A model reference adaptive moment of inertia identification method for arc-shaped permanent magnet motor

Abstract

The present invention relates to the field of permanent magnet motor parameter identification, and specifically to an arc-shaped permanent magnet motor model reference adaptive rotational inertia identification method, the method comprising: using the motion model of the arc-shaped motor, constructing the relationship between the motor position and the electromagnetic torque as an adjustable model for position estimation; using the actual position of the motor read by the encoder as a reference; subtracting the position reference value from the position estimation value to obtain an estimated error, and designing an adaptive rate according to the Popov superstability principle to make the estimated error converge to zero; when the motor runs at a low speed, the identification result is continuously corrected according to the read current, position and other signals to obtain the motor rotational inertia. Using the position signal as a reference avoids the influence of inaccurate speed measurement and high-frequency noise when the speed is used as a reference, so that the identification result is more stable and accurate at low speed.

Description

Technical Field

[0001] The invention relates to the field of permanent magnet motor parameter identification, and in particular to an arc-shaped permanent magnet motor model reference adaptive rotational inertia identification method. Background Art

[0002] The arc motor adopts a stator segmented splicing structure. Compared with ordinary permanent magnet motors of the same caliber, the arc motor has the advantages of saving materials, easy installation and repair, so it is widely used in robot joint drive and large-aperture astronomical telescope direct drive system. These applications require high-precision position tracking and often work at a very low given speed. There are very high requirements for the motor body, encoder measurement accuracy, and control strategy. In the control system, the design of the controller and disturbance observer requires the use of motor models. Establishing an accurate motion model of the arc motor helps to accurately control it. At low speeds, the influence of friction can be ignored. At this time, the main parameter of the motor motion equation is the moment of inertia of the rotor.

[0003] The identification of the moment of inertia is divided into two categories: offline and online. The offline identification method cannot be adjusted in real time according to the operating conditions of the motor, while the commonly used methods for online identification are the least squares method, the extended Kalman filter method, and the model reference adaptive method. Among them, the least squares and Kalman filter algorithms are relatively complex, with large calculations and difficulties in parameter debugging. In contrast, the model reference adaptive algorithm has a simple principle, but in existing applications, the rotor speed expression is used as a reference and adjustable expression, which requires high speed measurement accuracy of the encoder at low speeds and is affected by high-frequency noise in the speed measurement link. Summary of the invention

[0004] In order to solve the deficiencies mentioned in the above background technology, the object of the present invention is to provide a method for identifying the moment of inertia of an arc-shaped permanent magnet motor with a model reference adaptive method.

[0005] The purpose of the present invention can be achieved through the following technical solutions:

[0006] A method for identifying the moment of inertia of an arc-shaped permanent magnet motor by using a model reference adaptive method comprises the following steps:

[0007] S1. Establish a discrete motion model of the surface-mounted permanent magnet motor in dq axis coordinates at low speed;

[0008] S2, derive the reference model of the system based on the discrete motion model of S1, subtract the k-th motion equation from the k-1-th and k-2-th motion equations, and eliminate the load torque term;

[0009] S3, substitute the speed expression and torque expression obtained in S2 into the displacement expression, and take the coefficient containing the moment of inertia J as the parameter to be identified;

[0010] S4, taking the displacement expression derived in S3 as a reference model, and deriving an adjustable model from the reference model;

[0011] S5, correct the rotor position measurement value and use it as a position reference value;

[0012] S6. Establish an adaptive rate of the parameter to be identified according to Popov inequality, adjust the identification value according to the difference between the position reference and the position estimate, and update the identification result at the next moment.

[0013] Furthermore, the arc permanent magnet motor dq axis motion model established in S1 is based on the following conditions:

[0014] 1) When running at low speed, ignore the influence of friction coefficient;

[0015] 2) Adopting the id=0 control strategy, the electromagnetic torque is only generated by the q-axis current;

[0016] 3) The inductance and resistance of each phase winding are constant and equal.

[0017] Furthermore, the discrete motion model in S1 is as follows:

[0018]

[0019] In the formula, k is the kth sampling, T s is the sampling period, θ m is the rotor mechanical angle, ω m is the rotor mechanical angular velocity, T e is the electromagnetic torque, T L is the load torque, i q is the q-axis current, K t is the torque constant, J is the moment of inertia to be identified, and the influence of the friction coefficient is ignored at low speed.

[0020] Furthermore, the model expression for eliminating the load torque derived from S2 is:

[0021]

[0022] Furthermore, the displacement expression obtained by S3 is:

[0023]

[0024] In the formula, b is the parameter to be identified.

