A modeling and control method of current-continuous combined chopper switch

Abstract

The application relates to a modeling and control method of a current continuous combined chopper switch, which comprises the following steps: establishing a key of a current continuous combined chopper switch; establishing a key bond graph model of a BOOST circuit or a key bond graph model of a BUCK circuit; establishing a state equation of the circuit; and realizing the control of the circuit through model predictive control. The application is suitable for the combination of BUCK type and BOOST type chopper switches, realizes the unification of models in the on and off states, can establish an on-off key bond graph under the current continuous condition, distinguishes the "key" formed by the switch combination, sorts out the causal relationship in the key, divides the external key and the internal key, finally forms a model in which the external key is not affected by the internal key, solves the problem that the bond graph model changes with the switch state in the application of the circuit, expands the application range of the bond graph, and the time period is not limited to fault diagnosis, but can control the circuit based on the model.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of bond graph modeling, and in particular to a modeling and control method of a current continuous combined chopper switch. BACKGROUND

[0002] A bond graph model can establish a state equation of a system, and is widely applied to system optimization, control, fault tolerance and the like. However, it is difficult to model a switching device by using the bond graph model. For a modern power electronic converter, the application of the switching device is extremely important, which leads to the difficulty in applying the bond graph model to the power electronic converter and increases the difficulty in system modeling. At present, some technologies are used to model the switching device by using the bond graph model, but there are problems such as the need for approximation, the non-uniformity of the model in the on and off states and the like. Therefore, the overall circuit model established by using the switching device model has the limitations of low precision and complex model.

[0003] At present, the bond graph model in the circuit application has the problem of model change with the switching state. The existing on-off bond graph model can only be used for fault diagnosis and cannot be used for the control of the circuit. For the control of the circuit, the basis is to establish an accurate model which is not affected by the switching state and is stable in the continuous time domain. The current bond graph model cannot realize the unification of the model in the on and off states of the power switch tube, and therefore limits the application range of the model.

[0004] For a current continuous circuit, the current control method is usually voltage closed loop, current closed loop or voltage and current double closed loop control. The design of the controller depends on the small signal model of the circuit. However, the application of the small signal model has limitations, which leads to the fact that the controller cannot achieve the expected control effect. The parameter design also needs to consider the frequency domain response characteristics of the model, and the controller has poor robustness and is easily disturbed by parameter deviation. Although the model predictive control can solve these problems, the model established by using the existing small signal modeling method cannot obtain the state equation of the system, which leads to the fact that the model predictive control cannot be applied to the above-mentioned circuit. SUMMARY

[0005] In order to solve the problem that the existing technology needs approximation, the on and off states of the model cannot be unified, the purpose of the application is to provide a modeling and control method of a current continuous combined chopper switch which is suitable for the combination of BUCK and BOOST type chopper switches and realizes the unification of the model in the on and off states.

[0006] In order to achieve the above-mentioned purpose, the following technical scheme is adopted in the application: a modeling and control method of a current continuous combined chopper switch, which comprises the following sequential steps:

[0007] (1) establishing the bond of the current continuous combined chopper switch;

[0008] (2) According to the bonding of the current continuous type combined chopper switch, a BOOST circuit bonding graph model with bonding or a BUCK circuit bonding graph model with bonding is established;

[0009] (3) Establishing the circuit state equation based on the BOOST circuit bonding graph model with a bond or the BUCK circuit bonding graph model with a bond;

[0010] (4) Based on the state equation, circuit control is achieved through model predictive control.

[0011] The step (1) specifically includes the following steps in order:

[0012] (1a) Constructing a practical circuit for BOOST and BUCK type combination: For the combination of a continuous current combined chopper switch, the switch S and the diode D are equivalent to switches that are alternately turned on. Let the driving signal of the switch S be sw. When sw = 1, the switch S is turned on, the potential source Se = 0, and the diode D is cut off. The diode D is a current source, that is, the current source Sf = 0; when sw = 0, the switch S is cut off. The switch S is a current source, that is, Sf = 0. At this time, the diode D is turned on, and the diode D is a potential source, that is, Se = 0. There are two forms of combination of continuous current combined chopper switches: BOOST type and BUCK type.

