High-power electromagnetic detection transmitter direct-current power supply topology and model prediction-based control method thereof

Abstract

The invention discloses a high-power electromagnetic detection transmitter direct-current power supply topology and a model prediction-based control method thereof, which are characterized in that the direct-current power supply topology adopts a mode of combining four converter modules IPOS (input parallel connection and output series connection), and the modules adopt a Buck-LLC two-stage converter cascade structure. Each module is independently controlled through a model prediction control method, a discrete mathematical model of the Buck-LLC two-stage converter is constructed, a control time domain M and a prediction time domain P are introduced, a prediction output equation and a value function are established, the optimal duty ratio of a driving signal of an equivalent circuit switching tube of the Buck-LLC two-stage converter is obtained according to the value function, and the optimal duty ratio of the driving signal of the equivalent circuit switching tube of the Buck-LLC two-stage converter is calculated. The rear-stage LLC circuit works at a resonant frequency point in an open-loop mode. According to the invention, soft switching, low-voltage input and high-voltage high-power output are realized, and quick response is made to load change, so that the efficiency, the stability and the response speed of the system are improved.

Description

Technical Field

[0001] The invention belongs to the field of power electronics technology and energy detection, and in particular relates to a direct current power supply topology of a high-power electromagnetic detection transmitter and a control method thereof based on model prediction (MPC). Background Art

[0002] With the increasing demand for mineral resources and the rapid development of energy detection technology, electromagnetic method, as an efficient means of energy exploration, is widely used in the detection of underground and marine minerals. The electromagnetic method injects a primary field into the underground medium to excite the conductor to generate a secondary field, and reveals the distribution pattern of mineral resources through the analysis of the secondary field. However, the exploration depth of existing electromagnetic detection transmitters is generally limited by the transmission power, which is difficult to meet the needs of deep resource detection.

[0003] The core DC power supply of the electromagnetic transmitter needs to have high efficiency and fast dynamic response capabilities while ensuring high power output. However, the traditional PI-controlled power supply system has slow response speed and poor robustness, making it difficult to adapt to complex and changing working environments. Summary of the invention

[0004] In response to the above-mentioned technical problems, the present invention proposes a DC power supply topology for a high-power electromagnetic detection transmitter and a control method based on model prediction (MPC). Through modular design and model predictive control technology, it effectively achieves low-voltage input, high-voltage, high-power output, high efficiency, rapid response and precise control to meet the application requirements of high-power electromagnetic detection transmitters.

[0005] The present invention discloses a high-power electromagnetic detection transmitter DC power supply topology and a control method thereof based on model prediction, the method comprising the following steps:

[0006] Step 1: Use four converter modules IPOS to build a high-power DC power supply topology in a combination of input parallel connection and output series connection. The converter module adopts a Buck-LLC two-stage converter cascade structure;

[0007] Step 2: Set the transformer ratio of the LLC circuit at the rear stage of the converter module to 1:1, the voltage gain to 1, and the switching frequency to be approximately equal to the resonant frequency, so that the output voltage of the LLC circuit at the rear stage is equal to the input voltage, and the Buck-LLC two-stage converter is equivalent to a Buck circuit. Each module is independently controlled by the model predictive control method;

[0008] Step 3: Select the inductor current i of the front-stage Buck circuit L and output voltage V o Establish the equivalent state space expression of Buck-LLC two-stage converter for the state variables;

[0009] Step 4: Discretize the equivalent state-space expression obtained in Step 3 using the forward Euler formula to obtain the discrete mathematical model of the Buck-LLC two-stage converter;

[0010] Step 5: Introduce two parameters, the control time domain M and the prediction time domain P, to establish the prediction output equation of the equivalent circuit; among them, the prediction time domain P is the number of steps for predicting the system output, and the control time domain M is the number of steps for controlling the system, and the control time domain M ≤ the prediction time domain P;

[0011] Step 6: Establish the cost function J of the prediction output equation;

[0012] Step 7: Optimize the cost function J, and obtain the optimal duty cycle of the switch tube drive signal of the equivalent circuit of the Buck-LLC two-stage converter according to the cost function J, so that the latter-stage LLC circuit operates open-loop at the resonant frequency point.

