Method for Estimating Motor Rotor Position and Speed Based on Accelerated Nesterov Algorithm

Abstract

The present invention discloses a method for estimating the rotor position and speed of a motor based on the accelerated Nesterov algorithm, which specifically includes the following steps: Step 1, establish a discrete mathematical model of a high-speed permanent magnet synchronous motor, and construct a cost function for the rotor speed and position in the full speed range of the high-speed permanent magnet synchronous motor; Step 2, use the accelerated Nesterov to solve the minimum value of the cost function of the rotor speed and position in the full speed range constructed in Step 1; Step 3, estimate the rotor position and speed of the high-speed permanent magnet synchronous motor through a phase-locked loop by the minimum value obtained in Step 2. By constructing a cost function for the rotor speed and position in the full speed range with high convexity and using the accelerated Nesterov algorithm to solve the minimum value of the cost function of the rotor speed and position, the present invention solves the problems of low rotor position estimation accuracy in the high-speed region and easy oscillation of the rotor position and speed in the composite region in the existing rotor position and speed estimation methods for high-speed permanent magnet synchronous motors.

Description

Technical Field

[0001] The present invention relates to the technical field of high-speed permanent magnet synchronous motor control, and specifically to a method for estimating the rotor position and speed of a motor based on the accelerated Nesterov algorithm. Background Art

[0002] A permanent magnet synchronous motor with a rotational speed exceeding 10,000 r / min is called a high-speed permanent magnet synchronous motor. Due to its advantages such as high power density, high rotational speed, and small volume, high-speed permanent magnet synchronous motors are widely used in the military, aerospace, industrial and other fields. Usually, the rotor position and rotational speed of a high-speed permanent magnet synchronous motor are obtained by installing a mechanical encoder on the rotor. However, a high-speed permanent magnet synchronous motor requires the rotor to be as short as possible to ensure sufficient mechanical strength and stiffness of the rotor. Therefore, it is difficult to install a mechanical encoder on the rotor, and conventional mechanical encoders are difficult to detect the rotor position and rotational speed when the rotational speed of a high-speed permanent magnet synchronous motor exceeds 10,000 r / min. Therefore, it is particularly important to study a method for estimating the rotor position and rotational speed applicable to high-speed permanent magnet synchronous motors.

[0003] Currently, the methods for estimating the rotor position and rotational speed of high-speed permanent magnet synchronous motors mainly include: sliding mode observers, Kalman filters, model reference adaptive, etc. Since these methods have low-pass filtering characteristics, when a high-speed permanent magnet synchronous motor is operating at high speed, the estimated rotor position lags severely behind the actual rotor position, resulting in incomplete decoupling of the current loop and even system divergence. Moreover, currently, a single method for estimating the rotor position and rotational speed is difficult to estimate the rotational speed position and rotational speed in the full speed range of a high-speed permanent magnet synchronous motor. Usually, the rotor position and rotational speed in the full speed range of a high-speed permanent magnet synchronous motor are estimated by combining an estimation method suitable for low speeds and an estimation method suitable for medium and high speeds. However, the moment of inertia of a high-speed permanent magnet synchronous motor is small, and during rapid startup, the rotor position and rotational speed in the composite region of the two methods for estimating the rotor position and rotational speed are prone to oscillation and even startup failure. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for estimating the rotor position and rotational speed of a high-speed permanent magnet synchronous motor based on the accelerated Nesterov, which solves the problems of low accuracy of rotor position estimation in the high-speed region and easy oscillation of the rotor position and rotational speed in the composite region in the existing methods for estimating the rotor position and rotational speed of high-speed permanent magnet synchronous motors.

[0005] To achieve the above purpose, the technical solution adopted by the present invention is: a method for estimating the rotor position and speed of a motor based on the accelerated Nesterov algorithm, specifically including the following steps:

[0006] Step 1, establish a discrete mathematical model of a high-speed permanent magnet synchronous motor, and construct a cost function for the rotor speed and position in the full speed range of the high-speed permanent magnet synchronous motor;

[0007] Step 2: Use the accelerated Nesterov algorithm to solve for the minimum value of the full-speed range rotor speed and position cost function constructed in Step 1.

