A design method for high-speed motor rigid rotor system

Abstract

The present invention discloses a design method for a high-speed motor rigid rotor system, which includes establishing a state space model of the high-speed motor rigid rotor system; establishing a quadratic cost function according to the state and control input of the high-speed motor rigid rotor system; solving the Riccati equation according to the state space model and performance index of the high-speed motor rigid rotor system to obtain an optimal state feedback matrix K; calculating an optimal control input signal u by formula u=‑KZ; inputting the calculated optimal control input signal u into the system to implement an LQR controller. The present invention adopts minimization of a predefined cost function to achieve comprehensive optimization of system performance. The present invention can not only ensure the stability of the closed-loop system, but also resist changes in system parameters and external disturbances to a certain extent. The present invention can greatly reduce the noise of the entire high-speed motor rigid rotor system based on electromagnetic bearings by adopting an effective control or signal processing method.

Description

Technical Field

[0001] The invention belongs to the technical field of high-speed motor systems, and in particular relates to a design method for a high-speed motor rigid rotor system. Background Art

[0002] The combination of high-speed motors and active magnetic bearings (AMBs) has become an important technical solution, especially in those occasions where high precision, speed and reliability are required. Linear quadratic regulator (LQR), as a classic optimal control method, is widely used in various control systems due to its simple structure, intuitive design and easy implementation. The design and control of the electromagnetic bearing-high-speed motor rigid rotor system faces the following major challenges: Complex dynamic characteristics: The dynamic behavior of the rigid rotor, including its natural frequency, mode, etc., has an important impact on the stability and performance of the system. These characteristics need to be considered when designing the controller. Nonlinearity of the system: The nonlinear characteristics of the electromagnetic bearing increase the complexity of the control system design. High performance requirements: High-speed motor systems usually require high precision, high response speed and high reliability, which puts higher requirements on the control strategy. External disturbances and internal parameter changes: In practical applications, the system will be affected by various external disturbances, and the internal parameters may also change due to factors such as temperature and wear, which requires the controller to have good robustness and adaptability.

[0003] The patent publication number is CN113193801A, and the name is a patent application for a high-speed motor simulator control system and a high-speed motor simulator. The high-speed motor simulator solves the signal transmission delay problem through special hardware design and software delay compensation algorithm design to achieve accurate simulation of high-speed motors. It includes: the compensation control module receives the measured three-phase current and voltage average values, generates compensation voltage and compensation current under dq coordinates; the motor model calculation module uses the compensation voltage and current to calculate the motor model in real time, generates reference current, the speed and rotor position of the simulated motor; the current control module executes the current control algorithm according to the reference current and compensation current to generate PWM duty cycle; the virtual encoder simulates the photoelectric encoder to encode the rotor position and speed of the simulated motor; the synchronization signal generation module generates a PWM carrier synchronization pulse signal; the PWM module receives the synchronization signal and the PWM duty cycle, and modulates to generate a drive pulse. Although this patent application can realize the control of high-speed motors, it is not suitable for the control of high-speed motors with electromagnetic bearings. Summary of the invention

[0004] In order to overcome the problems existing in the above-mentioned prior art, the purpose of the present invention is to provide a design method for a high-speed motor rigid rotor system, which uses minimization of a predefined cost function to achieve comprehensive optimization of the performance of the high-speed motor rigid rotor system.

[0005] To achieve the above object, the technical solution adopted by the present invention is:

[0006] A method for designing a high-speed motor rigid rotor system, wherein the high-speed motor rigid rotor system has an electromagnetic bearing, comprises the following steps:

[0007] S1: Establish the state space model of the high-speed motor rigid rotor system;

[0008] S2: Establish a quadratic cost function based on the state and control input of the high-speed motor rigid rotor system;

[0009] S3: Solve the Riccati equation according to the state space model and performance index of the high-speed motor rigid rotor system to obtain the optimal state feedback matrix K;

[0010] S4: The optimal control input signal u is calculated by the formula u=-KZ, where Z is the state feedback control rate;

[0011] S5: Input the calculated optimal control input signal u into the system.

[0012] Optionally, the high-speed motor rigid rotor system has an electromagnetic bearing, characterized in that, in step S1, the state space model of the high-speed motor rigid rotor system is:

[0013]

[0014] Among them, A is the coefficient matrix of state variables, B is the coefficient matrix of input variables, C is the output matrix, D is the system feedback matrix, y is the system output, x is the state variable, and u is the linear quadratic optimal control quantity.

