A current prediction control algorithm for permanent magnet synchronous motor simulator

Abstract

The application provides a current prediction control algorithm for a permanent magnet synchronous motor simulator, which can effectively suppress parameter disturbance, improve the robustness of the control system and maintain system stability. In the control system, a state observer is constructed, the influence and delay compensation link caused by the parameter disturbance are abstracted as the observation of the current / voltage, on the one hand, the influence caused by the parameter disturbance is suppressed, and the robustness of the control system is improved; on the other hand, the synchronous calculation of the interface current prediction value is realized, and the real-time performance of the control system is improved. Based on the principle of Kalman filtering, the state observer is constructed, so that the observer gain can be adaptively adjusted with the change of the model parameters and the system parameters, without manual configuration, change and high-performance real-time stable operation of the observer.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of permanent magnet synchronous motor simulator control in electric drive system test, and particularly relates to an improved active disturbance rejection current prediction control algorithm applied to a permanent magnet synchronous motor simulator. BACKGROUND

[0002] The motor simulator plays a very important role in the power stage hardware-in-the-loop (PHIL) simulation test, which is mainly composed of a hardware circuit part (interface circuit + power stage inverter + sensor) and a signal simulation part (motor model + interface current control algorithm + modulation algorithm). The control signal is obtained through signal simulation, and the power interaction with the electric drive system to be tested is realized through the power stage inverter, so as to simulate the working of a real motor. In the signal simulation part, the interface current control algorithm as the inner loop of the current loop of the motor control system is the most core part in the whole motor simulator. The existing interface current control algorithm mostly adopts the traditional PID control to make the interface current track the expected value through the classical control theory. However, since the effect of the traditional PID control mainly depends on the parameter matching rather than the system mathematical model, and the control is prone to conflict with the current loop of the motor control system, the traditional PID control cannot meet the engineering requirements. If the prediction control based on the system mathematical model is adopted, the system will be unstable when the system parameters are disturbed and the actual parameters do not match the parameters of the control system mathematical model, so that the system robustness of this control mode is poor and is not conducive to wide application. SUMMARY

[0003] Therefore, aiming at the technical problems in the prior art, the application provides a current prediction control algorithm for a permanent magnet synchronous motor simulator, which specifically comprises the following steps:

[0004] Step one, the sensor is used to collect the three-phase current and three-phase voltage output by the electric drive system to be tested, the three-phase current and three-phase voltage output by the power stage inverter of the motor simulator, and the voltage at the element end of the interface circuit part, and convert them to the dq axis coordinate system; the interface circuit mathematical model and the corresponding interface voltage state space equation are established according to the topology structure of the interface circuit part; the interface voltage state space equation is discretized to obtain the current discrete time prediction model of the next moment input by the interface circuit from the electric drive system to be tested and output after filtering by the interface circuit;

[0005] Step two, the data collected by the sensor in step one are used to execute the deadbeat current prediction control algorithm, so that the prediction value of the output current of the electric drive system to be tested tracks the simulated reference current of the motor model, and the corresponding power stage inverter output voltage expected value is calculated; the modulation algorithm is executed considering the delay compensation to control the power stage inverter, so as to realize the control of the interface circuit output current;

[0006] Step 3: Considering that the interface parameter disturbance consists of two parts, the disturbance current and the disturbance voltage, a system parameter disturbance model is established; a state observer is constructed based on the Kalman filter, with the disturbance compensation current and the disturbance compensation voltage as one of the observed state quantities, and the delayed interface circuit input and output current prediction values ​​as the second observed state quantity;

[0007] Step 4. Compensate the disturbance compensation current and disturbance compensation voltage obtained by the state observer at the next moment to the simulated reference current value of the motor model and the expected value of the power stage inverter output voltage at the current moment to suppress parameter disturbances; and use the delayed interface circuit input and output current as the delayed input of the deadbeat current prediction control algorithm considering delay compensation to achieve synchronous calculation to ensure the real-time performance of the system.

