A parameter self-tuning method for permanent magnet synchronous motor servo system

Abstract

A method for self-tuning parameters of a permanent magnet synchronous motor servo system, which utilizes the collected servo system angle and current values ​​to identify the load torque and equivalent moment of inertia; based on the identified equivalent moment of inertia, combined with the speed loop bandwidth and time domain factor index, the speed loop PI controller parameters are self-tuned, and a speed loop bandwidth constraint equation is given to dynamically constrain the speed loop bandwidth. The present invention utilizes angle collection values ​​instead of speed values ​​to identify the parameters of the servo system, thus avoiding the influence of inaccurate speed measurement and differential noise; using the bandwidth constraint equation given by the present invention to constrain the bandwidth can reduce current saturation, and is more convenient for engineering applications based on the speed loop bandwidth and time domain factor index. The method for self-tuning parameters of a servo system proposed by the present invention can improve the dynamic response performance of transmission units of electromechanical systems such as numerical control equipment and robots.

Description

Technical Field

[0001] The invention discloses a servo parameter self-tuning method in the field of electromechanical system motion control, in particular a method for improving the response characteristics of a servo system by utilizing parameter online identification and speed loop PI parameter self-tuning technology. Background Art

[0002] Permanent magnet synchronous servo systems, due to their advantages such as high power density, high torque-to-inertia ratio, and wide speed regulation range, have been widely used in motion control applications such as industrial robots, CNC machine tools, and actuator systems. In engineering, permanent magnet synchronous servo systems often use PI controllers, which are simple to implement, offer good performance, and are insensitive to changes in the parameters of the controlled object. Improper PI controller parameter settings can directly impact control system performance. Therefore, studying PI controller parameter tuning algorithms for permanent magnet synchronous servo systems is an effective approach to improving these systems. Model analysis reveals that PI controller performance is sensitive to the moment of inertia parameter, highlighting the importance of combining inertia identification algorithms with PI parameter self-tuning methods. Because load torque can significantly interfere with inertia identification, developing identification algorithms that combine load torque and equivalent moment of inertia with PI parameter self-tuning methods is crucial for improving servo system performance.

[0003] Currently, research on PI parameter self-tuning methods is typically divided into model-based and rule-based approaches. Compared to rule-based tuning methods, model-based methods do not require complex control laws. Instead, they achieve superior control of both transient and steady-state servo system processes through frequency analysis and parameter solution of the model. Load torque and moment of inertia identification methods are categorized into two types: offline and online. Compared to offline methods, online identification methods eliminate the need for manual instructions and procedures and automatically acquire the parameters to be identified online, making them more flexible and more adaptable to the working environment. Currently, the main methods used include least squares, model reference adaptive, observer, and Kalman filtering. Compared to other methods, least squares is easier to implement and less sensitive to initial identification values ​​and adaptive parameters. However, its vulnerability to data saturation limits its application in variable parameter situations. Furthermore, least squares identification methods often use angular velocity for identification, which introduces differential noise, further limiting their application. When it comes to velocity loop PI parameter auto-tuning, the current loop is typically considered "1" when building the velocity loop model. This can introduce significant phase deviation when high velocity loop bandwidth requirements are required. Furthermore, typical tuning methods utilize only frequency-domain velocity loop parameters, failing to incorporate time-domain performance metrics, hindering engineering applications. Furthermore, the lack of velocity loop bandwidth constraints means that, in applications with heavy loads and high inertia, fixed-bandwidth tuning methods can lead to severe servo system current saturation, degrading system dynamic performance. Summary of the Invention

[0004] In response to the shortcomings of the above-mentioned prior art, the purpose of the present invention is to provide a method for improving the response characteristics of a servo system by utilizing parameter identification technology and speed loop PI parameter self-tuning technology. On the one hand, in response to the shortcomings of some load torque and moment of inertia identification methods, which are sensitive to identification initial values ​​and adaptive parameters, a recursive least squares method combined with an identification switch is selected for identification. The identification switch can reduce the shortcomings of the method being prone to data saturation, making it applicable to identification situations where parameters are variable. On the other hand, in response to the problem that some identification methods introduce differential noise when using angular velocity for identification, it is proposed to use angle to identify load torque and moment of inertia. In addition, in response to the shortcomings of some speed loop PI parameter self-tuning algorithms that only use speed loop frequency domain indicators for parameter tuning, an algorithm is proposed that combines time domain and frequency domain indicators for PI parameter self-tuning, and a speed loop bandwidth constraint equation is given to avoid current saturation.

