Permanent magnet synchronous motor control method based on linear active disturbance rejection and deadbeat prediction

Abstract

The invention discloses a permanent magnet synchronous motor control method based on linear active disturbance rejection and deadbeat prediction. The method comprises the following steps: step 1, establishing a mathematical model of a permanent magnet synchronous motor under a two-phase rotating coordinate system; 2, constructing a hyper-local model and a sliding mode observer, and combining the hyper-local model and the sliding mode observer to carry out model-free and dead-beat predictive control on a current inner loop; and 3, constructing linear active-disturbance-rejection control, wherein the linear active-disturbance-rejection control comprises a second-order linear expansion state observer, linear state error feedback and a total disturbance compensation mechanism, and performing linear active-disturbance-rejection control on a speed outer ring. The method has the advantages that the current control static tracking performance is good, the dynamic response is fast, various disturbances are effectively inhibited, and the robustness of the whole control system is improved.

Description

Technical Field

[0001] The design of the present invention relates to the technical field of permanent magnet synchronous motor control, and particularly to a control method for a permanent magnet synchronous motor based on a series correction function, double-feed linear active disturbance rejection, and deadbeat predictive current control. Background Art

[0002] As a core component of industrial manufacturing equipment such as intelligent manufacturing and high-end equipment manufacturing, as well as new energy vehicles, the permanent magnet synchronous motor (PMSM) will play an important role in promoting the transformation and upgrading of the manufacturing industry. At the same time, higher requirements are also put forward for the PMSM motion system. However, the PMSM is a complex nonlinear system with multiple variables, strong coupling, and time-variation. High-performance control strategies play a crucial role in the performance of the PMSM drive system.

[0003] The current loop of the permanent magnet synchronous motor adopts deadbeat predictive control, which does not require a cost function and has the advantages of simple structure, easy digital implementation, fixed switching frequency, good static tracking performance, and fast dynamic response. However, it depends on an accurate mathematical model, and problems such as steady-state tracking deviation will occur when the motor parameters deviate. Currently, to address the shortcoming of relying on an accurate mathematical model, many existing technologies adopt solutions such as introducing an error compensation term, introducing an observer, introducing a parameter identification algorithm, and reducing system delay.

[0004] The speed loop of the permanent magnet synchronous motor adopts linear active disturbance rejection control (LADRC). For problems such as speed fluctuations, noise, and increased torque ripple caused by external disturbances (load mutations) and internal disturbances (inverter nonlinearity, parameter mismatch, mechanical friction). The disturbance rejection ability of active disturbance rejection control is of great significance for suppressing disturbances during the operation of the PMSM. The disturbance rejection performance of active disturbance rejection control depends on the estimation accuracy of the extended state observer (ESO) for disturbances. The observation accuracy of the traditional ESO is not high, which will limit the speed tracking accuracy. Summary of the Invention

[0005] In view of the deficiencies in the prior art, the present invention provides a control method for a permanent magnet synchronous motor based on linear active disturbance rejection and deadbeat prediction to solve the technical problems of relying on an accurate mathematical model and low speed tracking accuracy in the prior art.

[0006] The present invention provides a control method for a permanent magnet synchronous motor based on linear active disturbance rejection and deadbeat prediction, including the following steps:

[0007] Step 1: Establish a mathematical model of the permanent magnet synchronous motor in the two-phase rotating coordinate system;

[0008] Step 2: Construct a super-local model and a sliding mode observer, and combine the super-local model with the sliding mode observer to perform model-free deadbeat predictive control on the current inner loop;

[0009] Step 3: Constructing the linear active disturbance rejection control includes: a second-order linear extended state observer, linear state error feedback, and a total disturbance compensation mechanism to perform linear active disturbance rejection control on the speed outer loop.

[0010] Furthermore, in the above Step 2, the constructed super-local model is:

[0011]

[0012] where i d and i q are the dq-axis currents; u d and u q are the dq current control outputs respectively; f d and f q are the disturbances on the dq-axis respectively; b = 1 / L.

[0013] Furthermore, in the above Step 2, the mathematical model of the sliding mode observer is:

[0014]

[0015] The sliding mode function of the sliding mode observer is:

[0016]

[0017] where is the estimated current value; is the estimated disturbance; U dsmo and U qsmo are the sliding mode functions to be designed; λ d and λ q are greater than 0 as the sliding mode gains; k 1 and k 2 are greater than 0.