[0013] (1b) Determination of causal relationships of BOOST and BUCK type combined keys: In either form, the SW of different switch states is different, and the causal relationships of internal keys are different, but the causal relationships of edge keys are determined; the edge keys include the first key, the fifth key, and the sixth key, and the internal keys include the second key, the third key, the fourth key, and the seventh key;

[0014] (1c) Constructing a mathematical model of the bond:

[0015] Node 0 is a common potential junction, used to connect variables with equal voltage in the circuit. For node 0, only one input is allowed to be potential, and the potentials of all bonds are the same. Node 1 is a common current junction, used to connect variables with equal current in the circuit. For node 1, only one input is allowed to be current, and the currents of all bonds are the same. Under the defined reference direction of energy flow, we have:

[0016]

[0017]

[0018] Where, u1 to u7 are the voltages from the first key to the seventh key, and i1 to i7 are the currents from the first key to the seventh key;

[0019] When sw=1,u7=0,i4=0,then:

[0020]

[0021] When sw=0,i7=0,u4=0,then:

[0022]

[0023] Then the potential-current relationship of the edge bond, i.e. the bond of the current continuous combined chopper switch, can be uniformly expressed as:

[0024]

[0025] u1=swu6+(1-sw)u5.

[0026] In step (2), the step of establishing a bonding graph model of a BOOST circuit with bonding specifically refers to:

[0027] For the inductor L, we have:

[0028]

[0029] For grounding points, there are:

[0030] u6=u8=0 (2)

[0031] For SD keys, there are:

[0032]

[0033] u1=(1-sw)u5=u2-u3 (4)

[0034] Transformed into:

[0035] u3=u2-u1=U in -(sw-1)u5 (5)

[0036] For output, we have:

[0037]

[0038] i4=i5-i7 (7)

[0039]

[0040] Where, u1 to u8 are the voltages of the first to eighth keys, i1 to i7 are the currents of the first to seventh keys, Uin is the input voltage of the BOOST circuit, R, C, and L are the equivalent load of the circuit, the output filter capacitor, and the boost inductor, respectively.

[0041] Equations (1) to (8) are the BOOST circuit bond graph model. Regardless of whether the driving signal sw of the switch S is a discrete PWM signal or a continuous variable representing the duty cycle, the input and output of the BOOST circuit bond graph model satisfy the BOOST circuit characteristics. Therefore, the switching signal is converted into a continuous signal, and the discrete system is treated as a continuous system.

[0042] In step (2), the step of establishing a bond graph model of a BUCK circuit with a bond specifically refers to:

[0043] For the inductor L, we have:

[0044]

[0045] For grounding points, there are:

[0046] u5=u8=0(10)

[0047] For SD keys, there are:

[0048]

[0049] u1=swu6=u2-u3 (12)

[0050] Transformed

[0051] u3=u2-u1=U in -swu6 (13)

[0052] For output, there are

[0053]

[0054] i4=-i2-i7 (15)

[0055]

[0056] Where, u1 to u8 are the voltages of the first to eighth keys, i1 to i7 are the currents of the first to seventh keys, Uin is the input voltage of the BOOST circuit, R, C, and L are the equivalent load of the circuit, the output filter capacitor, and the boost inductor, respectively.

[0057] Equations (9) to (16) are the buck circuit bond graph models. Similarly, regardless of whether the drive signal sw of the switch S is a discrete PWM signal or a continuous variable representing the duty cycle, the input and output of the buck circuit bond graph model satisfy the buck circuit characteristics. Therefore, the switching signal is converted into a continuous signal, and the discrete system is treated as a continuous system.

[0058] The step (3) specifically refers to: establishing a state equation according to the BOOST circuit bond graph model, and the input variable u(t) is:

[0059] u(t)=U in (t)

[0060] Where U in (t) is the input voltage of the BOOST circuit at time t;

[0061] The state variable x(t) is:

[0062]

[0063] Where q4 is the charge of capacitor C, p3 is the inductor flux, Then the first differential of the state variable is:

[0064]

[0065] u4 and i3 are represented as:

[0066]

[0067] For i4, there are:

[0068]

[0069] For u3, there are

[0070]

[0071] Among them, u3, u4, u5, and u7 are the voltages of the third, fourth, fifth, and seventh keys respectively; i1, i3, i4, i5, and i7 are the currents of the first, third, fourth, fifth, and seventh keys respectively; Uin is the input voltage of the BOOST circuit; R, C, and L are the equivalent load of the circuit, the output filter capacitor, and the boost inductor respectively; sw is the driving signal of the switch S;

[0072] The state equation of the system is obtained as follows:

[0073]

[0074] Where A and B are coefficient matrices, and R is the equivalent load of the circuit.

