Rotary motor limited space repeated learning control method

Abstract

The invention discloses a rotary motor limited space repeated learning control method, which aims at a rotary motor which needs to operate at a variable speed, can realize angular velocity tracking of the rotary motor with space periodic parameter uncertainty even if space periodic parameters are non-periodic along a time axis, and comprises the following steps of: firstly, establishing a kinetic model of a rotary motor system; a rotating motor system is converted from a time domain to a space domain through a space differential operator, and a limited space repeated learning controller is designed in the space domain, so that the rotating motor can be accurately learned under the condition that an initial error exists. The angular velocity tracking error of the rotating motor can be converged to a neighborhood near an original point in a limited rotating angle range of a motor rotor, and the angular velocity of the rotating motor can be quickly and accurately tracked on an expected track.

Description

Technical Field

[0001] The invention belongs to the technical field of permanent magnet synchronous motor control, and proposes a rotating motor control method based on limited space repeated learning technology to achieve fast and high-precision tracking of the motor angular velocity to a periodic desired trajectory. Background Art

[0002] In modern industrial production, rotating motors are widely used in aerospace, ship propulsion, industrial robots and other fields that require precise and efficient tracking control. In the design process of rotating motor controllers, the motor transient response speed and steady-state tracking accuracy are two key performance indicators. However, the uncertainty of the rotating motor system model in the time domain and external interference usually make it difficult to achieve the goal of fast and high-precision angular velocity tracking control. For example, for rotating motors, the interference caused by load eccentricity or cogging torque is essentially spatially periodic. Therefore, achieving high-precision trajectory tracking control of rotating motors is of great practical significance for improving the accuracy of automation equipment and processing and manufacturing.

[0003] In practice, the operating characteristics of a rotating motor have spatial periodicity about the angular position, that is, the motor rotor will return to the same angular position after an integer number of rotations. It presents a rotation with a fixed period of 2π. Therefore, the finite space repetitive learning control method can be used as a new control method to enable the angular velocity tracking error of the rotating motor to converge to the neighborhood near the origin within a limited angle range of the motor rotor rotation, solving the problem of fast and high-precision tracking, which has not been considered in previous rotating motors. Summary of the invention

[0004] In order to overcome the shortcomings of the existing technology and to achieve fast and high-precision tracking of the angular velocity of a rotating motor to a periodic desired trajectory, a finite space repetitive learning control method based on the Lyapunov method is proposed. The method introduces a spatial differential operator to convert the time domain non-periodic uncertainty of the rotating motor into a spatial periodic uncertainty related to the rotor position, and uses the full-limit spatial repetitive learning law to accurately compensate for the spatial periodic uncertainty. Considering the spatial periodic repetitive operation characteristics of the rotating motor with respect to the rotor angular position, the finite time control method is extended to the finite space control method to ensure that the angular velocity tracking error of the rotating motor can converge to a neighborhood near the origin within a limited angle range of the motor rotor rotation, so as to achieve fast and high-precision tracking of the angular velocity of the rotating motor to the desired trajectory.

[0005] The technical solutions proposed to solve the above technical problems are as follows:

[0006] A limited space repeated learning control method for a rotating motor comprises the following steps:

[0007] Step 1: Establish a dynamic model of the rotating motor system and initialize the system state and control parameters. The process is as follows:

[0008] 1.1 The mathematical model of the rotating motor in the rotating coordinate system is expressed as:

[0009]

[0010] Where J is the moment of inertia, B is the viscous friction coefficient, n p is the number of motor pole pairs, ψ f is the rotor flux, i q is the q-axis current, T L (θ) represents the load torque related to the position, d 1 (t) represents the bounded external disturbance, θ and ω are the rotor angular position and angular velocity of the rotating motor, respectively. and are the derivatives of θ and ω with respect to time t respectively;

[0011]

[0012] Then we get the following formula:

[0013]

[0014] in, Represents the motor load interference. Since the rotating motor operates repeatedly in the spatial domain and the direction of the motor load force remains unchanged, α(θ) is a periodic signal with the same period as θ, that is, a(θ) = α(θ-S), S = 2π;

