CN110112915A - The control method of Boost DC-DC converter based on Second Order Sliding Mode Control - Google Patents

Abstract

The control method for the Boost DC-DC converter based on Second Order Sliding Mode Control that the invention proposes a kind of, it include: step 1, the control variable of selected Boost establishes the differential equation according to selected control variable under different circuit structures, establishes the phase plane about control variable；Step 2, finite state machine controller based on Second Order Sliding Mode Control is established to Boost, set effective status and original state, effective status is set to correspond to the controller output quantity, according to the selected control variable analysis differential equation, without output overshoot, the finite state machine controller condition of convergence based on Second Order Sliding Mode Control is obtained；Step 3, according to the finite state machine controller based on Second Order Sliding Mode Control, the finite state machine controller for increasing time lag value is established, in finite frequency, control variable is set to converge to equalization point, i.e. given value in the agonic tracking of the output of Boost.

Description

Control Method of Boost DC-DC Converter Based on Second-Order Sliding Mode Control

technical field

The invention relates to the field of automatic control, in particular to a control method of a Boost DC-DC converter based on second-order sliding mode control.

Background technique

Pulse width modulation (PWM) control is widely used in direct current - direct current (DC-DC) converters. It obtains the output switching signal according to the output voltage and other state variables, and controls the DC-DC converter to track the reference voltage. This method requires the use of an integral term of the output error to ensure zero error at steady state. Its main advantage is that it enables the converter to operate at a constant switching frequency, making it very good electromagnetic compatibility (EMI). However, it also has some disadvantages:

1) The integral term may slow down the dynamic response of the converter;

2) It is a control method based on small signals, and the dynamic performance of the converter can only be guaranteed within a range near the balance point. Therefore, people began to study simple and fast control methods such as hybrid digital adaptive control, approximate time optimal control, boundary control, and Raster control.

Sliding mode control is a nonlinear control method, which has good robustness to parameter uncertainty and external disturbance, and can meet the large-signal and small-signal conditions of the converter. It is a kind of DC-DC converter PWM control. an alternative method. The traditional sliding mode control uses the sliding mode surface s=0 to divide the state control into two subspaces, and uses different control functions {U+, U-} in different subspaces to generate control outputs to adjust the converter, making the system dynamic The trajectory remains at s=0. Sliding mode control emphasizes the use of a switching function under different circuit structures, but since the Boost converter is a non-minimum phase system, it cannot be controlled with only one switching function under different circuit structures. The boundary control method, similar to the high-order sliding mode control method, uses high-order switching surfaces, which can achieve good control effects. But the boundary control method applied to the Boost converter still needs to measure the inductor current and the output current at the same time, which increases the cost of the control method.

Contents of the invention

The invention aims at at least solving the technical problems existing in the prior art, and particularly innovatively proposes a control method of a Boost DC-DC converter based on second-order sliding mode control.

The invention proposes a control method of a Boost DC-DC converter based on second-order sliding mode control. Based on the switching function idea of the second-order sliding mode, this method designs the switching functions under the two controller structures of the Boost converter respectively, so that the motion trajectory moves according to the specified trajectory under the limitation of the switching plane, and finally enters the steady-state limit cycle. This method adopts a controller based on a state machine structure, does not need to detect the output current, and uses the feedback of the output voltage and the inductor current, which can make the Boost converter have a good dynamic response, and has a strong resistance to parameter uncertainties and load disturbances. Good robustness. The control method with time delay proposed by the invention, combined with the controller of the finite state machine structure, realizes zero error in the steady state of the system under the condition of limited switching frequency.

In order to achieve the above-mentioned purpose of the present invention, the present invention provides a kind of control method based on the Boost DC-DC converter of second-order sliding mode control, and its key is, comprises:

Step 1, select the control variable of the Boost converter, establish a differential equation under different converter structures according to the selected control variable, and establish a phase plane about the control variable;

Step 2, establish a finite state machine controller based on second-order sliding mode control for the Boost converter, set the effective state and initial state, make the effective state correspond to the output of the controller, and analyze the differential equation according to the selected control variables , in the case of no output overshoot, obtain the convergence condition of the finite state machine controller based on the second-order sliding mode control;

Step 3, according to the finite state machine controller based on the second-order sliding mode control, establish a finite state machine controller with increased delay value, and make the control variable converge to the equilibrium point under the condition of limited frequency, that is, the boost converter Output the given value on tracking without deviation.

