Dual-vector model predictive control method for synchronous motor

Abstract

The invention provides a method for predicting a double-vector model of a synchronous motor, and solves the problems of difficulty in parameter setting, sensitivity to high-frequency noise and easiness in overshoot in traditional double-closed-loop control proportional-integral control. The model prediction method is applied to a static frequency conversion system of load commutation, an optimization algorithm is adopted to solve a cost function, a first sequence of the cost function comprises trigger angle data of a rectifier bridge and an inverter bridge, and double-vector control of the rectifier bridge and the inverter bridge is achieved.

Description

Technical Field

[0001] This invention belongs to the field of synchronous motor technology, and relates to synchronous motor speed control, specifically to a dual-vector model predictive control method for driving synchronous motors in load-commutated frequency converter systems. Background Technology

[0002] Load-commutated inverter (LCI) static frequency converter (SFD) synchronous motor control systems have become the preferred solution for many high-power drive control applications due to their high control efficiency, strong reliability, and low cost. They are widely used in high-power industrial applications such as main drives of hot strip mills, reversible units in pumped storage power stations, and blast furnace blast systems. In the operating scenario of hot strip mills, the motor drive system needs to achieve no-load start-up of the hot strip mill and possess good load-carrying capacity after reaching a stable speed, as well as good recovery capability under disturbance conditions. Furthermore, the blast furnace blast fan system also needs dynamic adjustment capability under surge conditions to achieve rapid over-run and ensure operational reliability. Although the economic advantages of LCI static frequency converter drive systems remain leading, the increasing complexity of their application scenarios and the increasing performance requirements have gradually revealed the shortcomings of traditional control strategies in terms of load adaptability, dynamic response, and multi-objective optimization.

[0003] Currently, many scholars are dedicated to researching Model Predictive Control (MPC) strategies for synchronous motors. Among these, the finite set MPC method has been widely applied in duty cycle optimization. This method, through the switching control of fully controlled devices, can obtain the spatially optimal control vector in any direction. However, load-commutated static inverter systems use semi-controlled devices. The system's bridge arms switch cyclically according to a specific timing sequence, and the resulting magnetomotive force is not a continuous rotational state, exhibiting a six-step jump characteristic. Therefore, the duty cycle optimization method is not applicable to load-commutated static inverter systems.

[0004] For high-precision, high-power transmission devices like finishing mills, traditional dual-closed-loop proportional-integral (PI) control suffers from drawbacks such as difficult parameter tuning, sensitivity to high-frequency noise, and susceptibility to overshoot. These limitations in practical applications lead to significant debugging costs. Therefore, model predictive control (MMC), with its high accuracy, good control performance, strong real-time capabilities, and high fault tolerance, has become a research hotspot. However, single-vector MMC employs a constant commutation lead angle, which lowers the upper limit of the system's dynamic performance. Addressing this issue by achieving better torque control and dynamic response performance of the motor while ensuring reliable commutation is of paramount importance. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a dual-vector model predictive control method for synchronous motors. This method is based on a load-commutated static frequency converter system. By controlling the voltage output of the LCI rectifier bridge and the control input of the inverter bridge, it improves the instantaneous tracking capability of speed changes under different loads while ensuring reliable commutation. The dual-vector MPC method enhances the dynamic performance of the LCI drive system.

[0006] This method involves simultaneously solving the equivalent voltage equation and the mechanical motion equation to construct a dual-vector model predictive control state equation; performing discrete modeling and analysis on the equation; predicting the time domain from k to k+p; and designing the objective function while considering the speed error term, the change in control input, and the cosine value of the control input. The dual-vector MPC control does not simply select the first term value, but adds the solved control increment to the control input from the previous time step to obtain the current control vector. At the next time step, it re-predicts and optimizes based on the new state, repeating the above process. Specifically, it includes the following steps:

[0007] S1: Construct the DC equivalent equation for voltage;

[0008] S2: Obtain electromagnetic torque;

[0009] S3: Construct the electromagnetic equation for torque;

[0010] S4: Construct the MPC state equations;

[0011] S5: Construct a discretized model;

[0012] S6: Construct the model to predict the dynamic equations from time k onwards;

[0013] S7: Establish the dual-vector MPC cost function;

[0014] S8: Set the commutation residual angle and the limit commutation angle;

[0015] S9: Constraint control quantity;

[0016] S10: Solve for the optimal control vector. Repeat the above operations to achieve rolling optimization of the system.