[0015] Step 2, taking the rotor angular position θ as the independent variable, transform the rotating motor system from the time domain to the space domain. The process is as follows:

[0016] 2.1 Rotating motor rotor angular position θ, its expression is:

[0017]

[0018] in, represents a function of time t;

[0019] 2.2 The angular velocity of the rotating motor always rotates in one direction during the entire operation process, and the angular velocity meets the following conditions:

[0020]

[0021] in, represents the derivative of the rotor angular displacement with respect to time t; this will ensure is a monotonically increasing function of time t, and t and θ are bijective, that is, there is an inverse function Therefore, any function about t can be expressed as a function about θ

[0022] 2.3 Considering that the rotating motor repeatedly operates in the spatial state θ domain, the state variables of the rotating motor in the spatial domain are defined as:

[0023]

[0024]

[0025] in, represents the angular velocity in the spatial domain with the rotor angular position θ as the independent variable, represents the control input with the rotor angular position θ as the independent variable in the spatial domain, represents a bounded external disturbance in the spatial domain with the rotor angular position θ as the independent variable;

[0026] 2.4 Define the differential operator with respect to the rotor angular position θ:

[0027]

[0028] in, represents the derivative with respect to the rotor angular position θ in the spatial domain;

[0029] 2.5 Substituting formula (4) into formula (8), we get:

[0030]

[0031] According to formula (9), we get:

[0032]

[0033] 2.6 Substituting equation (2) into equation (10) and equation (11), we get:

[0034]

[0035] 2.7 Substituting equations (5), (6) and (7) into equation (12), we get:

[0036]

[0037] Step 3, design a limited space repetitive learning controller to ensure that the angular velocity tracking error of the rotating motor can converge to a neighborhood near the origin within a limited angle range of the motor rotor rotation, so as to achieve fast and high-precision tracking of the angular velocity of the rotating motor to the desired trajectory.

[0038] Further, the process of step 3 is as follows:

[0039] 3.1 Define the angular velocity tracking error of the rotating motor rotor:

[0040]

[0041] in, represents a given desired angular velocity trajectory;

[0042] 3.2 Design space repetitive learning controller, the form is as follows:

[0043]

[0044] in, is the desired angular velocity trajectory given by The derivative with respect to the rotor angular position θ; It is a finite space control term, which is used to ensure that the angular velocity tracking error converges to the neighborhood of the origin in a finite space; is a fully limited repetitive learning control term to ensure accurate compensation of spatial periodic uncertainty α(θ), is a robust control term to ensure compensation of bounded external disturbances k 1 , k 2 , k 3 , ε, λ are control parameters, and their value range is k 1 >0, ε>0、0<λ<1, represents the upper bound of bounded external disturbance, and represents the estimated value of α(θ);

[0045] 3.3 Design the full-limit repeated learning law to estimate α(θ), which is in the following form:

[0046]

[0047] Among them, μ 0 yes The control gain is a positive constant; sat(·) is the limiting function, and the limiting value of α(θ) is Its expression is

[0048]

[0049] In formula (16), φ(θ) is a strictly increasing function defined on [0, +∞), and its expression is

[0050]

[0051] 3.6 Choose the following Lyapunov function:

[0052]

[0053] 3.7 The derivative of equation (19) with respect to the rotor angular position θ is:

[0054]

[0055] 3.8 Substituting formula (15) into formula (20), we get:

[0056]

[0057] in, That is, the system is determined to be actually finite space convergent.

[0058] 3.9 Select the following class of Lyapunov functions:

[0059]

[0060] 3.10 The derivative of equation (22) in the spatial domain with respect to the rotor angular position θ gives:

[0061]

[0062] 3.11 Substituting equation (21) and equation (16) into equation (23), we get in That is, the system is determined to be convergent.

[0063] The invention designs a limited space repetitive learning method for fast and high-precision tracking of the angular velocity of a rotating motor system to a desired angular velocity based on the Lyapunov method and the spatial full-amplitude limited repetitive learning method.