[0015] Optionally, in step S2, the cost function is:

[0016]

[0017] In the formula, Q is the state weight matrix in control, R is the control weight matrix, It is the control quantity corresponding to the state space equation of the high-speed motor rigid rotor system based on electromagnetic bearings with Z as the state variable, and Z is the system state variable of the state space model.

[0018] Optionally, the system state variables of the state space model Where, e is the rigid rotor vibration error, is the rate of change of error.

[0019] Optionally, the Riccati equation is A T P+PA+Q-PBR -1 B T P=0

[0020] Among them, Q is the state weight matrix in control, R is the control weight matrix, P is the constant matrix, A is the coefficient matrix of state variables, and B is the coefficient matrix of input variables. a 11 =a 22 =b1=c 12 =0,a 12 =c 11 =1,a 21 =k s / m a =33735,b2=k i / m a =21.3,x a and i xa are the rotor vibration and control current in the x direction of AMB-A end, k i and k s are the current stiffness coefficient and displacement stiffness coefficient of AMB, m a is half the mass of the rotor.

[0021] Optionally, Q is a 2nd-order matrix, R is a 1st-order matrix,

[0022] Optional, select Q 11 =1×10 -7 , Q 22 =1, R=10.

[0023] Optionally, the control rate of the optimal state feedback matrix K is:

[0024]

[0025] Where u is the control rate, e is the rigid rotor vibration error, is the rate of change of error, r is the rotor equilibrium position, k1 and k2 are e and The control coefficient of .

[0026] Compared with the prior art, the present invention has the following beneficial effects:

[0027] The present invention uses minimization of a predefined cost function to achieve comprehensive optimization of system performance. The present invention can not only ensure the stability of the closed-loop system, but also resist changes in system parameters and external disturbances to a certain extent. The present invention can greatly reduce the noise of the entire high-speed motor rigid rotor system based on electromagnetic bearings by adopting effective control or signal processing methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] The drawings described herein are for illustration purposes only and are not intended to limit the scope of the present disclosure in any way.

[0029] In the attached picture:

[0030] Figure 1 It is the structural block diagram of LQR in the present invention;

[0031] Figure 2 This is a block diagram of the principle of a high-speed motor rigid rotor system based on electromagnetic bearings based on LQR;

[0032] Figure 3 is the change of k1 and k2 when Q11 changes over the full range;

[0033] Figure 4 is the variation of k1 and k2 when Q22 varies over the full range;

[0034] Figure 5 It is a three-dimensional diagram of the rotor vibration at the full speed range of the AMB-A end;

[0035] Figure 6 It is a three-dimensional diagram of the rotor vibration at the full speed range of the AMB-B end;

[0036] Figure 7 is x A Comparison of rotor vibration envelopes in different directions;

[0037] Figure 8 is x B Comparison of rotor vibration envelopes in different directions. DETAILED DESCRIPTION

[0038] In order to enable those skilled in the art to better understand the technical solutions in the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings 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 should fall within the scope of protection of the present invention.

[0039] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as those generally understood by those skilled in the art of the present invention. The terms used herein in the specification of the present invention are only for the purpose of describing specific embodiments and are not intended to limit the present invention. The term "and / or" used herein includes any and all combinations of one or more related listed items.

[0040] It should be noted that in the claims, any reference signs placed between brackets shall not be construed as limiting the claims. The word "comprising" does not exclude the presence of components or steps not listed in the claims. The word "a" or "an" preceding a component does not exclude the presence of a plurality of such components. The present application may be implemented by means of hardware comprising several different components and by means of a suitably programmed computer. In a unit claim enumerating several means, several of these means may be embodied by the same item of hardware. The use of the words first, second, and third etc. does not indicate any order. These words may be interpreted as names.

[0041] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of the features. In the description of this application, the meaning of "plurality" is two or more, unless otherwise clearly and specifically defined.

[0042] The present invention is described in detail below with reference to the accompanying drawings.

[0043] A design method of a high-speed motor rigid rotor system of the present invention, wherein the high-speed motor rigid rotor system has an electromagnetic bearing, comprises the following steps:

[0044] Establish the state space model of the high-speed motor rigid rotor system;

[0045] A quadratic cost function is established according to the state and control input of the high-speed motor rigid rotor system;

[0046] Solve the Riccati equation based on the state space model and performance index of the high-speed motor rigid rotor system to obtain the optimal state feedback matrix K;

[0047] The optimal control input signal u is calculated by the formula u=-KZ, where Z is the state feedback control rate;

[0048] The calculated optimal control input signal u is input into the system to realize the LQR controller.

