Permanent magnet synchronous motor disturbance suppression control method based on double-observer design

Abstract

The invention provides a permanent magnet synchronous motor disturbance suppression control method based on double-observer design, and the method comprises the steps: firstly building a sliding-mode rotating speed controller according to a mathematical model of a permanent magnet synchronous motor, and obtaining a basic form of reference current through the sliding-mode rotating speed controller; and then a sliding mode load torque observer is used for compensating the reference current, and an extended state observer is used for realizing final compensation of the reference voltage, so that the problems of large current following error, harmonic content increase and the like caused by unknown disturbance ambiguity and motor parameter mismatch of the system can be effectively reduced; and the problem of motor control failure is avoided.

Description

Technical Field

[0001] The present invention belongs to the technical field of permanent magnet synchronous motor control, and in particular relates to a permanent magnet synchronous motor disturbance suppression control method based on a dual observer design of a sliding mode load torque observer and an extended observer. Background Art

[0002] At present, the speed loop control of permanent magnet synchronous motor usually adopts proportional integral control method, while the current loop control usually uses deadbeat predictive current control. Among them, proportional integral control has the advantages of being simple and easy to implement and convenient parameter adjustment; deadbeat predictive current control has the characteristics of fast dynamic response capability and low system control delay. However, in actual engineering applications, due to the limited anti-interference ability of proportional integral control, when the motor load torque changes continuously, it will cause large fluctuations in the actual speed, poor speed following performance, and thus deteriorate the speed performance of the motor. In addition, the actual parameters of the motor may change under harsh working conditions, and deadbeat predictive current control depends on the accuracy of the motor parameters. When the actual parameters do not match the model parameters, it will seriously affect the performance of the control system, leading to problems such as increased harmonic content of the output current and increased steady-state error. Summary of the invention

[0003] In view of this, in order to solve the technical problems existing in the art, the present invention provides a permanent magnet synchronous motor disturbance suppression control method based on dual observer design, which specifically includes the following steps:

[0004] Step 1: Establish an equivalent mathematical model of the permanent magnet synchronous motor in the dq axis coordinate system, including a voltage equation, a mechanical motion equation, and an electromagnetic torque equation; and establish a discretized permanent magnet synchronous motor deadbeat predictive control model based on the equivalent mathematical model to calculate a reference voltage;

[0005] Step 2: Based on the sliding mode variable structure control theory, a linear sliding surface and an exponential reaching law are designed, and on this basis, a sliding mode speed control model of a permanent magnet synchronous motor is established to predict and output a reference current;

[0006] Step 3: Using the same type of reaching law as in step 2 and based on the established mechanical motion equation and electromagnetic torque equation, a sliding mode load torque observer is designed to observe the motor load torque in real time; the reference current obtained in step 2 is compensated based on the observed motor load torque;

[0007] Step 4: Consider all unknown disturbances in the system, treat them as an expanded variable and the dq-axis stator current to form the system state variable, and establish an expanded observer to observe the unknown disturbances; use the observed unknown disturbances to compensate the deadbeat predictive control model established in step 1, and then obtain the compensated reference voltage.

[0008] Furthermore, in step 1, the following motor equivalent mathematical model is specifically established:

[0009] Voltage equation of surface-mounted permanent magnet synchronous motor:

[0010]

[0011] In the formula, u d 、u q are the stator voltages of the d and q axes respectively; i d 、i q are the stator currents of the d and q axes respectively; ψ f is the permanent magnet rotor flux; R s is the stator resistance; L s is the stator inductance; ω m is the rotor mechanical angular velocity; p is the number of pole pairs of the motor; t is the time variable;

[0012] Mechanical equation of motion:

[0013]

[0014] Where, J is the moment of inertia of the motor; T e is the electromagnetic torque of the motor; T L is the load torque of the motor;

[0015] Electromagnetic torque equation:

[0016]

[0017] To establish a discrete deadbeat predictive control model for permanent magnet synchronous motor, the dq axis current is discretized using the first-order forward Euler discretization equation to obtain:

[0018]

[0019] The specific form of establishing the deadbeat current prediction model at time k+1 is as follows:

[0020]

[0021] In the formula, i d (k+1), i q (k+1) are the predicted stator d and q axis currents at time k+1; i d (k), i q (k) are the stator d-axis and q-axis sampling currents at time k; u d (k),u q (k) are the d-axis and q-axis stator voltages acting at time k; T s is the sampling time;

[0022] Considering the delay link of the actual digital system, the control voltage is delayed and compensated, and the following reference voltage equation is obtained:

[0023]

[0024] In the formula, u d * 、u q * They are the predicted d-axis and q-axis reference voltages at time k+1 respectively.

[0025] Furthermore, the specific process of establishing the sliding mode speed control model in step 2 includes:

[0026] Before designing the sliding surface and reaching law, first use i d =0 control strategy, converting the voltage equation in the motor equivalent mathematical model into the following form:

[0027]

[0028] Define the following system status variables:

[0029]

[0030] In the formula, ω m * is the reference mechanical angular velocity of the motor; ω m is the actual mechanical angular velocity of the motor;

[0031] The state space expression of the system is as follows:

[0032]

[0033] Then, define the following linear sliding surface:

[0034] s=cx1+x2

[0035] In the formula, c>0 is the sliding mode parameter to be designed;

[0036] Combining the state space expression of the system with the sliding surface, we get:

[0037]

[0038] In the formula, D = i q * ; u=(3pψ f ) / 2J;

[0039] Define the following exponential reaching law:

[0040]

[0041] Where ε and λ are the sliding mode reaching law parameters to be designed, satisfying ε>0 and λ>0;

[0042] Combining the sliding surface and the reaching law equation, we get:

[0043]

[0044] Finally, the q-axis reference current value is expressed as:

[0045]

[0046] In the formula, i q * is the q-axis reference current value, which serves as the input variable of the current loop control.

[0047] Furthermore, the specific process of establishing the sliding mode load torque observer in step 3 includes:

[0048] First, based on the assumption that the load torque is a constant value within a cycle, combined with the mechanical motion equation in the motor equivalent mathematical model, we get:

[0049]

[0050] On this basis, the following sliding mode load torque observer is designed:

[0051]

[0052] In the formula, is the observed value of the motor’s mechanical angular velocity; is the observed value of the motor load torque; U m is the sliding mode control rate of the sliding mode load torque observer; k m is the gain parameter of load torque variation;

[0053] Subtract the above two equations to get:

[0054]

[0055] Then design the following sliding surface in the same form as step 2:

[0056]

[0057] Where m is the sliding surface parameter;

[0058] And design the following exponential reaching law:

[0059]

[0060] Where, k and q are the parameters of the sliding mode control law, satisfying k>0 and q>0;

[0061] Combining the above three formulas, U m It is expressed as:

[0062]

[0063] After discretization, we get:

[0064]

[0065] Where, T ω is the control period of the speed loop;

[0066] After discretizing the sliding mode load torque observer established above, the following expression is obtained:

[0067]

[0068] Finally, the following compensation current is obtained using the load torque observation value:

[0069]

[0070] In the formula, i qT is the compensation current value, which is equal to the reference current i calculated in step 2 q * Form a new reference current value.

[0071] Furthermore, the specific process of establishing the dilated observer in step 4 includes:

[0072] For the d-axis, all unknown disturbances f d is regarded as a new state variable, and the following system state variables are obtained:

[0073]

[0074] This expands the original first-order system into a second-order system, and the state space expression of the system is:

[0075]

[0076] Where x1 and x2 are the state variables of the d-axis system; the superscript · represents the derivative of the corresponding parameter; y is the output variable of the system; h(t) is the rate of change of the disturbance; A is related to the control variable u d Related parameters;

[0077] Then, the d-axis expansion state observer is designed as follows:

[0078]

