Multi-parameter Optimization Control System and Control Method for Dynamic Electromagnetic Loading Force of Water Lubricated Bearings

Abstract

The invention discloses a dynamic electromagnetic loading force control system for a water-lubricated bearing, which includes a pair of non-contact electromagnetic loading devices, a load device driver, an eddy current sensor, a torque and speed sensor, a piezoresistive force sensor, a load controller, and a current regulator. The load controller is connected to a database stored in the server hard disk. The invention has a higher control effect in the case of long-term operation. The invention also discloses a multi-parameter optimization control method for the dynamic electromagnetic loading force of a water-lubricated bearing. By reading the data collected under actual operation, using the path planning algorithm and the sliding mode control algorithm, and calculating the correction value of the coordinates and designing the form of the sliding mode surface, the effective value of the output current is obtained, which ensures the control accuracy, reduces the overshoot, and stabilizes the dynamic performance of the load system.

Description

Technical Field

[0001] The present invention belongs to the technical field of mechanical equipment condition monitoring, and specifically relates to a multi-parameter optimization control system for the dynamic electromagnetic loading force of a water-lubricated bearing, and also relates to a multi-parameter optimization control method for the dynamic electromagnetic loading force of a water-lubricated bearing. Background Art

[0002] Electromagnetic loading devices have been gradually widely used in the condition monitoring of mechanical equipment. Electromagnetic loading devices can provide non-contact loads. Compared with contact-type non-contact electromagnetic loading devices, they avoid problems such as friction and vibration, and have better application effects. During the process of dynamically applying electromagnetic loading force by the electromagnetic loading device, the loading force will be unstable due to factors such as shaft system speed, shaft center displacement, and magnetic field change, which has a great impact on load simulation and even bearing test experiments, and is a thorny problem currently faced. Therefore, it is of great significance and engineering application value to accurately control the dynamic electromagnetic loading force.

[0003] The invention patent with the application number CN201911147320.9 provides a control method and device for identifying and re-suspending the circumferential fall trajectory of a magnetic suspension, and proposes to identify the trajectory response by detecting the radial displacement of the shaft system and the expectation of the instantaneous frequency obtained by Hilbert transform.

[0004] The invention patent with the application number CN201710471181.X proposes a controller for controlling an active magnetic suspension bearing system and its control method, and proposes to control the current in two coils in a pair of active magnetic suspension bearings respectively through a three-stage cascade control structure and by introducing a single-layer neural network regulator.

[0005] The above patents propose methods for allowing the shaft system to re-enter stability when the shaft system has a radial displacement, but do not solve the problem of how to stabilize the loading force when the shaft system has a radial displacement in a certain direction. Summary of the Invention

[0006] The purpose of the present invention is to provide a control system for the dynamic electromagnetic loading force of a water-lubricated bearing, which has a higher control effect in terms of accuracy during long-term operation, and has a shorter adjustment time than a single control algorithm in different mutation situations.

[0007] Another purpose of the present invention is to provide a multi-parameter optimization control method for the dynamic electromagnetic loading force of a water-lubricated bearing, which ensures the control accuracy while reducing the overshoot and stabilizing the dynamic performance of the load system.

[0008] The technical solution adopted by the present invention is a dynamic electromagnetic loading force control system for a water-lubricated bearing, which includes a pair of non-contact electromagnetic loading devices respectively arranged at both ends of the bearing spindle. The non-contact electromagnetic loading device is connected to a load device driver. Eddy current sensors are also arranged at both ends of the bearing spindle, and a torque and speed sensor is arranged near the motor end of the bearing spindle. A piezoresistive force sensor is arranged at the bottom of the non-contact electromagnetic loading device. The eddy current sensor, the torque and speed sensor, and the piezoresistive force sensor are connected to a load controller. The load controller is connected to a database stored in the server hard disk. The load controller is also connected to a current regulator, and the current regulator is in turn connected to the load device driver.

[0009] The characteristics of the present invention also lie in that

[0010] The load controller is a three-dimensional path tracking controller;

[0011] The current regulator is a sliding mode controller;

[0012] The database is an Oracle database.

[0013] Another technical solution adopted by the present invention is a multi-parameter optimization control method for the dynamic electromagnetic loading force of a water-lubricated bearing. The dynamic electromagnetic loading force control system of the present invention is used for electromagnetic loading force control. A target loading force is set, and the readings of the torque and speed sensor, the piezoresistive force sensor, two pairs of eddy current sensors, and the load system controller are collected and the signals are transmitted to the load controller. The load controller reads the sensor readings and performs mean processing respectively to obtain the average measured value of the loading force of the piezoresistive force sensor signal The average measured value of the exciting current of the current sensor signal The average measured value of the rotational speed of the torque and speed sensor signal It is judged whether the non-contact electromagnetic loading force matches the set value. If it matches, the above process is continued for each sensor. If it does not match, the sensor signals after mean processing are used as query conditions to preprocess the database. After preprocessing, a data block is obtained. The load controller adopts a three-dimensional data path tracking algorithm optimized by a genetic algorithm, reads the data block and calculates to obtain the reference current I r , and the reference current I r is input into the current regulator. The current regulator uses a sliding mode algorithm to calculate the control output current I smc , and is input into the load device driver to control the electromagnetic loading force F of the non-contact electromagnetic loading device of the water-lubricated bearing, so as to achieve the purpose of improving the accuracy of the electromagnetic loading force and the robustness under different working conditions.