[0008] Step 3: Estimate the rotor position and speed of the high-speed permanent magnet synchronous motor from the minimum value obtained in Step 2 through a phase-locked loop.

[0009] Preferably, the specific steps of Step 1 are as follows:

[0010] Step 1.1: Establish a discrete mathematical model of the high-speed permanent magnet synchronous motor.

[0011] The voltage equation of the high-speed permanent magnet synchronous motor in the stationary coordinate system is shown in Equation (1) below:

[0012]

[0013] In Equation (1), v α is the component of the stator voltage on the α-axis; v β is the component of the stator voltage on the β-axis, i α is the component on the α-axis, i β is the component of the stator current on the β-axis, R is the stator resistance, p is the differential operator, φ m is the rotor flux linkage, ω e is the rotor electrical angular velocity, θ e is the rotor position; L α is the inductance on the α-axis, L αβ is the mutual inductance on the α-axis, L β is the inductance on the β-axis, L α 、L β 、L αβ are respectively expressed as:

[0014]

[0015] In Equation (2), L d is the d-axis inductance, L q is the q-axis inductance;

[0016] Discretize Equation (1) as shown in Equation (3) below:

[0017]

[0018] In Equation (3), Δθ re is the difference between the rotor position in this beat and the rotor position in the previous beat, k is the current beat sampling time, k - 1 is the previous beat sampling time, T s is the sampling period;

[0019] Step 1.2: Construct the full-speed range rotor speed and position cost function of the high-speed permanent magnet synchronous motor.

[0020] Square the left - hand side of formula (3) for the rotor speed ω e and the rotor position θ e As unknowns, the constructed cost function for the rotor speed ω e and the rotor position θ e can be written as shown in formula (4):

[0021]

[0022] In formula (4), H(θ e (k), ω e (k)) is the cost function for the rotor speed ω e and the rotor position θ e ;

[0023] The convexity of the cost function formula (4) decreases as the speed decreases. At zero speed and low speed, the convexity of the cost function is very small, almost a flat curve. The smaller the convexity of the cost function, the slower the convergence to solve the minimum value; To increase the convexity of the cost function at zero speed and low speed, a high - frequency square - wave voltage signal is injected on the d - axis below 10% of the rated speed. The injected high - frequency square - wave voltage signal is as shown in formula (5):

[0024]

[0025] In formula (5), u dh (k), u qh (k) are the components of the high - frequency square - wave voltage signal on the d - axis and q - axis respectively, and V h is the amplitude of the high - frequency square - wave voltage;

[0026] The high - frequency current responses on the α - axis and β - axis generated by the injected high - frequency square - wave voltage signal are as shown in formula (6):

[0027]

[0028] In formula (6), i αh (k) is the component of the high - frequency current response at the k - th sampling on the α - axis, and i βh (k) is the component of the high - frequency current response at the k - th sampling on the β - axis;

[0029] After injecting the high - frequency square - wave voltage, the cost function for the rotor speed ω e and the rotor position θ e is as shown in formula (7):

[0030]

[0031] In formula (7), i αh (k - 1) is the component of the high - frequency current at the (k - 1) - th sampling on the α - axis, i βh(k - 1) is the β-axis component of the high-frequency current sampled at the (k - 1)-th beat, i α (k - 1), i β (k - 1) are the α- and β-axis components of the stator current sampled at the (k - 1)-th beat, i β (k - 1) is the β-axis component of the stator current sampled at the (k - 1)-th beat;

[0032] When below 10% of the rated speed, the rotor speed ω e and the rotor position θ e The cost function is as shown in formula (7). Above 10% of the rated speed, the rotor speed and position cost function is as shown in formula (4). The full-speed range rotor speed ω e and the rotor position θ e The cost function is as shown in the following formula (8):

[0033] In formula (8), ω rate is the rated speed;

[0034] Formula (8) is a locally convex function. When the estimated speed and position are equal to the actual rotor speed and position, formula (8) reaches the minimum value;

[0035]

[0036] Estimating the rotor speed and position is equivalent to solving the minimum value of formula (8), as shown in the following formula (9):

[0037]

[0038] In formula (9), D is the search domain, is the estimated position, is the estimated speed, and the minimum value is obtained within the local range D.

