under different working conditions by optimizing the dynamic characteristics of the system.)
1. A four-switch three-phase inverter based on Cuk converters is characterized in that a topological structure of the four-switch three-phase inverter comprises a first bidirectional Cuk converter and a second bidirectional Cuk converter which are connected with each other, a first phase of a three-phase load is connected with an output end of the first bidirectional Cuk converter, a second phase of the three-phase load is connected with an output end of the second bidirectional Cuk converter, and a third phase of the three-phase load is connected with a negative electrode of a direct-current power supply.
2. The Cuk converter-based four-switch three-phase inverter of claim 1, wherein the sinusoidal modulations of the first and second bidirectional Cuk converters are staggered from each other by a phase angle of 120 °.
3. The Cuk-converter-based four-switch three-phase inverter according to claim 1, wherein the topology comprises a first direct current power source UDC1A second DC power supply UDC2A first inductor L1BA second inductor L2BA third inductor L1CA fourth inductor L2CA first polarity capacitor C1BA second polarity capacitor C2BA third polar capacitor C1CA fourth polarity capacitor C2CA first switch S1A second switch S2And a third switch S3And a fourth switch S4(ii) a Wherein:
the second DC power supply UDC2Is connected with the first direct current power supply UDC1The negative pole of the second direct current power supply UDC2And the positive electrode of the first DC power supply UDC1Is provided with a potential point O, and the second direct current power supply UDC2The negative electrode of the anode is connected with a potential point A;
the first inductor L1BOne end of the first DC power supply U is connected withDC1The positive electrode ofOne end is connected with the first switch S1And a first polarity capacitor C1BThe positive electrode of (1); the first switch S1Is connected to the potential point O; the first polarity capacitor C1BIs connected with the second inductor L2BAnd a second switch S2A cathode of (a); the second inductor L2BThe other end of the connecting rod is connected with a potential point B; the second switch S2The anode of (a) is connected with the potential point O;
the third inductor L1COne end of the first DC power supply U is connected withDC1The other end of the anode is connected with the third switch S3And a third polar capacitor C1CThe positive electrode of (1); the third switch S3Is connected to the potential point O; the third polarity capacitor C1CNegative pole of (3) is connected with the fourth inductor L2CAnd a fourth switch S4A cathode of (a); the fourth inductor L2CThe other end of the connecting rod is connected with a potential point C; the fourth switch S4The anode of (a) is connected with the potential point O;
the second polarity capacitor C2BThe anode of the anode is connected with the potential point O, and the cathode is connected with the potential point B; the fourth polarity capacitor C2CThe anode of the anode is connected with the potential point O, and the cathode is connected with the potential point C;
the potential points A, B, C are each connected to a zero potential point N through a resistor.
4. An integral sliding mode controller applied to a Cuk converter-based four-switch three-phase inverter according to any one of claims 1 to 3, and characterized by comprising a switch control unit (1), a linear control unit (2) and a nonlinear cancellation unit (3); the input of the switch control unit (1) and the input of the linear control unit (2) are tracking errors between reference output voltage and inverter output voltage, the input of the nonlinear counteracting unit (3) is inverter output voltage, and the outputs of the switch control unit (1) and the linear control unit (2) are used as the input of a preset dynamic equation after being superposed and counteracting the output of the nonlinear counteracting unit (3); the dynamic equation is used for controlling the output voltage of the first bidirectional Cuk converter and/or the second bidirectional Cuk converter.
5. An integrating sliding-mode controller according to claim 4, wherein the dynamic equation comprises the following formula:
y1(t)＝x1(t)；
whereinz1(t)＝i2(t)，z2(t)＝uC1(t) is a state variable, y1(t) is the output, u (t) D is the control input, f (x)1(t),z1(t)) and g (z)2(t)) is the system function and control gain, and v (t) is a bias term representing the concentration uncertainty;
f(x1(t),z1(t)) and g (z)2(t)) is expressed as:
v(t)＝Δv(x1(t),z1(t),z2(t),d(t))；
wherein R isoRepresenting the load resistance, d (t) is external disturbance;
v(t)∈span(g(z2(t)))。
6. the integral sliding mode controller according to claim 5, wherein the corresponding control law of the integral sliding mode controller is as follows:
wherein the feedback termThe closed loop system is stable within a unified error range; -g (z)2(t))-1(f(x1(t),z1(t))) term to eliminate system nonlinearities; switch input item-g (z)2(t))-1kSWsgn (s (t)) suppresses the bias term v (t); sign function sgn (·):
7. an integrating sliding-mode controller according to claim 6, characterized in that the sign function sgn () is smoothly approximated by:
sgn(s(t))→sat(s(t)/φ)；
where φ > 0 represents the thickness of the boundary layer, then the control law is:
Technical Field
The invention relates to the technical field of power electronic conversion, in particular to a Cuk converter-based four-switch three-phase inverter and an integral sliding mode controller.
