PD parameter self-tuning method and system for magnetic bearing system

Abstract

Disclosed are a PD parameter self-tuning method and system for a magnetic bearing system. The method comprises: determining initial values of P and D parameters of each degree of freedom of a magnetic bearing system, and taking the minimization of the normalized area of displacement per unit time and zero collisions per unit time as optimization objectives; and on the basis of the optimization objectives, establishing a self-tuning algorithm executed in parallel by an empirical compensator and a heuristic algorithm, and performing self-tuning on the P and D parameters of the magnetic bearing system, wherein the empirical compensator and the heuristic algorithm each take the optimization objectives as an input and the correction amounts of the P and D parameters as an output. The PD parameter self-tuning method for a magnetic bearing system can be applied to a magnetic bearing system with unknown parameters, is not restricted by the degree of freedom of a magnetic bearing, achieves easy acquisition of an evaluation index, and has the characteristics of not requiring priori knowledge, wide applicability, capability of online application, etc.

Description

A PD parameter self-tuning method and system for magnetic bearing system

Technical field

[0001] The present invention belongs to the field of magnetic bearing control, and more specifically, relates to a proportional-differential (PD) parameter self-tuning method and system for a magnetic bearing system. [Background Technology]

[0002] Magnetic bearings utilize electromagnetic force to levitate the rotor, enabling contactless operation between the rotor and stator. Magnetic bearings are frictionless, pollution-free, and have a long lifespan. They are suitable for high-speed and ultra-high-speed applications, as well as high-performance transmissions requiring contactless, lubricant-free, and pollution-free operation.

[0003] Magnetic bearings usually use proportional-integral-differential (PID) controllers for their displacement control. However, due to the physical characteristics of magnetic bearings, they are inherently open-loop unstable; they are difficult to process, have strong nonlinearity, and there is a large difference between actual parameters and design parameters; they have many degrees of freedom, usually more than 4. This makes it impossible to use the frequency domain method in classical control theory for parameter design of magnetic bearings. The parameters of the PID controller are difficult to select, and experienced engineers need to spend a lot of time to adjust them, which limits the use scenarios and usage thresholds of magnetic bearings. [Summary of the invention]

[0004] In response to the shortcomings of the prior art, the purpose of the present invention is to propose a proportional-differential (PD) parameter self-tuning method for a magnetic bearing system, aiming to accelerate the on-site parameter adjustment process of a magnetic bearing system that actually uses proportional-integral-differential (PID) displacement control, lower the usage threshold of the magnetic bearing system, and solve the problem of position closed-loop control parameter design under open-loop instability conditions of the magnetic bearing.

[0005] To achieve the above-mentioned objectives, the present invention provides a PD parameter self-tuning method for a magnetic bearing system, which determines the suspension performance evaluation index, optimization target and optimization object of the magnetic bearing system with PID displacement control; based on the optimization target and optimization object, a parameter self-tuning algorithm is established in which an empirical compensator and a heuristic algorithm are executed in parallel; a method for determining the starting point of the parameters at the beginning of self-tuning is provided; and a system protection method during the self-tuning process is provided, and the protection method does not affect the self-tuning process.

[0006] The present invention provides a PD parameter self-tuning method for a magnetic bearing system, wherein the magnetic bearing system uses PID displacement control, comprising:

[0007] (1) Determine the initial values ​​of the P and D parameters of each degree of freedom of the magnetic bearing system, with the optimization objectives of minimizing the normalized area per unit time of displacement and achieving zero collisions per unit time;

[0008] (2) Based on the optimization objective, a parameter self-tuning algorithm is established in which the empirical compensator and the heuristic algorithm are executed in parallel to self-tune the P and D parameters of the magnetic bearing system; wherein, both the empirical compensator and the heuristic algorithm take the optimization objective as input and the correction amount of the P parameter and the D parameter as output.

[0009] (3) The PD self-tuning algorithm continues to run until the magnetic bearing system can stably suspend the rotor.

[0010] During the tuning process, if a set of parameters causes the magnetic bearing system's collision count per unit time to exceed an upper threshold, the system immediately switches to the next set of parameters to prevent magnetic bearing system failure. Because the optimization targets are all based on a per-unit-time basis, the protection process does not require interrupting the auto-tuning process.