[0018] Furthermore, in the above Step 2, it also includes discretizing the sliding mode observer. The discretized sliding mode observer is:

[0019]

[0020] After one-step compensation and disturbance compensation of the discretized sliding mode observer, the output stator voltage is:

[0021]

[0022] where and are the predicted stator current values; and are the predicted disturbances; T s is the sampling time; u d (k + 1) and uq (k + 1) is the reference voltage value at the calculated (k + 1)-th moment.

[0023] Further, in the said step 3, the second-order linear extended state observer is:

[0024]

[0025] The linear state error feedback is:

[0026]

[0027] where k p is the proportional gain of the controller; β 1 , β 2 are the LESO feedback gain coefficients of the speed loop; b 0 is the control input coefficient; x 1 , x 2 are the estimated values of speed and total disturbance respectively; ω o ≈3 - 5ω c , ω c is the controller bandwidth; ω m is the system output.

[0028] Further, in the said step 3, it also includes optimizing the second-order linear extended state observer through the output feedback differential signal and the series correction function.

[0029] Further, the optimized second-order linear extended state observer is:

[0030]

[0031] where x 1 , x 2 are the estimated values of speed and total disturbance respectively; x 3 is the corrected total disturbance state variable, is the estimated value of x 3 .

[0032] Further, in the said step 3, it also includes optimizing the linear state error feedback through the reference signal differential feedforward and variable exponent.

[0033] Further, the optimized linear state error feedback is:

[0034]

[0035] where 0 < ε < 1, δ > 0; x 1 is the system state; A|s|sign(s) + ks is the variable exponent reaching law, A is the adaptive coefficient, and both A and k satisfy the stability condition.

[0036] Advantages of the present invention:

[0037] In the current inner-loop control of the present invention, the advantages of good static tracking performance and fast dynamic response of the deadbeat predictive current control are fully utilized. The super-local model is adopted to overcome the disadvantage of requiring an accurate mathematical model, and the sliding mode disturbance observer is used for compensation to improve the robustness of the control system.

[0038] In the speed outer-loop control of the present invention, the active disturbance rejection control is adopted. By improving the extended state observer and the error feedback control law, the estimation accuracy of the observer is improved, various disturbances are effectively suppressed, and the robustness of the entire control system is enhanced. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] The features and advantages of the present invention will be more clearly understood by referring to the accompanying drawings. The drawings are schematic and should not be construed as imposing any limitation on the present invention. In the drawings:

[0040] Figure 1 is the control block diagram in a specific embodiment of the present invention;

[0041] Figure 2 is the structural block diagram of the improved extended state observer in a specific embodiment of the present invention;

[0042] Figure 3 is the structural block diagram of the improved linear state error feedback in a specific embodiment of the present invention;

[0043] Figure 4 is the speed comparison diagram of the double-fed linear active disturbance rejection with series correction function and the unimproved linear active disturbance rejection in a specific embodiment of the present invention;

[0044] Figure 5 is the speed fluctuation comparison diagram of the double-fed linear active disturbance rejection with series correction function and the unimproved linear active disturbance rejection in a specific embodiment of the present invention;

[0045] Figure 6 is the d-axis current waveform diagram obtained by the double-fed linear active disturbance rejection with series correction function and the model-free deadbeat predictive control in a specific embodiment of the present invention;

[0046] Figure 7 is the q-axis current waveform diagram obtained by the double-fed linear active disturbance rejection with series correction function and the model-free deadbeat predictive control in a specific embodiment of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0047] To make the objectives, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0048] The present invention will be further clarified below with reference to specific embodiments. Those skilled in the art should understand that these embodiments are only used to illustrate the present invention and not to limit the scope of the present invention. Modifications to various equivalent forms of the present invention fall within the scope defined by the appended claims of this application.

[0049] The present invention provides a permanent magnet synchronous motor control method based on linear active disturbance rejection and deadbeat prediction, including the following steps:

[0050] Step 1: As Figure 1 shown, establish the mathematical model of the permanent magnet synchronous motor in the two-phase rotating coordinate system;

[0051] Establish the model of the permanent magnet synchronous motor in the rotating coordinate system,

[0052] Voltage equation:

[0053]

[0054] In the formula, u d and u q are respectively the direct-axis voltage and quadrature-axis voltage of the stator of the permanent magnet synchronous motor; R s is the stator resistance, L d , L q are the inductances on the dq axes equivalent to the rotating coordinate system. For a surface-mounted permanent magnet synchronous motor, L d = L q , i d , i q are the equivalent dq-axis currents, ψ f is the permanent magnet flux linkage, ω e is the electrical angular velocity;

[0055] Flux linkage equation:

[0056]

[0057] The motion equation without considering disturbances is:

[0058]

[0059] In the formula, T e is the electromagnetic torque, T Lis the load torque, and n p is the number of pole pairs, and J is the moment of inertia;

[0060] The surface-mounted permanent magnet synchronous motor generally adopts i d = 0 control. The internal magnetic flux of the motor is completely provided by the permanent magnet on the rotor. The direct-axis current is 0 A. The motor does not generate the armature reaction of the direct axis and does not generate additional reluctance torque. All the current in the motor is used to generate electromagnetic torque. By controlling the q-axis current component, the output torque of the motor can be controlled.