[0008] Furthermore, in step 1, the following voltage equation is established for the adopted LCL interface circuit topology:

[0009]

[0010]

[0011] Among them, u id 、u iq The d-axis and q-axis components of the output voltage of the electric drive system to be tested; i id 、i iq is the d-axis and q-axis components of the interface current; u od 、u oq are the d and q axis components of the motor simulator output voltage; i od 、i oq are the d-axis and q-axis components of the current after filtering by the interface circuit; ω e is the electrical angular velocity; t is the time variable; R i is the internal resistance of the inductor on the electric drive system side to be measured; R c is the damping resistance; L i L is the filter inductance of the electric drive system to be tested; o is the filter inductor on the motor simulator side; u c is the voltage across the filter capacitor;

[0012] Based on the above voltage equation, the interface voltage state space equation is established and discretized to obtain the following current i input to the interface circuit by the electric drive system under test at the next moment: i(k+1) And the output current i after filtering by the interface circuit o(k+1) Discrete-time prediction model for:

[0013]

[0014] in,

[0015]

[0016] Where, T s is the sampling period; k is the current moment; i o 、i i 、u o 、u i 、u C Are vectors, representing:

[0017] i i =[i id i iq ] T ,i o =[i od i oq ] T ,u i =[u id u iq ] T ,u o =[u od u oq ] T ,u c =[u cd u cq ] T .

[0018] Furthermore, in step 2, the predicted value of the output current of the electric drive system to be tested, that is, the input interface circuit current i i(k+1) Equal to the simulated reference current i* of the motor model i(k) , in order to track, and at the same time to get the expected value i* of the output current after the interface circuit is filtered o(k) :

[0019]

[0020] Let the interface circuit output current i after filtering o(k+1) Equal to the above i* o(k) , and calculate the corresponding power level inverter output voltage expected value u* o(k) :

[0021]

[0022] Considering the delay compensation, the modulation algorithm is executed to control the power stage inverter, and the output current of the interface circuit is controlled to meet the following relationship:

[0023]

[0024] Furthermore, when the system parameter disturbance model is established in step 3, the parameter disturbance is abstracted into the coefficient matrix disturbance ΔAi , ΔB i , ΔC i , ΔA o , ΔB o , ΔC o , we can get the following relationship:

[0025]

[0026] By comparing with the aforementioned i* o(k) 、u* o(k) By subtracting the formula, we can obtain the deviation of the expected value of the output current after interface filtering and the expected value of the output voltage of the power stage inverter after the parameter disturbance occurs, thereby converting the impact of the parameter disturbance into the deviation of the expected value of the interface current and the expected value of the output voltage, as shown in the following formula:

[0027]

[0028] The disturbance compensation current i l(k+1) and disturbance compensation voltage u l(k+1) As one of the observed state quantities, the delayed interface circuit input current i i(k+1) and the output current i o(k+1) The predicted value is used as the second observed state quantity, and two Kalman filter-based state observers, KFIO and KFVO, are constructed respectively;

[0029] Among them, the KFIO state observer is used to input the current i of the delayed interface circuit i(k+1) and disturbance compensation current i l(k+1) For observation, the system state equation and observation equation are:

[0030]

[0031] Where, v i(k) represents process noise, w i(k) represents the observation noise of KFIO, the two are independent of each other, Q i 、R i Represent the covariance matrix of the two respectively;

[0032] The prior estimation and covariance of the prediction link of the KFIO state observer are shown as follows:

[0033]

[0034] Where, Represents i i(k+1) 、i l(k+1) A priori estimate of Represents i i(k) 、i l(k) The observed value, Pi(k) represents the k-time error covariance in KFIO, Represents the prior error covariance in KFIO;

[0035] The Kalman gain, posterior estimation, and error covariance update of the correction link of the KFIO state observer are shown as follows:

[0036]

[0037] Where K i(k) represents the Kalman gain of KFIO, Represents i i(k+1) 、i l(k+1) The posterior estimate of P i(k+1) represents the updated error covariance;

[0038] Similarly, the KFVO state observer is used to output the current i of the delayed interface circuit. o(k+1) and disturbance compensation voltage u l(k+1) For observation, the system state equation and observation equation are:

[0039]

[0040] Where, v u(k) represents process noise, w u(k) represents the observation noise of KFVO, the two are independent of each other, Q u 、R u Represent the covariance matrix of the two respectively;

[0041] The prior estimation and covariance of the prediction link of the KFVO state observer are shown as follows:

[0042]

[0043] Where, Represents i o(k+1) 、u l(k+1) A priori estimate of Represent the observed values ​​of delayed current and compensation voltage at time k, P u(k) represents the error covariance at time k in KFVO, represents the prior error covariance in KFVO;

[0044] The Kalman gain, posterior estimation, and error covariance update of the correction link of the KFVO state observer are shown as follows:

[0045]

[0046] Where K u(k) represents the Kalman gain of KFVO, Represents i o(k+1) 、u l(k+1) The posterior estimate of P u(k+1) represents the updated error covariance.