[0011] Among them, the evaluation indicators of the suspension performance of the PID-controlled magnetic bearing system include the normalized area per unit time of displacement and the number of collisions per unit time. * Refers to:

[0012] Among them, -X p ~+X p is the displacement range of the magnetic bearing in this degree of freedom, N s is the number of sampling points for a single set of parameters during the self-tuning process, and x(n) is the distance from the center reference point of the rotor offset for the nth sampling point at each moment. The total number of collisions per unit time is:

[0013] Number of collisions per unit time = total number of collisions / single set parameter sampling time

[0014] The sampling time of a single set of parameters refers to the time it takes to record the displacement when the PID controller uses the current parameters. The statistical method for the total number of collisions is to assume that the displacement range of the degree of freedom is -X p ~+X p The distance of the rotor offset from the center reference point is greater than aX p or less than -aX p , a is a number greater than 0 and less than 1, the total number of collisions increases by one.

[0015] Based on the aforementioned evaluation criteria, the optimization objectives of this self-tuning method are to minimize the normalized area per unit time and to minimize the number of collisions per unit time. The optimization targets are the P and D parameters for each degree of freedom of the magnetic bearing system using PID displacement control. The I parameter is not optimized because it does not directly affect the performance of the magnetic bearing.

[0016] The present invention proposes a PD parameter self-tuning method for a magnetic levitation bearing system, which has a specific structure of a PD parameter self-tuning method that combines an empirical compensator with a heuristic algorithm in parallel, wherein the rules of the empirical compensator are as follows: when the number of collisions per unit time is 0, the P and D parameters are not affected; when the number of collisions per unit time is 1, the D parameter is reduced; when the number of collisions per unit time is small but not 0 or 1, the P parameter is increased; when the number of collisions per unit time is large, the P parameter is reduced; and in other cases, the P and D parameters are increased simultaneously.

[0017] The steps of the heuristic algorithm are as follows: in the same round of iteration, the P and D parameters of all parameter groups are applied to the magnetic levitation bearing system, and the normalized area per unit time of each group during its operation and sampling time is counted. Each degree of freedom should have multiple P and D parameter combinations; according to the normalized area per unit time, all parameter groups move toward the group of parameters with the smallest normalized area per unit time, and at the same time, all parameter groups move away from the group of parameters with the largest normalized area per unit time; except for the group of parameters with the smallest normalized area per unit time, all other parameter groups are randomly changed within a smaller range; and the correction values ​​of the P and D parameters are output according to the above rules.

[0018] The parameters output by the experience compensator and the heuristic algorithm are combined before starting a new round of iterations to achieve the purpose of parallel execution of the two.

[0019] The heuristic algorithm requires a set of initial value parameters for each degree of freedom. The method for determining the initial value parameters is as follows.

[0020] Two different differential control currents are injected into a single-degree-of-freedom winding, allowing it to run from one end to the other. The displacement during the process is recorded. The two sets of data can be used to solve the following two-variable linear equation:

[0021] Among them, x1 and x2 are the displacements obtained twice, T s is the sampling time, N is the number of sampling points, m is the weight of the rotor; k i is the unknown number 1, which is called the force / current coefficient; k x The unknown number 2 is called the force / displacement coefficient.

[0022] Thus, the starting parameter of this degree of freedom can be obtained as K P0 With KD0 , the calculation method is:

[0023] Based on the initial value of parameter K P0 With K D0 By randomly selecting parameters in a smaller range, the parameter group for the start of self-tuning of the degree of freedom can be obtained.

[0024] During the auto-tuning process, the number of rotor collisions is monitored in real time. If a parameter set is unstable and high-frequency rotor collisions are detected, the system immediately switches to the next parameter set. Since the evaluation metrics used in auto-tuning are all per unit time, data acquisition during the auto-tuning process is not affected. Furthermore, since the tuning of each degree of freedom is independent of each other, the proposed method can be applied to magnetic bearing systems with any degree of freedom.

[0025] The present invention also provides a PD parameter self-tuning system for a magnetic bearing system, comprising: a computer-readable storage medium and a processor;

[0026] The computer-readable storage medium is used to store executable instructions;

[0027] The processor is used to read the executable instructions stored in the computer-readable storage medium and execute the above-mentioned PD parameter self-tuning method for the magnetic bearing system.

[0028] In general, the above technical solutions conceived by the present invention can achieve the following beneficial effects compared with the prior art:

[0029] (1) The method proposed in the present invention can realize the self-tuning of the P and D parameters of the magnetic bearing system using PID displacement control, and provides a method for determining the self-tuning starting point parameters. It can also be used for magnetic bearing systems with unknown parameters, thereby lowering the threshold for the use of magnetic bearings.

[0030] (2) The method proposed in the present invention also includes a method for dealing with instability during the self-tuning process, and will not affect the normal progress of the self-tuning process, and is suitable for application in actual engineering.

Brief Description of the Drawings

[0031] FIG1 is a control block diagram of a magnetic bearing system applicable to an embodiment of the present invention.

[0032] FIG2 shows the insertion position of an example of the present invention in a control block diagram of a magnetic bearing system to which the present invention is applicable.