[0017] Furthermore, S1: Constructing the DC equivalent voltage equation: Based on the voltage and current measured by the rectifier bridge and inverter bridge of the LCI system, construct the DC circuit equivalent voltage equation, and collect the rectifier bridge voltage u1 and inverter bridge voltage u2 of the LCI static inverter system, and the DC bus current i d Construct the equivalent voltage equation of the DC loop for the LCI system using the data:

[0018]

[0019] Where u1 is the rectifier bridge terminal voltage, u2 is the inverter bridge terminal voltage, L is the smoothing reactance, R is the loop resistance, and i d This represents the bus current.

[0020] Furthermore, S2: obtains electromagnetic torque; acquires inverter bridge terminal voltage, ignores power loss due to commutation overlap angle during inverter bridge commutation, and obtains electromagnetic torque through inverter bridge terminal voltage u2 and bus current i. d The electromagnetic torque T is derived from the motor speed ω. e :

[0021] Furthermore, S3: Constructing the torque electromagnetic equation: Substituting Te into the mechanical motion equation of the motor,

[0022]

[0023] Among them, i d It is the bus current; J is the moment of inertia of the motor shaft system; B m It is the viscosity coefficient; ω r It is the mechanical rotational speed; U β It is the average voltage of the inverter bridge input; T L This is the load torque. Viscosity coefficient B m If the value is small enough, it can be ignored.

[0024] Furthermore, S4: Construct the MPC state equations; combine the equivalent voltage equations of the DC loop of the LCI system and the mechanical motion equations of the motor to construct a predictive model. The control input u = [u] of the dual-vector model predictive control method. α (t),u β (t)] T State variable x = [i d (t),ω(t)] T The system disturbance d = [0, T] L (t)] T The output y(t) = ω r (t), construct the two-vector model predictive control state equations:

[0025]

[0026] in, C = [0 1],

[0027] Where R is the DC resistance of the system's DC circuit; L d It is a DC circuit DC inductor; U β J is the average voltage input to the inverter bridge; J is the moment of inertia of the motor shaft system; Bm It is the viscosity coefficient; ω r It refers to the mechanical rotation speed.

[0028] Furthermore, in S5: a discretized model is constructed, and the rectifier-side output voltage and inverter-side input voltage of the control system exhibit periodic fluctuations in the time domain. A functional relationship between the firing angle and the average voltage is established to obtain the incremental state equation.

[0029]

[0030] in,

[0031] Where R is the DC resistance of the system loop; L d L is the DC inductance of the system's DC circuit; U is the system's equivalent inductance; β J is the average voltage input to the inverter bridge; J is the moment of inertia of the motor shaft system; B m It is the viscosity coefficient; ω r It refers to the mechanical rotational speed; t s It is the control cycle; U grid It is the effective value of the three-phase AC source phase voltage of the rectifier bridge; Δi d (k) is the DC loop current transformation quantity of the system; Δcosα rec It is the change in the rectification angle; Δcosβ inv It is the change in the inverse angle.

[0032] Furthermore, in S6: construct the model prediction dynamic equation from time k onwards, and predict the time domain from time k onwards until time k+p, predicting the system model for the time period from time k+1 to time k+p:

[0033] Y(k+p|k)=R x Δx(k)+R u ΔU(k)+Ey(k)

[0034] in,

[0035] Wherein, Δu(k) represents the change in control voltage from time k to time k+1 in the system control time domain;

[0036] Y(k+j|k+i) represents the predicted value of variable Y at time k+j obtained at time k+i.

[0037] Furthermore, in S7: a dual-vector MPC cost function is established and combined with the model predictive dynamic equations. A smaller lead commutation angle results in better torque characteristics and a higher power factor, i.e., a larger corresponding cosine value. Therefore, the design of the objective function must consider not only the speed error term and the change in control input, but also the cosine value of the control input.

[0038]

[0039] Among them, Γ y Γ represents the weighting coefficient of the control error at time k, representing the system input increment vector. u1 and Γ u2 This represents the weighting coefficient of the control error at time k, indicating the output vector increment.