[0039] Preferably, the specific process of step 2 is as follows:

[0040] The accelerated Nesterov algorithm is as shown in the following formula (10):

[0041]

[0042] In formula (10), n is the number of iterations, is the rotor speed ω at the (n - 1)-th iteration e and the rotor position θ e the partial derivative of the cost function with respect to the rotor position, is the rotor speed ω at the (n - 1)-th iteration e and the rotor position θ e the partial derivative of the cost function with respect to the rotational speed, y1 (n) is the momentum term of the rotor position at the n-th iteration, y1 (n)is the momentum term of the n-th iteration speed, y1 (k-1) is the momentum term of the rotor position at n-1 iterations, y2 (k-1) is the momentum term of the rotor speed for n-1 iterations, δ is the learning rate, and γ is the momentum parameter;

[0043] The size of the momentum parameter γ affects the speed of convergence. According to the characteristic of the cost function that the convexity increases with the increase of the rotation speed, the momentum parameter γ is adaptively adjusted, as shown in the following formula (11);

[0044]

[0045] In formula (11), is the gradient of the nth iteration, T is the transpose of the matrix, i is a constant, which refers to 1 and 2;

[0046] When the speed is less than 1046 rpm and When the momentum parameter is set to 0 to prevent iterative oscillation, when the speed is less than 1046 rpm and When , the initial value point is close to the optimal value, and the momentum parameter γ is set to 0.25. As the speed increases, the momentum parameter γ increases with the increase of the speed;

[0047] The iterative process of estimating rotor position and speed using the accelerated Nesterov algorithm is as follows:

[0048] Step 1) Given the initial value of iteration θ e (0) =θ e (k-1),ω e (0) =ω e (k-1), set the maximum number of iterations n max ≥1, convergence accuracy ε=1×10 -5 ;

[0049] Step 2) Calculate the full-speed rotor speed ω according to formula (8) e and the rotor position θ e Cost function;

[0050] Step 3) Calculate the momentum parameter γ according to formula (11);

[0051] Step 4) Calculate the rotor speed ω for this iteration according to formula (10): e and the rotor position θ e ;

[0052] Step 5) According to Determine whether it converges. If it satisfies Then the optimization is terminated and the rotor position θ of this shot is output. e (k) = θe (n) and speed ω e (k) = ω e (n) ; If not satisfied then determine whether the current iteration count n is greater than the maximum iteration count n max , if n ≥ n max then end the current optimization and output the rotor position θ of this beat e (k) = θ e (k - 1)+ω e (k - 1)T s and speed ω e (k) = ω e (k - 1), otherwise set n = n + 1 and return to step 2).

[0053] Preferably, the specific process of step 3 is as follows:

[0054] Take the difference between the rotor position θ e (k) of the k-th beat obtained in step 2 and the rotor position θ e_PLL (k - 1) output by the phase-locked loop in the previous beat, and after PI, the estimated rotational speed is as shown in the following formula (12):

[0055]

[0056] In formula (12), both the speed loop and the current loop have PI controllers, and PI is a proportional-integral controller; K p is the proportional coefficient, K i is the integral coefficient, ω e_PLL (k) is the speed output by the phase-locked loop at the k-th beat, and θ e_PLL (k - 1) is the rotor position output by the phase-locked loop at the (k - 1)-th beat;

[0057] The speed ω e_PLL (k) estimated by formula (12) is integrated to obtain the estimated rotor position as shown in the following formula (13):

[0058] θ e_PLL (k) = θ e_PLL (k - 1)+ω e_PLL (k)T s (13)

[0059] In formula (13), θ e_PLL (k) is the rotor position output by the phase-locked loop at the k-th beat.