[0049] The specific steps are as follows:

[0050] Step 1: Establish the state space model of the high-speed motor rigid rotor system based on active electromagnetic bearings (AMBs):

[0051] The rigid body translational modal single degree of freedom motion equation of the high-speed motor rigid rotor system based on active electromagnetic bearings (AMBs) is written as a state space equation:

[0052]

[0053] According to formula (1), we can get Figure 1 The LQR structure block diagram is shown.

[0054] LQR control belongs to negative feedback control, where y is the system output, x is the state variable, u is the linear quadratic optimal control quantity, and k is the optimal state feedback gain matrix.

[0055] make u=i xa , formula (1) can be further written as:

[0056]

[0057] Among them, a 11 =a 22 =b1=c 12 =0,a 12 =c 11 =1,a 21 =k s / m a ,b2=k i / m a ,x a and i xa are the rotor vibration and control current in the x direction at the A end of the electromagnetic bearing, k i and k s are the current stiffness coefficient and displacement stiffness coefficient of the electromagnetic bearing, m a is half the mass of the rotor.

[0058] Specifically, a 21 =k s / m a =33735,b2=k i / m a =21.3.

[0059] Take the rigid rotor vibration error e and the error change rate of the high-speed motor rigid rotor system based on electromagnetic bearings is a state variable, then the system state variable is:

[0060]

[0061] Among them, e reflects the steady-state performance, Reflects dynamic performance.

[0062] Step 2: Determine the performance index and define a performance index as a quadratic cost function of the state and control input:

[0063] The goal of LQR is to find a set of control variables u0, u1, ..., so that z0, z1, ..., are small enough, that is, the closed-loop system reaches a stable state, and u0, u1, ..., are also small enough, that is, the power amplifier current is as small as possible. The cost function is selected as:

[0064]

[0065] Where Q is a weighted matrix, which is semi-positive definite, and R is a positive definite matrix. Q represents the state weight in the control, R represents the control weight, and u is the control quantity corresponding to the state space equation of the high-speed motor rigid rotor system based on electromagnetic bearings with Z as the state variable.

[0066] Assuming that the rotor position reference input of the high-speed motor rigid rotor system based on electromagnetic bearing is r, and the eddy current displacement sensor output is y, the system error, error change rate and error change acceleration are expressed as:

[0067] z1=e=ry=rc 11 x1-c 12 x2=r-x1 (5)

[0068]

[0069]

[0070] And because x1=r-z1,a 22 =0, formula (7) is simplified to:

[0071]

[0072] According to equations (6) and (8), the state space expression of the high-speed motor rigid rotor system based on electromagnetic bearings constructed with error and error change rate as system state variables can be obtained as follows:

[0073]

[0074] Choose Q and R to be 2×2 and 1×1 matrices respectively, with Q usually being a positive semidefinite matrix and R being a positive definite matrix:

[0075]

[0076] Step 3: Solve the Riccati equation. According to the system model and performance indicators, the optimal state feedback matrix K can be calculated by solving the Riccati equation:

[0077] To solve K, first assume that there is a constant matrix P such that:

[0078]

[0079]

[0080] Because the closed-loop system is stable, that is, when t→∞, x(t)→0, the integral equation (11) can be solved directly, and the differential on the left side of equation (10) can be expanded to obtain:

[0081]

[0082] Simplified:

[0083] A T P+PA+Q+K T RK-K T B T P-PBK=0 (13)

[0084] Formula (13) is a quadratic form about K, and the solution process is relatively complicated. For the convenience of solution, let K = R -1 B T P, so that equation (13) can be simplified into a Riccati equation:

[0085] A T P+PA+Q-PBR -1 B T P=0 (14)

[0086] Although the quadratic form of K is omitted in formula (14), the value of K is related to P, so it is sufficient as long as the assumed P satisfies formula (14).

[0087] Step 4: Calculate the control input. The optimal control input can be calculated by using the state feedback control rate u=-KZ, where K is the state feedback matrix obtained by solving the Riccati equation:

[0088] Solving the Riccati equation using the matrix symbolic function method yields the quadratic optimal feedback matrix K, and the corresponding control quantity is:

[0089]

[0090] Also because

[0091]

[0092] Therefore, the control rate u of the high-speed motor rigid rotor system based on electromagnetic bearings is:

[0093]

[0094] The control rate u is given by equation (17).