[0064] The technical concept of the present invention is: through the differential operator of the rotor angular position, the rotating motor system is converted from the time domain to the space domain, and a limited space repetitive learning controller is designed in the space domain based on the Lyapunov method and the space full-limit repetitive learning method. The angular velocity tracking error of the rotating motor is realized to converge quickly to the neighborhood near the origin, and under the action of the space repetitive learning law, the angular velocity of the rotating motor is realized to track the desired angular velocity quickly and with high precision.

[0065] The beneficial effects of the present invention are as follows: for a rotating motor system with varying speed, even if the interference is non-periodic in the time domain but periodic in the space domain, the full-limit space repetitive learning law can suppress the spatial periodic interference and ensure the high-precision tracking performance of the angular velocity of the rotating motor system to the desired trajectory in the space domain. The finite space control law can enable the angular velocity tracking error of the rotating motor to converge to a neighborhood near the origin within a limited angle range of the motor rotor rotation. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1is a control flow chart of the present invention;

[0067] Figure 2 is the angular velocity Tracking the desired angular velocity trajectory effect;

[0068] Figure 3 is the angular velocity tracking error;

[0069] Figure 4 is an estimate of the uncertainty α(θ) associated with the angular position θ;

[0070] Figure 5 It is the control input of the rotating motor system. DETAILED DESCRIPTION

[0071] The present invention will be further described below in conjunction with the accompanying drawings.

[0072] Reference Figure 1-Figure 5 , a limited space repeated learning control method for a rotating motor, comprising the following steps:

[0073] Step 1: Establish a dynamic model of the rotating motor system and initialize the system state and control parameters. The process is as follows:

[0074] 1.1 The mathematical model of the rotating motor in the rotating coordinate system is expressed as:

[0075]

[0076] Where J is the moment of inertia, B is the viscous friction coefficient, n p is the number of motor pole pairs, ψ f is the rotor flux, i q is the q-axis current, T L (θ) represents the load torque related to the position, d 1 (t) represents the bounded external disturbance, θ and ω are the rotor angular position and angular velocity of the rotating motor, respectively. and are the derivatives of θ and ω with respect to time t respectively;

[0077] 1.2 In order to facilitate the design of subsequent controllers, remember d 2 (t) = hd 1 (t), Then we get the following formula:

[0078]

[0079] in, Represents the motor load interference. Since the rotating motor operates repeatedly in the spatial domain and the direction of the motor load force remains unchanged, α(θ) is a periodic signal with the same period as θ, that is, a(θ) = α(θ-S), S = 2π;

[0080] Step 2, taking the rotor angular position θ as the independent variable, transform the rotating motor system from the time domain to the space domain. The process is as follows:

[0081] 2.1 Rotating motor rotor angular position θ, its expression is:

[0082]

[0083] in, represents a function of time t;

[0084] 2.2 The angular velocity of the rotating motor always rotates in one direction during the entire operation process, and the angular velocity meets the following conditions:

[0085]

[0086] in, represents the derivative of the rotor angular displacement with respect to time t; this will ensure is a monotonically increasing function of time t, and t and θ are bijective, that is, there is an inverse function Therefore, any function about t can be expressed as a function about θ

[0087] 2.3 Considering that the rotating motor repeatedly operates in the spatial state θ domain, the state variables of the rotating motor in the spatial domain are defined as:

[0088]

[0089] in, represents the angular velocity in the spatial domain with the rotor angular position θ as the independent variable, represents the control input with the rotor angular position θ as the independent variable in the spatial domain, represents a bounded external disturbance in the spatial domain with the rotor angular position θ as the independent variable;

[0090] 2.4 Define the differential operator with respect to the rotor angular position θ:

[0091]

[0092] in, represents the derivative with respect to the rotor angular position θ in the spatial domain;

[0093] 2.5 Substituting formula (4) into formula (8), we get:

[0094]

[0095] According to formula (9), we get:

[0096]

[0097] 2.6 Substituting equation (2) into equation (10) and equation (11), we get:

[0098]

[0099] 2.7 Substituting equations (5), (6) and (7) into equation (12), we get:

[0100]

[0101] Step 3, design a limited space repetitive learning controller to ensure that the angular velocity tracking error of the rotating motor can converge to a neighborhood near the origin within a limited angle range of the motor rotor rotation, and realize fast and high-precision tracking of the angular velocity of the rotating motor to the desired trajectory. The process is as follows:

[0102] 3.1 Define the angular velocity tracking error of the rotating motor rotor:

[0103]

[0104] in, represents a given desired angular velocity trajectory;

[0105] 3.2 Design space repetitive learning controller, the form is as follows:

[0106]

[0107] in, is the desired angular velocity trajectory given by The derivative with respect to the rotor angular position θ; It is a finite space control term, which is used to ensure that the angular velocity tracking error converges to the neighborhood of the origin in a finite space; is a fully limited repetitive learning control term to ensure accurate compensation of spatial periodic uncertainty α(θ), is a robust control term to ensure compensation of bounded external disturbances k 1 , k 2 , k 3 , ε, λ are control parameters, and their value range is k 1 >0, ε>0、0<λ<1, represents the upper bound of bounded external disturbance, and represents the estimated value of α(θ);

[0108] 3.3 Design the full-limit repeated learning law to estimate α(θ), which is in the following form:

[0109]

[0110]

[0111] Among them, μ 0 yes The control gain is a positive constant; sat(·) is the limiting function, and the limiting value of α(θ) is Its expression is

[0112]

[0113] In formula (16), φ(θ) is a strictly increasing function defined on [0, +∞), and its expression is

[0114]

[0115] 3.6 Choose the following Lyapunov function:

[0116]

[0117] 3.7 The derivative of equation (19) with respect to the rotor angular position θ is:

[0118]

[0119] 3.8 Substituting formula (15) into formula (20), we get:

[0120]

[0121] in That is, the system is determined to be actually finite space convergent.

[0122] 3.9 Select the following class of Lyapunov functions:

[0123]

[0124] 3.10 The derivative of equation (22) in the spatial domain with respect to the rotor angular position θ gives:

[0125]

[0126] 3.11 Substituting equation (21) and equation (16) into equation (23), we get in That is, the system is determined to be convergent.

[0127] In order to verify the effectiveness of the proposed method, the present invention conducted an experiment on the proposed control method, and set the initial conditions and control parameters in the simulation experiment as follows: the system parameters are selected as J = 0.0275, n p =4,B=0.0012,ψ f =0.109; the controller parameter is selected as μ 0 =0.2,k 1 =0.4,k 2 =0.2,k 3 =0.05,ε=10 -4 ,λ=0.8,h=0.042,β=0.00183. The expected angular velocity trajectory is The initial state of the system is

[0128] In order to verify the effectiveness of the proposed method, the control effect of the limited space repetitive learning controller of the rotating motor is experimentally verified. The motor used in the experiment is a three-phase permanent magnet synchronous motor, whose rated load, voltage and power are 1.8N·m, 250VAC and 570W respectively. The three-phase inverter used to drive the permanent magnet synchronous motor is the intelligent power module (IPM) PS21A79, and the main control chip on the control board is the TMS320F28335 of Texas Together, which is connected to a PC with CCS12.0 programming environment. The rotor position is measured by an incremental encoder (resolution: 5000pulse / r), the phase current is measured by the TMS320F28335ADC module, and the 300V DC total voltage is provided by the DC power supply KPS3005D. The experimental data are sent to the PC via serial communication and processed by Matlab software. The sampling step size in the experiment is set to 0.001s, and the motor system parameters are selected as J=2.75×10 -4 kg·m 2 , T L =1.5sin(x 1 )N·m,φ f =0.109Wb,n p =4, B = 1.2 × 10 -4 .

[0129] Figure 2-Figure 5 is the experimental result diagram of limited space repetitive learning control of rotating motor system; Figure 2 is the angular velocity Tracking the desired angular velocity trajectory effect; Figure 3 is the angular velocity tracking error; Figure 4 is an estimate of the uncertainty α(θ) associated with the angular position θ; Figure 5is the control input of the rotating motor system; it shows that as the angular position of the rotating motor increases, the angular velocity tracking error gradually converges;

[0130] The above describes the effectiveness of the design of the present invention. Obviously, the present invention is not limited to the above examples, and various modifications can be made to implement it without departing from the basic spirit of the present invention and without exceeding the scope of the essential content of the present invention.