Background
A standard Six-Switch Three-Phase (SSTP) Voltage Source Inverter (VSI) is widely applied to various application fields such as electric/hybrid vehicles, renewable energy systems, and industrial drives. However, in some low power range applications, inverter topologies with fewer switches are preferred to reduce system size, complexity, losses, and cost. Some research efforts have been directed to developing inverter topologies that achieve the above goals. Research results show that it is feasible to implement a three-phase inverter with four switches. In a Four Switch Three Phase (FSTP) inverter, two Phase loads are powered by two leg inverters and the third Phase load is powered by the midpoint of two capacitors (C1 and C2) applied to the dc power supply.
In recent years, FSTP inverters have attracted considerable attention in terms of performance, control, and application. Compared to a standard SSTP inverter, the FSTP inverter has the following advantages: due to the reduction of the number of switches, the cost is reduced and the reliability is improved; omitting a complete branch reduces the switching losses of 1/3 and reduces the number of interface circuits providing PWM signals to the switches. The FSTP inverter may also utilize fault tolerant control to address open/short circuit faults of the SSTP inverter. However, conventional FSTP inverters also have some disadvantages that need to be considered. Like a standard SSTP inverter, the FSTP inverter only performs buck DC-AC conversion. If the voltages across the two capacitors (C1 and C2) of the dc link are not equal, the FSTP inverter will experience a non-linearity problem. In addition, the peak value of the phase voltage of the FSTP inverter is reduced to that of the SSTP inverter. In order to raise the phase voltage of the FSTP inverter to the phase voltage of the SSTP inverter, a typical solution is to insert a DC-DC boost converter between the FSTP inverter and the DC input source, which configuration is referred to as a two-stage inverter. The two-stage inverter generally utilizes any one of a Boost converter, a Buck-Boost converter, a Cuk converter, a Speic converter or a Zeta converter to improve the direct-current input voltage of the one-stage inverter, and then utilizes an SSTP inverter to realize the DC-AC conversion of the two-stage inverter. Furthermore, it is also capable of matching a wide range of input voltages, and is equally useful for various industrial applications such as UPS, heterogeneous renewable energy systems, active power filters and motor drives, etc. The complex structure makes the two-stage inverter system costly and bulky. Both the above-mentioned SSTP inverter and FSTP inverter require a dead zone to be inserted between two power switches of the same bridge arm, which may reduce the equivalent pwm voltage and cause distortion of the output waveform, and may reduce the energy transfer efficiency.
Disclosure of Invention
Aiming at the limitation of the prior art, the invention provides a four-switch three-phase inverter based on a Cuk converter and an integral sliding mode controller, and the invention adopts the technical scheme that:
a topology structure of the four-switch three-phase inverter based on Cuk converters comprises a first bidirectional Cuk converter and a second bidirectional Cuk converter which are connected with each other, wherein a first phase of a three-phase load is connected with an output end of the first bidirectional Cuk converter, a second phase of the three-phase load is connected with an output end of the second bidirectional Cuk converter, and a third phase of the three-phase load is connected with a negative electrode of a direct-current power supply.
Preferably, the sinusoidal modulations of the first and second bidirectional Cuk converters are offset from each other by a phase angle of 120 °.
