Rotational inertia identification and adaptive control method based on Lyapunov function

Abstract

The invention belongs to the technical field of permanent magnet synchronous motor control, and particularly relates to a rotational inertia identification and adaptive control method based on a Lyapunov function, and the method comprises the steps: 1, calculating a rotating speed error; step 2, updating an estimated value # imgabs0 # of a self-adaptive process parameter a (k) according to a self-adaptive law; step 3, updating an estimated value # imgabs1 # of a self-adaptive process parameter t (k) according to the self-adaptive law; step 4, calculating excitation torque; 5, calculating a reference model control quantity u0 (k); 6, updating the rotating speed output omega0 (k) of the reference model; 7, calculating a rotating speed output error of the reference model; and 8, updating the estimated value # imgabs2 # of the rotational inertia J (k) and the estimated value # imgabs3 # of the load torque T1 (k) according to the definition. According to the method, the rotational inertia and load torque parameters of the permanent magnet synchronous motor can be identified during operation, so that adaptive adjustment of the rotating speed ring parameters is realized, and the workload of calibration personnel is reduced.

Description

Technical Field

[0001] The present invention relates to the technical field of permanent magnet synchronous motor control, and particularly to a method for identifying rotational inertia and adaptive control based on Lyapunov function. Background Art

[0002] Permanent Magnet Synchronous Motor (PMSM) is a three-phase AC motor known for its excellent efficiency, power density, and control accuracy. This motor consists of three sets of stator windings with a phase difference of 120 degrees and a rotor equipped with permanent magnets. By sending PWM (Pulse Width Modulation) signals to the three-phase inverter, the switching state of IGBT (Insulated Gate Bipolar Transistor) is controlled, thereby generating voltage and three-phase current in the stator windings, and then generating the interaction between the stator magnetic field and the rotor magnetic field to drive the motor to rotate.

[0003] Currently, the speed loop of the permanent magnet synchronous motor generally uses a PI controller, which is calibrated by a calibration personnel on the test bench so that the speed response of the permanent magnet synchronous motor reaches the predetermined requirements. However, for different test benches, the parameters of the speed loop need to be recalibrated, greatly increasing the calibration workload of the permanent magnet synchronous motor.

[0004] Therefore, the present invention proposes a method for identifying rotational inertia and adaptive control based on Lyapunov function. Summary of the Invention

[0005] Aiming at the problems existing in the prior art, the present invention provides a method for identifying rotational inertia and adaptive control based on Lyapunov function.

[0006] To achieve the above object, the present invention adopts the following technical solutions:

[0007] A method for identifying rotational inertia and adaptive control based on Lyapunov function, the method comprising:

[0008] Step 1: Calculate the speed error: e ω (k) = ω * (k) - ω(k);

[0009] Step 2: Update the estimated value of the adaptive process parameter a(k) according to the adaptive law Specifically:

[0010] Step 3: Update the estimated value of the adaptive process parameter t(k) according to the adaptive law

[0011]

[0012] Step 4: Calculate the excitation torque:

[0013]

[0014] Step 5: Calculate the reference model control quantity u0(k), specifically:

[0015]

[0016] Step 6: Update the reference model speed output ω0(k), specifically:

[0017]

[0018] Step 7: Calculate the reference model speed output error:

[0019] e0(k) = ω(k) - ω0(k);

[0020] Step 8: Update the estimated value of the moment of inertia J(k) and the estimated value of the load torque Tl(k)

[0021]

[0022] where Trq is the excitation torque, Ts is the sampling period, (k) is the current period, (k - 1) is the previous period, ω is the mechanical angular velocity, a and t are parameters, and are the estimators of a and t respectively, J and Tl are the moment of inertia and the load torque, and are the estimators of J and Tl respectively.

[0023] Preferably, the design of the adaptation law is based on the Lyapunov function

[0024] Therefore, the adaptation law is designed as:

[0025]

[0026] ∴ where Tl is the load torque and J is the moment of inertia.

[0027] Preferably, the design of the reference model is:

[0028]

[0029] The error between the speed output by the reference model and the actual speed is e0 = ω - ω0, driving the convergence of the parameter estimation.

[0030] Preferably, the changes in the moment of inertia J and the load torque Tl are compensated by the adaptive update of the adaptive process parameters and .

[0031] Preferably, the sampling period Ts is the time interval of the discrete system

[0032] The above technical solution of the present invention has the following beneficial technical effects

[0033] 1. The present invention can identify the moment of inertia parameters of the permanent magnet synchronous motor during operation, thereby realizing the adaptive adjustment of the speed loop parameters and reducing the workload of the calibration personnel

[0034] 2. Due to the application of the parameter identification technology, the present invention can adjust the fluctuations of the moment of inertia during the actual process, thereby improving the control effect of the speed loop of the motor control BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 is the Simulink simulation model block diagram of the present invention

[0036] Figure 2 is the actual speed and reference model tracking curve graph DETAILED DESCRIPTION OF THE EMBODIMENTS

[0037] To make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below in conjunction with the specific embodiments and with reference to the accompanying drawings. It should be understood that these descriptions are exemplary only and are not intended to limit the scope of the present invention. In addition, in the following description, the descriptions of well-known structures and technologies are omitted to avoid unnecessarily obscuring the concepts of the present invention