The control method of the Boost DC-DC converter based on the second-order sliding mode control, preferably, the step 1 includes:

Step 1-1, establish differential equations under the controller OFF-state structure according to the selected control variables. The two selected control variables are the inductor current i _L and the output voltage V _o , according to the structural characteristics of the OFF-state controller, the input and output differential equations of the controller are transformed into the differential equations of i _L* and V _o to obtain Trajectory equation on the phase plane with the two control variables as axes.

Steps 1-2, according to the selected control variables to establish differential equations under the controller ON-state structure. The two selected control variables are the inductor current i _L and the output voltage V _o . According to the structural characteristics of the ON-state controller, the input and output differential equations of the controller are transformed into the differential equations of i _L* and V _o to obtain Trajectory equation on the phase plane with the two control variables as axes.

The control method of the Boost DC-DC converter based on the second-order sliding mode control, preferably, the step 2 includes:

Step 2-1, the input and output differential equations of the Boost converter are

Among them, u is the control quantity, when u=1, the controller is in the ON-state structure, and when u=0, the controller is in the OFF-state structure. The four valid states of the state machine There is a corresponding amount of control, and The corresponding control quantity u=0, and The corresponding control quantity u=1. When the system is powered on, the system is initialized and started from the initial state. When the output voltage V _o < V _ref , the state machine enters the left half plane to work, and the state driven, when the state machine is in If the output voltage V _o >V _ref , the state machine enters the right half-plane operation, and the state drive. when in state, if the output voltage V _o > V _ref , the state machine will re-enter the left half-plane operation.

Step 2-2, the differential equations about i _L and V _o obtained from step 1 can be distinguished as follows according to the controller structure. When the controller structure is in the OFF-state, the differential equation of the controller is

It can be seen that the trajectory of the controller in the phase plane under the OFF-state structure is a circular trajectory with (0, V _g ) as the center. When the controller structure is in the ON-state, the differential equation of the controller is

Among them, (i _L0 , V _o0 ) is the initial point of the trajectory, and it can be seen that the trajectory of the ON-state is a straight line with a negative slope. The working trajectories under each structure are obtained above, and the switching conditions for jumping between states can be obtained.

by state jump to Analysis of switching conditions: In the state, the controller is in the ON-state structure, and the motion trajectory is a straight line. In this state, the inductor is charged, and the load continues to flow through the output capacitor, the inductor current rises, and the output voltage drops at a very small rate. When the circular working trajectory of the working point passes the reference point, the charging is completed, and the state machine switches to the state The switching condition is obtained from the intersection of the circular trajectory and the linear trajectory passing through the reference point. The switching conditions are as follows

is the radius of the circular trajectory passing through the reference point, and its value is

by state jump to and Analysis of switching conditions: when the state machine is in When the output voltage rises, the inductor current drops. The motion trajectory in this state is a circular trajectory. When the inductor current drops below the reference value, the energy stored in the default inductor is not enough to make the output voltage continue to rise, and it needs to be charged. state, if the output voltage is less than the reference value and the inductor current is less than the reference value, the state machine is still working in the left half plane and switches to If the output voltage is greater than the reference value and the inductor current is greater than the reference value, the state machine enters the right half plane and switches to It can be obtained from the above description switch to The switching condition for i _L ≤i _Lref , switch to The switching condition for V _o ≥ V _ref .

by state jump to Analysis of switching conditions: The movement trajectory in the state is a circular trajectory, and the working point moves along the trajectory until the ON-state movement trajectory with the current point as the initial point passes the reference point, and the switching condition is met. It can also be understood as taking the current point as the initial point The switching condition is met when the slope of the straight line working track is less than or equal to the slope of the line connecting the current point and the reference point. The slope of the linear motion trajectory under the ON-state structure obtains different values depending on the initial point. From step 1, the equation of the ON-state motion trajectory is as follows

The slope of the straight line is related to the output voltage at the initial point and the controller parameters, and its value is

When the current point is the next starting point of the state When the motion trajectory passes the reference point, the state jumps, and the jump condition can be obtained as

The above formula can be transformed into

(i _Lref -i _L0 )*L*V _o0 ≤R*C*V _g *V _o0 -V _ref )

In order to further simplify the above formula, according to the input and output power conservation equation

Substitution can be obtained

Among them, i _L*ref is the converted inductor current reference value,

by state jump to and Analysis of switching conditions: in In this state, the inductor current rises and the output voltage drops. The main function of the state is the transition state of state switching. When the switching condition i _L* ≥ i L _*ref is satisfied and still working in the right half plane, switch to Switch to when the condition V _o ≤ V _ref and i _L* ≤ i L _*ref The state machine enters the left half plane to work.