[0079] Where, e is the observation error; and is the state variable i dand f d β1 and β2 are the gain parameters of the extended observer; g n (e) is the error feedback function, defined as:

[0080]

[0081] Combining the permanent magnet synchronous motor voltage equation and the d-axis extended state observer equation, the following form is obtained:

[0082]

[0083] After discretization, we get:

[0084]

[0085] Where, T s is the sampling period of the current loop;

[0086] The q-axis expansion observer is designed using the same process as the d-axis expansion state observer mentioned above, and its specific form is as follows:

[0087]

[0088] Where β3 and β4 are the extended observer gain parameters of the q-axis;

[0089] The predicted current and observed disturbances Substituting into the reference voltage expression of the deadbeat predictive current control, the reference voltage expression after compensation is finally obtained:

[0090]

[0091] In the formula, u dE * 、u qE * They are the d-axis and q-axis reference voltages based on the extended observer disturbance compensation.

[0092] The permanent magnet synchronous motor disturbance suppression control method based on the dual observer design provided by the present invention first establishes a sliding mode speed controller according to the mathematical model of the permanent magnet synchronous motor, and obtains the basic form of the reference current by the sliding mode speed controller; then, the reference current is compensated by the sliding mode load torque observer in turn, and the reference voltage is finally compensated by the extended state observer, thereby effectively reducing the problems of large current following error and increased harmonic content caused by unclear unknown disturbances and motor parameter mismatch in the system, and then avoiding the problem of motor control failure. BRIEF DESCRIPTION OF THE DRAWINGS

[0093] Figure 1A system flow diagram of the method provided by the present invention;

[0094] Figure 2 The actual speed and control current curve of the preferred embodiment of the present invention under load torque step condition;

[0095] Figure 3 The figure is a comparison between the actual current and reference current of the d and q axes under parameter mismatch conditions of a preferred embodiment of the present invention. DETAILED DESCRIPTION

[0096] The technical solution of the present invention will be described clearly and completely below in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0097] The present invention provides a permanent magnet synchronous motor disturbance suppression control method based on dual observer design, such as Figure 1 As shown, the specific steps include:

[0098] Step 1: Establish an equivalent mathematical model of the permanent magnet synchronous motor in the dq axis coordinate system, including a voltage equation, a mechanical motion equation, and an electromagnetic torque equation; and establish a discretized permanent magnet synchronous motor deadbeat predictive control model based on the equivalent mathematical model to calculate a reference voltage;

[0099] Step 2: Based on the sliding mode variable structure control theory, a linear sliding surface and an exponential reaching law are designed, and on this basis, a sliding mode speed control model of a permanent magnet synchronous motor is established to predict and output a reference current;

[0100] Step 3: Using the same type of reaching law as in step 2 and based on the established mechanical motion equation and electromagnetic torque equation, a sliding mode load torque observer is designed to observe the motor load torque in real time; the reference current obtained in step 2 is compensated based on the observed motor load torque;

[0101] Step 4: Consider all unknown disturbances in the system, treat them as an expanded variable and the dq-axis stator current to form the system state variable, and establish an expanded observer to observe the unknown disturbances; use the observed unknown disturbances to compensate the deadbeat predictive control model established in step 1, and then obtain the compensated reference voltage.

[0102] In a preferred embodiment of the present invention, in step 1, a motor equivalent mathematical model in the following form is specifically established:

[0103] Voltage equation of surface-mounted permanent magnet synchronous motor:

[0104]

[0105] In the formula, u d 、u q are the stator voltages of the d and q axes respectively; i d 、i q are the stator currents of the d and q axes respectively; ψ f is the permanent magnet rotor flux; R s is the stator resistance; L s is the stator inductance; ω m is the rotor mechanical angular velocity; p is the number of pole pairs of the motor; t is the time variable;

[0106] Mechanical equation of motion:

[0107]

[0108] Where, J is the moment of inertia of the motor; T e is the electromagnetic torque of the motor; T L is the load torque of the motor;