[0075] The step (4) specifically includes the following steps in order:

[0076] (4a) Determination of output equation and cost function

[0077] The output equation is:

[0078]

[0079] Then the cost function J is set to:

[0080]

[0081] Where Ts is the calculation period; u4 and u7 are the voltages of the fourth and seventh keys respectively, C is the output filter capacitor, and q4 is the charge of capacitor C;

[0082] (4b) Model predictive control based on state equation, output equation and cost function:

[0083] Sample u4 and the current i3 of the third key, calculate q4 and p3, and predict the state variables when sw is 0 and 1 respectively according to the following formula:

[0084]

[0085] Where p3 is the inductor flux, R and L are the equivalent load and boost inductor of the circuit respectively; Uin is the input voltage of the BOOST circuit; sw is the drive signal of switch S; x(t) is the state variable, and u(t) is the input variable;

[0086] Thus, the predicted value of q4 is calculated and substituted into the following formula:

[0087]

[0088] Take the sw corresponding to the minimum J to realize the control of the BOOST circuit.

[0089] It can be seen from the above technical solution that the beneficial effects of the present invention are: first, the present invention is applicable to both BUCK-type and BOOST-type chopper switch combinations, and realizes the unification of models in the on and off states, and can establish a switch key bonding diagram under the condition of continuous current; second, by distinguishing the "bonds" formed by the switch combination, sorting out the causal relationship within the bond, dividing the external bonds and internal bonds, and finally forming a model in which the external bonds are not affected by the changes of the internal bonds, it solves the problem that the current application of the bond diagram in the circuit has the problem that the model changes with the switch state, and expands the application scope of the bond diagram. The period is not only limited to fault diagnosis, but can also control the circuit based on the model; third, the established model does not need to simplify or equate the switching device, and is applicable to both continuous switching signals and discrete switching signals. Therefore, the model has high accuracy and the control algorithm based on the model is simple, which helps to improve the control accuracy of the power electronic converter and reduce the burden on the operation processor. BRIEF DESCRIPTION OF THE DRAWINGS

[0090] Figure 1 There are two forms of bonding;

[0091] Figure 2 It is a key causal relationship;

[0092] Figure 3 It is a key model of combined chopper switch;

[0093] Figure 4 It is the BOOST circuit bond diagram;

[0094] Figure 5 This is the BUCK circuit bonding diagram. DETAILED DESCRIPTION

[0095] A modeling method for a current continuous combined chopper switch includes the following steps in sequence:

[0096] (1) Establish the key of the current continuous type combined chopper switch;

[0097] (2) According to the bonding of the current continuous type combined chopper switch, a BOOST circuit bonding graph model with bonding or a BUCK circuit bonding graph model with bonding is established;

[0098] (3) Establishing the circuit state equation based on the BOOST circuit bonding graph model with a bond or the BUCK circuit bonding graph model with a bond;

[0099] (4) Based on the state equation, circuit control is achieved through model predictive control.

[0100] The step (1) specifically includes the following steps in order:

[0101] (1a) Construct a practical circuit for BOOST and BUCK type combination: For the combination of a continuous current combined chopper switch, the switch S and the diode D are equivalent to switches that are alternately turned on. Let the driving signal of the switch S be sw. When sw = 1, the switch S is turned on, the potential source Se = 0, and the diode D is cut off. The diode D is a current source, that is, the current source Sf = 0; when sw = 0, the switch S is cut off. The switch S is a current source, that is, Sf = 0. At this time, the diode D is turned on, the diode D is a potential source, that is, Se = 0; There are two forms of combination of continuous current combined chopper switches, namely BOOST type and BUCK type, as shown in Figure 1 As shown, no matter which form is used, the direction of the dotted arrow in the figure is defined as the positive direction of energy flow. Figure 1 The form of (a) is the same as the actual energy flow direction; Figure 1 The form of (b) is opposite to the actual energy flow direction. At this time, the two forms can be unified.