Preferably, the topology includes a first dc power source UDC1A second DC power supply UDC2A first inductor L1BA second inductor L2BA third inductor L1CA fourth inductor L2CA first polarity capacitor C1BA second polarity capacitor C2BA third polar capacitor C1CA fourth polarity capacitor C2CA first switch S1A second switch S2And a third switch S3And a fourth switch S4(ii) a Wherein:
the second DC power supply UDC2Is connected with the first direct current power supply UDC1The negative pole of the second direct current power supply UDC2And the positive electrode of the first DC power supply UDC1Is provided with a potential point O, and the second direct current power supply UDC2The negative electrode of the anode is connected with a potential point A;
the first inductor L1BOne end of the first DC power supply U is connected withDC1And the other end of the anode is connected with the first switch S1And a first polarity capacitor C1BThe positive electrode of (1); the first switch S1Is connected to the potential point O; the first polarity capacitor C1BIs connected with the second inductor L2BAnd a second switch S2A cathode of (a); the second inductor L2BThe other end of the connecting rod is connected with a potential point B; the second switch S2The anode of (a) is connected with the potential point O;
the third inductor L1COne end of the first DC power supply U is connected withDC1The other end of the anode is connected with the third switch S3And a third polar capacitor C1CThe positive electrode of (1); the third switch S3Is connected to the potential point O; the third polarity capacitor C1CNegative pole of (3) is connected with the fourth inductor L2CAnd a fourth switch S4A cathode of (a); the fourth inductor L2CThe other end of the connecting rod is connected with a potential point C; the fourth switch S4The anode of (a) is connected with the potential point O;
the second polarity capacitor C2BThe anode of the anode is connected with the potential point O, and the cathode is connected with the potential point B; the fourth polarity capacitor C2CThe anode of the anode is connected with the potential point O, and the cathode is connected with the potential point C;
the potential points A, B, C are each connected to a zero potential point N through a resistor.
An integral sliding mode controller applied to the four-switch three-phase inverter based on the Cuk converter comprises a switch control unit, a linear control unit and a nonlinear offset unit; the input of the switch control unit and the linear control unit is a tracking error between a reference output voltage and an inverter output voltage, the input of the nonlinear counteracting unit is an inverter output voltage, and the output of the switch control unit and the linear control unit is superposed and counteracted to be used as the input of a preset dynamic equation; the dynamic equation is used for controlling the output voltage of the first bidirectional Cuk converter and/or the second bidirectional Cuk converter.
As a preferred solution, the dynamic equation comprises the following formula:
y1(t)＝x1(t)；
whereinz1(t)＝i2(t)，z2(t)＝uC1(t) is a state variable, y1(t) is the output, u (t) D is the control input, f (x)1(t),z1(t)) and g (z)2(t)) is the system function and control gain, and v (t) is a bias term representing the concentration uncertainty;
f(x1(t),z1(t)) and g (z)2(t)) is expressed as:
v(t)＝Δv(x1(t),z1(t),z2(t),d(t))；
wherein R isoRepresenting the load resistance, d (t) is external disturbance;
v(t)∈span(g(z2(t)))。
further, the control law corresponding to the integral sliding mode controller is as follows:
wherein the feedback termThe closed loop system is stable within a unified error range; -g (z)2(t))-1(f(x1(t),z1(t))) term to eliminate system nonlinearities; switch input item-g (z)2(t))-1kSWsgn (s (t)) suppresses the bias term v (t); sign function sgn (·):
further, a smooth approximation is performed on the sign function sgn (·), that is:
sgn(s(t))→sat(s(t)/φ)；
where φ > 0 represents the thickness of the boundary layer, then the control law is:
compared with the prior art, the topological structure of the four-switch three-phase inverter based on the Cuk converter comprises two bidirectional Cuk converters, can provide pure sine output voltage, and does not need an output filter. Compared with the traditional FSTP inverter, the inverter provided by the invention improves the voltage utilization rate of an input direct-current power supply, provides higher output line voltage, and can be expanded to the full value of direct-current input voltage. In addition, since it is not necessary to insert a dead zone between the same bridge arm switches, distortion and nonlinearity of the output waveform can be significantly reduced. Meanwhile, the integral sliding mode controller provided by the invention can ensure the robustness of the system under different working conditions by optimizing the dynamic characteristics of the system; in addition, by performing smooth approximation on the sign function, the buffeting phenomenon can be suppressed, and the optimum balance between tracking performance and buffeting suppression can be achieved.
Drawings
FIG. 1 is a circuit topology diagram of a four-switch three-phase inverter based on a Cuk converter according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of an embodiment of the present invention implementing DC-AC conversion with four switches using two sinusoidally modulated bi-directional DC-DC converters;
FIG. 3 is a circuit topology diagram of a bidirectional Cuk converter;
FIG. 4 is a schematic diagram of an integral sliding mode controller according to an embodiment of the present invention;
FIG. 5 is a waveform of an output phase voltage of a steady state simulation result according to an embodiment of the present invention;
FIG. 6 is a waveform of an output current of a steady state simulation result according to an embodiment of the present invention;
FIG. 7 shows the dynamic simulation results of the load jump from 50 Ω to 100 Ω according to the embodiment of the present invention;
FIG. 8 shows the dynamic simulation results of the load jump from 100 Ω to 50 Ω according to the embodiment of the present invention.