[0109] Electromagnetic torque equation:

[0110]

[0111] To establish a discrete deadbeat predictive control model for permanent magnet synchronous motor, the dq axis current is discretized using the first-order forward Euler discretization equation to obtain:

[0112]

[0113] The specific form of establishing the deadbeat current prediction model at time k+1 is as follows:

[0114]

[0115] In the formula, i d (k+1), i q (k+1) are the predicted stator d and q axis currents at time k+1; i d (k), i q (k) are the stator d-axis and q-axis sampling currents at time k; u d (k),u q (k) are the d-axis and q-axis stator voltages acting at time k; T s is the sampling time;

[0116] Considering the delay link of the actual digital system, the control voltage is delayed and compensated, and the following reference voltage equation is obtained:

[0117]

[0118] In the formula, u d * 、u q * They are the predicted d-axis and q-axis reference voltages at time k+1 respectively.

[0119] In a preferred embodiment of the present invention, the specific process of step 2 of establishing the sliding mode speed control model includes:

[0120] Before designing the sliding surface and reaching law, first use i d =0 control strategy, converting the voltage equation in the motor equivalent mathematical model into the following form:

[0121]

[0122] Define the following system status variables:

[0123]

[0124] In the formula, ω m * is the reference mechanical angular velocity of the motor; ω m is the actual mechanical angular velocity of the motor;

[0125] The state space expression of the system is as follows:

[0126]

[0127] Then, define the following linear sliding surface:

[0128] s=cx1+x2

[0129] In the formula, c>0 is the sliding mode parameter to be designed;

[0130] Combining the state space expression of the system with the sliding surface, we get:

[0131]

[0132] In the formula, D = i q * ; u=(3pψ f ) / 2J;

[0133] Define the following exponential reaching law:

[0134]

[0135] Where ε and λ are the sliding mode reaching law parameters to be designed, satisfying ε>0 and λ>0;

[0136] Combining the sliding surface and the reaching law equation, we get:

[0137]

[0138] Finally, the q-axis reference current value is expressed as:

[0139]

[0140] In the formula, i q * is the q-axis reference current value, which serves as the input variable of the current loop control.

[0141] In a preferred embodiment of the present invention, the specific process of step 3 establishing the sliding mode load torque observer includes:

[0142] First, since the switching frequency of the controller is much greater than the frequency of change of the load torque, it is assumed that the load torque is a constant value within one cycle, and thus combined with the mechanical motion equation in the motor equivalent mathematical model, the following is obtained:

[0143]

[0144] On this basis, the following sliding mode load torque observer is designed:

[0145]

[0146] In the formula, is the observed value of the motor’s mechanical angular velocity; is the observed value of the motor load torque; U m is the sliding mode control rate of the sliding mode load torque observer; k m is the gain parameter of load torque variation;

[0147] Subtract the above two equations to get:

[0148]

[0149] Then design the following sliding surface in the same form as step 2:

[0150]

[0151] Where m is the sliding surface parameter;

[0152] And design the following exponential reaching law:

[0153]

[0154] Where, k and q are the parameters of the sliding mode control law, satisfying k>0 and q>0;

[0155] Combining the above three formulas, U m It is expressed as:

[0156]

[0157] After discretization, we get:

[0158]

[0159] Where, T ω is the control period of the speed loop;

[0160] After discretizing the sliding mode load torque observer established above, the following expression is obtained:

[0161]

[0162] Finally, the following compensation current is obtained using the load torque observation value:

[0163]

[0164] In the formula, i qT is the compensation current value, which is equal to the reference current i calculated in step 2 q * Form a new reference current value.

