A control method and control structure for a fractional-order inductor structure

Abstract

The present invention discloses a control method and a control structure for a fractional-order inductor structure, which are applied to a DC-DC converter including an LC or LC-like topology structure; the method includes: feeding forward the current of an equivalent real inductor L e , and connecting a virtual resistor r s in series with the inductor L BPF after passing through a first band-pass filter G e to form a current feedback loop, so as to realize adjustable order of the fractional-order inductor at any frequency; forming a voltage feedback loop through bus voltage feedback to realize adjustable impedance amplitude of the fractional-order inductor at any frequency. The control method of the fractional-order inductor structure of the present invention only needs to change the control structure of the DC-DC converter, and can arbitrarily adjust the impedance and order of the fractional-order inductor, and can be applied to various power occasions without any additional electronic components, greatly reducing the cost of constructing the fractional-order inductor.

Description

Technical Field

[0001] The present invention relates to the field of power electronic converter control, and particularly to a control method and a control structure for a fractional-order inductor configuration. Background Art

[0002] In the 1990s, the fractional-order nature of capacitors and inductors was discovered. An inductor is not a simple integer-order component, and its complex characteristics exhibit fractional-order behavior. The models obtained by modeling capacitors and inductors with fractional-order calculus are not only more accurate but also more complete compared with integer-order models. In addition, after modeling inductors and capacitors with fractional-order calculus, additional degrees of freedom can be extended in the form of any-order fractional order, that is, the order of the inductor is arbitrarily adjustable. The fractional-order inductor also has memory characteristics and genetic properties, and has broad application prospects in the electrical field.

[0003] Currently, the methods for constructing fractional-order inductors are mainly divided into four categories. The first category is to combine passive devices to simulate the characteristics of fractional-order inductor devices. For example, an inductor and a resistor in series can form a fractional-order inductor with an order less than 1. However, this method has great drawbacks. For example, the design is complex, and when changing the order of the fractional-order inductor, it is necessary to reselect and design device parameters, so it is inefficient and expensive. The second method is to construct a fractional-order inductor through an operational amplifier circuit. Although this method can achieve adjustable order of the fractional-order inductor, it can only be applied to low-power applications at the milliwatt level, which limits its application in the industrial electrical field. The third method is to manufacture a fractional-order inductor through a process method, such as making a fractional-order inductor by filling a highly conductive material. However, this method can also only achieve a fractional-order inductor with an order less than 1. When it is necessary to change the order and impedance of the inductor, it is necessary to redesign and manufacture. The fourth method is to realize a fractional-order inductor through a control method. This method can arbitrarily change the order and impedance of the fractional-order inductor by modifying the parameters of the controller, and can be applied to various power levels at the same time, and has broad application prospects. Summary of the Invention

[0004] In view of the above problems, the present invention provides a control method and a control structure for a fractional-order inductor configuration, which can achieve adjustable order and impedance of the inductor at any frequency, solve the problems of increased volume, complex design, non-arbitrary adjustment of order and impedance, and limited application power level brought by traditional fractional-order inductor construction methods. At the same time, the control method does not affect the original system dynamic performance of the DC-DC converter.

[0005] The technical solutions adopted by the present invention to solve the above technical problems are as follows:

[0006] On the one hand, a control method for a fractional-order inductor structure is applied to a DC-DC converter including an LC or LC-like topology; it is characterized in that it includes:

[0007] Feed forward the current of the equivalent real inductor L e , and a virtual resistor r s After passing through the first band-pass filter G BPF (s) is connected in series with the inductor L e To form a current feedback loop, realizing adjustable order of the fractional-order inductor at any frequency;

[0008] Form a voltage feedback loop through bus voltage feedback, realizing adjustable impedance amplitude of the fractional-order inductor at any frequency.

[0009] Preferably, the control method specifically includes:

[0010] Step 1), define the mathematical model of the fractional-order inductor, which is expressed as follows:

[0011]

[0012] It can be seen from the above formula that the fractional-order inductor is equivalent to an integer-order inductor L eq And a resistor R e In series, the equivalent inductor L eq And the equivalent series resistance R eq Are related to the order α and frequency, where 0 < α < 2; therefore, a virtual resistor r s Is connected in series to form a fractional-order inductor with adjustable order at any frequency;

[0013] Step 2), within a control period, collect the current e Value of the inductor L in the DC-DC converter , and return the sampling result to the controller;

[0014] Step 3), multiply the current value By the first band-pass filter G BPF (s) and the virtual resistor r s To obtain the feedback function of the current feedback loop The first band-pass filter G BPF (s) is expressed as follows:

[0015]

[0016] Among them, f b Is the bandwidth, and f c Is the center frequency of the band-pass filter;

[0017] Step 4), take Divided by the transfer function H of the current feedback loop 1 (s), and feed the obtained result forward to the output port of the controller; the transfer function H of the current feedback loop 1 (s) is expressed as follows:

[0018] H 1 (s) = G d (s)e(s)M(D) (3)

[0019] Among them, G d (s) is the equivalent transfer function of the controller delay; e(s) is the coefficient of the controlled voltage source in the unified small-signal model of the DC-DC converter; M(D) is the voltage gain of the DC / DC converter;

[0020] Thus, the expression of the current feedback loop constituting the virtual resistor is Based on steps 2), 3) and 4), the equivalent expression of the fractional-order inductor is

[0021] Z Le (s) = sL e +r s G BPF (s) (4)

[0022] Step 5), within one control period, collect the voltage value u of the bus capacitor C in the DC-DC converter b , and feed the sampling result forward to the controller through the voltage feedback loop; bus

[0023] Step 6), subtract the bus capacitor voltage u from the reference voltage u of the DC-DC converter r , and then multiply by the band-pass filter B bus (s); the second band-pass filter B R (s) is expressed as follows: R (s) is expressed as follows:

[0024]

[0025] Among them, K is the proportionality coefficient;

[0026] Through step 6), the transfer function H 2 (s) is obtained, and its expression is

[0027] H 2 (s) = (u r -u bus )B R (s) (6)

[0028] Step 7), subtract the bus capacitor voltage u from the reference voltage u of the DC-DC converter r ​​bus , subtract the transfer function H 2 (s) obtained in step 6) to get a new error error = (u r - u bus ) × (1 - B R (s));

[0029] Step 8), multiply the error error obtained in step 7) by the transfer function G v (s) of the controller. The transfer function of the controller G v (s) is expressed as follows:

[0030]

[0031] Step 9), multiply the bus capacitor voltage u bus by the band - pass filter B R (s) and then divide by the transfer function H 1 (s), and then feedback it to the output port of the controller;

[0032] Step 10), based on steps 2) to 9), the transfer function of the impedance of the equivalent fractional - order inductor is:

[0033]

[0034] In the above formula, K R (s) is expressed as follows:

[0035]

[0036] It can be seen from the expression of Z L (s) that the equivalent fractional - order inductor realizes arbitrary frequency tuning of impedance and order.

[0037] Preferably, the equivalent inductance value L e is related to the topological structure.

[0038] Preferably, it can be known from the transfer function of the impedance of the equivalent fractional - order inductor that by changing the center frequency of the band - pass filter and the value of the virtual resistor r s , the resistance value of the virtual resistor at the center frequency is changed, and the virtual resistor value at the non - center frequency is 0.

[0039] Preferably, it can be known from the transfer function of the impedance of the equivalent fractional - order inductor that by changing the center frequency of the band - pass filter and the value of the virtual resistor r s , the order α of the fractional - order inductor is changed.

[0040] Preferably, in step 4), the coefficient e(s) and the voltage gain M(D) of the controlled voltage source are related to the topological structure.

[0041] Preferably, in step 10), the impedance of the equivalent fractional-order inductor is adjusted by changing the coefficient K of K(s), and the value range of K is -1 ≤ K < ∞. R (s), and the value range of K is -1 ≤ K < ∞.

[0042] On the other hand, a control structure of a fractional-order inductor configuration is applied to a DC-DC converter including an LC or LC-like topology; characterized in that it includes a current feedback loop and a voltage feedback loop;

[0043] The current feedback loop is used to feed forward the current of the equivalent real inductor L e and connect a virtual resistor r s in series with the inductor L after passing through the first band-pass filter G BPF (s), so as to realize adjustable order of the fractional-order inductor at any frequency; e The voltage feedback loop is used to feedback the bus voltage to realize adjustable impedance amplitude of the fractional-order inductor at any frequency.