Detailed Description
The drawings are for illustrative purposes only and are not to be construed as limiting the patent;
it should be understood that the embodiments described are only some embodiments of the present application, and not all embodiments. All other embodiments obtained by a person of ordinary skill in the art based on the embodiments in the present application without any creative effort belong to the protection scope of the embodiments in the present application.
The terminology used in the embodiments of the present application is for the purpose of describing particular embodiments only and is not intended to be limiting of the embodiments of the present application. As used in the examples of this application and the appended claims, the singular forms "a", "an", and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It should also be understood that the term "and/or" as used herein refers to and encompasses any and all possible combinations of one or more of the associated listed items.
When the following description refers to the accompanying drawings, like numbers in different drawings represent the same or similar elements unless otherwise indicated. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present application. Rather, they are merely examples of apparatus and methods consistent with certain aspects of the application, as detailed in the appended claims. In the description of the present application, it is to be understood that the terms "first," "second," "third," and the like are used solely to distinguish one from another and are not necessarily used to describe a particular order or sequence, nor are they to be construed as indicating or implying relative importance. The specific meaning of the above terms in the present application can be understood by those of ordinary skill in the art as appropriate.
Further, in the description of the present application, "a plurality" means two or more unless otherwise specified. "and/or" describes the association relationship of the associated objects, meaning that there may be three relationships, e.g., a and/or B, which may mean: a exists alone, A and B exist simultaneously, and B exists alone. The character "/" generally indicates that the former and latter associated objects are in an "or" relationship. The invention is further illustrated below with reference to the figures and examples.
In order to solve the limitation of the prior art, the present embodiment provides a technical solution, and the technical solution of the present invention is further described below with reference to the accompanying drawings and embodiments.
Referring to fig. 1, a topology of a four-switch three-phase inverter based on Cuk converters includes a first bidirectional Cuk converter and a second bidirectional Cuk converter connected to each other, a first phase of a three-phase load is connected to an output terminal of the first bidirectional Cuk converter, a second phase of the three-phase load is connected to an output terminal of the second bidirectional Cuk converter, and a third phase of the three-phase load is connected to a negative electrode of a dc power supply.
In addition, the present embodiment further provides an integral sliding mode controller applied to the four-switch three-phase inverter based on the Cuk converter, which includes a switch control unit 1, a linear control unit 2, and a nonlinear cancellation unit 3; the input of the switch control unit 1 and the linear control unit 2 is a tracking error between a reference output voltage and an inverter output voltage, the input of the nonlinear counteracting unit 3 is an inverter output voltage, and the output of the switch control unit 1 and the linear control unit 2 is superposed and counteracted by the output of the nonlinear counteracting unit 3 to be used as the input of a preset dynamic equation; the dynamic equation is used for controlling the output voltage of the first bidirectional Cuk converter and/or the second bidirectional Cuk converter.
Compared with the prior art, the topological structure of the four-switch three-phase inverter based on the Cuk converter comprises two bidirectional Cuk converters, can provide pure sine output voltage, and does not need an output filter. Compared with the traditional FSTP inverter, the inverter provided by the invention improves the voltage utilization rate of an input direct-current power supply, provides higher output line voltage, and can be expanded to the full value of direct-current input voltage. In addition, since a dead zone does not need to be inserted between the switches of the same bridge arm, distortion and nonlinearity of an output waveform can be significantly reduced. And the corresponding integral sliding mode controller can ensure the robustness of the system under different working conditions by optimizing the dynamic characteristics of the system.
Specifically, the four-switch three-phase inverter based on the Cuk converter provided by the invention can be called as an FSTP Cuk inverter. It only needs to use four switches just can realize pure sinusoidal three-phase output, and does not need output filter. Compared with the traditional FSTP inverter, the FSTP Cuk inverter doubles the utilization rate of the direct-current bus. In addition, because the third phase load current of the topology is directly from the direct current power supply, the problem of voltage fluctuation between two capacitors of a direct current link is avoided. Moreover, the topology is indirectly connected between power switches in the same phase, so that no dead zone has to be inserted.