[0047] The current prediction control algorithm for a permanent magnet synchronous motor simulator provided by the present invention has the following beneficial effects compared to the prior art:

[0048] 1. The deadbeat current predictive control algorithm adopted in the present invention can effectively suppress parameter disturbances, improve the robustness of the control system and maintain system stability.

[0049] 2. By constructing a state observer in the control system, the impact of parameter disturbances and the delay compensation link are abstracted into current / voltage observations. On the one hand, this suppresses the impact of parameter disturbances and improves the robustness of the control system; on the other hand, it realizes the synchronous calculation of the interface current prediction value and improves the real-time performance of the control system.

[0050] 3. The state observer built based on the Kalman filter principle enables the observer gain to be adaptively adjusted as the model parameters and system parameters change, and high-performance, real-time and stable operation of the observer can be achieved without manual configuration or modification. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 This is a topological diagram of the permanent magnet synchronous motor simulator system of the present invention;

[0052] Figure 2 This is a schematic diagram of the single-phase topology of the LCL interface circuit used in the present invention;

[0053] Figure 3 This is a flow chart of a deadbeat current predictive control algorithm considering delay compensation on which the present invention is based;

[0054] Figure 4 This is a structural block diagram of the Kalman filter-based disturbance current state observer (KFIO) and disturbance voltage state observer (KFVO) described in the present invention;

[0055] Figure 5 The diagram is a schematic diagram of an improved auto-disturbance rejection deadbeat current prediction control algorithm implemented by the present invention. DETAILED DESCRIPTION

[0056] The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0057] The current prediction control algorithm provided by the present invention can be applied to various types of existing permanent magnet synchronous motor simulator systems. Figure 1 FIG. 1 shows a preferred system topology, which includes a hardware circuit part 1 and a signal simulation part 2. The hardware circuit part includes Figure 2 The LCL interface circuit, power stage inverter, sensor, and signal simulation part shown include a motor model, an interface current control algorithm, and a modulation algorithm running in a real-time controller (FPGA+DSP). The interface current control algorithm 3 is the core of the present invention. The specific working process is: the sensor collects the three-phase voltage, three-phase current, and terminal voltage of some components of the interface circuit output by the electric drive system to be tested in real time, and the input signal simulation part 2 performs high-speed real-time calculation to obtain the expected value of the output voltage of the power stage inverter, and realizes the simulation of the real motor interface characteristics by controlling the power stage inverter. The function of the LCL interface circuit is to realize the buffer isolation of the power stage inverters on both sides, avoid power interaction conflicts, and filter the interface current to improve the simulation accuracy.

[0058] The method of the present invention is as follows Figure 3 As shown, the specific steps include:

[0059] Step 1: Use sensors to collect the three-phase current and three-phase voltage output by the electric drive system to be tested, the three-phase current and three-phase voltage output by the motor simulator power stage inverter, and the terminal voltages of some components of the interface circuit, and convert them into a dq-axis coordinate system; establish an interface circuit mathematical model and a corresponding interface voltage state-space equation based on the topological structure of the interface circuit; discretize the interface voltage state-space equation to obtain a discrete-time prediction model of the current input by the electric drive system to the interface circuit at the next moment and the current output after filtering by the interface circuit;

[0060] Step 2: Using the data collected by the sensor in step 1 and executing a deadbeat current prediction control algorithm, the predicted value of the output current of the electric drive system to be tested tracks the simulated reference current of the motor model, and the expected value of the output voltage of the corresponding power stage inverter is calculated; considering delay compensation, a modulation algorithm is executed to control the power stage inverter to achieve control of the output current of the interface circuit;

[0061] Step 3: Considering that the interface parameter disturbance consists of two parts, the disturbance current and the disturbance voltage, a system parameter disturbance model is established; a state observer is constructed based on the Kalman filter, with the disturbance compensation current and the disturbance compensation voltage as one of the observed state quantities, and the delayed interface circuit input and output current prediction values ​​as the second observed state quantity;

[0062] Step 4. Compensate the disturbance compensation current and disturbance compensation voltage obtained by the state observer at the next moment to the simulated reference current value of the motor model and the expected value of the power stage inverter output voltage at the current moment to suppress parameter disturbances; and use the delayed interface circuit input and output current as the delayed input of the deadbeat current prediction control algorithm considering delay compensation to achieve synchronous calculation to ensure the real-time performance of the system.