[0095] A high-speed motor rigid rotor system with electromagnetic bearings is designed using the design method of the high-speed motor rigid rotor system and is constructed as follows: Figure 2 The rigid rotor system of a high-speed motor based on electromagnetic bearings based on an LQR controller is shown.

[0096] The sensor monitors the rotor position, speed, acceleration and other status information in real time, and feeds this information back to the controller. The controller processes and analyzes the sensor data, amplifies it through the power amplifier, and calculates the control signal to drive the AMBs system to generate sufficient electromagnetic force to make the rotor levitate and rotate without contact, achieving a frictionless and wear-free support method.

[0097] When the rotor displacement input signal r is a constant of 0, the feedforward part of the LQR controller loses its function, and the control effect of the entire controller depends only on k1 and k2, where the optimal feedback gain k = [k1, k2]. Moreover, k1 and k2 are similar to the proportional parameter P and differential parameter D in the PD controller. In other words, when the rotor displacement input signal of the high-speed motor rigid rotor system based on electromagnetic bearings is zero, the LQR controller is equivalent to the PD controller. When the rotor ends x A 、x B and A ,y B Directional rotor displacement and rotor reference position input r xA 、r xB and r yA 、r yB The difference is input into the controller. The proportional part calculates the difference between the current error and the set value and multiplies it by k1 to get an output signal. The differential part multiplies the change rate between the current error and the previous error by k2 to get another output signal. Finally, these two signals are added to get the final output control signal, and the control signal is input into the power amplifier to convert it into x A 、x B and A ,y B Direction of current i xa 、i xb and i ya 、i yb , and the disturbance current I d Together they are input into the electromagnetic bearing winding, thereby generating the corresponding electromagnetic force F xa 、F xband F ya 、F yb Keep the rotor in its specified position.

[0098] Depend on Figure 2 It can be seen that when the rotor displacement input signal r is a constant of 0, the feedforward part in the LQR controller loses its function, and the control effect of the entire controller depends only on k1 and k2. Moreover, k1 and k2 are similar to the proportional parameter P and differential parameter D in the PD controller. In other words, when the rotor displacement input signal of the high-speed motor rigid rotor system based on electromagnetic bearings is zero, the LQR controller is equivalent to the PD controller. So far, the LQR controller of the high-speed motor rigid rotor system based on electromagnetic bearings has been designed.

[0099] Step 5: Implement the controller, input the calculated control into the application system, implement the LQR controller, and qualitatively and quantitatively explore the influence of weighted arrays Q and R on k1 and k2 in the rigid rotor system of high-speed motor based on electromagnetic bearings, and then find out the parameter selection principle of LQR controller and its influence on the rotor vibration of the system:

[0100] Select Q 11 Gradually increases from 0 to 1×10 8 When comparing the experimental weights, Figure 3 The changes of elements k1 and k2 in the feedback matrix K are given, and four groups of optimal feedback matrices K are selected as shown in Table 1. It can be seen from Table 1 that although with the increase of Q 11 As the value increases, the rotor vibration gradually decreases.

[0101] Table 1

[0102] <![CDATA[Q 11 ]]> <![CDATA[2×10 7 ]]> <![CDATA[4×10 7 ]]> <![CDATA[6×10 7 ]]> <![CDATA[8×10 7 ]]> <![CDATA[k1]]> 6328.1 8103.7 9490.0 10667 <![CDATA[k2]]> 24.4 27.6 29.9 32

[0103] Select Q 22 When it increases gradually from 0 to 100, Figure 4 The changes of elements k1 and k2 in the feedback matrix K are given, and four groups of optimal feedback matrix K are selected as shown in Table 2. It can be seen from Table 2 that although with the increase of Q 22 increases, but k1 and k2 remain basically unchanged.

[0104] Table 2

[0105] <![CDATA[Q 22 ]]> 20 40 60 80 <![CDATA[k1]]> 5120.5 5120.5 5120.5 5120.5 <![CDATA[k2]]> 22.3 22.7 23.3 23.6

[0106] After the previous data analysis, in order to minimize the impact of noise on the system, Q 11 =1×10 -7 , Q 22=1, R=10, this set of LQR controller parameters is used to explore the vibration control of the rotor under floating and full speed operation. The corresponding k1 and k2 are 3456.9 and 18 respectively. In order to clearly reflect the control effect of LQR on rotor vibration, two vibration control methods, PID and PSC, are selected for comparison. The PID controller parameters P, I, and D are selected as 6400, 10000, and 3 respectively, and the polarity factor in the PSC controller is 0.0001.