The control method of the Boost DC-DC converter based on the second-order sliding mode control, preferably, the step 3 includes:

Step 3, according to the finite state machine controller based on the second-order sliding mode control, establish a finite state machine controller with an increased delay value, and make the control variable converge to the equilibrium point under the condition of limited frequency, that is, the Boost converter The output unbiasedly tracks the upper given value. Delay value is set to β, in the state jump to The following switching conditions can be obtained by adding a time lag value to the switching condition

After adding the delay value, the state machine can cross the boundary and enter the right half plane after a finite number of switching cycles, and can form a limit cycle centered on the reference point. After entering the equilibrium state, the relationship between the delay value β and the ripple coefficient of the output voltage ripple formed in the final steady state is explained by the following derivation. The final limit cycle has two state switching points, which are also the switching points when the controller structure switches, which are set to A(i _L*A , V _oA ), B(i _L*B , V _oB ). At the same time, set the target ripple coefficient of the output voltage as W, because the center of the limit cycle is the reference point, so the expression of the coordinates of the two points can be obtained, V _oA = V _ref -V _ref *W/2, V _oB = V _ref +V _ref *W/2, i _L*A ＝|K|*V _ref *W/2+i _L*ref , i _L*B ＝i _L*ref -|K|*V _ref *W/ 2. Because the two points A and B are two intersection points on the circular trajectory of the OFF-state and the linear trajectory of the ON-state. After calculating the coordinates of one of the points, the expression of the lag value can be calculated according to the following formula

In summary, owing to adopting above-mentioned technical scheme, the beneficial effect of the present invention is:

1. Improvement on the basis of sliding mode control method, no need to detect output current, only output voltage and inductor current are used as feedback;

2. In the start-up phase, only two switch switching actions are required under specific load conditions to make the output voltage track the upper reference signal; in the steady state, if there is a load disturbance, the output voltage will return to the steady state value in a short time ;

3. It has good robustness to the uncertainty of controller parameters;

Additional aspects and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention.

Description of drawings

The above and/or additional aspects and advantages of the present invention will become apparent and comprehensible from the description of the embodiments in conjunction with the following drawings, wherein:

Fig. 1 is the circuit diagram of the Boost DC-DC converter of the control method of the Boost DC-DC converter based on the second-order sliding mode control of the present invention;

Fig. 2 is the OFF-state structure circuit diagram of the Boost DC-DC converter of the control method of the Boost DC-DC converter based on the second-order sliding mode control of the present invention;

Fig. 3 is the ON-state structure circuit diagram of the Boost DC-DC converter of the control method of the Boost DC-DC converter based on the second-order sliding mode control of the present invention;

Fig. 4 is a schematic diagram of the circuit working trajectory when the starting point of the control method of the Boost DC-DC converter based on the second-order sliding mode control of the present invention is in the left half plane (V _o < V _ref );

Fig. 5 is a schematic diagram of the circuit working trajectory when the starting point of the control method of the Boost DC-DC converter based on the second-order sliding mode control of the present invention is in the right half plane (V _o > V _ref );

6 is a schematic diagram of switching conditions between states in the left half plane of the control method of the Boost DC-DC converter based on second-order sliding mode control in the present invention;

7 is a schematic diagram of switching conditions between the states of the right half plane of the circuit of the control method of the Boost DC-DC converter based on the second-order sliding mode control of the present invention;

Fig. 8 is the structure diagram of the state machine controller of the control method of the Boost DC-DC converter based on the second-order sliding mode control of the present invention;

Fig. 9 is a schematic diagram of steady-state analysis after adding a time lag value of the control method of the Boost DC-DC converter based on second-order sliding mode control in the present invention;

Fig. 10 is a method schematic diagram of a control method of a Boost DC-DC converter based on second-order sliding mode control in the present invention;

Fig. 11 is the example circuit diagram of the control method of the Boost DC-DC converter based on the second-order sliding mode control of the present invention;

Detailed ways

Embodiments of the present invention are described in detail below, examples of which are shown in the drawings, wherein the same or similar reference numerals designate the same or similar elements or elements having the same or similar functions throughout. The embodiments described below by referring to the figures are exemplary only for explaining the present invention and should not be construed as limiting the present invention.