The topological structure comprises a first direct current power supply UDC1A second DC power supply UDC2A first inductor L1BA second inductor L2BA third inductor L1CA fourth inductor L2CA first polarity capacitor C1BA second polarity capacitor C2BA third polar capacitor C1CA fourth polarity capacitor C2CA first switch S1A second switch S2And a third switch S3And a fourth switch S4(ii) a Wherein:
the second DC power supply UDC2Is connected with the first direct current power supply UDC1The negative pole of the second direct current power supply UDC2And the positive electrode of the first DC power supply UDC1Is provided with a potential point O, and the second direct current power supply UDC2The negative electrode of the anode is connected with a potential point A;
the first inductor L1BOne end of the first DC power supply U is connected withDC1The other end of the positive electrode is connected withIs connected with the first switch S1And a first polarity capacitor C1BThe positive electrode of (1); the first switch S1Is connected to the potential point O; the first polarity capacitor C1BIs connected with the second inductor L2BAnd a second switch S2A cathode of (a); the second inductor L2BThe other end of the connecting rod is connected with a potential point B; the second switch S2The anode of (a) is connected with the potential point O;
the third inductor L1COne end of the first DC power supply U is connected withDC1The other end of the anode is connected with the third switch S3And a third polar capacitor C1CThe positive electrode of (1); the third switch S3Is connected to the potential point O; the third polarity capacitor C1CNegative pole of (3) is connected with the fourth inductor L2CAnd a fourth switch S4A cathode of (a); the fourth inductor L2CThe other end of the connecting rod is connected with a potential point C; the fourth switch S4The anode of (a) is connected with the potential point O;
the second polarity capacitor C2BThe anode of the anode is connected with the potential point O, and the cathode is connected with the potential point B; the fourth polarity capacitor C2CThe anode of the anode is connected with the potential point O, and the cathode is connected with the potential point C;
the potential points A, B, C are each connected to a zero potential point N through a resistor.
Because the topological structure consists of two bidirectional Cuk converters, DC/AC conversion is obtained by adding two-phase loads to the output ends of the two Cuk converters, and the last phase load is connected to the negative input end of the direct current power supply. Both Cuk converters will produce a sine wave output with a dc bias, so each converter produces a unipolar voltage. In order to generate a three-phase balanced load voltage, the sinusoidal modulations of the two converters are staggered by 120 ° phase angle from each other, with a dc offset exactly equal to the input dc voltage. Since the load is differentially connected to the DC input power source via the two converters, the differential DC component across the load will be zero, and a waveform with a bipolar voltage is generated across the load, requiring the use of a bi-directional DC-DC converter.
Specifically, the FSTP inverter is composed of two bidirectional DC-DC converters, and a basic method for implementing DC-AC conversion with four switches using two sinusoidal modulated bidirectional DC-DC converters is shown in fig. 2. Two phases of a three-phase load are connected to the outputs of two sinusoidally modulated bidirectional DC-DC converters, while the third phase is directly connected to the input DC power source. The FSTP Cuk inverter provided by the invention consists of two bidirectional Cuk converters, the circuit topology of the bidirectional Cuk converters is shown in figure 3, the output voltage of the bidirectional Cuk converters can be smaller than or larger than the input voltage, and the output voltage depends on the duty ratio. The relationship between the output voltage and the input voltage is as follows:
wherein D is the duty cycle, UDCFor input voltage, UoIs the output voltage. The modulation wave of each Cuk converter is a sinusoidal signal U with direct current bias in formula (2)BOAnd UCO，
Wherein, UBO、UCOIs the reference voltage, U, of two Cuk convertersBrefAnd UCrefThe sinusoidal reference voltages of the B phase and the C phase are respectively added with-UDCThen, a reference voltage U with DC bias is formedBOAnd UCO。UmL-LIs the amplitude of the desired output sinusoidal line voltage and ω is the output voltage frequency. The line voltage obtained by a three-phase load is as follows (3):
see fig. 3 for a circuit topology of a bidirectional Cuk converter. When the switch S1Conduction, S2When turned off, flows through the inductor L1The current of (2) increases. Capacitor C1Providing energy to the output stage. Flowing through the inductor L2The current of (C) also increases, and the capacitance C1The voltage on will decrease. When the switch S1Off, S2When conducting, the two inductive currents are reduced, and the capacitor C1By passing a current i1And (6) charging. The state space equations in the above two cases are respectively equation (4) and equation (5):
in the formula i1(t) is the current flowing through the input inductance L1Current of (i)2(t) is the current flowing through the output inductor L2Current of (u)c1(t) is the transfer capacitance C1The voltage of (c). u. ofi(t) and uo(t) represents input and output voltages, RoRepresenting the load resistance.