[0005] In order to achieve the above technical objectives, the present invention will adopt the following technical solutions:

[0006] A method for self-tuning parameters of a permanent magnet synchronous motor servo system, comprising the following steps:

[0007] Step 1: parameter initialization, including giving the initial values ​​of the gain matrix and variance matrix of the identification algorithm;

[0008] Step 2: Perform servo parameter identification and calculation to start judgment, collect the servo system output angle and calculate the acceleration. When the acceleration is higher than the starting threshold, execute step 3, otherwise return to step 1;

[0009] Step 3: Sample the q-axis current and output angle, perform recursive identification calculations on the servo parameters, and then determine whether to exit the identification process. If the calculated real-time acceleration is less than the shutdown threshold, proceed to step 4; otherwise, continue the recursive identification calculations in this step.

[0010] Step 4: Determine whether the identification iteration has converged. If converged, output the identification result to step 5; otherwise, return to step 1.

[0011] Step 5: Input the identification results, the maximum current value of the servo system, and the operating speed into the speed loop bandwidth constraint equation to calculate the maximum allowable bandwidth of the speed loop and constrain the required bandwidth to be within the allowable bandwidth range.

[0012] Step 6: Substitute the identification results and the constrained bandwidth and time domain factor into the speed loop PI controller parameter self-tuning formula to calculate the PI controller parameter value.

[0013] In step 3, the servo parameter recursive identification calculation method is:

[0014]

[0015] in

[0016] is the parameter matrix to be identified at time k, is the parameter matrix to be identified at time k-1, K(k) is the gain matrix at time k, y(k-1) and is the input of the identification algorithm, P(k) is the variance matrix at time k, P(k-1) is the variance matrix at time k-1, I is the identity matrix, and the input parameter i q (k-1) is the q-axis current at time k-1, the input parameter θ(k) is the servo system angle at time k, θ(k-1) is the servo system angle at time k-1, θ(k-2) is the servo system angle at time k-2, K T is the torque coefficient, is the estimated value of the equivalent load moment of inertia J to be identified at time k, is the load torque T to be identified at time k l Estimated value, T s is the sampling interval.

[0017] In step 5, the speed loop bandwidth calculation formula considering current saturation is as follows:

[0018]

[0019] where ω scmax is the maximum allowable bandwidth of the speed loop, i qmax is the current loop saturation current, A N is the rated speed of the servo system, α is the speed attenuation coefficient determined by working conditions or test conditions, α≤1, is the load torque T to be identified l The estimated value of is the estimated value of the equivalent load moment of inertia J to be identified.

[0020] In step 6, the speed loop PI controller parameter self-tuning formula is:

[0021]

[0022]

[0023] where ω sc is the speed loop bandwidth after constraint, δ is the time domain factor, u is the transformation factor, which is a function of δ; According to the above formula, the PI controller parameters are obtained by identifying the equivalent moment of inertia and selecting the required parameters, that is, the proportional gain K sp and integral gain K si .

[0024] Based on the above technical solution, the present invention can achieve the following effects: the load torque and equivalent moment of inertia identification method used in the present invention is insensitive to the initial identification value and adaptive parameters, and the use of angle for identification can avoid the introduction of differential noise, facilitating the acquisition of better identification results. The speed loop PI parameter self-tuning method proposed in the present invention uses the speed loop bandwidth and time domain factor indicators for PI parameter tuning, which is more convenient for practical engineering applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 It is a flowchart of the execution process of the method of the present invention.

[0026] Figure 2 It is the control structure block diagram of permanent magnet synchronous servo system.

[0027] Figure 3 It is the identification excitation signal and tracking signal curve diagram; Among them, a is the load torque identification curve diagram, and b is the equivalent rotational inertia identification curve diagram.

[0028] Figure 4 It is the identification curve of load torque and equivalent moment of inertia.

[0029] Figure 5 It is the speed loop step response curve of different time domain factors.

[0030] Figure 6 This is the speed step response curve of the servo system after PI parameters are adjusted. DETAILED DESCRIPTION

[0031] In order to make the technical solutions and advantages of the present invention more clear, the technical solutions in the embodiments of the present invention are clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.

[0032] To implement the present invention's parameter self-tuning method for a permanent magnet synchronous motor servo system, the servo system's equations of motion are first established. A least-squares identification method using angles for load torque and moment of inertia is derived. Appropriate thresholds for starting and stopping the identification algorithm are set to mitigate data saturation. Next, the system's velocity loop transfer function is established, and a PI tuning formula based on the velocity loop bandwidth and time-domain factor is derived. Finally, a bandwidth constraint equation is established that takes current saturation into account.