Claims

1. A method for repeated learning control of a rotating electrical machine in a limited space, characterized in that: The method comprises the following steps: Step 1: Establish a dynamic model of the rotating motor system and initialize the system state and control parameters. The process is as follows: 1.1 The mathematical model of the rotating motor in the rotating coordinate system is expressed as: Where J is the moment of inertia, B is the viscous friction coefficient, n p is the number of motor pole pairs, ψ f is the rotor flux, i q is the q-axis current, T L (θ) represents the position-dependent load torque, d1(t) represents the bounded external disturbance, θ and ω are the rotor angular position and angular velocity of the rotating motor, respectively. and are the derivatives of θ and ω with respect to time t respectively; 1.2 Note d2(t)=hd1(t), Then we get the following formula: in, Represents the motor load interference. Since the rotating motor operates repeatedly in the spatial domain and the direction of the motor load force remains unchanged, α(θ) is a periodic signal with the same period as θ, that is, a(θ) = α(θ-S), S = 2π; Step 2, taking the rotor angular position θ as the independent variable, transform the rotating motor system from the time domain to the space domain. The process is as follows: 2.1 Rotating motor rotor angular position θ, its expression is: in, represents a function of time t; 2.2 The angular velocity of the rotating motor always rotates in one direction during the entire operation process, and the angular velocity meets the following conditions: in, represents the derivative of the rotor angular displacement with respect to time t; this will ensure is a monotonically increasing function of time t, and t and θ are bijective, that is, there is an inverse function Therefore, any function about t can be expressed as a function about θ 2.3 Considering that the rotating motor repeatedly operates in the spatial state θ domain, the state variables of the rotating motor in the spatial domain are defined as: in, represents the angular velocity in the spatial domain with the rotor angular position θ as the independent variable, represents the control input with the rotor angular position θ as the independent variable in the spatial domain, represents a bounded external disturbance in the spatial domain with the rotor angular position θ as the independent variable; 2.4 Define the differential operator with respect to the rotor angular position θ: in, represents the derivative with respect to the rotor angular position θ in the spatial domain; 2.5 Substituting formula (4) into formula (8), we get: According to formula (9), we get: 2.6 Substituting equation (2) into equation (10) and equation (11), we get: 2.7 Substituting equations (5), (6) and (7) into equation (12), we get: Step 3, design a limited space repetitive learning controller to ensure that the angular velocity tracking error of the rotating motor can converge to a neighborhood near the origin within a limited angle range of the motor rotor rotation, so as to achieve fast and high-precision tracking of the angular velocity of the rotating motor to the desired trajectory.

2. A rotating electrical machine limited space repeated learning control method as claimed in claim 1, characterized in that: The process of step 3 is as follows: 3.1 Define the angular velocity tracking error of the rotating motor rotor: in, represents a given desired angular velocity trajectory; 3.2 Design space repetitive learning controller, the form is as follows: in, is the desired angular velocity trajectory given by The derivative with respect to the rotor angular position θ; It is a finite space control term, which is used to ensure that the angular velocity tracking error converges to the neighborhood of the origin in a finite space; is a fully limited repetitive learning control term to ensure accurate compensation of spatial periodic uncertainty α(θ), is a robust control term to ensure compensation of bounded external disturbances k1, k2, k3, ε, and λ are control parameters, and their value range is k1>0, ε>0、0<λ<1, represents the upper bound of bounded external disturbance, and represents the estimated value of α(θ); 3.3 Design the full-limit repeated learning law to estimate α(θ), which is in the following form: Where μ0 is The control gain is a positive constant; sat(·) is the limiting function, and the limiting value of α(θ) is Its expression is In formula (16), φ(θ) is a strictly increasing function defined on [0, +∞), and its expression is 3.6 Choose the following Lyapunov function: 3.7 The derivative of equation (19) with respect to the rotor angular position θ is: 3.8 Substituting formula (15) into formula (20), we get: in, That is, the system is determined to be actually finite space convergent. 3.9 Select the following class of Lyapunov functions: 3.10 The derivative of equation (22) in the spatial domain with respect to the rotor angular position θ gives: 3.11 Substituting equation (21) and equation (16) into equation (23), we get in That is, the system is determined to be convergent.

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