[0014] The characteristics of the present invention also lie in that

[0015] Calculate the average measured value of the axial center distance of the eddy current sensor signal within the sampling period The calculation formula is as follows:

[0016]

[0017] In formula (1), k is the number of points collected within one sampling period, x r (i) is the value of the axial center distance in all horizontal directions collected by the eddy current sensor installed horizontally within one sampling period, y r (i) is the value of the axial center distance in all vertical directions collected by the eddy current sensor installed vertically within one sampling period, and δ(i) is the value of the axial center distance without direction collected within one sampling period;

[0018] Calculate the average value of the loading force measured by the piezoresistive force sensor signal within the sampling period The calculation formula is as follows:

[0019]

[0020] In formula (2), k is the number of points collected within one sampling period, and F(i) is the value of all loading forces collected within one sampling period;

[0021] Calculate the average value of the exciting current measured by the current sensor signal within the sampling period The calculation formula is as follows:

[0022]

[0023] In formula (3), k is the number of points collected within one sampling period, and I e (i) is the value of all exciting currents collected within one sampling period;

[0024] Calculate the average value of the rotational speed measured by the torque & rotational speed sensor signal within the sampling period The calculation formula is as follows:

[0025]

[0026] In formula (4), k is the number of points collected within one sampling period, and n(i) is the value of all rotational speeds collected within one sampling period;

[0027] By comparing the average value of the electromagnetic loading force measured by the non-contact electromagnetic loading device within the sampling period with the threshold F 0 *ε 1 to determine whether the non-contact electromagnetic loading force matches the set value, the discrimination formula is as follows:

[0028]

[0029] is the measured average value of the electromagnetic loading force, F 0 is the target electromagnetic loading force, ε 1 is the electromagnetic force fluctuation threshold.

[0030] The database consists of a data storage end, a pre-called data area, multiple processing processes, a user process, a server process, and a backup log file. The data storage end includes: a data table space composed of actual test data, a parameter table space composed of optimization parameters, and a shared pool composed of call statements, table headers, table descriptions, etc.;

[0031] The data table space composed of actual test data is composed of a test data table and a data index segment. The test data table stores the test data of the electromagnetic loading force F measured actually at different axial center distances δ, different rotational speeds n, and different excitation currents I. Taking the axial center distance δ as the primary query condition, the test data table is divided into three-dimensional data tables under different axial center distances. These three-dimensional data tables are all composed of three-dimensional data composed of the rotational speed n, the excitation current I, and the electromagnetic loading force F;

[0032] The three-dimensional data table is subdivided into multiple data blocks according to the rotational speed range, the excitation current range, and the loading force range. Among them, the axial center distance δ is the primary query condition, the loading force interval is the secondary query condition, and the rotational speed interval and the excitation current interval are the tertiary query conditions. The data index segment is composed of index keywords, and the index keywords are composed of the primary query condition, the secondary query condition, and the tertiary query condition;

[0033] The parameter table space is composed of an optimization parameter table and a parameter index segment. The optimization parameter table stores each optimization parameter, such as the maximum step size λ max , the maximum viewing distance s max , the step size gain coefficient K, the curve path weight ζ 1 , ζ 2 , ζ 3 , η 1 , η 2 , η 3 , and are stored in a data table in the form of a stack respectively with the category as the primary query condition.

[0034] Specifically, preprocessing the database to obtain data blocks means

[0035] Issuing a call instruction, first querying with the average value of the axial center distance as the primary query condition to specify the data table space; with the average value of the current loading force as the secondary query condition, after specifying the data area, querying whether the value of the loading force F at the target coordinate point is located in this data area. If it is located in this data area, then this data area is the pre-called data area. If it is not located in this data area, then call the target loading force F to the average value of the current loading force All data areas constitute the pre-call data area; through the current operating condition speed and the excitation current As the three-level query conditions, specify a data segment in the pre-call data area, read the data segment and put it into the local data located in the pre-call data area together with the index segment to obtain the preprocessed data block, waiting for the load controller to read.

[0036] The load controller adopts a three-dimensional data path tracking algorithm optimized by a genetic algorithm, which consists of a global path planning layer, a local path planning layer, a path reconstruction layer, and a behavior execution layer. Specifically,

[0037] The load controller initializes, wakes up the database, and reads the center distance shaft speed excitation current loading force input value, call the data segment of the local data stored in the pre-call data area, enter the global path planning layer, establish a three-dimensional map, determine the current input value coordinate point and the target value coordinate point, and plan the global path; enter the local path planning layer, add constraint conditions, and find the optimal path in the global path; enter the behavior execution layer, read the optimal path, judge whether to use the point-to-point tracking method or the point-to-line tracking method, and optimize them with the simulated annealing algorithm and the particle swarm algorithm respectively. Calculate the reference current I according to the coordinate change value of the excitation current r , and the reference current I r is output to the current controller;

[0038] At the same time, continuously judge whether the average value of the center distance changes. If it changes, enter the path reconstruction layer, replace the table space in the database, no longer perform indexing, directly call the specified data segment in the table space, enter the local path planning layer again, perform path re-planning, add constraint conditions, and find the optimal path in the global path; enter the behavior execution layer, read the optimal path, select the optimal path and determine the path tracking method, and calculate the reference current I according to the coordinate change value of the excitation current r .

[0039] The local path planning layer, as the local planning part of the three-dimensional data path tracking algorithm, receives the local map information generated by the global map from the three-dimensional coordinates of the electromagnetic loading force under the current operating condition to the three-dimensional coordinates of the target electromagnetic loading force, adds constraint conditions to select the local optimal path, and the obtained optimal path is stored in the specified data block of the database for convenient real-time update. Specifically,

[0040] Call three low-order curve path weights ζ stored in the database 1 , ζ 2 , ζ 3 and three high-order curve path weights η 1, η 2 , η 3 , read the three-dimensional data map, confirm the current coordinates and the target coordinates, calculate the electromagnetic loading force error e, and make the following judgments based on this error:

[0041] Whether the error e is within 30% of the target electromagnetic force. If the error is less than 30% of the target electromagnetic force, determine the weight ζ of the low-order curve path 1 as parameter 1; otherwise, determine the weight η of the high-order curve path 1 as parameter 1; whether there are discontinuous points on the three-dimensional data map, judged by whether the derivative is continuous. If there are discontinuous points, determine the weight ζ of the low-order curve path 2 as parameter 2; otherwise, determine the weight η of the high-order curve path 2 as parameter 2; whether a slight change in the working condition is allowed, and the control system accuracy is within the range of the target value ±2% to ±5%. If the speed fluctuation is within the control system accuracy when the optimal path is a low-order curve, determine the weight η of the low-order curve path 3 as parameter 3; otherwise, determine the weight η of the high-order curve path 3 as parameter 3;

[0042] Integrate the path weights ζ 1 , ζ 2 , ζ 3 , η 1 , η 2 , η 3 , the selected path weights are iteratively optimized through the genetic algorithm, adjust the parameters, and sum the weights ζ of the low-order curve paths 1 , ζ 2 , ζ 3 to obtain the total weight ζ of the low-order curve path, and the weights η of the high-order curve paths 1 , η 2 , η 3 to obtain the total weight η of the high-order curve path;

[0043] If ζ is greater than η, it is determined to search for the optimal low-order curve path group; otherwise, it is determined to search for the optimal high-order curve path group, and calculate the weight difference Δ = |η - ζ|, and adjust the weight difference threshold Δ through the genetic algorithm * , to judge whether to select the relatively higher-order or relatively lower-order one in the optimal curve group, and the judgment conditions are as follows:

[0044]

[0045] The optimal high-order curve path group is selected using the D*Lite path search algorithm, while the optimal low-order curve path group is selected using the Dijkstra algorithm.

[0046] Enter the behavior execution layer, read the optimal path, determine whether to use the point-to-point tracking method or the point-to-line tracking method, and optimize them using the simulated annealing algorithm and the particle swarm optimization algorithm respectively. Calculate the reference current I based on the change value of the excitation current coordinates r Specifically,

[0047] Read the line-of-sight s, maximum line-of-sight s max from the database, step size λ, maximum step size λ max and step size gain coefficient K, as well as the optimal path L obtained from the local path planning layer, and determine whether the order m of the optimal path L is greater than 2;

[0048] If m>2, then select the point-to-line tracking method. The process of this method is as follows: Judge the relationship between the current signal error e and the maximum line-of-sight s max ; if e<s max , then select the forward point on the optimal path with the maximum step size λ max ; if e>s max , that is, the target point can be "seen" at this time. At this time, the step size gain coefficient K is corrected according to the size of the error e through the particle swarm optimization algorithm, and the product of the corrected step size gain coefficient and the maximum step size λ max is calculated to obtain the step size λ, so as to select the forward point on the optimal path. When reaching the point before the target point, the step size λ should be 0; if there are discontinuous points within the step size λ, then use the discontinuous points as the forward points and perform path tracking in segments; obtain the excitation current coordinates of each step, and calculate the respective reference current I rn for each step, and gradually reach the final reference current I r ;

[0049] If m<2, then select the point-to-point tracking method. The process of this method is as follows: Adjust the number of segmentation points q through the particle swarm optimization algorithm according to the size of the current signal error e; according to the number of segmentation points q, divide the optimal low-order curve into the current point A, intermediate points A 1 , A 2 , …, A q , and the target point B; set the intermediate point A 1 as the next target point, confirm the correction value of the excitation current coordinates, and calculate the reference current I r1 ; perform point by point to obtain the reference currents I r2 , I r3 , …, I rq respectively, and finally obtain the reference current I r of the target point.

[0050] The current controller is a sliding mode controller and is designed based on the following mathematical model:

[0051]

[0052] In Equation (5), R is the outer radius of the loading disk, is the thickness of the loading disk, and μ 0 is the vacuum permeability, N is the number of turns of the coil, I is the excitation current, l is the air-gap length, n is the harmonic order, and v x is the linear velocity of the loading disk;

[0053] The sliding-mode variable s of the sliding-mode controller is selected as:

[0054]

[0055] In Equation (6), c is the speed of adjusting the error, and the current signal error e = I r -I e ,

[0056] The sliding-mode controller is designed by using the reaching law, and the reaching law is:

[0057]

[0058] In Equation (7), k s and γ are both positive constants, and sgn(s) is the sign function;

[0059] The control output current I of the sliding-mode controller is calculated as smc follows:

[0060] I smc = ce + k s + γsgn(s) (8).

[0061] The beneficial effects of the present invention are:

[0062] The dynamic electromagnetic loading force control system of the water-lubricated bearing of the present invention has a higher control accuracy in the case of long-term operation compared with the control system of traditional single control algorithms, and has a shorter adjustment time than the single control algorithm in different mutation cases; a database is used to store a large amount of test data and optimized parameters, which can not only view historical data, but also correct non-contact electromagnetic loading devices with different structures, expanding the application range; the query method of the table space is designed to directly call the specified data segment when switching the table space, simplifying the query steps and saving time and memory; during the movement of the shafting, the air gap changes continuously, and the design of the database ensures the sensitivity and response speed of the control system during the dynamic operation of the shafting; and the database adopts the Oracle form, and one of its characteristics is the lock mechanism strategy, that is, the write operation of parameters will not block the read operation, which means that during the real-time operation, the internal parameters of the database can be reasonably corrected through an optimization algorithm, thereby continuously improving the control accuracy, robustness under complex working conditions, and adaptability to mutation working conditions.