[0063] In a preferred embodiment of the present invention, in step 1, the following voltage equation is established for the adopted LCL interface circuit topology:

[0064]

[0065]

[0066] Among them, u id 、u iq The d-axis and q-axis components of the output voltage of the electric drive system to be tested; i id 、i iq is the d-axis and q-axis components of the interface current; u od 、u oq are the d and q axis components of the motor simulator output voltage; i od 、i oq are the d-axis and q-axis components of the current after filtering by the interface circuit; ω e is the electrical angular velocity; t is the time variable;

[0067] Based on the above voltage equation, the interface voltage state space equation is established and discretized to obtain the following current i input to the interface circuit by the electric drive system under test at the next moment: i(k+1) And the output current i after filtering by the interface circuit o(k+1) Discrete-time prediction model for:

[0068]

[0069] in,

[0070]

[0071] Where, T s is the sampling period; k is the current moment; i o 、i i 、u o 、u i 、u C Are vectors, representing:

[0072] i i =[i id i iq ] T ,i o=[i od i oq ] T ,u i =[u id u iq ] T ,u o =[u od u oq ] T ,u c =[u cd u cq ] T .

[0073] In a preferred embodiment of the present invention, in step 2, the predicted value of the output current of the electric drive system to be tested, that is, the input interface circuit current i i(k+1) Equal to the simulated reference current i* of the motor model i(k) , in order to track, and at the same time to get the expected value i* of the output current after the interface circuit is filtered o(k) :

[0074]

[0075] Let the interface circuit output current i after filtering o(k+1) Equal to the above i* o(k) , and calculate the corresponding power level inverter output voltage expected value u* o(k) :

[0076]

[0077] Considering the delay compensation, the modulation algorithm is executed to control the power stage inverter, and the output current of the interface circuit is controlled to meet the following relationship:

[0078]

[0079] In a preferred embodiment of the present invention, when the system parameter disturbance model is established in step 3, the parameter disturbance is abstracted into a coefficient matrix disturbance ΔA. i , ΔB i , ΔC i , ΔA o , ΔB o , ΔC o , we can get the following relationship:

[0080]

[0081] By comparing with the aforementioned i* o(k) 、u* o(k)By subtracting the formula, we can obtain the deviation of the expected value of the output current after interface filtering and the expected value of the output voltage of the power stage inverter after the parameter disturbance occurs, thereby converting the impact of the parameter disturbance into the deviation of the expected value of the interface current and the expected value of the output voltage, as shown in the following formula:

[0082]

[0083] The disturbance compensation current i l(k+1) and disturbance compensation voltage u l(k+1) As one of the observed state quantities, the delayed interface circuit input current i i(k+1) and the output current i o(k+1) The predicted value serves as the second observed state variable, and two Kalman filter-based state observers, KFIO and KFVO, are constructed. The state observers are based on the Kalman filter principle, taking into account its small size, low computational complexity, and wide application in optimal estimation problems. Furthermore, the Kalman gain is used as the state observer gain, which can be adaptively adjusted according to the covariance matrix during the correction process, avoiding the randomness of manually configuring the observer gain.

[0084] Among them, the KFIO state observer framework is as follows Figure 4 (a) shows the input current i of the interface circuit for delay i(k+1) and disturbance compensation current i l(k+1) For observation, the system state equation and observation equation are:

[0085]

[0086] Where, v i(k) represents process noise, w i(k) represents the observation noise of KFIO, the two are independent of each other, Q i 、R i Represent the covariance matrix of the two respectively;

[0087] The prior estimation and covariance of the prediction link of the KFIO state observer are shown as follows:

[0088]

[0089] Where, Represents i i(k+1) 、i l(k+1) A priori estimate of Represents i i(k) 、i l(k) The observed value, P i(k) represents the k-time error covariance in KFIO, Represents the prior error covariance in KFIO;

[0090] The Kalman gain, posterior estimation, and error covariance update of the correction link of the KFIO state observer are shown as follows:

[0091]

