High-precision Rotor Position Acquisition Method for a Resolver All-digital Axial Angle Conversion System

Abstract

The present invention discloses a method for obtaining high-precision rotor position in a resolver all-digital shaft angle conversion system. The method comprises the following steps: Step 1, generation of resolver excitation signal: A sine pulse width modulation waveform is generated by a digital signal processor and input into the resolver excitation winding through a conditioning circuit to obtain the sine and cosine signals output by the resolver; Step 2, demodulation of the resolver output signal: The sine and cosine signals output by the resolver are demodulated by phase-sensitive demodulation to obtain low-frequency sine and cosine signals containing rotor position information; Step 3, acquisition of rotor position: A steady-state extended Kalman filter is used as an observer for the resolver rotor position information to extract the rotor position information contained in the sine and cosine signals after phase-sensitive demodulation. This method can effectively improve the position detection accuracy, calculation efficiency and response speed of the resolver shaft angle conversion system, and has high application value in industrial fields with resolvers as rotor position sensors.

Description

Technical Field

[0001] The present invention relates to a method for obtaining high-precision rotor position of a resolver full-digital shaft angle conversion (RDC) system, and particularly to a method for obtaining rotor position based on a steady-state extended Kalman filter (SSEKF), which can be used to improve the position detection accuracy, calculation efficiency and response speed of the resolver full-digital shaft angle conversion system. Background Art

[0002] In a resolver full-digital shaft angle conversion system, the method for obtaining rotor position affects the comprehensive performance of resolver position detection. The arctangent method and the angle tracking observer method are two common methods for obtaining rotor position. The arctangent method has less code volume, but since it is an open-loop system, it is more susceptible to noise. The angle tracking observer method has strong anti-noise performance, higher accuracy and can directly obtain speed information from it, and is widely used in various special resolver decoding chips. However, this method has more integral operations, the calculation efficiency is relatively low, and there is also a certain phase lag, which affects the accuracy of resolver position detection. If the angle tracking observer is second-order, there will be a certain steady-state error when tracking acceleration input, which affects the tracking performance of the RDC system.

[0003] In summary, it is necessary to design a method for obtaining resolver rotor position with strong anti-noise performance, high calculation efficiency, high position detection accuracy and good dynamic performance to improve the overall performance of the RDC system. Summary of the Invention

[0004] Considering the disadvantages such as phase lag and low calculation efficiency when using the traditional angle tracking observer method (ATO) to obtain rotor position information, the present invention provides a method for obtaining high-precision rotor position of a resolver full-digital shaft angle conversion system. This method can effectively improve the position detection accuracy, calculation efficiency and response speed of the resolver shaft angle conversion system, and has high application value in the industrial field with a resolver as the rotor position sensor.

[0005] The object of the present invention is achieved by the following technical solutions:

[0006] A method for obtaining high-precision rotor position of a resolver full-digital shaft angle conversion system includes the following steps:

[0007] Step 1, generation of resolver excitation signal: A sine pulse width modulation (SPWM) waveform is generated by a digital signal processor (DSP) and input into the resolver excitation winding through a conditioning circuit to obtain the sine and cosine signals output by the resolver;

[0008] Step 2, demodulation of the resolver output signal: The sine and cosine signals output by the resolver are demodulated by phase-sensitive demodulation to obtain low-frequency sine and cosine signals containing rotor position information;

[0009] Step 3. Obtaining the rotor position: Use the steady-state extended Kalman filter (SSEKF) as the observer for the resolver rotor position information, and extract the rotor position information contained in the sine and cosine signals after phase-sensitive demodulation. The specific steps are as follows:

[0010] Step 3-1. Modeling of the SSEKF rotor position acquisition system:

[0011] Select the resolver rotor position θ, rotational speed ω r and angular acceleration a as state variables. Then, the discrete process equation of the resolver rotor position acquisition system is:

[0012]

[0013] where x(k + 1) is the state variable of the SSEKF rotor position acquisition system at the (k + 1)-th moment; θ(k) is the rotor position of the resolver at the k-th moment (rad); ω r (k) is the angular velocity of the resolver at the k-th moment (rad / s); a(k) is the angular acceleration of the resolver at the k-th moment (rad / s 2 ); T is the sampling period (s); ω(k) is the process noise at the k-th moment;

[0014] Denote the resolver rotor position acquisition system matrix F as:

[0015]