[0102] (1b) Determination of BOOST and BUCK type causal relationships: In either form, sw is different in different switch states, e.g. Figure 2As shown, the causal relationships of the internal keys are different, but the causal relationships of the edge keys are determined; the edge keys include the first key, the fifth key, and the sixth key, and the internal keys include the second key, the third key, the fourth key, and the seventh key;

[0103] (1c) Constructing a mathematical model of the bond:

[0104] Node 0 is a common potential junction, used to connect variables with equal voltage in the circuit. For node 0, only one input is allowed to be potential, and the potentials of all bonds are the same. Node 1 is a common current junction, used to connect variables with equal current in the circuit. For node 1, only one input is allowed to be current, and the currents of all bonds are the same. Under the defined reference direction of energy flow, we have:

[0105]

[0106] Where, u1 to u7 are the voltages from the first key to the seventh key, and i1 to i7 are the currents from the first key to the seventh key;

[0107] for Figure 2 In Figure (a), when sw=1,u7=0,i4=0,then:

[0108]

[0109] for Figure 2 In Figure (b), when sw=0, i7=0, u4=0, then:

[0110]

[0111] like Figure 3 As shown, the potential-current relationship of the edge bond, that is, the bond of the current continuous combined chopper switch, is uniformly expressed as:

[0112]

[0113] u1=swu6+(1-sw)u5.

[0114] In step (2), the step of establishing a bonding graph model of a BOOST circuit with bonding specifically refers to:

[0115] For the BOOST circuit, its bonding diagram is as follows Figure 4 As shown:

[0116] For the inductor L, we have:

[0117]

[0118] For grounding points, there are:

[0119] u6=u8=0 (2)

[0120] S is a switch, D is a diode, and the switch S and diode D are connected as Figure 1 , and converted into Figure 2 The bond graph model is the SD bond. For the SD bond, there are:

[0121]

[0122] u1=(1-sw)u5=u2-u3 (4)

[0123] Transformed into:

[0124] u3=u2-u1=U in -(sw-1)u5 (5)

[0125] For output, we have:

[0126]

[0127] i4=i5-i7 (7)

[0128]

[0129] Where, u1 to u8 are the voltages of the first to eighth keys, i1 to i7 are the currents of the first to seventh keys, Uin is the input voltage of the BOOST circuit, R, C, and L are the equivalent load of the circuit, the output filter capacitor, and the boost inductor, respectively.

[0130] Equations (1) to (8) are the BOOST circuit bond graph model. Regardless of whether the driving signal sw of the switch S is a discrete PWM signal or a continuous variable representing the duty cycle, the input and output of the BOOST circuit bond graph model satisfy the BOOST circuit characteristics. Therefore, the switching signal is converted into a continuous signal, and the discrete system is treated as a continuous system.

[0131] In step (2), the step of establishing a bond graph model of a BUCK circuit with a bond specifically refers to:

[0132] For the BUCK circuit, its bonding diagram is as follows Figure 5 As shown:

[0133] For the inductor L, we have:

[0134]

[0135] For grounding points, there are:

[0136] u5=u8=0 (10)

[0137] For SD keys, there are:

[0138]

[0139] u1=swu6=u2-u3 (12)

[0140] Transformed

[0141] u3=u2-u1=U in -swu6 (13)

[0142] For output, there are

[0143]

[0144] i4=-i2-i7 (15)

[0145]

[0146] Where, u1 to u8 are the voltages of the first to eighth keys, i1 to i7 are the currents of the first to seventh keys, Uin is the input voltage of the BOOST circuit, R, C, and L are the equivalent load of the circuit, the output filter capacitor, and the boost inductor, respectively.

[0147] Equations (9) to (16) are the buck circuit bond graph models. Similarly, regardless of whether the drive signal sw of the switch S is a discrete PWM signal or a continuous variable representing the duty cycle, the input and output of the buck circuit bond graph model satisfy the buck circuit characteristics. Therefore, the switching signal is converted into a continuous signal, and the discrete system is treated as a continuous system.

[0148] The step (3) specifically refers to: establishing a state equation according to the BOOST circuit bond graph model, and the input variable u(t) is:

[0149] u(t)=U in (t)

[0150] Where U in (t) is the input voltage of the BOOST circuit at time t;

[0151] The state variable x(t) is:

[0152]

[0153] Where q4 is the charge of capacitor C, p3 is the inductor flux, Then the first differential of the state variable is:

[0154]

[0155] u4 and i3 are represented as:

[0156]

[0157] For i4, there are:

[0158]

[0159] For u3, there are

[0160]

[0161] Among them, u3, u4, u5, and u7 are the voltages of the third, fourth, fifth, and seventh keys respectively; i1, i3, i4, i5, and i7 are the currents of the first, third, fourth, fifth, and seventh keys respectively; Uin is the input voltage of the BOOST circuit; R, C, and L are the equivalent load of the circuit, the output filter capacitor, and the boost inductor respectively; sw is the driving signal of the switch S;

[0162] The state equation of the system is obtained as follows:

[0163]

[0164] Where A and B are coefficient matrices, and R is the equivalent load of the circuit.