[0063] The multi-parameter optimization control method for the dynamic electromagnetic loading force of the water-lubricated bearing of the present invention adopts decentralized control, and different excitation currents are used to drive different non-contact electromagnetic loading devices, and has a more accurate control effect than centralized control in the case of axis offset caused by complex working conditions and large load conditions, improving the stiffness of the shafting; avoiding problems such as difficult decoupling, reading the data collected under actual operation, using path planning algorithms and sliding mode control algorithms, and obtaining the effective value of the output current by calculating the correction value of the coordinates and designing the form of the sliding mode surface. It not only does not require decoupling in mathematical modeling between rotational speed, current and electromagnetic loading force, but also the data already contains static losses and dynamic losses under the current working conditions, and no further compensation is required. While effectively ensuring the control effect, this method simplifies the control difficulty; three parameters of "line of sight", step size and step size gain are designed to ensure a higher "speed" in the initial stage of the change process, thus ensuring an overall lower adjustment time; at the same time, during the process of reducing the line of sight, the step size gain parameter also decreases, ensuring the control accuracy while reducing the overshoot and stabilizing the dynamic performance of the load system. Brief Description of the Drawings

[0064] Figure 1 is the structure diagram of the dynamic electromagnetic loading force control system of the water-lubricated bearing of the present invention;

[0065] Figure 2 is the control flow chart of the multi-parameter optimization control method for the dynamic electromagnetic loading force of the water-lubricated bearing of the present invention;

[0066] Figure 3 is the structure diagram of the Oracle database;

[0067] Figure 4 is the structure diagram of the data table space;

[0068] Figure 5 is the flow chart of database call;

[0069] Figure 6 is the structure of the pre - call data area;

[0070] Figure 7 is the flow chart of the three - dimensional data path tracking algorithm;

[0071] Figure 8 is the flow chart of the local path planning algorithm;

[0072] Figure 9 is the flow chart of the behavior execution layer algorithm;

[0073] Figure 10 is the global three - dimensional view of the embodiment;

[0074] Figure 11 is the local three - dimensional view of the embodiment. Specific implementation manners

[0075] The present invention will be described in detail below in conjunction with the accompanying drawings and specific implementation manners.

[0076] The dynamic electromagnetic loading force control system of the water - lubricated bearing of the present invention, as Figure 1 shown, includes a pair of non - contact electromagnetic loading devices respectively arranged at both ends of the bearing spindle. The non - contact electromagnetic loading device is connected with a load device driver. The load controller is a three - dimensional path tracking controller. Eddy current sensors are also arranged at both ends of the bearing spindle, and a torque and speed sensor is arranged near the motor end of the bearing spindle. A piezoresistive force sensor is arranged at the bottom of the non - contact electromagnetic loading device. The eddy current sensors, the torque and speed sensor and the piezoresistive force sensor are connected with the load controller through a data acquisition card and an analog - to - digital converter. The load controller is connected with an Oracle database stored in the server hard disk. The load controller is also connected with a current regulator. The current regulator is a sliding - mode controller, and the current regulator is further connected with the load device driver.

[0077] The multi - parameter optimization control method for the dynamic electromagnetic loading force of the water - lubricated bearing of the present invention uses the dynamic electromagnetic loading force control system of the water - lubricated bearing of the present invention to control the electromagnetic loading force. As Figure 2 shown, after the system is initialized, the target loading force is set. The readings of the torque and speed sensor, the piezoresistive force sensor, two pairs of eddy current sensors and the load system controller are collected and the signals are transmitted to the load controller. The load controller reads the sensor readings and performs mean processing respectively to obtain the average measured value of the loading force of the piezoresistive force sensor signal the average measured value of the exciting current of the current sensor signal Average rotational speed measurement of torque rotational speed sensor signal Determine whether the non-contact electromagnetic loading force matches the set value. If it matches, each sensor continues to repeat the above process. If it does not match, the sensed signal after mean processing is used as a query condition to preprocess the database. After preprocessing, a data block is obtained. The load controller uses a three-dimensional data path tracking algorithm optimized by a genetic algorithm to read the data block and calculate the reference current I r , the reference current I r is input into the current regulator. The current regulator uses a sliding mode algorithm to calculate the control output current I smc , and is input into the load device driver to control the electromagnetic loading force F of the water-lubricated bearing non-contact electromagnetic loading device, so as to achieve the purpose of improving the accuracy of the electromagnetic loading force and the robustness under different working conditions.

[0078] Calculate the average axial center distance measurement of the eddy current sensor signal within the sampling period The calculation formula is as follows:

[0079]

[0080] In formula (1), k is the number of points collected within a sampling period, and x r (i) are all the axial center distance values in the horizontal direction collected by the horizontally installed eddy current sensor within a sampling period, and y r (i) are all the axial center distance values in the vertical direction collected by the vertically installed eddy current sensor within a sampling period, and δ(i) are all the non-directional axial center distance values collected within a sampling period;

[0081] Calculate the average loading force measurement of the piezoresistive force sensor signal within the sampling period The calculation formula is as follows:

[0082]

[0083] In formula (2), k is the number of points collected within a sampling period, and F(i) are all the loading force values collected within a sampling period;

[0084] Calculate the average exciting current measurement of the current sensor signal within the sampling period The calculation formula is as follows:

[0085]

[0086] In formula (3), k is the number of points collected within a sampling period, and I e (i) are all the exciting current values collected within a sampling period;

[0087] Calculate the average rotational speed measurement of the torque & rotational speed sensor signals within the sampling period The calculation formula is as follows:

[0088]

[0089] In formula (4), k is the number of points collected within one sampling period, and n(i) is all the rotational speed values collected within one sampling period;

[0090] By comparing the average measurement of the electromagnetic loading force of the non-contact electromagnetic loading device within the sampling period with the threshold F 0 *ε 1 to determine whether the non-contact electromagnetic loading force matches the set value, the discrimination formula is as follows:

[0091]

[0092] is the average measurement of the electromagnetic loading force, F 0 is the target electromagnetic loading force, ε 1 is the electromagnetic force fluctuation threshold.