[0092] Where K i(k) represents the Kalman gain of KFIO, Represents i i(k+1) 、i l(k+1) The posterior estimate of P i(k+1) represents the updated error covariance;

[0093] Similarly, the KFVO state observer structure is as follows Figure 4 (b) is shown, which is used to output the current i of the interface circuit for delay o(k+1) and disturbance compensation voltage u l(k+1) For observation, the system state equation and observation equation are:

[0094]

[0095] Where, v u(k) represents process noise, w u(k) represents the observation noise of KFVO, the two are independent of each other, Q u 、R u Represent the covariance matrix of the two respectively;

[0096] The prior estimation and covariance of the prediction link of the KFVO state observer are shown as follows:

[0097]

[0098] Where, Represents i o(k+1) 、u l(k+1) A priori estimate of Represent the observed values ​​of delayed current and compensation voltage at time k, P u(k) represents the error covariance at time k in KFVO, represents the prior error covariance in KFVO;

[0099] The Kalman gain, posterior estimation, and error covariance update of the correction link of the KFVO state observer are shown as follows:

[0100]

[0101] Where K u(k) represents the Kalman gain of KFVO, Represents i o(k+1) 、u l(k+1)The posterior estimate of P u(k+1) represents the updated error covariance.

[0102] The compensation current i obtained by observing KFIO and KFVO l(k+1) , compensation voltage u l(k+1) Compensation to the control system analog current reference value i * i(k) , the expected value of the power stage inverter output voltage u * o(k) In order to suppress the parameter disturbance, the observed delay current i i(k+1) 、i o(k+1) As the delay link input of the deadbeat current predictive control algorithm considering delay compensation, it can realize synchronous calculation and well ensure the real-time performance of the system.

[0103] The invention can realize improved self-disturbance rejection and deadbeat current prediction control for the permanent magnet synchronous motor simulator. The algorithm principle block diagram is as follows: Figure 5 shown.

[0104] In a specific implementation of the present invention, the motor simulator interface circuit can adopt an LCL structure, and the power-stage inverter adopts a three-phase two-level SiC MOSFET module with high switching frequency and low dead time characteristics; the signal simulation part includes an FPGA chip and a DSP chip, the FPGA is responsible for running the electromagnetic simulation part such as the motor model, and the DSP is responsible for running the control algorithm, modulation algorithm, etc., and has high real-time computing capabilities.

[0105] It should be understood that the size of the serial numbers of the steps in the embodiment of the present invention does not mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiment of the present invention.