[0013] Furthermore, in Step 2, the state equations for the on and off states of the switch tube of the equivalently obtained Buck circuit are respectively:

[0014] When 0 < t < DT, the state equation of the circuit in the case of the switch tube being on is:

[0015]

[0016] When DT < t < T, the state equation of the circuit in the case of the switch tube being off is:

[0017]

[0018] In the formula, i L is the current of the inductor L of the front-stage Buck circuit, C is the output filter capacitor of the front-stage Buck circuit, V o is the output voltage of the Buck-LLC two-stage converter, V s is the input voltage, D is the duty cycle of the switch tube, i b is the output current of the front-stage Buck circuit, and T is the sampling period.

[0019] Step 3 further includes:

[0020] Denote the transmission efficiency as λ, and there is:

[0021]

[0022] i b = i o / λ;

[0023] i o = V o / R o ;

[0024] The state equations of the switch on and off are averaged by the state space averaging method, and the equivalent state space expression of the Buck-LLC two-stage converter is obtained as follows:

[0025]

[0026] Where V b is the output voltage of the previous Buck circuit, i o is the system output current, R o is the system equivalent load.

[0027] Furthermore, in step 4, the process of obtaining the discrete mathematical model of the equivalent Buck circuit includes:

[0028] The equivalent state space expression of the Buck-LLC two-stage converter is transformed into a discrete state equation through the forward Euler formula:

[0029]

[0030] make u(k)=D(k), we get:

[0031] x(k+1)=Ax(k)+Bu(k);

[0032] The output voltage at time k is the controlled output variable y(k), and its relationship with the inductor current and capacitor voltage is:

[0033] y(k)=Zx(k);

[0034] Where Z =

[01] ;

[0035] The state space model of the Buck circuit in discrete time is obtained as follows:

[0036]

[0037] Where T is the sampling period; x(k+1) is the state variable; u(k) is the control input variable; y(k) is the controlled output variable.

[0038] Step 5 further includes:

[0039] Change the state space model of the Buck circuit in discrete time to an incremental model:

[0040]

[0041] Among them: Δx(k)=x(k)-x(k-1), Δu(k)=u(k)-u(k-1);

[0042] Introduce two parameters: control time domain M and prediction time domain P;

[0043] The incremental model predicts the state of the Buck-LLC two-stage converter from time k+1 to k+P and the state of the output equation y(k) from time k+1 to k+P;

[0044] Define the P-step prediction output vector Y(k+1|k) as:

[0045]

[0046] Define the expression of the M-step input vector ΔU(k) ​​as:

[0047]

[0048] The output equations at time k+1 to k+P are transformed into:

[0049] Y(k+1|k)=GΔx(k)+HΔU(k)+Iy(k);

[0050] Where, the expressions of G, H and I matrices are as follows:

[0051]

[0052]

[0053] Furthermore, in step 6, the value function of the prediction output equation is established as:

[0054]

[0055] Wherein, w(k+i) is the reference value of the given reference input sequence at time k+i; q is the weighting factor of the predictive control output error, and r is the weighting factor of the predictive control increment.

[0056] Furthermore, in step 7, the process of optimizing the value function J includes the following steps:

[0057] Convert the cost function of the Buck-LLC two-stage converter into a matrix-vector form:

[0058] J=Q|Y(k+1|k)-W(k+1)| 2 +R|ΔU(k)| 2 ;

[0059] The expressions of weighted matrices Q and R are: Q = diag (q1, q2, ..., q P ), R = diag(r1,r2,(,r M ), where q1,q2,…,q PWeighting factors of predictive control output error, r1, r2, …, r M is the weighting factor for the predictive control increment.

[0060] The reference input sequence W(k+1) is:

[0061]

[0062] The optimal duty cycle of the converter model predictive control strategy is:

[0063] ΔU * (k)=(H T Q T QH+R T R) -1 H T Q T QE(k+1|k);

[0064] In the formula, E(k+1|k)=W(k+1)-GΔx(k)-Iy(k);

[0065] Closed-loop control is introduced, and the first element of the calculated open-loop optimal control sequence is applied to the system. The optimal control increment is defined as:

[0066] Δu(k)=ηΔU * (k) = η(H T Q T QH+R T R) -1 H T Q T QE(k+1|k);

[0068] Where η=[1 0 … 0] 1×M .