[0033] Therefore, the permanent magnet servo system parameter self-tuning method based on load parameter identification of the present invention first obtains the estimated values ​​of the load torque and equivalent rotational inertia through inertia identification, and then establishes a speed loop PI controller parameter self-tuning calculation method.

[0034] Specifically, the present invention comprises the following steps:

[0035] Step 1: Parameter initialization. This involves initializing the variance matrix of the identification algorithm and the matrix of parameters to be identified. For example, the identification algorithm is the aforementioned least squares identification method using load torque and moment of inertia with respect to angle. In this example, the variance matrix is ​​initialized to 10I, and the parameters to be identified are initialized to 0.

[0036] Step 2: Identification start judgment. If the identification start condition is met, execute step 3. Otherwise, return to step 1. For example, after the servo parameter identification parameter initialization is performed, the judgment is started, the servo system output angle is collected, the acceleration is calculated and filtered. If the acceleration is higher than the start threshold, execute step 3. Otherwise, return to step 1. The method for calculating acceleration in this step is as follows:

[0037]

[0038] Where a(k) is the calculated acceleration value at time k, θ(k), θ(k-1), and θ(k-2) are the system output angles at time k, k-1, and k-2, respectively. s is the sampling interval.

[0039] In this step, a second-order Butterworth filter is used to filter the acceleration, with a filtering frequency of 30 Hz.

[0040] For example, the start threshold can be set to 200rad / s 2 .

[0041] Step 3: Execute the servo parameter identification calculation process. When the identification process calculation closing condition is met, execute step 4. Otherwise, continue to execute the identification calculation.

[0042] Specifically, in this step, the servo parameter identification calculation is a recursive identification calculation process. The closing condition here refers to: calculating the real-time acceleration based on the sampled q-axis current and output angle, and executing step four when the result is less than the closing threshold, otherwise continue to execute the recursive identification calculation in this step.

[0043] Since when the load damping is ignored, the motion equation of the servo system is

[0044]

[0045] Where T e is the driving torque, T l and J are the load torque and equivalent load moment of inertia to be identified, and ω is the mechanical angular velocity.

[0046] Assuming that the load torque and equivalent load moment of inertia change slowly, the identification algorithm of the load torque and equivalent load moment of inertia can be obtained based on the least squares method. Integrating both ends of equation (1) yields:

[0047] ∫T e dt-∫T l dt=J(ω(t)-ω(0)) (3)

[0048] Where ω(0) is the initial angular velocity of the identification process.

[0049] Discretizing Equation (2) yields:

[0050]

[0051] One step of recursion can be obtained:

[0052]

[0053] Subtracting formula (4) from formula (3) yields:

[0054] T e (k-1)·T s -T l ·T s =J(ω(k)-ω(k-1)) (6)

[0055] In discrete form

[0056]

[0057] After substituting formula (6) into formula (5), formula (5) can be rewritten as:

[0058]

[0059] In permanent magnet synchronous motors d = 0 current control strategy, T e =K T i q , where K T is the torque coefficient, i q is the q-axis current. Then, after reorganizing equation (7), we can obtain:

[0060]

[0061] According to formula (8), the recursive least squares identification equation can be established:

[0062]

[0063] in, is the parameter matrix to be identified at time k, is the parameter matrix to be identified at time k-1, K(k) is the gain matrix at time k, y(k-1) and is the input of the identification algorithm, P(k) is the variance matrix at time k, P(k-1) is the variance matrix at time k-1, I is the identity matrix, and the input parameter i q (k-1) is the q-axis current at time k-1, the input parameter θ(k) is the servo system angle at time k, θ(k-1) is the servo system angle at time k-1, θ(k-2) is the servo system angle at time k-2, K T is the torque coefficient, is the estimated value of the equivalent load moment of inertia J to be identified at time k, is the load torque T to be identified at time k l Estimated value, T s is the sampling interval.

[0064] For example, the acceleration calculation and filtering in this step are the same as those in step 2, and the closing threshold is the same as the opening threshold in step 2.

[0065] Step 4: Perform convergence judgment on the identification result. When the result converges, output the identification result. Otherwise, return to step 1.

[0066] For example, the convergence condition of the identification result in this step is set as follows: the difference between the two identification results is less than 1×10 -4 kgm 2 , which is 10% of the no-load moment of inertia in the example. When the identification result meets this condition, the algorithm determines that the result has converged.