[0106] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A current predictive control algorithm for a permanent magnet synchronous motor simulator, characterized by: The specific steps include: Step 1: Use sensors to collect the three-phase current and three-phase voltage output by the electric drive system to be tested, the three-phase current and three-phase voltage output by the motor simulator power stage inverter, and the terminal voltages of some components of the interface circuit, and convert them into a dq-axis coordinate system; establish an interface circuit mathematical model and a corresponding interface voltage state-space equation based on the topological structure of the interface circuit; discretize the interface voltage state-space equation to obtain a discrete-time prediction model of the current input by the electric drive system to the interface circuit at the next moment and the current output after filtering by the interface circuit; Specifically, the following voltage equation is established using an LCL-type interface circuit topology: Among them, u id 、u iq The d-axis and q-axis components of the output voltage of the electric drive system to be tested; i id 、i iq is the d-axis and q-axis components of the interface current; u od 、u oq are the d and q axis components of the motor simulator output voltage; i od 、i oq are the d-axis and q-axis components of the current after filtering by the interface circuit; ω e is the electrical angular velocity; t is the time variable; R i is the internal resistance of the inductor on the electric drive system side to be measured; R c is the damping resistance; L i L is the filter inductance of the electric drive system to be tested; o is the filter inductor on the motor simulator side; u c is the voltage across the filter capacitor; Based on the above voltage equation, the interface voltage state space equation is established and discretized to obtain the following current i input to the interface circuit by the electric drive system under test at the next moment: i(k+1) And the output current i after filtering by the interface circuit o(k+1) Discrete-time prediction model for: in, Where, T s is the sampling period; k is the current moment; i o 、i i 、u o 、u i 、u C Are vectors, representing: and i =[and id and iq ] T ,and o =[and od and oq ] T ,in i =[in id in iq ] T ,in o =[in od in oq ] T ,in c =[in cd in cq ] T ; Step 2: Using the data collected by the sensor in step 1 and executing a deadbeat current prediction control algorithm, the predicted value of the output current of the electric drive system to be tested tracks the simulated reference current of the motor model, and the expected value of the output voltage of the corresponding power stage inverter is calculated; considering delay compensation, a modulation algorithm is executed to control the power stage inverter to achieve control of the output current of the interface circuit; Specifically, it is the predicted value of the output current of the electric drive system to be tested, that is, the input interface circuit current i i(k+1) Equal to the simulated reference current i* of the motor model i(k) To track, and at the same time get the expected value i* of the output current after filtering of the interface circuit o(k) : Let the interface circuit output current i after filtering o(k+1) Equal to the above i* o(k) , and calculate the corresponding power level inverter output voltage expected value u* o( k ) : Considering the delay compensation, the modulation algorithm is executed to control the power stage inverter, and the output current of the interface circuit is controlled to meet the following relationship: Step 3: Considering that the interface parameter disturbance consists of two parts, the disturbance current and the disturbance voltage, a system parameter disturbance model is established; a state observer is constructed based on the Kalman filter, with the disturbance compensation current and the disturbance compensation voltage as one of the observed state quantities, and the delayed interface circuit input and output current prediction values ​​as the second observed state quantity; The specific process includes: when the parameter perturbation model is established, the parameter perturbation is abstracted into the coefficient matrix perturbation ΔA i , ΔB i , ΔC i , ΔA o , ΔB o , ΔC o , we get the following relationship: By comparing with the aforementioned i* o(k) 、u* o(k) By subtracting the formula, we can obtain the deviation of the expected value of the output current after interface filtering and the expected value of the output voltage of the power stage inverter after the parameter disturbance occurs, thereby converting the impact of the parameter disturbance into the deviation of the expected value of the interface current and the expected value of the output voltage, as shown in the following formula: The disturbance compensation current i l(k+1) and disturbance compensation voltage u l(k+1) As one of the observed state quantities, the delayed input interface circuit current i i(k+1) and the output current i o(k+1) The predicted value is used as the second observed state quantity, and two Kalman filter-based state observers, KFIO and KFVO, are constructed respectively; Among them, the KFIO state observer is used to analyze the delayed input interface circuit current i i(k+1) and disturbance compensation current i l(k+1) For observation, the system state equation and observation equation are: Where, v i(k) represents process noise, w i(k) represents the observation noise of KFIO, the two are independent of each other, Q i 、R i Represent the covariance matrix of the two respectively; The prior estimation and covariance of the prediction link of the KFIO state observer are shown as follows: Where, Represents i i(k+1) 、i l(k+1) A priori estimate of Represents i i(k) 、i l(k) The observed value, P i(k) represents the k-time error covariance in KFIO, Represents the prior error covariance in KFIO; The Kalman gain, posterior estimation, and error covariance update of the correction link of the KFIO state observer are shown as follows: Where K i(k) represents the Kalman gain of KFIO, Represents i i(k+1) 、i l(k+1) The posterior estimate of P i(k+1) represents the updated error covariance; Similarly, the KFVO state observer is used to output the current i of the delayed interface circuit. o(k+1) and disturbance compensation voltage u l(k+1) For observation, the system state equation and observation equation are: Where, v u(k) represents process noise, w u(k) represents the observation noise of KFVO, the two are independent of each other, Q u 、R u Represent the covariance matrix of the two respectively; The prior estimation and covariance of the prediction link of the KFVO state observer are shown as follows: Where, Represents i o(k+1) 、u l(k+1) A priori estimate of Represent the observed values ​​of delayed current and compensation voltage at time k, P u(k) represents the error covariance at time k in KFVO, represents the prior error covariance in KFVO; The Kalman gain, posterior estimation, and error covariance update of the correction link of the KFVO state observer are shown as follows: Where K u(k) represents the Kalman gain of KFVO, Represents i o(k+1) 、u l(k+1) The posterior estimate of P u(k+1) represents the updated error covariance; Step 4. Compensate the disturbance compensation current and disturbance compensation voltage obtained by the state observer at the next moment to the simulated reference current value of the motor model and the expected value of the power stage inverter output voltage at the current moment to suppress parameter disturbances; and use the delayed interface circuit input and output current as the delayed input of the deadbeat current prediction control algorithm considering delay compensation to achieve synchronous calculation to ensure the real-time performance of the system.

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