[0060] Advantages of the present invention: The method for estimating the rotor position and speed of a motor based on the accelerated Nesterov algorithm provided by the present invention constructs a rotor speed and position cost function with high convexity in the full speed range, and uses the accelerated Nesterov algorithm to solve the minimum value of the rotor speed and position cost function, thereby improving the rotor position estimation accuracy in the high-speed region. A single method is used to estimate the rotor position and speed in the full speed range, fundamentally solving the problem that the rotor position and speed are prone to oscillation in the composite region of the full speed range. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 is a control system block diagram of the method for estimating the rotor position and speed of a motor based on the accelerated Nesterov algorithm of the present invention;

[0062] Figure 2 are simulation results of the rotor speed and position cost function at different speeds when no high-frequency square wave voltage is injected at zero speed and low speed;

[0063] Figure 3 are comparative simulation results of the rotor speed and position cost function with and without injecting high-frequency square wave voltage at a low speed of 50 rpm;

[0064] Figure 4 is a phase-locked loop block diagram adopted by the method for estimating the rotor position and speed of a motor based on the accelerated Nesterov algorithm of the present invention;

[0065] Figure 5 is a flowchart of the iterative process for estimating the rotor position and speed using the accelerated Nesterov method adopted by the method for estimating the rotor position and speed of a motor based on the accelerated Nesterov algorithm of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0066] The technical solutions in the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0067] As Figures 1-5 shown;

[0068] Through u α (k), u β (k), i α (k), i β (k) in the two-phase stationary coordinate system and the previous beat's ω e (k - 1) and θ e (k - 1) are used as the inputs of the accelerated Nesterov estimator for rotor position and speed module as Figure 5 shown. The outputs of the accelerated Nesterov estimator for rotor position and speed module are the rotor position θ e (k) and the rotational speed ω e (k); The rotor position θ e (k) is used as Figure 4The output of the phase-locked loop is the estimated rotor position θ. e_PLL (k) and speed ω e_PLL (k); given speed and speed ω e_PLL (k) The difference is used as the input of the speed loop PI, and the output of the speed loop PI is the given q-axis stator current The three-phase stationary coordinate system stator current i is detected by the current Hall sensor a (k), i b (k), i c (k); Detected three-phase stator current i a (k), i b (k), i c (k) The current value i in the two-phase stationary coordinate system is obtained by abc / αβ transformation α (k), i β (k);i α (k), i β (k) The current value i in the two-phase synchronous rotating coordinate system is obtained by αβ / dq transformation d (k), i q (k); given q-axis stator current With the current value i q (k) The difference is used as the input of the q-axis current loop PI, and the output of the q-axis current loop PI is the q-axis voltage command u q (k); given d-axis stator current With the current value i d (k) The difference is used as the input of the d-axis current loop PI, and the output of the d-axis current loop PI is the d-axis voltage command u d (k); if the speed ω e _ PLL (k) Less than or equal to 10% of the rated speed, d-axis voltage command u d (k) and high-frequency voltage u dh The sum of (k) and q-axis voltage command u q (k) The voltage command u in the two-phase stationary coordinate system is obtained through dq / αβ transformation α (k),u β (k); if the speed ω e _ PLL (k) Greater than 10% of the rated speed, d-axis voltage command u d (k) and q-axis voltage command u q (k) The voltage command u in the two-phase stationary coordinate system is obtained through dq / αβ transformation α (k),u β (k);u α (k),u β(k) As the input of space vector modulation, it controls the operation of a three-phase inverter to drive a high-speed permanent magnet synchronous motor through space vector modulation.