[0069] The beneficial effects of the present invention are:

[0070] First, the DC power supply topology of the high-power electromagnetic detection transmitter of the present invention and its control method based on model prediction (MPC) adopts modular IPOS combination design to achieve low-voltage input and high-voltage output, improve power density and system reliability, and meet the application requirements of high-power electromagnetic detection transmitters; the converter module adopts Buck-LLC two-stage converter, which combines the efficient voltage regulation capability of Buck circuit with the resonant and efficient transmission characteristics of LLC circuit, and is an ideal choice for high-voltage, high-power and high-efficiency applications. It not only optimizes efficiency, but also significantly reduces system complexity and operating costs. .

[0071] Second, the high-power electromagnetic detection transmitter DC power supply topology of the present invention and its control method based on model prediction (MPC). In the Buck-LLC two-stage converter, model predictive control combines the advantages of equivalent modeling, real-time optimization and multi-objective control, which not only significantly improves the control performance, but also adapts to the stringent requirements of high-voltage and high-power scenarios on response speed and robustness. BRIEF DESCRIPTION OF THE DRAWINGS

[0072] Figure 1 It is the main circuit topology and control block diagram of the present invention.

[0073] Figure 2 The invention discloses a flow chart of a direct current power supply topology of a high-power electromagnetic detection transmitter and a control method thereof based on model prediction (MPC).

[0074] Figure 3 1 is a simulation waveform diagram of the output voltage of the Buck-LLC two-stage converter of the present invention. DETAILED DESCRIPTION

[0075] The following examples will enable those skilled in the art to more fully understand the present invention, but are not intended to limit the present invention in any way.

[0076] See also Figure 1 and Figure 2 The present invention discloses a high-power electromagnetic detection transmitter DC power supply topology and a control method thereof based on model prediction, comprising the following steps:

[0077] Step 1: The high-power DC power supply topology adopts a combination of four converter modules IPOS (input parallel, output series), each module adopts a Buck-LLC two-stage converter cascade structure, and is independently controlled by the model predictive control method.

[0078] Step 2: The high-power converter is in a high-voltage and high-current working environment, and the voltage and current ripples are small, so the Buck circuit will not be intermittent. Therefore, the CCM mode is selected to analyze the Buck circuit equivalent to the Buck-LLC two-stage converter.

[0079] Step 3: Select the inductor current i of the front-stage Buck circuit L and output voltage V o Establish the equivalent state space expression of Buck-LLC two-stage converter for the state variables;

[0080] Step 4: Discretize the state space expression obtained in step 2 using the forward Euler formula to obtain a discrete mathematical model of the equivalent circuit;

[0081] Step 5: Introduce two parameters, the control time domain M and the prediction time domain P, and establish the prediction output equation of the circuit. By reasonably adjusting the values of M and P, the dynamic response speed of the system can be increased, the computational load of the system can be reduced, and the control accuracy of the system can be improved;

[0082] Step 6: To be able to track the target output voltage quickly and smoothly, establish an appropriate cost function J;

[0083] Step 7: Optimize the cost function J to obtain the optimal solution Δu(k) of the control quantity;

[0084] As one of the preferred examples, the derivation process of the discrete mathematical model is as follows:

[0085] The state equations for the on and off states of the switching tubes for constructing the equivalent circuit are respectively:

[0086] For 0 < t < DT, the state equation of the circuit when the switching tube is on:

[0087]

[0088] For DT < t < T, the state equation of the circuit when the switching tube is off:

[0089]

[0090] Considering that the actual transmission efficiency of the LLC circuit is between 95% and 98%, and denoting the transmission efficiency as λ. Then there is:

[0091]

[0092] So, i b = i o / λ;

[0093] And, i o = V o / R o .