[0061] Step 2: Construct a super-local model and a sliding mode observer, and combine the super-local model with the sliding mode observer to perform model-free deadbeat predictive control on the current inner loop;

[0062] The derivation process of the deadbeat predictive control for the current inner loop of the permanent magnet synchronous motor and the model-free deadbeat predictive control based on the sliding mode observer is as follows:

[0063] The discrete-time model of the PMSM can be described by the first-order Taylor series. According to Equation (1), the discrete current prediction model of the PMSM is obtained as:

[0064]

[0065] Among them,

[0066]

[0067] In the formula, i d (k), i q (k) are the current values at the current moment. In order to make the motor track the given value at the next moment, let i d (k + 1) = i dref , i q (k + 1) = i qref . The stator voltage of the motor that makes the actual current vector reach the reference current is:

[0068] u(k) = B -1 (i ref (k) - Ai(k) - D(k)) (5)

[0070] For the control delay problem, a "two-step prediction" scheme is adopted for delay compensation. The output voltage vector after compensation is:

[0071] u(k + 1) = B -1 (i(k + 2) - Ai pre (k + 1) - D(k + 1)) (6)

[0072] In the formula, when considering the delay compensation, it is necessary to make the feedback current at the (k + 2)th moment track the given current at the kth moment. Therefore, let i(k + 2) = i ref (k). Since the control period is very short and the mechanical time constant of the motor is much larger than the electrical constant, it is assumed that the rotational speed remains unchanged within two adjacent control periods, that is, ω(k + 1) = ω(k). The unknown quantity i(k + 1) needs to be estimated and predicted at the kth moment. According to Equation (4), the current value i pre (k + 1) at the (k + 1)th moment is:

[0073]

[0074] Then:

[0075] u(k + 1) = B -1 (i ref (k) - Ai pre (k + 1) - D(k)) (8)

[0077] In order to completely get rid of the dependence on parameters, model-free deadbeat predictive current control (MF-DPCC) is adopted, which greatly reduces the dependence of controller design on parameters. A sliding mode observer is used to estimate the total disturbance.

[0078] The super-local model used in the deadbeat predictive current control is:

[0079]

[0080] It can be seen from Equation (1) that in the current control of PMSM, the constructed super-local model is:

[0081]

[0082] In the formula, i d and i q are the dq-axis currents; u d and u q are the dq-current control outputs respectively; f d and f q are the disturbances of the dq-axis respectively; b = 1 / L.

[0083] The mathematical model design of the adopted sliding mode observer is:

[0084]

[0085] In the formula, is the estimated current value; is the estimated disturbance; U dsmo and U qsmo are the sliding mode functions to be designed; λ d, λ q Greater than 0 is the sliding mode gain.

[0086] Combining Equation (10) and Equation (11), the error equation is obtained as:

[0087]

[0088] Wherein, is the current estimation error; is the disturbance estimation error.

[0089] The sliding mode surface is designed as:

[0090]

[0091] The exponential reaching law adopted is:

[0092]

[0093] Wherein, k 1 , k 2 Greater than 0 are the sliding mode coefficients.

[0094] Combining Equation (13) and Equation (14), the expression of the sliding mode function can be obtained as:

[0095]

[0096] Discretizing the sliding mode observer gives:

[0097]

[0098] Wherein, and represent the predicted stator current values; and represent the predicted disturbances; T s is the sampling time;

[0099] After one-step compensation and disturbance compensation for the discretized sliding mode observer, the output stator voltage is:

[0100]

[0101] Wherein, u d (k + 1) and u q (k + 1) represent the calculated reference voltage values at the (k + 1)-th moment.

[0102] Step 3: Construct a linear active disturbance rejection control, including: a second-order linear extended state observer, linear state error feedback, and a total disturbance compensation mechanism, and perform linear active disturbance rejection control on the speed outer loop.