[0107] Take the AMB-A end x direction and -B end x direction as an example, Figure 5 and Figure 6 A three-dimensional diagram of the rotor system vibration is given. It can be seen that the vibration at both ends of the rotor is almost completely suppressed under LQR control. This is because the damping introduced in the control system is too large. Figure 7 and Figure 8 The rotor vibration envelope is given, and it can be clearly seen that in the full speed range including rigid body translation and rigid body cone modes, the maximum rotor vibration under PID, PSC and LQR control is 3.6×10 -6 m, 2.4×10 -6 m and 0.8×10 -6 m, the rotor vibration under LQR control is very small, and there is no overshoot in the entire speed range.

[0108] When the LQR controller is used, the eigenvalue of the rigid closed-loop rotor system is a negative real number or the damping ratio is greater than 0.707. LQR control is not easy to implement for AMBs because overdamping will amplify the noise and interference of sensors, power amplifiers and other links, making the AMBs-rigid rotor system unable to work stably. However, LQR can be used as an external damper for the rigid rotor system of high-speed motors based on electromagnetic bearings.

[0109] It should be understood by those skilled in the art that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the present application can adopt the form of complete hardware embodiments, complete software embodiments, or embodiments in combination with software and hardware. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that contain computer-usable program code.

[0110] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0111] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0112] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0113] Unless otherwise specified, the working modes or control modes involved in the above embodiments are all conventional working modes or control modes in the art.

[0114] Although the preferred embodiments of the present application have been described, those skilled in the art may make other changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications falling within the scope of the present application.

[0115] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Other modifications or equivalent substitutions made to the technical solution of the present invention by ordinary technicians in the field should be included in the scope of the claims of the present invention as long as they do not depart from the spirit and scope of the technical solution of the present invention.

Claims

1. A design method for a high-speed motor rigid rotor system, wherein the high-speed motor rigid rotor system has an electromagnetic bearing, characterized in that: The following steps are involved: S1: Establish the state space model of the high-speed motor rigid rotor system; the state space model of the high-speed motor rigid rotor system is: in, A is the coefficient matrix of the state variables, B is the coefficient matrix of the input variables, C is the output matrix, D is the system feedback matrix, y is the system output, x is the state variable, and u is the linear quadratic optimal control quantity; , , which can be further written as: in, a 11 = a 22 = b 1= c 12 =0, a 12 = c 11 =1, a 21 = k s / m a , b 2= k i / m a , x a and i xa The A end of the electromagnetic bearing x Directional rotor vibration and control current, k i and k s are the current stiffness coefficient and displacement stiffness coefficient of the electromagnetic bearing respectively, m a is half of the rotor mass; S2: Establish a quadratic cost function based on the state and control input of the high-speed motor rigid rotor system; The cost function is: In the formula, Q is the state weight matrix in control, R is the control weight matrix, It is the control quantity corresponding to the state space equation of the high-speed motor rigid rotor system based on electromagnetic bearings with Z as the state variable, and Z is the system state variable of the state space model; S3: Solve the Riccati equation based on the state space model and performance index of the high-speed motor rigid rotor system to obtain the optimal state feedback matrix K; the Riccati equation is Among them, Q is the state weight matrix in control, R is the control weight matrix, P is the constant matrix, A is the coefficient matrix of the state variables, B is the coefficient matrix of the input variables; ; S4: The optimal control input signal u is calculated by the formula u=-KZ, where K is the state feedback matrix obtained by solving the Riccati equation; the control rate of the optimal state feedback matrix K is: Where u is the control rate, e is the rigid rotor vibration error, is the rate of change of error, r is the rotor equilibrium position, k 1 and k 2 are e and The control coefficient of S5: Input the calculated optimal control input signal u into the system.

2. The design method of a high-speed motor rigid rotor system according to claim 1, characterized in that: The system state variables of the state space model , where e is the rigid rotor vibration error, is the rate of change of error.

3. The design method of a high-speed motor rigid rotor system according to claim 1, characterized in that: Q is a 2nd-order matrix, R is a 1st-order matrix, .

4. The design method of a high-speed motor rigid rotor system according to claim 3, characterized in that: Select Q 11 =1×10 -7 , Q 22 =1, R= 10.

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