[0040]

[0041] Furthermore, S8: Set the commutation residual angle and the limiting commutation angle. For the thyristor to turn off, the current flowing through it must drop below the holding current and withstand reverse voltage for a period of time; otherwise, commutation failure will occur. For the commutation limit of the LCI static inverter system, the limiting commutation angle of the system is set to ensure reliable commutation of the thyristor. The time t corresponding to the thyristor turn-off is collected. f Commutation overlap angle μ and motor speed ω f ,

[0042] Commutation residual angle γ of the inverter bridge c Greater than the time t corresponding to the thyristor turn-off f :

[0043] γ c ≥Kω r t f

[0044] The system's limiting commutation angle β min :

[0045] β min =Kω r t f +0.5μ

[0046] Where K is the safety margin value of the remaining commutation angle, K≥1, ω r It is the mechanical rotational speed, and μ is the commutation overlap angle.

[0047] Furthermore, S9: Constraint control quantity:

[0048]

[0049] Among them, i dIt is the bus current; α is the rectification angle; β is the inverter angle; Δcosα min and Δcosα max These are the lower and upper limits of the control increment Δcosα, respectively; Δcosβ min and Δcosβ max These are the lower and upper limits of the control increment Δcosβ, respectively.

[0050] In the optimization design of model predictive control, in addition to imposing soft constraints on speed deviation tracking and control input changes in the objective function, it is also necessary to impose insurmountable hard boundary constraints on key state variables. Only by ensuring that the control commands are kept within a preset range can the system always operate within a controllable range, thus guaranteeing system stability.

[0051] Furthermore, in step S10: based on the optimal control algorithm, the optimal control vector is solved, and the first element Δu(k) is selected and superimposed with the current control signal u(k), i.e., the control signal u(k) = Δu(k) + u(k-1), and applied to the LCI static variable frequency dual-vector MPC system. The calculation is repeated at the next time step, and so on.

[0052] The features of this invention are:

[0053] 1. This invention is applied to a static frequency converter system with load switching, which can effectively reduce the fluctuations caused by load disturbances in synchronous motors and significantly improve the dynamic performance of the system.

[0054] 2. This invention is applied to a static frequency converter system with load switching. It uses an optimization algorithm to solve the cost function. Its first sequence contains the firing angle data of the rectifier bridge and the inverter bridge, realizing dual vector control of the rectifier bridge and the inverter bridge.

[0055] 3. This invention is applied to load-commutated static inverter systems, and does not produce significant fluctuations when different levels of load are introduced, exhibiting excellent dynamic performance. It demonstrates the feasibility of the dual-vector model predictive control method for LCI static inverter systems. Attached Figure Description

[0056] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0057] Figure 1 This is a flowchart of the method of the present invention.

[0058] Figure 2This is a block diagram of a dual-vector MPC control strategy.

[0059] Figure 3 The waveform diagram for the two-vector model predictive control of the load commutation drive system.

[0060] Figure 4 This is an enlarged waveform diagram under a 33% step load disturbance.

[0061] Figure 5 This is an enlarged waveform diagram under a 66% step load disturbance.

[0062] Figure 6 This is an enlarged waveform diagram under a 100% step load disturbance.

[0063] Figure 7 The waveforms of the speed under load for PI control, single-vector MPC, and dual-vector MPC are shown.

[0064] Figure 8 The waveform diagrams are enlarged for three methods: PI control, single-vector MPC, and dual-vector MPC, under a 33% step load disturbance.

[0065] Figure 9 The waveforms are enlarged for three methods: PI control, single-vector MPC, and dual-vector MPC, under a 66% step load disturbance.

[0066] Figure 10 The waveform diagrams are enlarged for three methods: PI control, single-vector MPC, and dual-vector MPC, under 100% step load disturbance. Detailed Implementation

[0067] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0068] Example 1:

[0069] A method for two-vector model predictive control of a synchronous motor, see [link to relevant documentation]. Figure 1 See the block diagram of the dual-vector MPC control strategy. Figure 2 The method includes the following steps:

[0070] S1: Collect the rectifier bridge voltage u1 and inverter bridge voltage u2 of the LCI static inverter system, and the DC bus current i. d Constructing the equivalent voltage equation for the DC loop of the LCI system:

[0071]

[0072] S2: Collect the inverter bridge terminal voltage, ignoring the power loss due to the commutation overlap angle during inverter bridge switching, and obtain the inverter bridge voltage u2 and bus current i. d The electromagnetic torque T is obtained from the motor speed ω. e :

[0073]

[0074] S3: Take the T obtained above e Substituting the equations of motion of the electric motor, we obtain the following equation:

[0075]

[0076] Where J is the moment of inertia of the motor shaft system; B m It is the viscosity coefficient; ω r It refers to the mechanical rotational speed. Viscosity coefficient B m If the value is small enough, it can be ignored.