[0033] FIG3 is a flowchart of an algorithm in actual application of an example of the present invention. [Specific implementation method]

[0034] In order to make the objectives, technical solutions, and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined and reordered as long as they do not conflict with each other.

[0035] The present invention provides a PD parameter self-tuning method for a magnetic bearing system, wherein the magnetic bearing system uses PID displacement control, comprising:

[0036] (1) Determine the initial values ​​of the P and D parameters of each degree of freedom of the magnetic bearing system, with the optimization objectives of minimizing the normalized area per unit time of displacement and achieving zero collisions per unit time;

[0037] (2) Based on the optimization objective, a parameter self-tuning algorithm is established in which the empirical compensator and the heuristic algorithm are executed in parallel to self-tune the P and D parameters of the magnetic bearing system; wherein, both the empirical compensator and the heuristic algorithm take the optimization objective as input and the correction amount of the P parameter and the D parameter as output.

[0038] (3) The PD self-tuning algorithm continues to run until the magnetic bearing system can stably suspend the rotor.

[0039] Figure 1 shows a system block diagram of a magnetic bearing. Its displacement control section uses a PID controller. The PID controller's input is the reference position signal minus the displacement feedback signal from the displacement sensor, and its output is a command current signal. This command current signal enters a current controller, which drives a power amplifier, which converts the command current signal into actual winding current for control. This type of magnetic bearing control system can utilize the algorithm of the present invention.

[0040] Figure 2 shows the position where the self-tuning algorithm proposed in the present invention is inserted into the magnetic bearing control system. The self-tuning algorithm of the present invention requires the system to input a displacement signal, and it outputs P and D control parameters and is applied to the PID displacement controller of the magnetic bearing system.

[0041] Figure 3 shows a flow chart of the self-tuning algorithm proposed in the present invention. In practical applications, the self-tuning algorithm proposed in the present invention can follow the process shown in Figure 3, or the calculation process can be adjusted to suit the controller. The process steps shown in Figure 3 are as follows.

[0042] The first step is to inject two different differential control currents into the winding with a single degree of freedom, so that it can run from one end to the other, and record the displacement during the process. The two sets of data are used to solve and estimate the force / displacement parameter k iand force / current parameter k x The linear equation of two variables:

[0043] Among them, x1 and x2 are the displacements obtained twice, T s is the sampling time, N is the number of sampling points, and m is the weight of the rotor. The starting parameter of this degree of freedom is K P0 With K D0 , the calculation method is:

[0044] Based on the starting parameter K P0 With K D0 By randomly selecting parameters in a smaller range, the parameter group for the start of self-tuning of the degree of freedom can be obtained.

[0045] In the second step, starting from the first set of parameters in the starting parameter group, they are applied to the magnetic bearing system in sequence, and the displacement during the process is recorded to obtain the number of collisions per unit time and the normalized area per unit time until all the parameters in the starting parameter group are applied.

[0046] The third step is to determine whether the system has converged and entered a stable suspension state. If it has entered a stable suspension state, the self-tuning ends; otherwise, proceed to the next step.

[0047] In the fourth step, based on the previously obtained number of collisions per unit time and normalized area per unit time, the parameter group is adjusted using the experience compensator and heuristic algorithm to obtain a new set of parameters.

[0048] The rules of the experience compensator are as follows: when the number of collisions per unit time is 0, the P and D parameters are not affected; when the number of collisions per unit time is 1, the D parameter is reduced; when the number of collisions per unit time is small (single digit) but not 0 or 1, the P parameter is increased; when the number of collisions per unit time is large (three digits or more), the P parameter is reduced; in all other cases, the P and D parameters are increased at the same time.

[0049] The steps of the heuristic algorithm are as follows: in the same round of iteration, the P and D parameters of all parameter groups are applied to the magnetic bearing system, and the normalized area per unit time of each group during its operation and sampling time is counted. Each degree of freedom should have multiple P and D parameter combinations; according to the normalized area per unit time, all parameter groups move toward the group of parameters with the smallest normalized area per unit time, and at the same time, all parameter groups move away from the group of parameters with the largest normalized area per unit time; except for the group of parameters with the smallest normalized area per unit time, all other parameter groups are randomly changed within a smaller range; and a new round of iteration is started until the magnetic bearing can operate stably.

[0050] In the fifth step, a new round of iteration is started based on the new parameter set obtained in the fourth step, and then the process returns to the first step.

[0051] The collision count statistics are always running, and the displacement collision count is counted in real time. If the displacement collision count is large, it will immediately switch to the next set of parameters to obtain the current collision count per unit time and the normalized area per unit time, and continue to run the self-tuning algorithm.