[0016] The measurement equation of the resolver rotor position acquisition system is given by the output signals of the demodulated resolver sine and cosine windings:

[0017]

[0018] where y(k) is the output variable of the SSEKF rotor position acquisition system at the k-th moment; y1(k) and y2(k) are the demodulated resolver sine and cosine output signals respectively; v(k) is the measurement noise of the system at the k-th moment;

[0019] Denote the measurement equation output matrix h(x(k)) of the resolver rotor position acquisition system as:

[0020]

[0021] The state-space expression of the resolver rotor position acquisition system is:

[0022]

[0023] Step 3-2. Simplification of the SSEKF rotor position acquisition system:

[0024] Introduce the Park transformation matrix T(θ):

[0025]

[0026] The linearized expression of the measurement equation output matrix h(x(k)) of the resolver rotor position acquisition system is:

[0027]

[0028]

[0029] where is the predicted state variable of the SSEKF rotor position acquisition system at the k-th moment, where is the predicted value of the resolver rotor position at the k-th moment (rad); is the predicted value of the resolver angular velocity at the k-th moment (rad / s); is the predicted value of the resolver angular acceleration at the k-th moment (rad / s 2 );

[0030] Refer to the steps of updating the error covariance matrix P k of the Kalman filter. The update expression of the error covariance matrix of the resolver rotor position acquisition system is:

[0031] P k+1 = FP k F T + Q - K k H k P k F T ;

[0032] Further simplify:

[0033]

[0034] Let the prior error covariance matrix be simplified by the following steps for K k :

[0035]

[0036] where T k represents

[0037] Let Then the Kalman gain K k is divided into two parts: the time-invariant part and the time-varying part T k ;

[0038] Since the first row of the matrix H is all 0, let is:

[0039]

[0040] In the formula, k1, k2 and k3 are all preset constants, and the following expressions are given:

[0041]

[0042] Define the deviation Then:

[0043]

[0044] Step 33. According to Step 32, obtain the optimal estimation value update expression of the steady-state extended Kalman filter:

[0045]

[0046]

[0047] In the formula, the optimal state prediction value at the (k + 1)-th moment (i.e., the latest moment) is the optimal prediction value of the resolver rotor position at the latest moment, is the optimal prediction value of the resolver angular velocity at the latest moment, is the optimal prediction value of the resolver angular acceleration at the latest moment.

[0048] Compared with the prior art, the present invention has the following advantages:

[0049] The method proposed by the present invention only needs to write a software program on the basis of the original all-digital shaft angle conversion system hardware circuit without adding any additional hardware, without causing any additional cost and energy loss; it remains unchanged in terms of operation, control, use, etc., and only needs to change the program of the rotor position acquisition module; applying it to the resolver shaft angle conversion system can effectively improve the position detection accuracy, dynamic performance and calculation efficiency of the resolver shaft angle conversion system. Brief Description of the Drawings

[0050] Figure 1 is a schematic diagram of the RDC system;

[0051] Figure 2 is a block diagram of the SSEKF structure;

[0052] Figure 3 is the unit step response of the four angle observer systems and the SSEKF. Detailed Embodiment

[0053] The technical solution of the present invention will be further described below in conjunction with the accompanying drawings, but it is not limited thereto. Any modification or equivalent replacement of the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention shall be covered by the protection scope of the present invention.

[0054] The present invention provides a high-precision rotor position acquisition method for a resolver all-digital shaft angle conversion system. As Figure 1 shown, in order to achieve the all-digital shaft angle conversion of the resolver, the following three steps need to be completed through a hardware circuit and a software algorithm:

[0055] (1) Generation of the resolver excitation signal: A sine pulse width modulation (SPWM) waveform is generated by a digital signal processor (DSP) and input into the resolver excitation winding through a conditioning circuit to obtain the sine and cosine signals output by the resolver.

[0056] (2) Demodulation of the resolver output signal: In order to remove the high-frequency excitation signal in the resolver output signal, the sine and cosine signals output by the resolver are passed through a phase-sensitive demodulation (also known as frequency shift technology) to obtain low-frequency sine and cosine signals containing rotor position information.