In describing the present invention, it should be understood that the terms "longitudinal", "transverse", "upper", "lower", "front", "rear", "left", "right", "vertical", The orientation or positional relationship indicated by "horizontal", "top", "bottom", "inner", "outer", etc. are based on the orientation or positional relationship shown in the drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than Nothing indicating or implying that a referenced device or element must have a particular orientation, be constructed, and operate in a particular orientation should therefore not be construed as limiting the invention.

In the description of the present invention, unless otherwise stipulated and limited, it should be noted that the terms "installation", "connection" and "connection" should be understood in a broad sense, for example, it can be a mechanical connection or an electrical connection, or it can be two The internal communication of each element can be directly connected or indirectly connected through an intermediary, and those of ordinary skill in the art can understand the specific meanings of the above terms according to specific situations.

Figure 1 shows the circuit structure of the Boost DC-DC converter, and the different states of the switches S1 and S2 determine the different states of the circuit. When the switch tube S1 is turned off and S2 is turned on, the controller is in an OFF-state structure, and the control variable u=0. From the input and output differential equations of the controller, the following differential equations can be obtained

In order to simplify the analysis, it is assumed that there is no load, that is, R→∞, the above equation can be simplified as

Taking the two coordinate axes of the i _L and V _o phase planes, the above formula can be transformed into the controller working trajectory equation under the OFF-state structure

For the convenience of geometric analysis, let

The final working trajectory equation of the controller is the expression of a circle

The Boost DC-DC controller in the OFF-state structure is shown in Figure 2.

Figure 3 shows a diagram of the Boost DC-DC controller in the ON-state structure. At this time, the switch S1 is turned on and the switch S2 is turned off. The control quantity u=1, the following differential equations can be obtained from the input and output differential equations of the controller

Here, an intermediate quantity in the derivation process is introduced, the energy E stored in the inductor and capacitor, and its expression is as follows

E＝L*i _L ² /2+C*V _o ² /2

Deriving from E gives The expression of is as follows:

To simplify the analysis, in Setting R→∞ in the formula, the above equation can be simplified as

right Derived to get The expression of is as follows:

Integrate both sides of formula (21) at the same time (i _L0 is the initial value of the current):

i _L ＝(V _g /L)*t+i _L0 (22)

The expression of the output voltage V _o can be obtained by deriving (21) (V _o0 is the initial value of the voltage):

Equation (22) and Equation (23) eliminate time t at the same time to obtain the relationship between i _L and V _o :

ln(V _o /V _o0 )＝-L*(i _L -i _L0 )/R*C*V _g (24)

In this state, the value of the output voltage drop is very small, and the value of V _o /V _o0 is approximately equal to 1, which can be approximated

ln(V _o /V _o0 )≈V _o /V _o0 -1 (25)

Put formula (25) into (24) to get:

Figure 4 shows the schematic diagram of the controller’s working trajectory when the starting point is in the left half plane (V _o < V _ref ). In the figure, the initial value of the output voltage is set to 0, and the first valid state after startup is Since the initial value of the voltage of the output capacitor is 0 and the MOSFET has the characteristics of an equivalent parallel diode, the track appears "abnormal", that is, the output voltage also rises while the inductor current rises. When the switching condition is met , the state switches to in state Under , if the controller is in an ideal state, that is, there is no loss and parameter changes, the controller will move along a circular trajectory to reach the reference point. However, due to the loss and parameter changes of the actual controller, its motion trajectory is always within the reference circle. When the switching condition i _L ≤ i _Lref is satisfied and the controller is still working in the left half plane, it switches back to state. So far, the movement of one switching cycle is completed. enter again To charge the inductor, the initial voltage of the remaining output capacitor is greater than the input voltage, so the current The trajectory is a "normal" trajectory, where the output voltage decreases while the inductor current increases. The movement of the trajectory is the same as the above switching period, repeating the movement period, and finally forms a stable limit cycle in the left half plane area near the reference point due to reasons such as circuit loss.