[0094] Average the state equations in the on and off states of the switching tube through the state space averaging method to obtain the state equation of the circuit:

[0095]

[0096] In the formula, i L is the current of the inductor L of the front-stage Buck circuit, C is the output filter capacitor of the front-stage Buck circuit, V b is the output voltage of the front-stage Buck circuit, V o is the output voltage of the Buck-LLC two-stage converter, V s is the input voltage, D is the duty cycle of the switching tube, i ois the system output current, i b is the output current of the previous Buck circuit, R o is the system equivalent load.

[0097] By using the Euler forward method, the state equation of the circuit is transformed into a discrete state equation:

[0098]

[0099] make u(k)=D(k), we get:

[0100] x(k+1)=Ax(k)+Bu(k);

[0101] The output voltage is the controlled output variable y(k), and its relationship with the inductor current and capacitor voltage is:

[0102] y(k)=Zx(k);

[0103] Where Z =

[01] .

[0104] The state space model of the circuit in discrete time is expressed as follows:

[0105]

[0106] Where T is the sampling period, x(k+1) is the state variable, u(k) is the control input variable, and y(k) is the controlled output variable.

[0107] As a preferred example, the prediction output equation derivation process is as follows:

[0108] In order to reduce or eliminate the static error of the system, the state space model of the circuit in discrete time can be changed to an incremental model:

[0109]

[0110] Among them: Δx(k)=x(k)-x(k-1), Δu(k)=u(k)-u(k-1);

[0111] In model predictive control, two important parameters, control time domain M and prediction time domain P, need to be introduced. The prediction time domain is the number of steps to predict the system output, and the control time domain is the number of steps to control the system. In engineering, in order to consider the dynamic characteristics of the system and reduce the amount of calculation, the control time domain M is generally set to be less than the prediction time domain P. By reasonably adjusting the values ​​of M and P, the dynamic response speed of the system can be accelerated, the amount of calculation of the system can be reduced, and the control accuracy of the system can be increased.

[0112] According to the basic principle of model predictive control, in order to derive the system output equation of the Buck-LLC two-stage converter, we need to make the following assumptions:

[0113] (1) Except for the control time domain P, the other control quantities remain unchanged;

[0114] (2) The system is not interfered by external factors.

[0115] When the current time is k, the measured value is x(k), and Δx(k)=x(k)-x(k-1) can be calculated. This Δx(k) will serve as the starting point for predicting the future dynamics of the system. Therefore, based on assumptions 1 and 2, the incremental model can predict the state of the Buck-LLC two-stage converter from time k+1 to k+P, and the prediction results are as follows:

[0116]

[0117] The state of the output equation y(k) from time k+1 to time k+P can be predicted, and the prediction results are as follows:

[0118]

[0119]

[0120] According to the above prediction equation, the expression of the P-step prediction output vector Y(k+1|k) is defined as follows:

[0121]

[0122] The expression of the M-step input vector ΔU(k) ​​is defined as follows:

[0123]

[0124] Finally, the output equations at time k+1 to k+P can be transformed into the following expression:

[0125] Y(k+1|k)=GΔx(k)+HΔU(k)+Iy(k);

[0126] In the formula, the expressions of G, H and I matrices are as follows:

[0127]

[0128] Build the value function of the prediction model:

[0129]

[0130] Among them, w(k+i) is the reference value of the given reference input sequence at time k+i; q is the weighting factor of the predictive control output error. The larger the q, the more attention the controller will pay to reducing the system output error, so that the system output is closer to the desired reference trajectory, which helps to improve the tracking accuracy and response speed of the system. r is the weighting factor of the predictive control increment. The larger the r, the more stable the controller will tend to be, which helps to avoid system instability or over-response caused by excessive control action. By reasonably adjusting the size of q and r, the model predictive control can enable the system to achieve the design requirements of small output error without excessive overshoot and oscillation.

[0131] In order to make the cost function correspond to the equation set of the Buck-LLC two-stage converter at the time k+1 to k+P, the cost function of the Buck-LLC two-stage converter is now converted into a matrix vector form, namely:

[0132] J=Q|Y(k+1|k)-W(k+1)| 2 +R|ΔU(k)| 2 ;

[0133] The expressions of weighted matrices Q and R are: Q = diag (q1, q2, ..., q P ), R = diag(r1, r2, …, r M ), where q1,q2,…,q P Weighting factors of predictive control output error, r1, r2, …, r M is the weighting factor for the predictive control increment.