[0057] (3) Acquisition of the resolver rotor position: In order to extract the rotor position information contained in the sine and cosine signals after phase-sensitive demodulation, the present invention proposes to use a steady-state extended Kalman filter (SSEKF) as an observer for the resolver rotor position information. The basic structure block diagram is as Figure 2 shown. In the figure, y1(k) and y2(k) are the output values of the cosine signal and sine signal obtained by the phase-sensitive demodulation method at the k-th moment respectively. The method for acquiring the resolver rotor position is the research focus of the present invention.

[0058] The specific steps are as follows:

[0059] 1. Modeling of the SSEKF rotor position acquisition system:

[0060] Select the resolver rotor position θ, rotational speed ω r and acceleration a as state variables. Then the discrete process equation of the resolver rotor position acquisition system is:

[0061]

[0062] In the formula, x(k + 1) is the state variable of the SSEKF rotor position acquisition system at the (k + 1)-th moment; θ(k) is the rotor position (rad) of the resolver at the k-th moment; ω r (k) is the angular velocity (rad / s) of the resolver at the k-th moment; a(k) is the angular acceleration (rad / s 2 ) of the resolver at the k-th moment; T is the sampling period (s); ω(k) is the process noise at the k-th moment.

[0063] In the above process equation, the speed ω of the resolver r is the double integral of the process noise ω(k). Therefore, theoretically, there is no steady-state error when it tracks a uniformly accelerating input; if the resolver speed is only the single integral of the process noise ω(k), there will be a steady-state error when it tracks a uniformly accelerating input.

[0064] Denote the system matrix F as:

[0065]

[0066] The measurement equation of the system is given by the output signals of the demodulated resolver sine and cosine windings:

[0067]

[0068] where y(k) is the output variable of the SSEKF rotor position acquisition system at the k-th moment; y1(k) and y2(k) are the demodulated resolver sine and cosine output signals respectively; v(k) is the measurement noise of the system at the k-th moment.

[0069] Denote h(x(k)) as:

[0070]

[0071] The state space expression of the resolver rotor position acquisition system is:

[0072]

[0073] Assume that the system process noise ω(k) follows a Gaussian distribution with a variance of 1, and its error covariance matrix Q is shown as follows:

[0074]

[0075] Assume that the measurement noise v(k) follows a Gaussian distribution with an error covariance matrix R shown as follows:

[0076]

[0077] where λ is an adjustment factor, and the noise suppression ability of the resolver rotor position acquisition system can be adjusted through λ.

[0078] 2. Simplification of the SSEKF rotor position acquisition system:

[0079] Introduce the Park transformation matrix T(θ):

[0080]

[0081] The linearized expression of the measurement equation output matrix h(x(k)) of this system is:

[0082]

[0083]

[0084] In the formula, is the estimated state variable of the SSEKF rotor position acquisition system at the k-th moment, where is the estimated value of the resolver rotor position at the k-th moment (rad); is the estimated value of the resolver angular velocity at the k-th moment (rad / s); is the estimated value of the resolver angular acceleration at the k-th moment (rad / s 2 ).

[0085] Use T k to represent

[0086] Referring to the steps of updating the error covariance matrix P k of the Kalman filter, the update expression of the error covariance matrix of this resolver rotor position acquisition system is:

[0087] P k+1 = FP k F T + Q - K k H k P k F T ;

[0088] Further simplify:

[0089]

[0090] It can be seen from the above formula that all Park transformation matrices T(θ) can be eliminated, and P k+1 no longer changes with time. That is, when the resolver rotor position acquisition system gradually converges to the steady state, P k+1 will also converge to the steady-state solution At this time, although the Kalman gain K k is still time-varying, let the prior error covariance matrix can simplify K k through the following steps:

[0091]

[0092] Let The Kalman gain K k is then divided into two parts, the time-invariant part and the time-varying part T k . Since the first row of the matrix H is all 0, so it can be set as:

[0093]

[0094] Wherein, k1, k2 and k3 are all constants that can be preset in advance, and the following expressions can be given:

[0095]

[0096] Define the deviation Then:

[0097]

[0098] 3. According to the above simplification steps, the optimal estimated value update expression of the steady-state extended Kalman filter can be obtained:

[0099]

[0100]

[0101] That is, the optimal predicted value of the rotor position obtained by SSEKF. Just input the above formula into the DSP for application.