Figure 5 shows the schematic diagram of the circuit working trajectory when the starting point is in the right half plane (V _o > V _ref ). The initial value of the output capacitance is greater than the reference value, and the first valid state entered after startup is The operating point of the controller moves along the circular trajectory, the output voltage drops, and the inductor current also decreases (reversely increases). When the switching condition is met, switch to In the state, the output voltage drops and the inductor current increases. If the switching conditions are met, it will switch back to So far, a complete switching cycle is completed. It can be seen from the figure that due to the loss and the change of controller parameters, after a finite number of switching cycles, the motion trajectory crosses the boundary and enters the left half plane.

FIG. 6 shows a schematic diagram of the derivation process of switching conditions between states in the left half plane, the starting point is in the left half plane and the initial value of the capacitance at the output terminal is 0. The first valid state is In this state, the inductor is charged, the inductor current rises, and the output voltage also rises. If the circuit is ideal and there is no loss, then the distance between the current operating point and the center of the circle (0, V _g ) is equal to the radius of the circular trajectory passing through the reference point, which means that the inductance is fully charged. If you switch to The working point will move along the track of the reference circle to reach the reference point. Therefore, according to the above principle, the state can be obtained switch to switching condition in The square of the radius of the reference circle The switching point is shown as point C in the figure. However, there are losses in the actual circuit, so the actual trajectory always moves within the reference circle trajectory. In order to make the inductance discharge fully and as fast as possible close to the reference point, switch to The switching condition of is i _L ≤ i _Lref . The switching point is shown as point D in the figure. When the conditions are met, the default is that the inductor discharge energy is completed. Afterwards, the switching cycle is repeated until a stable limit cycle is formed near the reference point, and high-frequency oscillation will be formed at the same time. The effect of adding the delay value is to make the trajectory cross the boundary into the right plane, and avoid forming a high-frequency oscillatory limit cycle in the end.

FIG. 7 is a schematic diagram showing the derivation of switching conditions between states in the right half plane. As shown in the figure, the starting point is in the right half plane, and the first valid state after startup is In this state, the voltage drops and the inductor current decreases. The trajectory of is approximately a straight line, and its slope formula is as follows:

Different switching points (i _L*0 , V _o0 ) can obtain straight lines with different slopes. The above formula represents a straight line cluster, and the straight line passing through the reference point needs to be selected. The figure shows different switching points (i _L*1 , V _o1 ), (i _L*2 , V _o2 ), (i _L*3 , V _o3 ), etc., and different switching points correspond to straight lines with different slopes , assuming that the straight line where one point M(i _L*4 , V _o4 ) is located passes through the reference point. The straight line passing through the reference point corresponds to the slope of the line connecting the switching point and the reference point being equal to the slope of the straight line trajectory. According to the above principle, it can be obtained switch to switching condition

Switch to The straight line that satisfies the switching conditions will pass through the reference point (i _L*ref , V _ref ) when there is no loss and parameter changes in the circuit, but in actual situations, the trajectory may reach the reference point due to delay, loss, and parameter fluctuations. Before the point crosses V _o =V _ref and enters the left half plane or reaches a point near the reference point that belongs to the right half plane area. For the convenience of calculation, the above formula can be transformed into

According to the conservation of input and output power, that is Substitute into the above formula to get

switch to _Afterwards , the working point moves along a straight line _trajectory , and switches to Wherein A is a constant greater than 0. In order to make the motion trajectory approach the reference point quickly, the value of A should be as small as possible, and A=0. so Towards The switching condition is i _L ≥ i _Lref .

Figure 8 shows a schematic structural diagram of a state machine, which consists of four valid states and one initial state. The switching conditions between states have been explained in detail above. After startup, the state machine drives the jump between states according to the feedback inductor current and output voltage. After entering the steady state, the limit cycle corresponds to the one-way state of the four effective states. Loop jump.