[0093] The Oracle database is stored in the server hard disk, waiting at any time for the upper computer to send user instructions for calling. The database structure is as Figure 3 shown. The Oracle database consists of a data storage end, a pre-called data area, multiple processing processes, user processes, server processes, and backup log files. Among them, the data storage end stores the complete data table space, the complete parameter table space, and the corresponding index files; the called parameters, the data blocks obtained after preprocessing, as well as the library name files, mirror files, etc. are stored in the pre-called data area waiting for call instructions; the processing processes include the CKPT process, SMON process, LGWR process, DBWN process, ARCN process, and PMON process, which are responsible for functions such as inspection, call, recording, deletion, etc.; the user process is the call instruction or modification instruction sent by the upper computer, and then modifies the database after being processed by the server process.

[0094] The data storage end includes: the data table space composed of actual test data, the parameter table space composed of optimized parameters, and the shared pool composed of call statements, table headers, table descriptions, etc.;

[0095] The data table space composed of actual test data consists of test data tables and data index segments. The test data tables store the test data of the measured loading force F at different axial distances δ, different rotational speeds n, and different excitation currents I. Taking the axial distance δ as the primary query condition, the test data tables are divided into three-dimensional data tables under different axial distances, and these three-dimensional data tables are all composed of three-dimensional data composed of the rotational speed n, excitation current I, and electromagnetic loading force F;

[0096] The data table space structure is as follows Figure 4 shown. The three-dimensional data table is subdivided into multiple data blocks according to the rotational speed range, excitation current range, and loading force range. Among them, the center distance δ is the first-level query condition, the loading force interval is the second-level query condition, and the rotational speed interval and excitation current interval are the third-level query conditions. The data index segment is composed of index keywords, and the index keywords are composed of the first-level query condition, the second-level query condition, and the third-level query condition;

[0097] The parameter table space is composed of an optimization parameter table and a parameter index segment. The optimization parameter table stores various optimization parameters, such as the maximum step size λ max 、the maximum viewing distance s max 、the step size gain coefficient K, the curve path weight ζ 1 、ζ 2 、ζ 3 、η 1 、η 2 、η 3 , with the category as the first-level query condition, and are stored in the data table in the form of a stack respectively.

[0098] Each process plays a different role in the process of reading the three-dimensional database. At the data storage end, after the CKPT process checks the database integrity, the SMON process clears the unused temporary segments to ensure that the database has enough data space to record the modification records. During the operation, the DBWR process saves the old parameters generated during the optimization process in the modification records. If there are data modifications in the data table space, they will also be saved in the modification records. The database is limited, and the modification records and the modified data will be sent back to the data storage end through the LGWR process and the DBWN process respectively for separate storage. And the modification records are time-limited. In order to ensure that the long-term change curve of the parameters can be generated, the ARCN process will call the modification records in the database for separate storage.

[0099] The call flow chart is as follows Figure 5 shown. Combining Figure 4 , the user process issues a call instruction, first queries the first-level query condition - the average value of the center distance to specify the data table space; uses the current average loading force to confirm the second-level query condition. After specifying the data area, it queries whether the value of the loading force F at the target coordinate point is within this data area. If it is not within this data area, it will call all data areas from the target loading force F to the current average loading force to form a pre-call data area, and its structure is as follows Figure 6 shown; through the current working condition - rotational speed and excitation current Confirm the three-level query conditions, specify a data segment in the pre-called data area, read the data segment and put it together with the index segment into the local data located in the pre-called data area, and wait for reading.

[0100] Preprocess the database to obtain a data block specifically as follows:

[0101] Issue a call instruction, first use the average value of the axial center distance as the first-level query condition for querying, and specify the data table space; use the average value of the current loading force as the second-level query condition. After specifying the data area, query whether the value of the loading force F at the target coordinate point is within this data area. If it is within this data area, then this data area is the pre-called data area. If it is not within this data area, then call all the data areas from the target loading force F to the average value of the current loading force to form the pre-called data area; use the current working condition speed and the excitation current as the third-level query conditions, specify a data segment in the pre-called data area, read the data segment and put it together with the index segment into the local data located in the pre-called data area to obtain the preprocessed data block, and wait for the load controller to read.

[0102] The load controller adopts a three-dimensional data path tracking algorithm optimized by a genetic algorithm, which consists of a global path planning layer, a local path planning layer, a path reconstruction layer, and a behavior execution layer, as shown in Figure 7 shown. Specifically as follows:

[0103] Initialize the load controller, wake up the database, and read the axial center distance shaft speed excitation current loading force input values, call the data segment of the local data stored in the pre-called data area, enter the global path planning layer, establish a three-dimensional map, determine the current input value coordinate point and the target value coordinate point, and plan the global path; enter the local path planning layer, add constraint conditions, and find the optimal path in the global path; enter the behavior execution layer, read the optimal path, judge whether to use the point-to-point tracking method or the point-to-line tracking method, and optimize them respectively using the simulated annealing algorithm and the particle swarm algorithm. Calculate the reference current I r according to the coordinate change value of the excitation current, and output the reference current I r to the current controller;

[0104] At the same time, continuously judge the average value of the axial center distance Whether it changes, if it changes, enter the path reconstruction layer, replace the tablespace in the database, no longer perform indexing, directly call the specified data segment in the tablespace, enter the local path planning layer again, perform path re-planning, add constraint conditions, and find the optimal path in the global path; enter the behavior execution layer, read the optimal path, select the optimal path and determine the path tracking method, and calculate the reference current I according to the change value of the excitation current coordinates r 。

[0105] As the local planning part of the three-dimensional data path tracking algorithm, the local path planning layer receives the local map information of the three-dimensional coordinates of the electromagnetic loading force to the three-dimensional coordinates of the target electromagnetic force generated by the global map under the current working conditions, adds constraint conditions to select the local optimal path, and stores the obtained optimal path in the specified data block of the database for convenient real-time update, as Figure 8 shown, specifically,