[0044] The beneficial effects of the present invention are as follows:

[0045] (1) By changing the parameters of the controller, the impedance and order of the fractional-order inductor can be arbitrarily changed, overcoming the defects of complex design, high cost, fixed and unchangeable order and impedance, and low power level in the traditional method;

[0046] (2) By modifying the resistance value of the virtual resistor, the order of the fractional-order inductor can be arbitrarily changed, and by changing the coefficient K of the band-pass filter, the impedance of the fractional-order inductor can be arbitrarily changed;

[0047] (3) By changing the center frequency f of the band-pass filter

[0048] the impedance and order of the fractional-order inductor at different frequencies can be arbitrarily changed, and the order and impedance of the inductor at non-center frequencies are not affected; c the impedance and order of the fractional-order inductor at different frequencies can be arbitrarily changed, and the order and impedance of the inductor at non-center frequencies are not affected;

[0049] (4) Both the inductor current feedback loop and the voltage feedback loop of the present invention include band-pass filters, and the use of the band-pass filters does not affect the original dynamic performance of the DC-DC converter. Description of the Drawings

[0050] Figure 1 is the unified small-signal model of the existing DC-DC converter;

[0051] Figure 2 is the voltage closed-loop control block diagram of the existing DC-DC converter;

[0052] Figure 3 is the closed-loop control block diagram of the fractional-order inductor applied to the DC-DC converter configuration in the embodiment of the present invention;

[0053] Figure 4 is the first band-pass filter G of the embodiment of the present invention BPF (s) Bode plot;

[0054] Figure 5 is the second band-pass filter B of the embodiment of the present invention R (s) Bode plot;

[0055] Figure 6 is for the embodiment of the present invention when K = 1, L e = 1mH, at 100Hz, the relationship diagram of the order of the fractional-order inductor varying with r s ;

[0056] Figure 7 is for the embodiment of the present invention when r s = 1Ω, L e = 1mH, at 100Hz, the Bode plot of the fractional-order inductor under different K;

[0057] Figure 8 is for the embodiment of the present invention when r s = 1Ω, L e = 1mH, K = 1, the Bode plot of the fractional-order inductor at different center frequencies f of the band-pass filter c ;

[0058] Figure 9 is the unified small-signal model of the DC-DC converter containing a fractional-order inductor in the embodiment of the present invention. Detailed implementation manners

[0059] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and not to limit the scope of the present invention. After reading the present invention, various equivalent modifications made by those skilled in the art fall within the scope defined by the appended claims of this application.

[0060] In this embodiment, a control method for a fractional-order inductor structure is provided. The controlled object is a DC-DC converter containing an LC circuit or a similar LC circuit, including but not limited to buck, boost, buck-boost and their derivative topologies.

[0061] Referring to Figure 1 shown is the unified small-signal model of an existing DC-DC converter, where L e is the equivalent real inductor, C b is the bus capacitor, e(s) and j(s) are the coefficients of the control voltage source and the control current source respectively, and M(D) is the voltage gain of the DC-DC converter. Among them, L e, The expressions of e(s), j(s), and M(D) are shown in the following table. Among them, L b is the true inductance value of the DC-DC converter, and I Lb is the current passing through the inductor L b . N is the turns ratio of the transformer. For a non-isolated DC-DC converter, N = 1. The expressions of L e , e(s), j(s), and M(D) for each topology are shown in Table 1 below.

[0062] Table 1

[0063]

[0064] See Figure 2 shown in Figure 1 the closed-loop control block diagram of the unified small-signal model of the DC-DC converter shown. It can be seen from Figure 2 that the equivalent inductor L e of the DC-DC converter is an inductor of integer first order. Therefore Figure 2 the order and impedance of the closed-loop control block diagram shown cannot be changed.

[0065] See Figure 3 shown in the closed-loop control block diagram for controlling the fractional-order inductor with arbitrarily adjustable order and impedance of the DC-DC converter. The specific implementation steps of the control method proposed by the present invention include:

[0066] Step 1), Build the small-signal model and closed-loop control block diagram of the DC-DC converter; the mathematical model of the fractional-order inductor is expressed as follows:

[0067]

[0068] It can be seen from the above formula that the fractional-order inductor is equivalent to a series connection of an integer-order inductor L eq and a resistor R eq . The equivalent inductor L eq and the equivalent series resistor R eq are related to the order α and the frequency, where 0 < α < 2; therefore, a virtual resistor r s is connected in series with the integer-order inductor to form a fractional-order inductor with adjustable order at any frequency.

[0069] Step 2), In each sampling period, the current e of the inductor L is sampled by the sensor and the sampling result is input into the controller for further data processing.

[0070] Step 3), Multiply the current value by the first band-pass filter G BPF (s) and the virtual resistor rs , obtain the feedback function of the current feedback loop Band-pass filter G BPF (s) is expressed as

[0071]

[0072] In the above formula, f b is the bandwidth, f c is the center frequency of the band-pass filter.