[0134] The reference input sequence W(k+1) is:

[0135]

[0136] The optimal duty cycle of the converter model predictive control strategy is:

[0137] ΔU * (k)=(H T Q T QH+R T R) -1 H T Q T QE(k+1|k);

[0138] In the formula, E(k+1|k)=W(k+1)-GΔx(k)-Iy(k).

[0139] Due to factors such as model error and weak nonlinear characteristics, when the model predicts open-loop control, ΔU *(k) It is not possible to closely track the reference input sequence if ΔU is used multiple times. * (k) Controlling the system will result in large deviations and fail to suppress system disturbances. Therefore, closed-loop control is required, that is, the first element of the calculated open-loop optimal control sequence is applied to the system. In this case, the optimal control increment can be defined as:

[0140] Δu(k)=ηΔU * (k) = η(H T Q T QH+R T R) -1 H T Q T QE(k+1|k);

[0142] In the above formula, η=[1 0 … 0] 1×M .

[0143] like Figure 1 As shown, the actual output voltage V o , reference output voltage V o-ref And the inductor current i of the previous stage L As the input of the MPC controller, Δu(k) acts as the control output of the MPC controller on the switch tube of the front-stage Buck circuit, so that the overall system outputs a stable and adjustable voltage.

[0144] like Figure 3 As shown in the figure, the output voltage is set to 400V. During the simulation, the load resistance is first changed from 5Ω to 10Ω. After the system is stable, the load resistance is restored from 10Ω to 5Ω. The output voltage waveforms under different control strategies are obtained. It can be seen from the figure that when a small range of load mutation occurs, the overshoot and adjustment time of the output voltage under the model predictive control are better than those of the traditional PI control. Therefore, the introduction of model predictive control is beneficial to improving the output dynamic performance of the converter to a certain extent.

[0145] The above are only preferred embodiments of the present invention, and the protection scope of the present invention is not limited to the above embodiments. All technical solutions under the concept of the present invention belong to the protection scope of the present invention. It should be pointed out that for ordinary technicians in this technical field, some improvements and modifications without departing from the principle of the present invention should be regarded as the protection scope of the present invention.

Claims

1. A high-power electromagnetic detection transmitter DC power supply topology and a control method based on model prediction, characterized in that: The method includes the following steps: Step 1: Use four converter modules IPOS to construct a high-power DC power supply topology in a combination of input parallel and output series. The converter module adopts a cascaded structure of a Buck-LLC two-stage converter; Step 2: Set the transformer turns ratio of the LLC circuit at the rear stage of the converter module to 1:1, the voltage gain to 1, and the switching frequency approximately equal to the resonance frequency, so that the output voltage of the rear-stage LLC circuit is equal to the input voltage, and the Buck-LLC two-stage converter is equivalent to a Buck circuit. Each module is independently controlled by the model predictive control method; Step 3: Select the inductor current i of the front-stage Buck circuit L and output voltage V o Establish the equivalent state space expression of Buck-LLC two-stage converter for the state variables; Step 4: Discretize the equivalent state space expression obtained in Step 3 using the forward Euler formula to obtain the discrete mathematical model of the Buck-LLC two-stage converter; Step 5: Introduce two parameters, the control time domain M and the prediction time domain P, to establish the prediction output equation of the equivalent circuit; where the prediction time domain P is the number of steps for predicting the system output, and the control time domain M is the number of steps for controlling the system, and the control time domain M ≤ the prediction time domain P; Step 6: Establish the cost function J of the prediction output equation; Step 7: Optimize the cost function J, and obtain the optimal duty cycle of the switching tube drive signal of the equivalent circuit of the Buck-LLC two-stage converter according to the cost function J, so that the rear-stage LLC circuit operates open-loop at the resonance frequency point.