Figure 9 shows the schematic diagram of the steady-state limit cycle after adding the delay value. The trajectory of the ON-state structure of the controller is a straight line, and the trajectory of the OFF-state structure is a circular trajectory. After entering the steady state, ON-state and OFF- The two intersection points of the state trajectory are set as A(i _L*A , V _oA ) and B(i _L*B , V _oB ) in the figure. Since the limit cycle is centered on the reference point, the ripple coefficient according to the performance index of the circuit The coordinates of the two intersection points can be obtained. Assuming that the target ripple coefficient of the output voltage is W, the coordinate expressions of points A and B can be obtained as follows

V _oB =V _ref -V _ref *W/2

i _L*B ＝|K|*V _ref *W/2+i _L*ref

V _oA =V _ref +V _ref *W/2

i _L*A ＝i _L*ref -|K|*V _ref *W/2

Among them, K is the slope of the linear working trajectory of the controller under the ON-state structure. According to the coordinates of one point, the calculation formula of the time lag value can be obtained

Figure 10 shows a schematic diagram of the control method of the Boost DC-DC converter based on the second-order sliding mode control, which is improved based on the idea of switching function of the second-order sliding mode, and this control method is realized by three major steps. From the transformation of the input and output differential equations of the Boost controller, the working trajectory equation under the phase plane with the control variable as the coordinate axis is obtained, and then combined with the structure of the state machine and the characteristics of the working trajectory of the controller, the switching conditions between states in the state machine are obtained. Three The big step fully describes the design flow and workflow of the state machine controller.

Figure 11 shows an example circuit diagram where the inductor current and output voltage are returned as feedback signals to the state machine controller, which outputs control signals to two switching MOSFETs. The controller adopts FPGA of Altera Cyclone IV series. The analog-to-digital converter used for the output voltage and inductor current measurement has a conversion frequency of 30MHz, a resolution of 10 bits, and a 0-2V input range.

In the description of this specification, descriptions referring to the terms "one embodiment", "some embodiments", "example", "specific examples", or "some examples" mean that specific features described in connection with the embodiment or example , structure, material or characteristic is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials or characteristics described can be combined in any suitable manner in any one or more embodiments or examples.

Although the embodiments of the present invention have been shown and described, those skilled in the art can understand that various changes, modifications, substitutions and variations can be made to these embodiments without departing from the principle and spirit of the present invention. The scope of the invention is defined by the claims and their equivalents.

Claims (8)