[0165] The step (4) specifically includes the following steps in order:

[0166] (4a) Determination of output equation and cost function

[0167] The output equation is:

[0168]

[0169] Then the cost function J is set to:

[0170]

[0171] Where Ts is the calculation period; u4 and u7 are the voltages of the fourth and seventh keys respectively, C is the output filter capacitor, and q4 is the charge of capacitor C;

[0172] (4b) Model predictive control based on state equation, output equation and cost function:

[0173] Sample u4 and the current i3 of the third key, calculate q4 and p3, and predict the state variables when sw is 0 and 1 respectively according to the following formula:

[0174]

[0175] Where p3 is the inductor flux, R and L are the equivalent load and boost inductor of the circuit respectively; Uin is the input voltage of the BOOST circuit; sw is the drive signal of switch S; x(t) is the state variable, and u(t) is the input variable;

[0176] Thus, the predicted value of q4 is calculated and substituted into the following formula:

[0177]

[0178] Take the sw corresponding to the minimum J to realize the control of the BOOST circuit.

[0179] The control method for the corresponding buck circuit is the same as that for the boost circuit. That is, the state equation of the circuit is established based on the bond graph model of the buck circuit with a bond. Based on the state equation, the circuit is controlled through model predictive control.

[0180] In summary, the present invention is applicable to both BUCK-type and BOOST-type chopper switch combinations, and realizes the unification of models in the on and off states, and can establish a switch key bonding diagram under the condition of continuous current; by distinguishing the "bonds" formed by the switch combination, sorting out the causal relationship within the bond, dividing the external bonds and internal bonds, and finally forming a model in which the external bonds are not affected by the changes of the internal bonds, it solves the problem that the model changes with the switch state when the bond diagram is currently applied in the circuit, and expands the application scope of the bond diagram. The period is not limited to fault diagnosis, but can control the circuit based on the model; the established model does not need to simplify or equate the switching device, and is applicable to both continuous switching signals and discrete switching signals. Therefore, the model has high accuracy and the control algorithm based on the model is simple, which helps to improve the control accuracy of the power electronic converter and reduce the burden on the operation processor.

Claims

1. A modeling and control method for a current-continuous combined chopper switch, characterized in that: The method comprises the following steps in sequence: (1) Establish the key of the current continuous type combined chopper switch; (2) According to the bonding of the current continuous type combined chopper switch, a BOOST circuit bonding graph model with bonding or a BUCK circuit bonding graph model with bonding is established; (3) Establishing the circuit state equation based on the BOOST circuit bonding graph model with a bond or the BUCK circuit bonding graph model with a bond; (4) Based on the state equation, circuit control is achieved through model predictive control; The step (1) specifically includes the following steps in order: (1a) Constructing a practical circuit for BOOST and BUCK type combination: For the combination of a continuous current combined chopper switch, the switch S and the diode D are equivalent to switches that are alternately turned on. Let the driving signal of the switch S be sw. When sw = 1, the switch S is turned on, the potential source Se = 0, and the diode D is cut off. The diode D is a current source, that is, the current source Sf = 0; when sw = 0, the switch S is cut off. The switch S is a current source, that is, Sf = 0. At this time, the diode D is turned on, and the diode D is a potential source, that is, Se = 0. There are two forms of combination of continuous current combined chopper switches: BOOST type and BUCK type. (1b) Determination of causal relationships of BOOST and BUCK type combined keys: In either form, the SW of different switch states is different, and the causal relationships of internal keys are different, but the causal relationships of edge keys are determined; the edge keys include the first key, the fifth key, and the sixth key, and the internal keys include the second key, the third key, the fourth key, and the seventh key; (1c) Constructing a mathematical model of the bond: Node 0 is a common potential junction, used to connect variables with equal voltage in the circuit. For node 0, only one input is allowed to be potential, and the potentials of all bonds are the same. Node 1 is a common current junction, used to connect variables with equal current in the circuit. For node 1, only one input is allowed to be current, and the currents of all bonds are the same. Under the defined reference direction of energy flow, we have: Where, u1 to u7 are the voltages from the first key to the seventh key, and i1 to i7 are the currents from the first key to the seventh key; When sw=1,u7=0,i4=0,then: When sw=0,i7=0,u4=0,then: Then the potential-current relationship of the edge bond, i.e. the bond of the current continuous combined chopper switch, can be uniformly expressed as: u1=swu6+(1-sw)u5.