[0073] Step 4), let be divided by the transfer function H 1 (s) of the current feedback loop, and feed the obtained result forward to the output port of the controller; the transfer function H 1 (s) of the current feedback loop is expressed as follows:

[0074] H 1 (s) = G d (s)e(s)M(D) (3)

[0075] where, G d (s) is the delay equivalent transfer function of the controller; e(s) is the coefficient of the controlled voltage source in the unified small-signal model of the DC-DC converter; M(D) is the voltage gain of the DC / DC converter;

[0076] Thus, the expression of the current feedback loop constituting the virtual resistor is Based on Step 2), Step 3) and Step 4), the equivalent expression of the fractional-order inductor is obtained as

[0077] Z Le (s) = L e + r s G BPF (s) (4)

[0078] The closed-loop feedback loop constructed in Step 3) and Step 4) refers to the loop above the main control structure in Figure 3 .

[0079] Step 5), within one control period, collect the voltage value u b of the bus capacitor C bus in the DC-DC converter, and return the sampling result to the controller.

[0080] Step 6), subtract the bus capacitor voltage u r from the reference voltage u bus of the DC-DC converter, and then multiply by the band-pass filter B R (s). The expression of the band-pass filter B R (s) is

[0081]

[0082] In the above formula, K is the proportionality coefficient. The transfer function H 2 (s) is obtained through step 6), and its expression is

[0083] H 2 (s) = (u r - u bus )B R (s) (6)

[0084] Step 7), subtract the bus capacitor voltage u r from the reference voltage u bus of the DC-DC converter, and then subtract the transfer function H 2 (s) obtained in step 6) to get a new error error = (u r - u bus ) × (1 - B R (s)).

[0085] Step 8), multiply the error error obtained in step 7) by the transfer function G v (s) of the PI controller. The transfer function of the PI controller G v (s) is

[0086]

[0087] Step 9), divide the bus capacitor voltage u bus by the feedback path transfer function H 1 (s), and then feedback it to the output port of the PI controller.

[0088] It should be noted that in this embodiment, the reference voltage u r and the bus capacitor voltage u bus represent instantaneous signals, representing the sum of large signals and small signals, while Figure 3 in and represent small signals.

[0089] The closed-loop feedback loop constructed in steps 5) to 9) is shown in the loop below the main control structure in Figure 3 .

[0090] See Figure 4 shown, which is the Bode plot of the band-pass filter G BPF (s) of this embodiment, and its gain at the center frequency f c is 1.

[0091] See Figure 5 shown, which is the band-pass filter K of this embodimentR Bode plot of (s), with the center frequency f c having a gain of K at.

[0092] See Figure 6 As shown, for K = 1, L e = 1mH, at 100Hz, the relationship between the order of the fractional - order inductor and r s changing. It can be seen from the figure that the order of the fractional - order inductor can be changed by adjusting the value of r s , and the change range of the order α of the fractional - order inductor is 0 - 2.

[0093] See Figure 7 As shown, for r s = 0.2Ω, L e = 1mH, at 100Hz, the Bode plots of the fractional - order inductor at different K values. It can be seen from the figure that the impedance of the fractional - order inductor can be changed by changing the value of the gain K.

[0094] See Figure 8 As shown, for r s = 0.2Ω, L e = 1mH, K = 1, the Bode plots of the fractional - order inductor at different center frequencies f c of the band - pass filter. It can be seen from the figure that the order and impedance of the fractional - order inductor can be changed by changing the center frequency fc of the band - pass filter, and other frequencies are not affected.

[0095] See Figure 9 As shown, the unified small - signal model of the DC - DC converter containing the fractional - order inductor constructed in this embodiment.

[0096] The above is only a specific embodiment of the present invention, but the design concept of the present invention is not limited thereto. Any non - substantial modification made to the present invention using this concept shall fall within the scope of infringement of the protection of the present invention.