1. a control method based on the Boost DC-DC converter of second-order sliding mode control, it is characterized in that, comprising: S1, select the control variable of the Boost converter, establish a differential equation under different circuit structures according to the selected control variable, and establish a phase plane about the control variable; S2, establishing a finite state machine controller based on second-order sliding mode control for the Boost converter, setting the effective state and the initial state so that the effective state corresponds to the output of the controller, and analyzing the differential equation according to the selected control variable, In the case of no output overshoot, obtain the convergence condition of the finite state machine controller based on the second-order sliding mode control; S3, according to the finite state machine controller based on the second-order sliding mode control, establish a finite state machine controller with an increased time lag value, and in the case of limited frequency, make the control variable converge to the equilibrium point, that is, the output of the Boost converter Unbiased tracking of the upper given value. 2. the control method based on the Boost DC-DC converter of second-order sliding mode control according to claim 1, is characterized in that, described S1 comprises: S1-1, according to the selected control variables to establish a differential equation under the OFF-state shutdown structure of the controller; the two selected control variables are the inductor current i _L and the output voltage V _o , according to the OFF-state controller structure Features, the input and output differential equations of the controller are transformed into differential equations of i _L and V _o , so as to obtain the trajectory equation on the phase plane with the two control variables as coordinate axes; S1-2, according to the selected control variables, establish the differential equation under the ON-state open structure of the controller; the two selected control variables are the inductor current i _L and the output voltage V _o , according to the structural characteristics of the ON-state controller , transform the input and output differential equations of the controller into the differential equations of i _L and V _o , so as to obtain the trajectory equation on the phase plane with the two control variables as coordinate axes. 3. the control method based on the Boost DC-DC converter of second-order sliding mode control according to claim 2, is characterized in that, described S1-1 comprises: S1-A, it is known that the input and output differential equations under the OFF-state structure of the Boost converter are In order to simplify the analysis, it is assumed that there is no load, that is, R→∞, the above equation can be simplified as Here, an intermediate quantity in the derivation process is introduced, the energy E stored in the inductor and capacitor, and its expression is as follows E＝L*i _L ² /2+C*V _o ² /2 (3) Deriving from E gives The expression of is as follows: right Derived to get The expression of is as follows: Multiply formula (4) and formula (5) to get command parameters Both sides of equation (6) are integrated with respect to time t at the same time: Substitute formula (4) into formula (7): is an unknown constant whose value is related to the state of the controller; for the convenience of geometric expression, let Substitute formula (9) into formula (8): It can be seen that formula (10) is an expression of a circle. So far, the trajectory equation of the controller OFF-state structure in the coordinate system of the two control variables i _L* and V _o has been established, where L is the inductance, C Is the capacitance, R is the resistance, and V _g is the input voltage. 4. the control method of the Boost DC-DC converter based on second-order sliding mode control according to claim 1, is characterized in that, described S1-2 comprises: S1-B, it is known that the input and output differential equations under the ON-state structure of the Boost converter are Here, an intermediate quantity in the derivation process is introduced, the energy E stored in the inductor and capacitor, and its expression is as follows E＝L*i _L ² /2+C*V _o ² /2 (12) Deriving from E gives The expression of is as follows: To simplify the analysis, in Setting R→∞ in the formula, the above equation can be simplified as to the first order Derivative to get the second derivative The expression of is as follows: The following formula is obtained by integrating both sides of formula (11), where i _L0 is the initial value of the current: i _L ＝(V _g /L)*t+i _L0 (16) The expression of the output voltage V _o can be derived by formula (11), where V _o0 is the initial value of the voltage: Equation (16) and Equation (17) eliminate time t at the same time to get the relationship between i _L and V _o : ln(V _o /V _o0 )＝-L*(i _L -i _L0 )/R*C*V _g (18) In this state, the value of the output voltage drop is very small, and the value of V _o /V _o0 is approximately equal to 1, which can be approximated ln(V _o /V _o0 )≈V _o /V _o0 -1 (19) Put formula (19) into (18) to get: 5. the control method based on the Boost DC-DC converter of second-order sliding mode control according to claim 1, is characterized in that, described S2 comprises: S2-1, set the effective state and initial state of the state machine, so that the effective state corresponds to the output of the state machine controller; the state machine has four effective states as and an initial state; when the output voltage V _o < V _ref , the system works in the left half plane, and the state machine consists of the state and drive; when the output voltage V _o > V _ref , the system works in the right half plane, and the state machine consists of the state and drive; and Indicates that the controller is in an OFF-state structure, the symbol "-" represents the left half-plane, and the symbol "+" represents the right half-plane; and Indicates that the controller is in the ON-state structure, the symbol "-" represents the left half-plane, and the symbol "+" represents the right half-plane; S2-2, according to the differential equations about i _L and V _o obtained in S1, combined with geometric analysis in the phase plane, the switching conditions for jumping between states are obtained, that is, the switching planes under different controller structures are obtained. 