[0103] The present invention does not adopt a tracking differentiator. The constructed linear active disturbance rejection control (LADRC) includes: a second-order linear extended state observer (LESO), a linear state error feedback (LSEF), and a total disturbance compensation mechanism. The specific construction process is as follows:

[0104] The differential expression of the motion equation is:

[0105]

[0106] According to Equation (18), the system output ω m is selected as the state variable, and its state equation is described as:

[0107]

[0108] In the formula, The total disturbance f includes the external and internal disturbances suffered by the system. Among them, the external disturbance refers to the disturbance imposed by the external system, such as the given disturbance and the load disturbance; the internal disturbance refers to the changes inside the system, such as structural changes, temperature drift, zero drift, system parameter changes, etc. In the formula, δ is the external disturbance, and the error ΔJ generated by the actual value and the nominal value of the moment of inertia is used as the internal disturbance in the total disturbance.

[0109] Let, x 1 = ω m , x 2 = f, then the state space equation of the system is:

[0110]

[0111] Its matrix form is:

[0112]

[0113] In the formula, c = [1 0].

[0114] According to Equation (20) and Equation (21), a second-order linear extended state observer can be established as:

[0115]

[0116] In the formula, x = [x 1 x 2 T are the estimated values of the speed and the total disturbance respectively; L = [β 1 β 2 T is the LESO feedback gain coefficient of the speed loop, and when expanded, it is:

[0117] ​​

[0118] Through pole placement, the observer feedback gain coefficient is configured at the bandwidth ω of the second-order linear extended state observer 0 to obtain:

[0119] s 2 +β 1 s + β 2 =(s + ω 0 ) 2 (24)

[0120] It can be obtained that β 1 = 2ω 0 , β 2 = ω 0 2 .

[0121] The linear feedback error control rate is:

[0122] u 0 = k p (ω * m - x 1 ) (25)

[0123] In the formula, k p is the proportional gain of the controller, and its value is determined by the controller bandwidth ω c , which affects the dynamic response speed and anti-interference ability of the system. Usually, ω o ≈(3 - 5)ω c .

[0124] After compensating for the disturbance observed by the second-order linear extended state observer, it is:

[0125]

[0126] Then, the speed loop control design based on LADRC is:

[0127]

[0128] The second-order linear extended state observer adopts the output feedback differential compensation (FBDC) method. At this time, the LESO is:

[0129]

[0130] According to the aforementioned derivation method, it can be known that the LESO changes as:

[0131]

[0132] Through pole placement, the observer feedback gain coefficient is configured at the bandwidth ω of the second-order linear extended state observer 0 to obtain:

[0133] (s + β 1 )(s + β 2 )=(s + ω 0 ) 2 (30)

[0134] It can be obtained that β 1 =β 2 =ω 0 。

[0135] Widen the estimation range of the LESO for the total disturbance and solve the system oscillation problem caused by too large ω 0 , and a series lead compensation function (SCLC) is used to correct the second-order linear extended state observer.

[0136] As can be seen from Equation (27), the s-domain expression of the observer obtained according to the Laplace transform is:

[0137]

[0138] From the above reasoning, it can be obtained that

[0139]

[0140] In order to more effectively handle the deviation of the disturbance term reconstruction and obtain higher robustness under uncertainty and disturbance conditions, a correction of the disturbance is introduced. After , a cascade correction function is connected, and then the corrected Φ 1 (s) is:

[0141]

[0142] where T a is the lead correction time constant; α is the correction coefficient, and α > 1.

[0143] From Equation (32), the second-order linear extended state observer after the series lead compensation function as shown in Figure 2 is obtained:

[0144]

[0145] where x 3 is the corrected total disturbance state variable; is the estimated value of x 3 .

[0146] By optimizing the linear state error feedback through reference signal difference feedforward and variable exponents, the optimized linear state error feedback is:

[0147]

[0148] where \(0 < \varepsilon < 1\), \(\delta>0\); \(x\) 1 is the system state; \(A|s|\text{sign}(s)+ks\) is the variable exponent reaching law, \(A\) is the adaptive coefficient, and both \(A\) and \(k\) satisfy the stability conditions. The reference signal feedforward is introduced into the original linear error feedback control law to enhance the signal tracking ability, and at the same time, the variable structure part is added to enhance the disturbance rejection ability.

[0149] According to Equation (36), the block diagram of the improved linear feedback error control law is as Figure 3 shown.