[0102] The closed-loop transfer function Φ(s) of the traditional angle observer method is shown as follows:

[0103]

[0104] Essentially, it is a low-pass filter, so there is a certain phase lag. And it can be calculated by the final value theorem that when tracking a uniformly accelerating input θ = kt 2 (R(s) = 2 / s 3 ) The steady-state error existing:

[0105]

[0106] The SSEKF rotor position acquisition method proposed by the present invention can make SSEKF have no steady-state error when tracking a uniformly accelerating input through a reasonable modeling method; at the same time, since the Kalman filter is an algorithm for optimal state estimation, if the system model and the observation model are correct, the Kalman filter is a real-time estimation. Therefore, theoretically, it can achieve a high-precision and fast-response resolver shaft angle conversion effect. Figure 3The unit step responses of four systems (System1 - System4) of SSEKF and the traditional angle observer method are shown. It can be seen that the SSEKF has the fastest response speed, that is, the amplitude quickly converges to 1, and there is basically no overshoot phenomenon and steady-state error; since the calculation of the Kalman filter is quite efficient, and through reasonable simplification, the calculation efficiency of SSEKF can be greatly improved. In summary, the rotor position acquisition method based on SSEKF of the present invention can improve the comprehensive performance of the resolver position detection system.

Claims

1. A method for obtaining high-precision rotor position in a resolver all-digital shaft angle conversion system, characterized in that The method includes the following steps: Step 1, generation of resolver excitation signal: A sine pulse width modulation waveform is generated by a digital signal processor and input into the resolver excitation winding through a conditioning circuit to obtain the sine and cosine signals output by the resolver; Step 2, demodulation of the resolver output signal: The sine and cosine signals output by the resolver are demodulated by phase-sensitive demodulation to obtain low-frequency sine and cosine signals containing rotor position information; Step 3, acquisition of rotor position: The steady-state extended Kalman filter is used as an observer for the resolver rotor position information to extract the rotor position information contained in the sine and cosine signals after phase-sensitive demodulation. The specific steps are as follows: Step 3-1, modeling of the SSEKF rotor position acquisition system: Select the resolver rotor position θ, speed ω r and acceleration a as state variables. Then the discrete process equation of the resolver rotor position acquisition system is as follows: where \(x(k + 1)\) is the state variable of the SSEKF rotor position acquisition system at the \((k + 1)\)-th moment; \(\theta(k)\) is the rotor position of the resolver at the \(k\)-th moment; \(\omega\) r (k) is the angular velocity of the resolver at the \(k\)-th moment; \(a(k)\) is the angular acceleration of the resolver at the \(k\)-th moment; \(T\) is the sampling period; \(\omega(k)\) is the process noise at the \(k\)-th moment; Denote the system matrix F of the resolver rotor position acquisition system as: The measurement equation of the resolver rotor position acquisition system is given by the output signals of the demodulated resolver sine and cosine windings: In the formula, y(k) is the output variable of the SSEKF rotor position acquisition system at the k-th moment; y1(k) and y2(k) are the demodulated resolver sine and cosine output signals respectively; v(k) is the measurement noise of the system at the k-th moment; Denote the output matrix h(x(k)) of the measurement equation of the resolver rotor position acquisition system as: The state space expression of the resolver rotor position acquisition system is: Step 3-2, simplification of the SSEKF rotor position acquisition system: Introduce the Park transformation matrix T(θ): The linearized expression of the output matrix h(x(k)) of the measurement equation of this resolver rotor position acquisition system is: In the formula, is the estimated state variable of the SSEKF rotor position acquisition system at the k-th moment, is the estimated value of the resolver rotor position at the k-th moment; Refer to the steps for updating the error covariance matrix P of the Kalman filter. k The update expression of the error covariance matrix of the resolver rotor position acquisition system is as follows: P k+1 = FP k F T + Q - K k H k P k F T ; Further simplification: Let the prior error covariance matrix K can be simplified by the following steps k : where T k represents Let Then the Kalman gain K k is divided into two parts: the time-invariant part and the time-varying part T k ; Since the first row of matrix H is all 0, let be: In the formula, k1, k2, and k3 are all preset constants, and the following expression is given: Define deviation Then: Step 3-3, according to Step 3-2, obtain the update expression of the optimal estimation value of the steady-state extended Kalman filter: In the formula, the optimal state prediction value at the (k + 1)-th moment, i.e., the latest moment is the optimal predicted value of the resolver rotor position at the latest moment, is the optimal predicted value of the resolver angular velocity at the latest moment, is the optimal predicted value of the resolver angular acceleration at the latest moment.

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