Combining equation (4) and equation (5), a state space averaging method is used, and the average model equation can be described as follows:
the above dynamic equations may be used to construct a sliding mode controller. However, the design of the controller by directly using the dynamic equation is too complex, because four parameters need to be measured to solve the four-dimensional matrix. The following simplified dynamic equations are used here to control the output voltage of the Cuk converter.
y1(t)＝x1(t) (9)
Whereinz1(t)＝i2(t)，z2(t)＝uC1(t) is a state variable, y1(t) is the output, u (t) D is the control input, f (x)1(t),z1(t)) and g (z)2(t)) is the system function and control gain, v (t) is the concentration uncertainty; f (x)1(t),z1(t)) and g (z)2(t)) is expressed as:
v(t)＝Δv(x1(t),z1(t),z2(t),d(t)) (12)
where d (t) is an unknown external perturbation. This uncertainty satisfies the matching condition:
v(t)∈span(g(z2(t))) (13)
the goal of the controller is to drive the output voltage of the Cuk converter to follow the reference output voltage with uncertain parameters and unknown disturbances. The collective uncertainty v (t) can degrade control performance and even cause system instability. To overcome this problem, the present invention provides an Integral Sliding Mode Controller (ISMC) applied to the FSTP Cuk inverter. The purpose of ISMC is to limit the output voltage of the Cuk converter to a sliding surface with s (t) equal to 0, so that the error is kept within a prescribed dynamic range.
The sliding mode controller has the main characteristic of robustness to parameter uncertainty and external interference[20]. The conventional slip plane is defined as s (t),
wherein n represents the system order, e1(t)＝y1d(t)-y1(t) represents a tracking error, λ being a positive constant; y is1dAnd (t) is a reference output voltage.
In addition to being robust to parameter uncertainties and disturbances, ISMC also improves steady state accuracy by adding integration effects on conventional slip planes. The integration broadening sliding surface is represented by the formula (15):
wherein k isiIs a positive constant.
Setting the system order n to 2, and taking the derivative of the integral amplification sliding surface s (t) with respect to time:
substituting formula (7) and formula (8) for formula (16) to obtain:
by setting upThe obtained equivalent control law is as follows:
in the formula (18), λ and k are selectediSo that the polynomialBecoming a herwitz matrix (Hurwitz). Substituting the control law formula (18) into the formula (17) to obtain an error dynamic equationComprises the following steps:
whereinIs the upper bound of the bias term. If the bias term v (t) is zero, the ideal error dynamic equation is obtained as:
however, the bias term v (t) prevents tracking error e1(t) converges to zero. To suppress this bias term, the switch control inputs are used as:
uSW(t)＝g-1(z2(t))kSWsgn(s(t)) (21)
wherein k isswIs a positive constant, ksw≧ v + η, where η is a positive constant, the sign function sgn (·) is defined as:
combining the equivalent control law and the on-off control law to obtain a complete control law which is as follows:
the control system consists of three parts, and a specific control scheme is shown in figure 4. Feedback itemThe closed loop system is stable within a unified error range; -g (z)2(t))-1(f(x1(t),z1(t))) term to eliminate system nonlinearities; switch input item-g (z)2(t))-1kSWsgn (s (t)) suppresses the bias term v (t).
It is worth noting here that discontinuous switching control often results in chattering, which may excite undesirable high frequencies. By performing smooth approximation on the sign function, the phenomenon of buffeting can be suppressed. The saturation function may be used as an example, replacing the sign function with equation (24):
sgn(s(t))→sat(s(t)/φ) (24)
where φ > 0 represents the thickness of the boundary layer, which should be adjusted to achieve the best balance of tracking performance and jitter suppression. The resulting control law can then be written as:
the FSTP Cuk inverter provided by the invention is simulated under the steady-state and dynamic working conditions by adopting the integral sliding mode control method. The simulation parameters are set as follows: input direct voltage UDC200V, switching frequency fs10kHz, inductance L1B＝L1C＝0.2mH，L2B＝L2C0.1mH, capacitance C1B＝C1C＝100μF，C2B＝C2C60 muf, 50 Ω load resistance Ro, reference voltageλ＝2×107，ki＝4×104，ksw＝4.6×104Phi is 0.1. Fig. 5 is an output phase voltage waveform of a steady state simulation result, and fig. 6 is an output current waveform of the steady state simulation result. Fig. 7 shows the dynamic simulation result of the load from 50 Ω to 100 Ω, and fig. 8 shows the dynamic simulation result of the load from 100 Ω to 50 Ω.
It should be understood that the above-described embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. And are neither required nor exhaustive of all embodiments. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be included in the protection scope of the claims of the present invention.
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