[0025] Furthermore, the adjustable model obtained in S4 is:

[0026]

[0027] In the formula, is the estimated value of the rotor position at the kth sampling time, is the estimated value of the kth parameter b to be identified.

[0028] Furthermore, the value obtained after position correction in S5 is:

[0029] θ′ m (k) = θ m (k)+ω m (k)T s (5)

[0030] Where θ′ m (k) is the kth corrected rotor position, and the corrected value replaces the encoder sampling position as the reference value.

[0031] Further, the adaptive rate established in S6 is:

[0032]

[0033] In the formula, the error β is the adaptive gain parameter, when When converged, the moment of inertia is calculated by equation (7):

[0034]

[0035] Beneficial effects of the present invention:

[0036] 1. The present invention adopts the rotor displacement type as the reference model and the adjustable model type, which can avoid the influence of speed measurement accuracy and speed measurement algorithm noise on the identification result at low speed;

[0037] 2. The present invention adopts a three-step position signal to offset the load torque in the displacement equation, thus avoiding the need for an additional load disturbance observer;

[0038] 3. The present invention corrects the position signal to make the rotor displacement more continuous. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative work.

[0040] Figure 1 It is a schematic diagram of the principle of the model reference moment of inertia identification module of the present invention;

[0041] Figure 2It is a schematic diagram of the overall system principle of the arc motor vector control to which the present invention is applicable;

[0042] Figure 3 It is a schematic diagram comparing the effects of the present invention and the speed-based model reference adaptive identification method. DETAILED DESCRIPTION

[0043] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. 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.

[0044] like Figure 1 and Figure 2 As shown, the arc motor vector control of the present invention adopts a double closed-loop control structure, the outer loop is a speed loop, using a PI controller, the inner loop is a current loop using an id=0 control strategy, the three-phase current is transformed by park to obtain the dq axis current, the q axis current and the encoder position signal are used as the input of the inertia identification algorithm, and the identification result is used to construct a disturbance observer, a Kalman speed observer, etc. Among them, the steps of the arc permanent magnet motor model reference adaptive rotation inertia identification method are as follows:

[0045] S1. Establish a discrete motion model of the surface-mounted permanent magnet motor in dq axis coordinates at low speed;

[0046] The dq axis motion model of the arc permanent magnet motor in S1 is based on the following conditions:

[0047] 1) When running at low speed, ignore the influence of friction coefficient;

[0048] 2) Adopting the id=0 control strategy, the electromagnetic torque is only generated by the q-axis current;

[0049] 3) The inductance and resistance of each phase winding are constant and equal.

[0050] The derived discrete motion model of the permanent magnet arc motor is as follows:

[0051]

[0052] In the formula, k is the kth sampling, T s is the sampling period, θ m is the rotor mechanical angle, ω m is the rotor mechanical angular velocity, T e is the electromagnetic torque, T L is the load torque, i q is the q-axis current, K tis the torque constant, J is the moment of inertia to be identified, and the influence of the friction coefficient is ignored at low speed.

[0053] S2, derive the reference model of the system based on the discrete motion model of S1, subtract the k-th motion equation from the k-1-th and k-2-th motion equations, and eliminate the load torque term;

[0054] The derived model expression for eliminating load torque is:

[0055]

[0056] The rotor position of the current sampling period is constructed using the rotor position and speed difference of the previous three sampling periods. Compared with the ordinary motion model of S1, this model offsets the influence of load torque and other interference torques, avoiding the trouble of additional torque observation.

[0057] S3, substitute the speed expression and torque expression obtained in S2 into the displacement expression, and take the coefficient containing the moment of inertia J as the parameter to be identified;

[0058] The displacement expression is:

[0059]

[0060] Formula (3) corresponds to Figure 1 The reference model in , where b is the parameter to be identified.

[0061] S4, taking the displacement expression derived in S3 as a reference model, and deriving an adjustable model from the reference model;

[0062] The adjustable model obtained by S4 is:

[0063]

[0064] Formula (4) corresponds to Figure 1 The adjustable model in the formula is is the estimated value of the rotor position at the kth sampling time, is the estimated value of the kth parameter b to be identified.

[0065] S5, correct the rotor position measurement value and use it as a position reference value;

[0066] The value after position correction in S5 is:

[0067] θ′ m (k) = θ m (k)+ω m (k)T s (5)

[0068] Where θ′ m(k) is the kth corrected rotor position, which aims to make the step position signal measured by the encoder close to a smooth curve, which is more consistent with the continuity of the actual rotation of the rotor. This value is used instead of the encoder sampling position as a reference value.