2. The high-power electromagnetic detection transmitter DC power supply topology and its model prediction-based control method according to claim 1 is characterized in that: In Step 2, the state equations for the conduction and cutoff of the switching tube of the equivalently obtained Buck circuit are respectively: When 0 < t < DT, the state equation of the circuit when the switching tube is conducting is: When DT < t < T, the state equation of the circuit when the switching tube is cutoff is: In the formula, i L is the current of the inductor L of the front-stage Buck circuit, C is the output filter capacitor of the front-stage Buck circuit, V o is the output voltage of the Buck-LLC two-stage converter, V s is the input voltage, D is the duty cycle of the switch, i b is the output current of the previous Buck circuit, and T is the sampling period.

3. The high-power electromagnetic detection transmitter DC power supply topology and its model prediction-based control method according to claim 2 is characterized in that: Step 3 further includes: Denote the transmission efficiency as λ, and there is: i b =i o / λ; i o =V o / R o ; Average the state equations in the cases of switching tube conduction and cutoff through the state space averaging method to obtain the equivalent state space expression of the Buck-LLC two-stage converter as: Where V b is the output voltage of the previous Buck circuit, i o is the system output current, R o is the system equivalent load.

4. The high-power electromagnetic detection transmitter DC power supply topology and its control method based on model prediction according to claim 1 is characterized in that: In Step 4, the process of obtaining the discrete mathematical model of the equivalently obtained Buck circuit includes: Convert the equivalent state space expression of the Buck-LLC two-stage converter into a discrete state equation through the forward Euler formula: make u(k)=D(k), we get: x(k + 1) = Ax(k) + Bu(k); Denote the output voltage at time k as the controlled output variable y(k), and its relationship with the inductor current and capacitor voltage is: y(k) = Zx(k); Where Z = [0 1]; Obtain the state space model of the Buck circuit in discrete time as: Where T is the sampling period; x(k + 1) is the state variable; u(k) is the control input variable; y(k) is the controlled output variable.

5. The high-power electromagnetic detection transmitter DC power supply topology and its control method based on model prediction according to claim 4 is characterized in that: Step 5 further includes: Change the state space model of the Buck circuit in discrete time to an incremental model: Where: Δx(k) = x(k) - x(k - 1), Δu(k) = u(k) - u(k - 1); Introduce two parameters, the control time domain M and the prediction time domain P; Predict the states of the Buck-LLC two-stage converter at times k + 1 to k + P and the states of the output equation y(k) at times k + 1 to k + P from the incremental model; Define the expression of the P-step prediction output vector Y(k + 1|k) as: Define the expression of the M-step input vector ΔU(k) ​​as: The output equations at time k+1 to k+P are transformed into: Y(k+1|k)=GΔx(k)+HΔU(k)+Iy(k); Where, the expressions of G, H and I matrices are as follows:

6. The high-power electromagnetic detection transmitter DC power supply topology and its model prediction-based control method according to claim 5 is characterized in that: In step 6, the value function of the prediction output equation is established as: Wherein, w(k+i) is the reference value of the given reference input sequence at time k+i; q is the weighting factor of the predictive control output error, and r is the weighting factor of the predictive control increment.

7. The high-power electromagnetic detection transmitter DC power supply topology and its model prediction-based control method according to claim 6 is characterized in that: In step 7, the process of optimizing the value function J includes the following steps: Convert the cost function of the Buck-LLC two-stage converter into a matrix-vector form: J=Q|Y(k+1|k)-W(k+1)| 2 +R|ΔU(k)| 2 ; The expressions of weighted matrices Q and R are: Q = diag (q1, q2, ..., q P ), R = diag(r1, r2, …, r M ), where q1,q2,…,q P Weighting factors of predictive control output error, r1, r2, …, r M is the weighting factor of the predictive control increment; The reference input sequence W(k+1) is: The optimal duty cycle of the converter model predictive control strategy is: ΔU * (k)=(H T Q T QH+R T R) -1 H T Q T QE(k+1|k); In the formula, E(k+1|k)=W(k+1)-GΔx(k)-Iy(k); Closed-loop control is introduced, and the first element of the calculated open-loop optimal control sequence is applied to the system. The optimal control increment is defined as: Δu(k)=ηΔU * (k)=η(H T Q T QH+R T R) -1 H T Q T QE(k+1|k); Where η=[1 0 … 0] 1×M .

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