[0069] Finally, it should be noted that the above are only the preferred embodiments of the present invention and are not used to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions recorded in the foregoing embodiments or perform equivalent replacements for some of the technical features. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for estimating the position and speed of a motor rotor based on an accelerated Nesterov algorithm, characterized in that, Specifically, it includes the following steps: Step 1: Establish a discrete mathematical model of the high-speed permanent magnet synchronous motor, and construct a cost function for the rotor speed and position in the full speed range of the high-speed permanent magnet synchronous motor; Step 2: Use the accelerated Nesterov algorithm to solve the minimum value of the cost function of the rotor speed and position in the full speed range constructed in Step 1; Step 3: Estimate the rotor position and speed of the high-speed permanent magnet synchronous motor through a phase-locked loop based on the minimum value obtained in Step 2; The specific process of Step 2 is as follows: The accelerated Nesterov algorithm is shown in the following formula (10): In Equation (10), n is the number of iterations, is the rotor speed ω at the (n - 1)-th iteration e and the rotor position θ e the partial derivative of the cost function with respect to the rotor position, is the rotor speed ω at the (n - 1)-th iteration e and the rotor position θ e the partial derivative of the cost function with respect to the rotational speed, y1 (n) is the momentum term of the rotor position at the n-th iteration, y1 (n) is the momentum term of the speed at the n-th iteration, y1 (k-1) is the momentum term of the rotor position at the (n - 1)-th iteration, y2 (k-1) is the momentum term of the rotor speed at the (n - 1)-th iteration, δ is the learning rate, and γ is the momentum parameter; The magnitude of the momentum parameter γ affects the convergence speed. According to the characteristic that the convexity of the cost function increases with the increase of the rotational speed, the momentum parameter γ is adaptively adjusted as shown in the following formula (11); In formula (11), is the gradient of the nth iteration, T is the transpose of the matrix, and i is a constant, referring to 1 and 2; When the rotational speed is less than 1046 rpm and , the momentum parameter is set to 0 to prevent iterative oscillation. When the rotational speed is less than 1046 rpm and , the initial value point is close to the optimal value, and the momentum parameter γ is set to 0.

25. As the rotational speed increases, the momentum parameter γ is increased with the increase of the rotational speed; The iterative process of estimating the rotor position and speed using the accelerated Nesterov algorithm is as follows: Step 1) Given the initial iteration value θ e (0) = θ e (k - 1), ω e (0) = ω e (k - 1), set the maximum number of iterations n max ≥ 1, the convergence accuracy ε = 1 × 10 -5 ; Step 2) Calculate the full-speed range rotor speed ω according to formula (8) e and the rotor position θ e Cost function Step 3): Calculate the momentum parameter γ according to formula (11); Step 4) Calculate the rotor speed ω for this iteration according to formula (10) e and the rotor position θ e ; Step 5) According to judge whether it converges. If it meets then end this optimization and output the rotor position θ e (k)=θ e (n) and the speed ω e (k)=ω e (n) ; if it does not meet then judge whether the number of iterations n of this time is greater than the maximum number of iterations n max , if n≥n max then end this optimization and output the rotor position θ e (k)=θ e (k - 1)+ω e (k - 1)T s and the speed ω e (k)=ω e (k - 1), otherwise set n=n + 1 and return to Step 2).