6. the control method based on the Boost DC-DC converter of second-order sliding mode control according to claim 5, is characterized in that, described S2-1 comprises: S2-A, the input and output differential equations of the Boost converter are Among them, u is the control quantity, when u=1, the controller is in the ON-state structure, when u=0, the controller is in the OFF-state structure; the four effective states of the state machine There is a corresponding amount of control, and The corresponding control quantity u=0, and The corresponding control quantity u=1; when the system is powered on, the system is initialized and started from the initial state. When the output voltage V _o < V _ref , the state machine enters the left half-plane operation, and the state driven, when the state machine is in If the output voltage V _o >V _ref , the state machine enters the right half-plane operation, and the state drive; when in In the state, if the output voltage V _o >V _ref , the state machine will re-enter the left half-plane operation. 7. the control method based on the Boost DC-DC converter of second-order sliding mode control according to claim 5, is characterized in that, described S2-2 comprises: S2-B, the differential equations about i _L and V _o obtained from step 1 can be distinguished as follows according to the controller structure; when the controller structure is in the OFF-state, the differential equation of the controller is It can be seen that the trajectory of the controller in the phase plane under the OFF-state structure is a circular trajectory with (0, V _g ) as the center; when the controller structure is in the ON-state, the differential equation of the controller is Among them, (i _L0 , V _o0 ) is the initial point of the trajectory, and it can be seen that the trajectory of the ON-state is a straight line with a negative slope; the working trajectory under each structure is obtained above, and the switching conditions for jumping between states can be obtained; by state jump to Analysis of switching conditions: In this state, the controller is in the ON-state structure, and the motion trajectory is a straight line; in this state, the inductor is charged, the load is continuously flowed by the output capacitor, the inductor current rises, and the output voltage drops at a small rate; when the operating point is in a circular When the working trajectory passes the reference point, the charging is completed, and the state machine switches to the state The switching condition is obtained by the intersection of the circular trajectory passing through the reference point and the straight line trajectory; the switching condition is as follows is the radius of the circular trajectory passing through the reference point, and its value is by state jump to and Analysis of switching conditions: when the state machine is in , the output voltage rises and the inductor current drops; the motion trajectory in this state is a circular trajectory. When the inductor current drops below the reference value, the energy stored in the default inductor is not enough to make the output voltage continue to rise, and it needs to be charged; state, if the output voltage is less than the reference value and the inductor current is less than the reference value, the state machine is still working in the left half plane and switches to If the output voltage is greater than the reference value and the inductor current is greater than the reference value, the state machine enters the right half plane and switches to It can be obtained from the above description switch to The switching condition for i _L ≤i _Lref , switch to The switching condition of V _o ≥ V _ref ; by state jump to Analysis of switching conditions: The movement trajectory in the state is a circular trajectory, and the working point moves along the trajectory until the ON-state movement trajectory with the current point as the initial point passes the reference point, and the switching condition is met; it can also be understood as the current point as the initial point. When the slope of the straight-line working track is less than or equal to the slope of the line connecting the current point and the reference point, the switching condition is satisfied; the slope of the straight-line motion track under the ON-state structure obtains different values according to the difference of the initial point. From S1, ON- The motion trajectory equation of the state is as follows The slope of the straight line is related to the output voltage at the initial point and the controller parameters, and its value is Take the current point as the next starting point of the state When the motion track passes the reference point, the state jumps, and the jump condition is The above formula can be transformed into (i _Lref -i _L0 )*L*V _o0 ≤R*C*V _g *(V _o0 -V _ref ) In order to further simplify the above formula, according to the input and output power conservation equation Substitution can be obtained Among them, i _L*ref is the converted inductor current reference value, by state jump to and Analysis of switching conditions: in In the state, the inductor current rises and the output voltage drops; The main function of the state is the transition state of state switching. When the switching condition i _L* ≥ i L _*ref is satisfied and still working in the right half plane, switch to Switch to when the condition V _o ≤ V _ref and i _L* ≤ i L _*ref The state machine enters the left half plane to work. 8. the control method based on the Boost DC-DC converter of second-order sliding mode control according to claim 1, is characterized in that, described S3 comprises: S3-1, according to the finite state machine controller based on the second-order sliding mode control, establish a finite state machine controller with an increased time lag value, and make the control variable converge to the equilibrium point under the condition of limited frequency, that is, Boost transformation The output of the controller tracks the upper given value without deviation; the time lag value is set to β, in the state jump to The following switching conditions can be obtained by adding a time lag value to the switching condition After adding the delay value, the state machine can cross the boundary and enter the right half plane after a finite number of switching cycles, and can form a limit cycle centered on the reference point; after entering the equilibrium state, the output voltage formed by the delay value β and the final steady state The relationship between the ripple coefficient of the ripple is explained by the following derivation; the final limit cycle has two switching points, which are also the switching points when the controller structure is switched, which is set to A(i _L*A , V _oA ), B(i _L*B , V _oB ); at the same time, set the target ripple coefficient of the output voltage to W, because the center of the limit cycle is the reference point, so the expression of the coordinates of the two points can be obtained, V _oA =V _ref -V _ref *W/2, V _oB ＝V _ref +V _ref *W/2, i _L*A ＝|K|*V _ref *W/2+i _L*ref , i _L*B ＝i _{L* ref} -|K|*V _ref *W/2; because the two points A and B are the two intersection points on the circle trajectory of OFF-state and the straight line trajectory of ON-state; after calculating the coordinates of one point, according to the following The formula is able to calculate the expression of the lag value