[0052] After obtaining the parameters that can support the stable suspension of the magnetic bearing system, the magnetic bearing system enters a closed-loop stable state, and the system can be swept or other model fitting can be performed for further analysis and optimization design.

[0053] It will be easily understood by those skilled in the art that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A PD parameter self-tuning method for a magnetic bearing system, wherein the magnetic bearing system uses PID displacement control, characterized in that: include: (1) Determine the initial values ​​of the P and D parameters of each degree of freedom of the magnetic bearing system, with the optimization objectives of minimizing the normalized area per unit time of displacement and achieving zero collisions per unit time; (2) Based on the optimization objective, a parameter self-tuning algorithm is established in which the empirical compensator and the heuristic algorithm are executed in parallel to self-tune the P and D parameters of the magnetic bearing system; wherein both the empirical compensator and the heuristic algorithm take the optimization objective as input and the correction amount of the P parameter and the D parameter as output.

2. According to the PD parameter self-tuning method for a magnetic bearing system according to claim 1, if a certain set of parameters causes the number of collisions per unit time of the magnetic bearing system to exceed the upper limit threshold, the next set of parameters is immediately switched to avoid failure of the magnetic bearing system.

3. The PD parameter self-tuning method for a magnetic bearing system according to claim 2, characterized in that: The normalized area per unit time of displacement is: Among them, the displacement range of this degree of freedom of the magnetic bearing is -X p ~+X p , the number of sampling points of a single group of parameters during the self-tuning process is N s At each moment, the distance that the rotor of this degree of freedom deviates from the center reference point is x(n).

4. The PD parameter self-tuning method for a magnetic bearing system according to claim 2, characterized in that: The number of collisions per unit time refers to: Number of collisions per unit time = total number of collisions / single set parameter sampling time Among them, the sampling time of a single set of parameters refers to the time when the PID controller uses the current parameters to record the displacement; the statistical method for the total number of collisions is to assume that the displacement range of the degree of freedom is -X p ~+X p If the distance of the rotor deviation center reference point of this degree of freedom is greater than the upper threshold or less than the lower threshold, the total number of collisions increases by one.

5. According to the PD parameter self-tuning method for a magnetic bearing system according to claim 1, the empirical compensator is: When the number of collisions per unit time is 0, the P and D parameters are not affected; when the number of collisions per unit time is 1, the D parameter is reduced; when the number of collisions per unit time is less than the preset value but not 0 or 1, the P parameter is increased; when the number of collisions per unit time is not less than the preset value, the P parameter is reduced; in other cases, both the P and D parameters are increased.

6. The PD parameter self-tuning method for a magnetic bearing system according to claim 1, wherein the heuristic algorithm is: In the same round of iteration, the P and D parameters of all parameter groups are applied to the magnetic bearing system, and the normalized area per unit time of each group during its operation and sampling time is counted. Each degree of freedom should have multiple P and D parameter combinations. According to the normalized area per unit time, all parameter groups move toward the group of parameters with the smallest normalized area per unit time, and at the same time, all parameter groups move away from the group of parameters with the largest normalized area per unit time; Except for the set of parameters with the smallest normalized area per unit time, all other parameter sets are randomly changed within the preset range; Output the P and D parameter correction values ​​according to the above rules.

7. According to the PD parameter self-tuning method for a magnetic bearing system described in claim 6, before the start of a new round of iteration, the P and D parameter corrections output by the empirical compensator and the heuristic algorithm are added, the parameters are updated, and applied to the PID controller until the magnetic bearing can operate stably.

8. According to the PD parameter self-tuning method for a magnetic bearing system of claim 1, determining the initial values ​​of the P and D parameters of each degree of freedom of the magnetic bearing system comprises: injecting two different differential control currents into a winding of a single degree of freedom, causing it to run from one end to the other, and recording the displacement during the process. The two sets of data are used to solve the following two-variable linear equation: in, x1 and x2 are the displacements obtained twice, T s is the sampling time, N is the number of sampling points, m is the weight of the rotor; k i is the unknown number 1, which is called the force / current coefficient; k x is the unknown number 2, which is called the force / displacement coefficient; Thus, the initial value of the parameter of this degree of freedom is K P0 With K D0 , the calculation method is: From the initial value of parameter K P0 With K D0 , randomly fluctuates within the preset range, and the parameter group at the beginning of the self-tuning of this degree of freedom is obtained.

9. A PD parameter self-tuning system for a magnetic bearing system, characterized in that: include: Computer-readable storage media and processor; The computer-readable storage medium is used to store executable instructions; The processor is used to read the executable instructions stored in the computer-readable storage medium and execute the PD parameter self-tuning method for a magnetic bearing system according to any one of claims 1 to 8.

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