[0106] Call three low-order curve path weights ζ 1 、ζ 2 、ζ 3 and three high-order curve path weights η 1 、η 2 、η 3 stored in the database, read the three-dimensional data map, confirm the current coordinates and target coordinates, calculate the electromagnetic loading force error e, and make the following judgments based on this error:

[0107] Whether the error e is within 30% of the target electromagnetic force. If the error is less than 30% of the target electromagnetic force, determine that the low-order curve path weight ζ 1 is parameter 1; otherwise, determine that the high-order curve path weight η 1 is parameter 1; whether there are discontinuous points on the three-dimensional data map, judged by whether the derivative is continuous. If there are discontinuous points, determine that the low-order curve path weight ζ 2 is parameter 2; otherwise, determine that the high-order curve path weight η 2 is parameter 2; whether a slight change in the working condition is allowed, and the control system accuracy is within the range of the target value ±2% to ±5%. If the rotational speed fluctuation is within the control system accuracy when the optimal path is a low-order curve, determine that the low-order curve path weight η 3 is parameter 3; otherwise, determine that the high-order curve path weight η 3 is parameter 3;

[0108] Integrate the path weights ζ 1 、ζ 2 、ζ 3 、η 1 、η 2 、η 3 The selected path weights are iteratively optimized by the genetic algorithm, adjust the parameters, and the low-order curve path weight ζ1 and ζ 2 and ζ 3 Sum them up to obtain the total weight ζ of the low - order curve path and the weight η of the high - order curve path 1 and η 2 and η 3 Sum them up to obtain the total weight η of the high - order curve path;

[0109] If ζ is greater than η, it is determined to search for the optimal low - order curve path group; otherwise, it is determined to search for the optimal high - order curve path group, and calculate the weight difference Δ = |η - ζ|, and adjust the weight difference threshold Δ through the genetic algorithm * , to determine whether to select the relatively higher - order or relatively lower - order one in the optimal curve group. The judgment conditions are as follows:

[0110]

[0111] The optimal high - order curve path group is selected by using the D*Lite path search algorithm, while the optimal low - order curve path group is selected by using the Dijkstra algorithm.

[0112] Enter the behavior execution layer, read the optimal path, determine whether to use the point - to - point tracking method or the point - to - line tracking method, and optimize them respectively with the simulated annealing algorithm and the particle swarm algorithm, and calculate the reference current I according to the change value of the excitation current coordinates r , as Figure 9 shown, specifically

[0113] Read the line - of - sight distance s, the maximum line - of - sight distance s max , step size λ, the maximum step size λ max and step - size gain coefficient K from the database, and the optimal path L obtained from the local path planning layer, and determine whether the order m of the optimal path L is greater than 2;

[0114] If m > 2, then select the point - to - line tracking method. The process of this method is as follows: Determine the relationship between the current signal error e and the maximum line - of - sight distance s max ; if e < s max , then select the forward point on the optimal path with the maximum step size λ max ; if e > s max , that is, at this time, the target point can be "seen". At this time, the particle swarm optimization algorithm is used to correct the step - size gain coefficient K according to the size of the error e, and calculate the product of the corrected step - size gain coefficient and the maximum step size λ max to obtain the step size λ, so as to select the forward point on the optimal path. When reaching the point before the target point, the step size λ should be 0; if there are discontinuous points within the step size λ, then use the discontinuous points as the forward points and perform path tracking in segments; obtain the excitation current coordinates of each step, and calculate the respective reference current I for each step rn, gradually reach the final reference current I r ;

[0115] If m < 2, the point-by-point tracking method is selected. The process is as follows: According to the magnitude of the current signal error e, adjust the number of segmentation points q through the particle swarm optimization algorithm; According to the number of segmentation points q, divide the optimal low-order curve into the current point A, the intermediate points A 1 , A 2 , …, A q , and the target point B; Set the intermediate point A 1 as the next target point, confirm the correction value of the excitation current coordinate, and calculate the reference current I r1 ; Perform point by point to obtain the reference currents I r2 , I r3 , …, I rq , and finally obtain the reference current I r of the target point.

[0116] The current controller is a sliding mode controller designed based on the following mathematical model:

[0117]

[0118] In Equation (5), R is the outer radius of the loading disk, is the thickness of the loading disk, μ 0 is the vacuum permeability, N is the number of turns of the coil, I is the excitation current, l is the air gap length, n is the harmonic order, v x is the linear velocity of the loading disk;

[0119] The sliding mode variable s of the sliding mode controller is selected as:

[0120]

[0121] In Equation (6), the sliding mode variable s is obtained through the design of the sliding mode surface , where x is the state vector, C is the matrix [c 1 …c n-1 1] T , in the sliding mode control, the parameters c 1 c 2 …c n-1 should satisfy that the polynomial p n-1 +c n-1 p n-2 +…+c 2 p + c 1 is hurwitz, where p is the laplace operator. In this equation, n is taken as 2, and x 2 is Adjusting the magnitude of c can regulate the speed at which the state approaches zero. The larger c is, the faster the adjustment error is, and the current signal error e = I r -I e ,

[0122] The sliding mode controller is designed using the reaching law approach, and the reaching law is:

[0123]

[0124] In Equation (7), k s and γ are both positive constants, and sgn(s) is the sign function;

[0125] The control output current I smc of the sliding mode controller is calculated as:

[0126] I smc = ce + k s + γsgn(s) (8).