2. The method for estimating the position and speed of a motor rotor based on the accelerated Nesterov algorithm according to claim 1, wherein The specific steps of Step 1 are as follows: Step 1.1: Establish a discrete mathematical model of the high-speed permanent magnet synchronous motor; The voltage equation of the high-speed permanent magnet synchronous motor in the stationary coordinate system is shown in the following formula (1): In Equation (1), v α is the component of the stator voltage on the α-axis; v β is the component of the stator voltage on the β-axis, i α is the component on the α-axis, i β is the component of the stator current on the β-axis, R is the stator resistance, p is the differential operator, φ m is the rotor flux linkage, ω e is the electrical angular velocity of the rotor, θ e is the rotor position; L α is the inductance on the α-axis, L αβ is the mutual inductance on the α-axis, L β is the inductance on the β-axis, L α 、L β 、L αβ are respectively expressed as: In Equation (2), L d is the d-axis inductance, and L q is the q-axis inductance; The discretization of formula (1) is shown in the following formula (3): In formula (3), Δθ re is the difference between the rotor position of this beat and the rotor position of the previous beat. k is the current beat sampling moment, k - 1 is the previous beat sampling moment, and T s is the sampling period; Step 1.2: Construct a cost function for the rotor speed and position in the full speed range of the high-speed permanent magnet synchronous motor; Taking the square of the norm of the left - hand side of Equation (3), the rotor speed ω e and the rotor position θ e As unknowns, the constructed cost function of the rotor speed ω e and the rotor position θ e is written as shown in Equation (4): In Equation (4), H(θ e (k), ω e (k)) is the cost function of the rotor speed ω e and the rotor position θ e ; The convexity of the cost function formula (4) decreases with the decrease of the speed. At zero speed and low speed, the convexity of the cost function is very small, almost a flat curve. The smaller the convexity of the cost function, the slower the convergence of solving the minimum value; In order to increase the convexity of the cost function at zero speed and low speed, a high-frequency square wave voltage signal is injected into the d-axis below 10% of the rated speed. The injected high-frequency square wave voltage signal is shown in the following formula (5): In Equation (5), u dh (k), u qh (k) are the components of the high-frequency square-wave voltage signal on the d-axis and q-axis respectively, and V h is the amplitude of the high-frequency square-wave voltage; The high-frequency current responses of the α and β axes generated by the injected high-frequency square wave voltage signal are shown in formula (6): In Equation (6), i αh (k) is the component of the high-frequency current response at the k-th sampling instant on the α-axis, and i βh (k) is the component of the high-frequency current response at the k-th sampling instant on the β-axis; Rotor speed ω after injecting a high-frequency square-wave voltage e and rotor position θ e The cost function is as shown in Equation (7): In Equation (7), i αh (k - 1) is the α-axis component of the high-frequency current sampled at the (k - 1)-th beat, i βh (k - 1) is the β-axis component of the high-frequency current sampled at the (k - 1)-th beat, i α (k - 1), i β (k - 1) are the α- and β-axis components of the stator current sampled at the (k - 1)-th beat, i β (k - 1) is the β-axis component of the stator current sampled at the (k - 1)-th beat; When it is below 10% of the rated speed, the rotor speed ω e and the rotor position θ e The cost function is as shown in formula (7); Above 10% of the rated speed, the rotor speed and position cost function is shown in formula (4); Full - speed - range rotor speed ω e and rotor position θ e The cost function is shown in the following formula (8): In formula (8), ω rate is the rated speed; Formula (8) is a locally convex function, and when the estimated speed and position are equal to the actual rotor speed and position, formula (8) reaches its minimum value; Estimating the rotor speed and position is equivalent to solving the minimum value of formula (8), as shown in the following formula (9): In formula (9), D is the search domain, is the estimated position, is the estimated speed, and the minimum value is obtained within the local range D.

3. The method for estimating the position and speed of the motor rotor based on the accelerated Nesterov algorithm according to claim 1, characterized in that, The specific process of Step 3 is as follows: The rotor position θ at the k-th beat obtained in step 2 e (k) is subtracted from the rotor position θ e_PLL (k-1) output by the phase-locked loop in the previous beat, and the estimated rotational speed is obtained after passing through a PI as shown in the following formula (12): In Equation (12), both the speed loop and the current loop have PI controllers, where PI is a proportional-integral controller; K p is the proportionality coefficient, and K i is the integral coefficient. ω e_PLL (k) is the speed output by the phase-locked loop at the k-th beat, and θ e_PLL (k - 1) is the rotor position output by the phase-locked loop at the (k - 1)-th beat; The speed ω estimated by formula (12) e_PLL (k) is integrated to obtain the estimated rotor position as shown in formula (13) below: θ e_PLL (k) = θ e_PLL (k - 1)+ω e_PLL (k)T s (13) In Equation (13), θ e_PLL (k) is the rotor position output by the k-th beat phase-locked loop.

Images