[0077] S4: Combine the equivalent voltage equation of the DC loop of the LCI system with the mechanical motion equation of the motor to construct a predictive model. The control input u = [u] of the two-vector model predictive control method. α (t),u β (t)] T State variable x = [i d (t),ω(t)] T The system disturbance d = [0, T] L (t)] T The output y(t) = ω r The two-vector model predictive control state equations are constructed as follows:

[0078]

[0079] in, C = [0 1],

[0080] S5: Analyze the discretized modeling and construct the incremental state equations under steady-state conditions as shown below:

[0081]

[0082] in,

[0083] S6: Based on the numerical values ​​obtained from the state equation, the time domain from k to k+p is predicted. The dynamic equation for the system model prediction from time k+1 to time k+p can be expressed as follows:

[0084] Y(k+p|k)=Rx Δx(k)+R u ΔU(k)+Ey(k)

[0085] in,

[0086] S7: Substituting the above formula into the two-vector model predictive control cost function, we obtain the following function:

[0087]

[0088] Among them, Γ y , Γ u1 ,Γ u2 These are the weighting coefficients.

[0089] S8: Collect the time t corresponding to the thyristor turn-off. f Commutation overlap angle μ and motor speed ω f For the commutation limit of the LCI static inverter system, the limiting commutation angle of the system is as follows:

[0090] β min =Kω r t f +0.5μ

[0091] Where K is the safety margin value of the remaining commutation angle, K≥1.

[0092] S9: Hard constraints on the control variables of the dual-vector MPC:

[0093]

[0094] S10: The optimal control vector u(k) = [u α (k),u β (k)] T This process is applied to the system. In the next cycle, the above operations are repeated to achieve rolling optimization of the system.

[0095] Figures 3-6 The enlarged waveform diagram under step load disturbance shows that under a 33% step load disturbance, the time to return to the preset speed is 52ms and the maximum speed drops by 14rpm. Under unload conditions, the time to return to the preset speed is 62ms and the maximum speed drops by 14rpm.

[0096] Under a 66% step load disturbance, the time to return to the preset speed is 71ms and the maximum speed drop is 24rpm. Under unload conditions, the time to return to the preset speed is 64ms and the maximum speed drop is 25rpm.

[0097] Under a 100% step load disturbance, the time to return to the preset speed is 82ms, and the maximum speed drop is 38rpm. Under unload conditions, the time to return to the preset speed is 100ms, and the maximum speed drop is 36rpm.

[0098] Figures 7-10 The waveforms for PI control, single-vector MPC, and dual-vector MPC are shown. It can be seen that under a 100% step load disturbance, the maximum control drop speed of PI control is 135 rpm, the maximum rise speed is 70 rpm, the load settling time is much greater than 1000 ms, the unloading time is also much greater than 1000 ms, and the load steady-state error is 20 rpm. Under single-vector MPC control, the maximum control drop speed is 107 rpm, the maximum rise speed is 51 rpm, the load settling time is 186 ms, the unloading time is 271 ms, and the load steady-state error is close to 0 rpm. Under dual-vector MPC control, the maximum control drop speed is 38 rpm, the maximum rise speed is 36 rpm, the load settling time is 82 ms, the unloading time is 100 ms, and the load steady-state error is close to 0 rpm. It can be seen that the settling time and control performance of dual-vector and single-vector control are far superior to PI control, with load steady-state errors close to 0. The control accuracy is high, ensuring that after the system reaches a stable state during loading, the actual output is completely consistent with the expected target, meeting the set value and improving product quality.

[0099] In summary, it can be seen that compared with single-vector MPC and PI control, the dual-vector MPC method exhibits more subtle speed changes under load conditions and requires less settling time. It also shows significant improvements in terms of speed difference changes and settling time during load testing.

[0100] Those skilled in the art will understand that the features described in the various embodiments and / or claims of the present invention can be combined or combined in various ways, even if such combinations or combinations are not explicitly described in the present invention. In particular, the features described in the various embodiments and / or claims of the present invention can be combined or combined in various ways without departing from the spirit and teachings of the present invention. All such combinations and / or combinations fall within the scope of the present invention.