[0127] Embodiment

[0128] In this embodiment, according to the multi-parameter optimization control method for the dynamic electromagnetic loading force of the water-lubricated bearing, the target loading force is set, and the readings of the torque and speed sensor, piezoresistive force sensor, two pairs of eddy current sensors, and the load system controller are collected and the signals are transmitted to the load controller. The load controller reads the sensor readings and performs mean processing respectively to obtain the average measured value of the loading force of the piezoresistive force sensor signal The average measured value of the exciting current of the current sensor signal The average measured value of the rotational speed of the torque and speed sensor signal It is judged whether the non-contact electromagnetic loading force matches the set value. If it matches, the above process is repeated for each sensor; if it does not match, the sensor signals after mean processing are used as query conditions to preprocess the database. After preprocessing, a data block is obtained. The load controller uses a three-dimensional data path tracking algorithm optimized by the genetic algorithm, reads the data block and calculates the reference current I r , and the reference current I r is input into the current regulator, and the control output current I smc of the current regulator is calculated using the sliding mode algorithm, and is input into the load device driver to control the electromagnetic loading force F of the non-contact electromagnetic loading device of the water-lubricated bearing, so as to achieve the purpose of improving the accuracy of the electromagnetic loading force and the robustness under different working conditions.

[0129] As Figure 10 shown, it is a three-dimensional diagram converted from the table space data composed of the exciting current, rotational speed, and electromagnetic loading force under a certain air gap. The coordinate form of all points on the three-dimensional diagram is: (I e, n, F), the formation of this 3D map includes two steps: calling the database and the global path planning layer. Assume that the current working condition coordinate is point A and the target working condition coordinate is point B. It is necessary to construct an optimal path on this 3D map and move the current working condition coordinate point to point B in the form of changing the horizontal coordinate. First, enter the local path planning layer and extract the data segment to which point A to point B belongs, such as Figure 11 as shown.

[0130] Figure 11 At the same time, 3 possible optimal paths L 1 , L e , L 3 are given, where L 1 , L 2 are high-order curve paths passing through the surface of the 3D map; L 3 is a low-order curve path passing through the interior of the 3D map, and both L 3 and L 1 have turning points. The path planning layer starts to judge according to the following conditions:

[0131] 1) Whether the error e is within 30% of the target electromagnetic force;

[0132] 2) Whether there are discontinuous points on the 3D data map;

[0133] 3) Whether a small change in the working condition is allowed;

[0134] Assume the current selections are:

[0135] 1) The error e is within 30% of the target electromagnetic force;

[0136] 2) There are no discontinuous points on the 3D data map;

[0137] 3) A small change in the working condition is allowed;

[0138] At this time, the selection of path weights is:

[0139] 1) Low-order curve path weight 1 - ζ 1

[0140] 2) High-order curve path weight 2 - η 2 ;

[0141] 3) Low-order curve path weight 3 - ζ 3 ;

[0142] After iterating through the genetic algorithm and summing respectively to obtain the total weight ζ of the low-order curve path and the total weight η of the high-order curve path, judge the magnitudes of ζ and η. At this time, η > ζ, and Δ > Δ * , select L 2As the optimal curve path, it is stored in the specified data block in the database, waiting to be called by the behavior execution layer.

[0143] After the behavior execution layer calls the optimal curve L 2 , it first judges the order of L 2 . Obviously, the order of L 2 is greater than 2. Therefore, the point-line tracking method is selected. Read the visual distance s, the maximum visual distance s max , the step size λ, the maximum step size λ max and the step size gain coefficient K from the database. Starting from the starting point A, with point A as the center and the maximum visual distance s max as the radius, form a visual distance circle O s , and find the intersection point of the visual distance circle O s and the optimal curve L 2 . Using this intersection point as the intermediate target point, move forward in multiple steps through the step size λ corresponding to the visual distance s.

[0144] Since there are inflection points in the visual distance circle, move forward with the inflection point A 1 as the target point to ensure that during the transformation of the coordinate points (I A , n A , F A ), only the exciting current I or the rotational speed n changes at the same time, avoiding the instability of the shafting caused by simultaneous changes. As shown, from the kth forward point A Figure 9 to the (k + 1)th forward point A k , there are no inflection points or discontinuous points on the path. Therefore, |A k+1 , A k | = s k+1 , and the step size is the maximum step size λ max . And in the section from the forward point A max to the target point B, since |A n , B| < s n , the step size λ = K * λ max . Select forward points on the optimal path to obtain the exciting current coordinates of each step, and calculate the respective reference current I max for each step, and gradually reach the final reference current I rn , and finally reach the reference current I r .

Claims

1. Water-lubricated bearing dynamic electromagnetic loading force control system, Characterized in that, It includes a pair of non-contact electromagnetic loading devices respectively arranged at both ends of the bearing spindle. The non-contact electromagnetic loading device is connected with a load device driver. Eddy current sensors are also arranged at both ends of the bearing spindle. And a torque and speed sensor is arranged near the motor end of the bearing spindle. A piezoresistive force sensor is arranged at the bottom of the non-contact electromagnetic loading device. The eddy current sensor, the torque and speed sensor and the piezoresistive force sensor are connected with a load controller. The load controller is connected with a database stored in the server hard disk. The load controller is also connected with a current regulator. The current regulator is in turn connected with the load device driver.

2. The water-lubricated bearing dynamic electromagnetic loading force control system according to claim 1, Characterized in that, The load controller is a three-dimensional path tracking controller; The current regulator is a sliding mode controller; The database is an Oracle database.

3. Water-lubricated bearing dynamic electromagnetic loading force multi-parameter optimization control method, which uses the water-lubricated bearing dynamic electromagnetic loading force control system according to claim 1 to control the electromagnetic loading force, Characterized in that, Set the target loading force, collect the readings of the torque and speed sensor, piezoresistive force sensor, two pairs of eddy current sensors and the load system controller, and transmit the signals to the load controller. The load controller reads the sensor readings and performs mean processing respectively to obtain the average loading force measurement of the piezoresistive force sensor signal , the average excitation current measurement of the current sensor signal , the average speed measurement of the torque and speed sensor signal , determine whether the non-contact electromagnetic loading force matches the set value. If it matches, the above process is repeated for each sensor. If it does not match, the sensor signals after mean processing are used as query conditions to preprocess the database. After preprocessing, a data block is obtained. The load controller uses a three-dimensional data path tracking algorithm optimized by a genetic algorithm, reads the data block and calculates the reference current , and the reference current is input into the current regulator. The current regulator uses a sliding mode algorithm to calculate the control output current , and is input into the load device driver to control the electromagnetic loading force of the water-lubricated bearing non-contact electromagnetic loading device , so as to achieve the purpose of improving the accuracy of the electromagnetic loading force and the robustness under different working conditions.