[0067] Step 5: Calculate bandwidth constraints. Input the identification results, the maximum current value of the servo system, and the operating speed into the speed loop bandwidth constraint equation, calculate the maximum allowable bandwidth of the speed loop, and constrain the required bandwidth to be within the allowable bandwidth range. The bandwidth constraint equation derivation process is as follows:

[0068] Assume that the speed command input is a sinusoidal signal: ω ref =αA N sin(ωt), where ω is the angular frequency of the input command, A N is the rated speed of the servo system, α is the speed attenuation coefficient, which is determined by the working conditions or test conditions, and α≤1.

[0069] From the definition of bandwidth, we can know that when the frequency of the speed loop input command is the system bandwidth, the output speed is:

[0070]

[0071] Where β is the output phase delay.

[0072] Substituting formula (11) into formula (1), we can obtain:

[0073]

[0074] To avoid current saturation, the speed loop bandwidth must meet the following requirements:

[0075]

[0076] Among them, i qmax is the current loop saturation current.

[0077] The theoretical inertia and torque are replaced by the load equivalent inertia and torque obtained by identification, so the speed loop bandwidth constraint equation considering current saturation is:

[0078]

[0079] Among them, ω scmax It is the maximum allowable bandwidth of the speed loop under the current load.

[0080] Step 6: Substitute the identification results and the constrained bandwidth and time domain factor into the speed loop PI controller parameter self-tuning formula to calculate the PI controller parameter value.

[0081] In this step, the current loop is equivalent to a first-order inertial joint, the velocity loop transfer function is established, and the relationship between frequency domain indicators (cutoff frequency and phase margin) and PI parameters is established using frequency domain analysis. On this basis, the relationship between the frequency domain indicator phase margin and the time domain indicator time factor is established. The time domain factor is used to characterize the combined characteristics of the velocity loop overshoot and adjustment time. A PI parameter tuning method based on the velocity loop bandwidth and time domain factor is established, and a velocity loop bandwidth constraint equation considering current saturation is given.

[0082] Specifically, the PI auto-tuning formula is obtained from the following process:

[0083] The speed loop PI controller is:

[0084]

[0085] like Figure 2 The structure block diagram shown can obtain the speed loop open-loop transfer function:

[0086]

[0087] in, is the current loop closed-loop transfer function.

[0088] Note co Indicates the speed loop open loop cut-off frequency, represents the phase margin, then:

[0089]

[0090]

[0091] Since usually In order to ensure that the speed loop has sufficient intermediate frequency width, the PI controller zero point Therefore, formula (17) can be simplified as:

[0092]

[0093] Define γ=atg(T c ω co ), formula (18) can be rewritten as:

[0094]

[0095] According to equations (19) and (20), the PI tuning formula can be preliminarily obtained:

[0096]

[0097]

[0098] The following derivation process links the PI parameters with the time domain factor and the speed loop bandwidth. When , the speed loop will obtain the maximum phase margin, where is the current loop bandwidth.

[0099] Time domain factor Then there is It reflects the comprehensive requirements for overshoot and adjustment time. Substituting it into formula (22) yields a new tuning formula:

[0100]

[0101] The relationship between the speed loop bandwidth and the speed loop open-loop cutoff frequency is further derived.

[0102] The closed-loop transfer function is obtained from the open-loop transfer function of the speed loop in formula (16):

[0103]

[0104] Note sc represents the speed loop bandwidth after constraint, then according to the bandwidth definition,

[0105]

[0106] Common requirements Therefore, the influence of the current link can be ignored when calculating the amplitude-frequency, and it can be regarded as "1", so:

[0107]

[0108] Substituting equations (21) and (23) into equation (26), we can calculate the transformation factor u, which is a function of δ:

[0109]

[0110] Substituting Equation (27) into Equations (21) and (23), we can obtain the final speed loop PI controller parameter self-tuning equation:

[0111]

[0112]

[0113] Among them, the time domain factor δ is Figure 5 According to the above formula, the PI controller parameters are obtained by identifying the equivalent moment of inertia and selecting the required parameters, that is, the proportional gain K sp and integral gain K si .

[0114] According to the above method provided by the embodiment of the present invention, a simulation experiment is carried out on the identification of load parameters and the self-tuning of speed loop PI parameters. The simulation experiment block diagram is shown as follows: Figure 2 As shown, in the experiment, the servo system resistance is 0.0976Ω, the d-axis inductance is 0.525mH, the q-axis inductance is 1.2mH, the magnetic flux is 0.1827Wb, the number of pole pairs is 4, and the no-load moment of inertia is 0.001kgm 2 The sampling frequency is 20K and the torque coefficient is 1.0962Nm / A.