2. The modeling and control method of the current continuous type combined chopper switch according to claim 1, characterized in that: In step (2), the step of establishing a bonding graph model of a BOOST circuit with bonding specifically refers to: For the inductor L, we have: For grounding points, there are: u6=u8=0 (2) For SD keys, there are: u1=(1-sw)u5=u2-u3 (4) Transformed into: u3=u2-u1=U in -(sw-1)u5 (5) For output, we have: i4=i5-i7 (7) Where, u1 to u8 are the voltages of the first to eighth keys, i1 to i7 are the currents of the first to seventh keys, Uin is the input voltage of the BOOST circuit, R, C, and L are the equivalent load of the circuit, the output filter capacitor, and the boost inductor, respectively. Equations (1) to (8) are the BOOST circuit bond graph model. Regardless of whether the driving signal sw of the switch S is a discrete PWM signal or a continuous variable representing the duty cycle, the input and output of the BOOST circuit bond graph model satisfy the BOOST circuit characteristics. Therefore, the switching signal is converted into a continuous signal, and the discrete system is treated as a continuous system.

3. The modeling and control method of the current continuous type combined chopper switch according to claim 1, characterized in that: In step (2), the step of establishing a bond graph model of a BUCK circuit with a bond specifically refers to: For the inductor L, we have: For grounding points, there are: u5=u8=0 (10) For SD keys, there are: u1=swu6=u2-u3 (12) Transformed u3=u2-u1=U in -swu6 (13) For output, there are i4=-i2-i7 (15) Where, u1 to u8 are the voltages of the first to eighth keys, i1 to i7 are the currents of the first to seventh keys, Uin is the input voltage of the BOOST circuit, R, C, and L are the equivalent load of the circuit, the output filter capacitor, and the boost inductor, respectively. Equations (9) to (16) are the buck circuit bond graph models. Similarly, regardless of whether the drive signal sw of the switch S is a discrete PWM signal or a continuous variable representing the duty cycle, the input and output of the buck circuit bond graph model satisfy the buck circuit characteristics. Therefore, the switching signal is converted into a continuous signal, and the discrete system is treated as a continuous system.

4. The modeling and control method of the current continuous type combined chopper switch according to claim 1, characterized in that: The step (3) specifically refers to: establishing a state equation according to the BOOST circuit bond graph model, and the input variable u(t) is: u(t)=U in (t) Where U in (t) is the input voltage of the BOOST circuit at time t; The state variable x(t) is: Where q4 is the charge of capacitor C, p3 is the inductor flux, Then the first differential of the state variable is: u4 and i3 are represented as: For i4, there are: For u3, there are Among them, u3, u4, u5, and u7 are the voltages of the third, fourth, fifth, and seventh keys respectively; i1, i3, i4, i5, and i7 are the currents of the first, third, fourth, fifth, and seventh keys respectively; Uin is the input voltage of the BOOST circuit; R, C, and L are the equivalent load of the circuit, the output filter capacitor, and the boost inductor respectively; sw is the driving signal of the switch S; The state equation of the system is obtained as follows: Where A and B are coefficient matrices, and R is the equivalent load of the circuit.

5. The modeling and control method of the current continuous combined chopper switch according to claim 1, characterized in that: The step (4) specifically includes the following steps in order: (4a) Determination of output equation and cost function The output equation is: Then the cost function J is set to: Where Ts is the calculation period; u4 and u7 are the voltages of the fourth and seventh keys respectively, C is the output filter capacitor, and q4 is the charge of capacitor C; (4b) Model predictive control based on state equation, output equation and cost function: Sample u4 and the current i3 of the third key, calculate q4 and p3, and predict the state variables when sw is 0 and 1 respectively according to the following formula: Where p3 is the inductor flux, R and L are the equivalent load and boost inductor of the circuit respectively; Uin is the input voltage of the BOOST circuit; sw is the drive signal of switch S; x(t) is the state variable, and u(t) is the input variable; Thus, the predicted value of q4 is calculated and substituted into the following formula: Take the sw corresponding to the minimum J to realize the control of the BOOST circuit.

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