Claims

1. A method for two-vector model predictive control of a synchronous motor, characterized in that: Includes the following steps: S1: Construct the DC equivalent equation for voltage; S2: Obtain electromagnetic torque; S3: Construct the electromagnetic equation for torque; S4: Construct the MPC state equations; S5: Construct a discretized model; S6: Construct the model to predict the dynamic equations from time k onwards; S7: Establish the dual-vector MPC cost function; S8: Set the commutation residual angle and the limit commutation angle; S9: Constraint control quantity; S10: Solve for the optimal control vector. Repeat the above operations to achieve rolling optimization of the system.

2. The method for dual-vector model predictive control of a synchronous motor according to claim 1, characterized in that: S1: Constructing the DC equivalent voltage equation: Based on the voltage and current measured by the rectifier bridge and inverter bridge of the LCI system, construct the DC loop equivalent voltage equation: Where u1 is the rectifier bridge terminal voltage, u2 is the inverter bridge terminal voltage, L is the smoothing reactance, R is the loop resistance, and i d This represents the bus current.

3. The method for dual-vector model predictive control of a synchronous motor according to claim 1, characterized in that: S2: Obtaining electromagnetic torque; through inverter bridge terminal voltage u2 and bus current i d The electromagnetic torque T is derived from the motor speed ω. e :

4. The method for dual-vector model predictive control of a synchronous motor according to claim 1, characterized in that: S3: Constructing the torque electromagnetic equation: Among them, i d It is the bus current; J is the moment of inertia of the motor shaft system; B m It is the viscosity coefficient; ω r It is the mechanical rotational speed; U β It is the average voltage of the inverter bridge input; T L It is the load torque.

5. The method for dual-vector model predictive control of a synchronous motor according to claim 1, characterized in that: S4: Construct the MPC state equations; in, C = [0 1], Where R is the DC resistance of the system's DC circuit; L d It is a DC circuit DC inductor; U β J is the average voltage input to the inverter bridge; J is the moment of inertia of the motor shaft system; B m It is the viscosity coefficient; ω r It refers to the mechanical rotation speed.

6. The method for dual-vector model predictive control of a synchronous motor according to claim 1, characterized in that: S5: Constructing a discretized model: in, Where R is the DC resistance of the system loop; L d L is the DC inductance of the system's DC circuit; U is the system's equivalent inductance; β J is the average voltage input to the inverter bridge; J is the moment of inertia of the motor shaft system; B m It is the viscosity coefficient; ω r It refers to the mechanical rotational speed; t s It is the control cycle; U grid It is the effective value of the three-phase AC source phase voltage of the rectifier bridge; Δi d (k) is the DC loop current transformation quantity of the system; Δcosα rec It is the change in the rectification angle; Δcosβ inv It is the change in the inverse angle.

7. The method for dual-vector model predictive control of a synchronous motor according to claim 1, characterized in that: S6: Construct the model prediction dynamic equations from time k onwards: Y(k+p|k)=R x Δx(k)+R u ΔU(k)+Ey(k) in, Wherein, Δu(k) represents the change in control voltage from time k to time k+1 in the system control time domain; Y(k+j|k+i) represents the predicted value of variable Y at time k+j obtained at time k+i.

8. The method for dual-vector model predictive control of a synchronous motor according to claim 1, characterized in that: S7: Establish a dual-vector MPC cost function and combine it with the model prediction dynamic equation: Among them, Γ y Γ represents the weighting coefficient of the control error at time k, representing the system input increment vector. u1 and Γ u2 The weighting coefficients representing the control error of the output vector increment at time k are:

9. The method for dual-vector model predictive control of a synchronous motor according to claim 1, characterized in that: S8: Set the commutation residual angle and the limiting commutation angle. Commutation residual angle γ of the inverter bridge c Greater than the time t corresponding to the thyristor turn-off f : c c ≥Kω r t f The system's limiting commutation angle β min : b min =Kω r t f +0.5m Where K is the safety margin value of the remaining commutation angle, K≥1, ω r It is the mechanical rotation speed, and μ is the commutation overlap angle.

10. The method for dual-vector model predictive control of a synchronous motor according to claim 1, characterized in that: S9: Constraint control quantity: Among them, i d It is the bus current; α is the rectification angle; β is the inverter angle; Δcosα min and Δcosα max These are the lower and upper limits of the control increment Δcosα, respectively; Δcosβ min and Δcosβ max These are the lower and upper limits of the control increment Δcosβ, respectively.

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