[0165] In a preferred embodiment of the present invention, the specific process of establishing the dilation observer in step 4 includes:

[0166] For the d-axis, all unknown disturbances f d is regarded as a new state variable, and the following system state variables are obtained:

[0167]

[0168] This expands the original first-order system into a second-order system, and the state space expression of the system is:

[0169]

[0170] Where x1 and x2 are the state variables of the d-axis system; the superscript · represents the derivative of the corresponding parameter; y is the output variable of the system; h(t) is the rate of change of the disturbance; A is related to the control variable u d Related parameters;

[0171] Then, the d-axis expansion state observer is designed as follows:

[0172]

[0173] Where, e is the observation error; and is the state variable i d and f d β1 and β2 are the gain parameters of the extended observer; gn (e) is the error feedback function, defined as:

[0174]

[0175] Combining the permanent magnet synchronous motor voltage equation and the d-axis extended state observer equation, the following form is obtained:

[0176]

[0177] After discretization, we get:

[0178]

[0179] Where, T s is the sampling period of the current loop;

[0180] The q-axis expansion observer is designed using the same process as the d-axis expansion state observer mentioned above, and its specific form is as follows:

[0181]

[0182] Where β3 and β4 are the extended observer gain parameters of the q-axis;

[0183] The predicted current and observed disturbances Substituting into the reference voltage expression of the deadbeat predictive current control, the reference voltage expression after compensation is finally obtained:

[0184]

[0185] In the formula, u dE * 、u qE * They are the d-axis and q-axis reference voltages based on the extended observer disturbance compensation.

[0186] In a preferred embodiment of the present invention, a permanent magnet synchronous motor disturbance suppression control method based on a dual observer design is provided. When the inverter DC voltage supply is 130V, the stator resistance R s is 0.365Ω, stator inductance L s is 0.001225H, rotor flux ψ f The actual speed and control current curves obtained by executing this method are as follows: Figure 2 As shown in the figure, when the motor parameter mismatch occurs (R s0 =2R s , Ls0 =2L s , ψ f0 =2ψ f ) The actual d and q axis currents are compared with the reference currents. Figure 3 As shown, it can be seen that the method provided by the present invention can increase the anti-disturbance capability and robustness of the motor under load torque step and parameter mismatch conditions.

[0187] 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.

[0188] Although 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 the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A disturbance suppression control method for a permanent magnet synchronous motor based on a dual observer design, characterized in that: The specific steps include: Step 1: Establish an equivalent mathematical model of the permanent magnet synchronous motor in the dq axis coordinate system, including a voltage equation, a mechanical motion equation, and an electromagnetic torque equation; and establish a discretized permanent magnet synchronous motor deadbeat predictive control model based on the equivalent mathematical model to calculate a reference voltage; Step 2: Based on the sliding mode variable structure control theory, a linear sliding surface and an exponential reaching law are designed, and on this basis, a sliding mode speed control model of a permanent magnet synchronous motor is established to predict and output a reference current; Step 3: Using the same type of reaching law as in step 2 and based on the established mechanical motion equation and electromagnetic torque equation, a sliding mode load torque observer is designed to observe the motor load torque in real time; the reference current obtained in step 2 is compensated based on the observed motor load torque; Step 4: Consider all unknown disturbances in the system, treat them as an expanded variable and the dq-axis stator current to form the system state variable, and establish an expanded observer to observe the unknown disturbances; use the observed unknown disturbances to compensate the deadbeat predictive control model established in step 1, and then obtain the compensated reference voltage.

2. The method according to claim 1, characterized in that: In step 1, the following motor equivalent mathematical model is established: Voltage equation of surface-mounted permanent magnet synchronous motor: In the formula, u d 、u q are the stator voltages of the d and q axes respectively; i d 、i q are the stator currents of the d and q axes respectively; ψ f is the permanent magnet rotor flux; R s is the stator resistance; L s is the stator inductance; ω m is the rotor mechanical angular velocity; p is the number of pole pairs of the motor; t is the time variable; Mechanical equation of motion: Where, J is the moment of inertia of the motor; T e is the electromagnetic torque of the motor; T L is the load torque of the motor; Electromagnetic torque equation: To establish a discrete deadbeat predictive control model for permanent magnet synchronous motor, the dq axis current is discretized using the first-order forward Euler discretization equation to obtain: The specific form of establishing the deadbeat current prediction model at time k+1 is as follows: In the formula, i d (k+1), i q (k+1) are the predicted stator d and q axis currents at time k+1; i d (k), i q (k) are the stator d-axis and q-axis sampling currents at time k; u d (k) and u q (k) are the d-axis and q-axis stator voltages acting at time k; T s is the sampling time; Considering the delay link of the actual digital system, the control voltage is delayed and compensated, and the following reference voltage equation is obtained: In the formula, u d * 、u q * They are the predicted d-axis and q-axis reference voltages at time k+1 respectively.