[0069] S6. Establishing the adaptive rate of the parameter to be identified according to the Popov inequality, adjusting the identification value according to the difference between the position reference and the position estimate, and updating the identification result at the next moment;

[0070] The adaptive rate established in S6 is;

[0071]

[0072] The above formula corresponds to Figure 1 The adaptation rate in is, where the error β is the adaptive gain parameter, when When converged, the moment of inertia is calculated by equation (7):

[0073]

[0074] In S4, the rotor position is used as a reference. According to the error between the observed position and the actual rotor position measured by the encoder, the identification result is adjusted in real time in combination with the adaptive rate designed by S6. Compared with other model reference adaptive moment of inertia identification methods, this method can effectively avoid the calculation of the speed, thereby avoiding the influence of inaccurate speed calculation and noise caused by position difference during low-speed operation.

[0075] The present invention adopts the rotor displacement formula as a reference model and an adjustable model formula, which can avoid the influence of speed measurement accuracy and speed measurement algorithm noise on the identification result at low speed; adopts a three-step position signal, offsets the load torque in the displacement equation, and avoids the need for an additional load disturbance observer; and corrects the position signal to make the rotor displacement more continuous.

[0076] like Figure 3 As shown in the figure, j1 is the identification result of the present invention, j2 is the identification result based on the speed signal, and j is the calibrated moment of inertia, whose value is 2.833×10 -4 (kgm 2 ), Figure 3 In (a), the rotor speed is 0.5 rpm. After 15 seconds, the rotor is clamped and then released. The identification algorithm based on speed is greatly affected by the interference and cannot converge to the correct value after stabilization. When the speed drops to 0.1 rpm, Figure 3 As shown in (b), the inaccurate speed makes j2 unable to converge to the true value when it is close to the critical speed that can be measured. However, in this process, j1 uses the angle as a reference, which can not only converge to the true value quickly, but also be less affected by interference.

[0077] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments, and the above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, and these changes and improvements all fall within the scope of the present invention to be protected.

Claims

1. A method for identifying the moment of inertia of an arc-shaped permanent magnet motor based on a model reference, characterized in that: The identification method comprises the following steps: S1. Establish a discrete motion model of the surface-mounted permanent magnet motor in dq axis coordinates at low speed; S2, derive the reference model of the system based on the discrete motion model of S1, subtract the k-th motion equation from the k-1-th and k-2-th motion equations, and eliminate the load torque term; S3, substitute the speed expression and torque expression obtained in S2 into the displacement expression, and take the coefficient containing the moment of inertia J as the parameter to be identified; S4, taking the displacement expression derived in S3 as a reference model, and deriving an adjustable model from the reference model; S5, correct the rotor position measurement value and use it as a position reference value; S6. Establishing the adaptive rate of the parameter to be identified according to the Popov inequality, adjusting the identification value according to the difference between the position reference and the position estimate, and updating the identification result at the next moment; The discrete motion model in S1 is as follows: In the formula, k is the kth sampling, T s is the sampling period, θ m is the rotor mechanical angle, ω m is the rotor mechanical angular velocity, T e is the electromagnetic torque, T L is the load torque, i q is the q-axis current, K t is the torque constant, J is the moment of inertia to be identified, and the influence of friction coefficient is ignored at low speed; The model expression for eliminating load torque derived from S2 is: The displacement expression obtained by S3 is: In the formula, b is the parameter to be identified.

2. The method for identifying the moment of inertia of an arc-shaped permanent magnet motor model referenced by claim 1 is characterized in that: The arc permanent magnet motor dq axis motion model established in S1 is based on the following conditions: 1) When running at low speed, ignore the influence of friction coefficient; 2) Adopting the id=0 control strategy, the electromagnetic torque is only generated by the q-axis current; 3) The inductance and resistance of each phase winding are constant and equal.

3. The method for identifying the moment of inertia of an arc-shaped permanent magnet motor model referenced by claim 1 is characterized in that: The adjustable model obtained by S4 is: In the formula, is the estimated value of the rotor position at the kth sampling time, is the estimated value of the kth parameter b to be identified.

4. The method for identifying the moment of inertia of an arc-shaped permanent magnet motor model referenced by claim 1, characterized in that: The value obtained after position correction in S5 is: i m ′(k)=θ m (k)+ω m (k)T s (5) In the formula, θ m ′(k) is the kth corrected rotor position, and the corrected value replaces the encoder sampling position as the reference value.

5. The method for identifying the moment of inertia of an arc-shaped permanent magnet motor model referenced by an adaptive method according to claim 1, characterized in that: The adaptive rate established in S6 is: In the formula, the error β is the adaptive gain parameter, when When converged, the moment of inertia is calculated by equation (7):

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