[0038] As Figure 1 and Figure 2 shown, the present invention provides a moment of inertia identification and adaptive control method based on the Lyapunov function, and the method includes

[0039] The method includes

[0040] Step 1: Calculate the speed error: e ω (k) = ω * (k) - ω(k);

[0041] Step 2: Update the estimated value of the adaptive process parameter a(k) according to the adaptive law Specifically

[0042]

[0043] Step 3: Update the estimated value of the adaptive process parameter t(k) according to the adaptation law

[0044] Step 4: Calculate the excitation torque:

[0045]

[0046] Step 5: Calculate the reference model control quantity u0(k), specifically:

[0047]

[0048] Step 6: Update the reference model speed output ω0(k), specifically:

[0049]

[0050] Step 7: Calculate the reference model speed output error:

[0051] e0(k) = ω(k) - ω0(k);

[0052] Step 8: Update the estimated value of the moment of inertia J(k) according to the definition and the estimated value of the load torque Tl(k)

[0053]

[0054] where Trq is the excitation torque, Ts is the sampling period, (k) is the current period, (k - 1) is the previous period, ω is the mechanical angular velocity, a and t are adaptive process parameters, and are the estimators of a and t respectively, J and Tl are the moment of inertia and the load torque, and are the estimators of J and Tl respectively.

[0055] Specifically:

[0056] The known motion equation of the permanent magnet synchronous motor is:

[0057]

[0058] where Trq is the excitation torque, Tl is the load torque, J is the moment of inertia, ω is the mechanical angular velocity, is the mechanical angular acceleration.

[0059] Therefore, let: We can get:

[0060]

[0061] Let the rotational speed command be ω * , and the rotational speed error be e ω = ω * - ω, Therefore, design the Lyapunov function:

[0062]

[0063] Therefore, it can be obtained that:

[0064]

[0065] Since the moment of inertia and the load torque are both unknown, the parameters a and t are unknown. Therefore, design the estimators of a and t as and So the torque Trq at this time is:

[0066]

[0067] Since the parameters a and t need to be estimated, design a reference model and adaptively estimate the parameters in the reference model and such that the estimated rotational speed ω0 output by the reference model can converge to the actual feedback rotational speed ω, thereby realizing the estimation of the parameters and can converge to the actual parameters a and t. Therefore, design the reference model as:

[0068]

[0069] Let the error between the rotational speed output by the reference model and the actual rotational speed be e0 = ω - ω0, Therefore, design the Lyapunov function as:

[0070]

[0071] From this, it can be obtained that the input u0 of the reference model is:

[0072]

[0073] Also, since the parameters a and t are unknown, u0 is:

[0074]

[0075] Design the error of the parameter estimation as Its derivative is Therefore, design the Lyapunov function as:

[0076]

[0077]

[0078] Therefore, the adaptive law is designed as follows:

[0079]

[0080] ∴

[0081] The system is stable, which is proved.

[0082] In summary, let the sampling period of the discrete system be Ts, (k) be the current period, and (k - 1) be the previous period.

[0083] The motor speed loop control law designed by the present invention can automatically identify the motor inertia, greatly saving the calibration burden of the calibration personnel and avoiding the problem of frequently adjusting the PI parameters under different inertia conditions.

[0084] The above are only the preferred embodiments of the present invention and are not intended 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 described in the foregoing embodiments or perform equivalent replacements for some of the technical features. Any modification, equivalent replacement, improvement, 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 identifying moment of inertia and adaptive control based on Lyapunov function, characterized in that The method includes: Step 1: Calculate the rotational speed error: e ω (k) = ω * (k) - ω(k); Step 2: Update the estimated value of the adaptive process parameter a(k) according to the adaptation law Specifically: Step 3: Update the estimated value of the adaptive process parameter t(k) according to the adaptation law Step Four: Calculate the excitation torque: Step Five: Calculate the reference model control quantity u0(k), specifically: Step Six: Update the reference model speed output ω0(k), specifically: Step Seven: Calculate the reference model speed output error: e0(k) = ω(k) - ω0(k); Step Eight: Update the estimated value of the moment of inertia J(k) according to the definition and the estimated value of the load torque Tl(k) Among them, Trq is the excitation torque, Ts is the sampling period, (k) is the current period, (k - 1) is the previous period, ω is the mechanical angular velocity, a and t are adaptive process parameters, and are the estimators of a and t respectively, J and Tl are the moment of inertia and the load torque, and are the estimators of J and Tl respectively.

2. The method for identifying the moment of inertia and adaptive control based on the Lyapunov function according to claim 1, wherein The design of the adaptation law is based on the Lyapunov function Therefore, the adaptive law is designed as: ∴ where Tl is the load torque and J is the moment of inertia.

3. The method for identifying moment of inertia and adaptive control based on Lyapunov function according to claim 2, characterized in that, The design of the reference model is: The error between the output speed of the reference model and the actual speed is \(e_0=\omega - \omega_0\). Convergence of the drive parameter estimation.

4. The method for identifying moment of inertia and adaptive control based on Lyapunov function according to claim 2, wherein, The changes in the moment of inertia J and the load torque Tl are compensated by the adaptive update of the adaptive process parameters and .

5. The method for identifying moment of inertia and adaptive control based on Lyapunov function according to claim 1, wherein The sampling period Ts is the time interval of the discrete system.

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