3. The method according to claim 2, characterized in that: The specific process of step 2 to establish the sliding mode speed control model includes: Before designing the sliding surface and reaching law, first use i d =0 control strategy, converting the voltage equation in the motor equivalent mathematical model into the following form: Define the following system status variables: In the formula, ω m * is the reference mechanical angular velocity of the motor; ω m is the actual mechanical angular velocity of the motor; The state space expression of the system is as follows: Then, define the following linear sliding surface: s=cx1+x2 In the formula, c>0 is the sliding mode parameter to be designed; Combining the state space expression of the system with the sliding surface, we get: Where D = i q * ; u=(3pψ f ) / 2J; Define the following exponential reaching law: Where ε and λ are the sliding mode reaching law parameters to be designed, satisfying ε>0 and λ>0; Combining the sliding surface and the reaching law equation, we get: Finally, the q-axis reference current value is expressed as: In the formula, i q * is the q-axis reference current value, which serves as the input variable of the current loop control.

4. The method according to claim 3, characterized in that: Step 3: The specific process of establishing the sliding mode load torque observer includes: First, based on the assumption that the load torque is a constant value within a cycle, combined with the mechanical motion equation in the motor equivalent mathematical model, we get: On this basis, the following sliding mode load torque observer is designed: In the formula, is the observed value of the motor’s mechanical angular velocity; is the observed value of the motor load torque; U m is the sliding mode control rate of the sliding mode load torque observer; k m is the gain parameter of load torque variation; Subtract the above two equations to get: Then design the following sliding surface in the same form as step 2: Where m is the sliding surface parameter; And design the following exponential reaching law: Where, k and q are the parameters of the sliding mode control law, satisfying k>0 and q>0; Combining the above three formulas, U m It is expressed as: After discretization, we get: Where, T ω is the control period of the speed loop; After discretizing the sliding mode load torque observer established above, the following expression is obtained: Finally, the following compensation current is obtained using the load torque observation value: In the formula, i qT is the compensation current value, which is equal to the reference current i calculated in step 2 q * Form a new reference current value.

5. The method according to claim 4, characterized in that: The specific process of establishing the dilated observer in step 4 includes: For the d-axis, all unknown disturbances f d is regarded as a new state variable, and the following system state variables are obtained: This expands the original first-order system into a second-order system, and the state space expression of the system is: Where x1 and x2 are the state variables of the d-axis system; the superscript · represents the derivative of the corresponding parameter; y is the output variable of the system; h(t) is the rate of change of the disturbance; A is related to the control variable u d Related parameters; Then, the d-axis expansion state observer is designed as follows: Where, e is the observation error; and is the state variable i d and f d β1 and β2 are the gain parameters of the extended observer; g n (e) is the error feedback function, defined as: Combining the permanent magnet synchronous motor voltage equation and the d-axis extended state observer equation, the following form is obtained: After discretization, we get: Where, T s is the sampling period of the current loop; The q-axis expansion observer is designed using the same process as the d-axis expansion state observer mentioned above, and its specific form is as follows: Where β3 and β4 are the extended observer gain parameters of the q-axis; The predicted current and observed disturbances Substituting into the reference voltage expression of the deadbeat predictive current control, the reference voltage expression after compensation is finally obtained: In the formula, u dE * 、u qE * They are the d-axis and q-axis reference voltages based on the extended observer disturbance compensation.

Images