[0115] In the simulation experiment, the moment of inertia is from 0.003kgm 2 becomes 0.005kgm 2 , the load torque changes from -10Nm to -5Nm, and the acceleration threshold for identification opening and closing is set to 200rad / s 2 (The threshold value needs to be selected according to the actual working conditions of the servo system), identify the excitation signal and the speed output signal such as Figure 3 As shown in the figure, the inertia identification results are as follows: Figure 4 As shown in FIG, it can be seen from the identification results that the identification method proposed in the present invention can quickly and accurately identify the load torque and equivalent moment of inertia.

[0116] In the simulation experiment of the servo system PI controller parameter self-tuning, the bandwidth is 300Hz and the equivalent moment of inertia is 0.003kgm 2 , the time domain factor δ is 4 (from Figure 5 (Selected from), using formula (27) we can calculate the u value 1.24, and using formulas (28) and (29) we can calculate the proportional gain K sp is 4.16, the integral gain is 1578, and the speed tracking curve is as follows Figure 6 As shown, the speed tracking curve before tuning ( Figure 2 ), the overshoot is reduced to a certain extent, and the adjustment time is significantly reduced, which verifies that the PI parameter tuning method proposed in the present invention enables the servo system to obtain better dynamic performance.

[0117] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent replacement or modification made by anyone familiar with the art within the technical scope disclosed by the present invention and based on the technical solution and inventive concept of the present invention shall be covered by the scope of protection of the present invention.

Claims

1. A method for self-tuning parameters of a permanent magnet synchronous motor servo system, characterized in that: The following steps are involved: Step 1: parameter initialization, including giving the initial value of the variance matrix of the identification algorithm and the initial value of the parameters to be identified; Step 2: Perform servo parameter identification and calculation to start judgment, collect the servo system output angle and calculate the acceleration. When the acceleration is higher than the starting threshold, execute step 3, otherwise return to step 1; Step 3: Sample the q-axis current and output angle, perform recursive identification calculations on the servo parameters, and then determine whether to exit the identification process. If the calculated real-time acceleration is less than the shutdown threshold, proceed to step 4; otherwise, continue the recursive identification calculations in this step. Step 4: Determine whether the identification iteration has converged. If converged, output the identification result to step 5; otherwise, return to step 1. Step 5: Input the identification results, the maximum current value of the servo system, and the operating speed into the speed loop bandwidth constraint equation to calculate the maximum allowable bandwidth of the speed loop and constrain the required bandwidth to be within the allowable bandwidth range. The speed loop bandwidth calculation formula considering current saturation is as follows: where ω scmax K is the maximum allowable bandwidth of the speed loop. T is the torque coefficient, i qmax is the current loop saturation current, A N is the rated speed of the servo system, α is the speed attenuation coefficient determined by working conditions or test conditions, α≤1, is the load torque T to be identified l The estimated value of is the estimated value of the equivalent load moment of inertia J to be identified; Step 6: Substitute the identification results and the constrained bandwidth and time domain factor into the speed loop PI controller parameter self-tuning formula to calculate the PI controller parameter value. The speed loop PI controller parameter self-tuning formula is: where ω sc is the speed loop bandwidth after constraint, δ is the time domain factor, u is the transformation factor, which is a function of δ; According to the above formula, the PI controller parameters are obtained by identifying the equivalent moment of inertia and selecting the required parameters, that is, the proportional gain K sp and integral gain K si .

2. A method for self-tuning parameters of a permanent magnet synchronous motor servo system according to claim 1, characterized in that: In step 3, the servo parameter recursive identification calculation method is: in, is the parameter matrix to be identified at time k, is the parameter matrix to be identified at time k-1, K(k) is the gain matrix at time k, y(k-1) and is the input of the identification algorithm, P(k) is the variance matrix at time k, P(k-1) is the variance matrix at time k-1, I is the identity matrix, and the input parameter i q (k-1) is the q-axis current at time k-1, the input parameter θ(k) is the servo system angle at time k, θ(k-1) is the servo system angle at time k-1, and θ(k-2) is the servo system angle at time k-2. is the estimated value of the equivalent load moment of inertia J to be identified at time k, is the load torque T to be identified at time k l Estimated value, T s is the sampling interval.

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