[0150] The present invention is verified in Matlab / Simulink. According to the derivation of the above steps, its simulation model is built. Figure 4 is the speed comparison diagram of the improved linear active disturbance rejection and the unimproved linear active disturbance rejection proposed by the present invention for the PMSM speed loop. The initial given speed is 1000 rmp. It is found that the improved scheme of the present invention has a faster starting speed. When the same torque load is given at 0.1 s, the scheme of the present invention has a smaller speed drop. When the load is unloaded at 0.2 s, the scheme of the present invention has a smaller speed overshoot. Figure 5 is the speed fluctuation comparison diagram of the improved linear active disturbance rejection and the unimproved linear active disturbance rejection proposed by the present invention for the PMSM speed loop. It is found that the scheme proposed by the present invention has a smaller speed jitter. Figure 6 and Figure 7 are the dq-axis current waveform diagrams obtained by the double-fed linear active disturbance rejection and the model-free deadbeat predictive control of the series correction function proposed by the present invention, respectively.

[0151] Although the embodiments of the present invention have been described with reference to the accompanying drawings, those skilled in the art can make various modifications and variations without departing from the spirit and scope of the present invention. Such modifications and variations fall within the scope defined by the appended claims.

Claims

1. A permanent magnet synchronous motor control method based on linear auto-disturbance rejection and deadbeat prediction, characterized in that: The steps include: Step 1: Establish a mathematical model of the permanent magnet synchronous motor in a two-phase rotating coordinate system; Step 2: Construct a hyperlocal model and a sliding film observer, and combine the hyperlocal model and the sliding film observer to perform model-free deadbeat predictive control on the current inner loop; Step 3: Construct a linear active disturbance rejection control including: a second-order linear extended state observer, a linear state error feedback and a total disturbance compensation mechanism to perform linear active disturbance rejection control on the speed outer loop.

2. The permanent magnet synchronous motor control method based on linear auto-disturbance rejection and deadbeat prediction according to claim 1, characterized in that: In step 2, the hyperlocal model constructed is: In the formula, i d 、i q is the dq axis current; u d 、u q They are dq current control output respectively; f d 、f q are the disturbances of dq axis respectively; b=1 / L.

3. The permanent magnet synchronous motor control method based on linear auto-disturbance rejection and deadbeat prediction according to claim 1 or 2, characterized in that: In step 2, the mathematical model of the synovial membrane observer is: The sliding mode function of the sliding film observer is: In the formula, is the estimated current value; is the estimated disturbance; U dsmo , U qsmo is the sliding mode function to be designed; d , q Greater than 0 is sliding mode gain; k1 and k2 are greater than 0.

4. The permanent magnet synchronous motor control method based on linear auto-disturbance rejection and deadbeat prediction as claimed in claim 3, characterized in that: The step 2 also includes discretizing the synovial observer, and the discretized synovial observer is: After the discretized synovial observer performs one-beat compensation and disturbance compensation, the output stator voltage is: In the formula, and is the predicted stator current value; and is the predicted disturbance; T s is the sampling time; u d (k+1) and u q (k+1) is the calculated reference voltage value at the k+1th moment.

5. The permanent magnet synchronous motor control method based on linear auto-disturbance rejection and deadbeat prediction according to claim 1, characterized in that: In step 3, the second-order linear extended state observer is: The linear state error feedback is: In the formula, k p The proportional gain of the controller; β1 and β2 are the LESO feedback gain coefficients of the speed loop; b0 is the control input coefficient; x1 and x2 are the estimated values ​​of the speed and total disturbance respectively; ω o ≈3~5ω c ,ω c is the controller bandwidth; ω m Output for the system.

6. The permanent magnet synchronous motor control method based on linear auto-disturbance rejection and deadbeat prediction according to claim 1 or 5, characterized in that: The step 3 also includes optimizing the second-order linear extended state observer by outputting a feedback differential signal and a series correction function.

7. The permanent magnet synchronous motor control method based on linear auto-disturbance rejection and deadbeat prediction according to claim 6, characterized in that: The optimized second-order linear extended state observer is: In the formula, x1 and x2 are the estimated values ​​of speed and total disturbance respectively; x3 is the corrected total disturbance state variable, is the estimated value of x3.

8. The permanent magnet synchronous motor control method based on linear auto-disturbance rejection and deadbeat prediction according to claim 1 or 5, characterized in that: The step 3 also includes optimizing the linear state error feedback through reference signal differential feedforward and variable exponent.

9. The permanent magnet synchronous motor control method based on linear auto-disturbance rejection and deadbeat prediction as claimed in claim 8, characterized in that: The optimized linear state error feedback is: Where, 0<ε<1, δ>0; x1 is the system state; A|s|sign(s)+ks is the variable exponential reaching law, A is the adaptive coefficient, and A and k both meet the stability conditions.

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