Claims

1. A control method for a fractional-order inductor structure, characterized in that, it is applied to a DC-DC converter including an LC or LC-like topology; characterized in that it includes: Feed forward the current of the equivalent real inductor L e , and pass a virtual resistor r s through the first band-pass filter G BPF (s) and then connect it in series with the inductor L e to form a current feedback loop, so as to realize adjustable order of the fractional-order inductor at any frequency; forming a voltage feedback loop through bus voltage feedback to achieve adjustable impedance amplitude of the fractional-order inductor at any frequency; The control method specifically includes: Step 1), defining the mathematical model of the fractional-order inductor, expressed as follows: It can be seen from the above formula that the fractional-order inductor is equivalent to an integer-order inductor L eq and a resistor R eq in series. The equivalent inductor L eq and the equivalent series resistance R eq are related to the order α and the frequency, where 0 < α < 2; therefore, a virtual resistor r s is connected in series with the integer-order inductor to form a fractional-order inductor with adjustable order at any frequency; Step 2), within a control period, collect the current e of the inductor L in the DC-DC converter and return the sampling result to the controller; Step 3), multiply the current value by the first band-pass filter G BPF (s) and the virtual resistance r s to obtain the feedback function of the current feedback loop The first band-pass filter G BPF (s) is expressed as follows: where f b is the bandwidth, and f c is the center frequency of the band-pass filter; Step 4), divide by the transfer function H 1 (s) of the current feedback loop, and feed forward the obtained result to the output port of the controller; the transfer function H 1 (s) of the current feedback loop is expressed as follows: Among them, G d (s) is the delay equivalent transfer function of the controller; e(s) is the coefficient of the controlled voltage source in the unified small-signal model of the DC-DC converter; M(D) is the voltage gain of the DC / DC converter; The expression of the current feedback loop constituting the virtual resistor is thus obtained as Based on steps 2), 3) and 4), the equivalent expression of the fractional-order inductor is obtained as Z Le (s) = sL e + r s G BPF (s) (4) Step 5), within a control period, collect the voltage value u of the bus capacitor C in the DC-DC converter b and feed the sampling result forward to the controller through the voltage feedback loop; bus ​ Step 6), subtract the bus capacitor voltage u r from the reference voltage u of the DC-DC converter bus , and then multiply by the band-pass filter B R (s); The second band-pass filter B R (s) is expressed as follows: where K is the proportionality coefficient; The transfer function H 2 (s) is obtained through step 6), and its expression is H 2 (s) = (u r -u bus )B R (s) (6) Step 7), subtract the bus capacitor voltage u r from the reference voltage u of the DC-DC converter bus , and then subtract the transfer function H 2 (s) obtained in step 6) to get a new error error = (u r - u bus ) × (1 - B R (s)); Step 8), multiply the error error obtained in step 7) by the transfer function G v (s) of the controller, and the transfer function of the controller G v (s) is expressed as follows: Step 9), multiply the bus capacitor voltage u bus by the band-pass filter B R (s) and then divide by the transfer function H 1 (s), and then feedback to the output port of the controller; Step 10), based on Steps 2) to 9), obtaining the transfer function of the impedance of the equivalent fractional-order inductor as: In the above formula, K R (s) is expressed as follows: From Z L As can be seen from the expression of (s), the equivalent fractional-order inductor realizes arbitrary frequency tuning of impedance and order.

2. The control method for a fractional-order inductor structure according to claim 1, characterized in that, Equivalent inductance value L e Is related to the topology structure.

3. The control method for a fractional-order inductor structure according to claim 1, characterized in that, It can be seen from the transfer function of the impedance of the equivalent fractional-order inductor that the resistance value of the virtual resistor at the center frequency is changed by changing the center frequency of the band-pass filter and the value of the virtual resistor r s instead of the virtual resistor value at the center frequency being 0.

4. The control method for a fractional-order inductor structure according to claim 1, characterized in that, It can be seen from the transfer function of the impedance of the equivalent fractional-order inductor that by changing the center frequency of the band-pass filter and the value of the virtual resistor r s the order α of the fractional-order inductor can be changed.

5. The control method for a fractional-order inductor structure according to claim 1, characterized in that, in Step 4), the coefficient e(s) and voltage gain M(D) of the controlled voltage source are related to the topology.

6. The control method for a fractional-order inductor structure according to claim 1, characterized in that, Step 10) The impedance of the equivalent fractional-order inductor is adjusted by changing the coefficient K of K(s), where the value range of K is -1 ≤ K < ∞. R (s). The value range of K is -1 ≤ K < ∞.

7. A control structure for a fractional-order inductor structure, characterized in that, it is applied to a DC-DC converter including an LC or LC-like topology; characterized in that it includes a current feedback loop and a voltage feedback loop for implementing the control method for a fractional-order inductor structure described in any one of claims 1 to 6; The current feedback loop is used to perform current feedforward of the equivalent true inductance L e and feed forward the current of a virtual resistor r s After passing through the first band-pass filter G BPF (s), it is connected in series with the inductor L e to achieve adjustable order of the fractional-order inductor at any frequency; The voltage feedback loop is used to feedback the bus voltage to achieve adjustable impedance amplitude of the fractional-order inductor at any frequency.

Images