4. The water-lubricated bearing dynamic electromagnetic loading force multi-parameter optimization control method according to claim 3, Characterized in that, Calculate the average value of the shaft center distance measurement of the eddy current sensor signal within the sampling period The calculation formula is as follows: （1） In formula (1), is the number of points collected within one sampling period, is the value of the axial center distance in all horizontal directions collected by the eddy current sensor installed horizontally within one sampling period, is the value of the axial center distance in all vertical directions collected by the eddy current sensor installed vertically within one sampling period, is the value of all non-directional axial center distances collected within one sampling period; Calculate the average value of the applied force measured by the piezoresistive force sensor signal within the sampling period The calculation formula is as follows: （2） In formula (2), is the number of points collected within one sampling period, is the value of all the applied forces collected within one sampling period; Calculate the average measured value of the exciting current of the current sensor signal within the sampling period The calculation formula is as follows: （3） In formula (3) is the number of points collected within one sampling period, is the values of all exciting currents collected within one sampling period; Calculate the average rotational speed measurement of the torque & rotational speed sensor signals within the sampling period The calculation formula is as follows: （4） In formula (4) is the number of points collected within one sampling period, is the value of all rotational speeds collected within one sampling period; By taking the average value of the loading force measured by the non-contact electromagnetic loading device within the sampling period and the threshold value are compared to determine whether the non-contact electromagnetic loading force matches the set value. The discrimination formula is as follows: is the average value of the loading force measurement, is the target electromagnetic loading force, is the electromagnetic force fluctuation threshold.

5. The water-lubricated bearing dynamic electromagnetic loading force multi-parameter optimization control method according to claim 3, Characterized in that, The database consists of a data storage end, a pre-called data area, multiple processing processes, user processes, server processes and backup log files. The data storage end includes: a data table space composed of actual test data, a parameter table space composed of optimization parameters, and a shared pool composed of call statements, table headers, table descriptions, etc.; The data table space composed of the actual test data is composed of a test data table and a data index segment. The test data table stores the actually measured electromagnetic loading forces at different axial center distances , different rotational speeds , and different excitation currents . Using the axial center distance as the primary query condition, the test data table is divided into three-dimensional data tables at different axial center distances. These three-dimensional data tables are all composed of three-dimensional data formed by the rotational speed , the excitation current , and the electromagnetic loading force . The three-dimensional data table is subdivided into multiple data blocks according to the rotational speed range, exciting current range, and loading force range. Among them, the axial distance is the primary query condition, the loading force interval is the secondary query condition, the rotational speed interval and the exciting current interval are the tertiary query conditions, the data index segment is composed of index keywords, and the index keywords are composed of the primary query condition, the secondary query condition, and the tertiary query conditions; The parameter table space consists of an optimized parameter table and a parameter index segment. The optimized parameter table stores various optimization parameters, such as the maximum step size , the maximum viewing distance , the step size gain coefficient , the curve path weight . Using the category as the primary query condition, they are respectively stored in a stack-form data table.

6. The water-lubricated bearing dynamic electromagnetic loading force multi-parameter optimization control method according to claim 3, Characterized in that, Specifically, the pretreatment of the database to obtain data blocks is as follows, Send a call instruction, first use the average value of the axial center distance as the first-level query condition to query and specify the data table space; use the average value of the current loading force as the second-level query condition. After specifying the data area, query whether the value of the loading force at the target coordinate point is located in this data area. If it is located in this data area, then this data area is the pre-called data area. If it is not located in this data area, then call the target loading force to the average value of the current loading force measurement of all data areas to form the pre-called data area; use the average value of the current working condition speed measurement and the average value of the excitation current measurement as the third-level query condition, specify a data segment in the pre-called data area, read this data segment and put it together with the index segment into the local data located in the pre-called data area to obtain a preprocessed data block, and wait for the load controller to read.

7. The water-lubricated bearing dynamic electromagnetic loading force multi-parameter optimization control method according to claim 6, Characterized in that, The three-dimensional data path tracking algorithm optimized by the genetic algorithm adopted by the load controller consists of a global path planning layer, a local path planning layer, a path reconstruction layer and a behavior execution layer. Specifically, The load controller is initialized, the database is awakened, and the average value of the axial center distance is read , the average value of the rotational speed measurement , the average value of the excitation current measurement , the average value of the loading force measurement Input values, call the data segment of the local data stored in the pre-called data area, enter the global path planning layer, establish a 3D map, determine the current input value coordinate point and the target value coordinate point, and plan the global path; Enter the local path planning layer, add constraint conditions, and find the optimal path in the global path; enter the behavior execution layer, read the optimal path, judge whether to use the point-to-point tracking method or the point-to-line tracking method, and optimize them respectively with the simulated annealing algorithm and the particle swarm algorithm, and calculate the reference current according to the change value of the excitation current coordinates , and output the reference current to the current controller; Meanwhile, the average value of the axial center distance is judged in real time to determine whether it changes. If it changes, enter the path reconstruction layer, replace the tablespace in the database, stop indexing, directly call the specified data segment in the tablespace, enter the local path planning layer again, perform path replanning, add constraint conditions, and search for the optimal path in the global path; enter the behavior execution layer, read the optimal path, select the optimal path and determine the path tracking method, and calculate the reference current based on the change value of the excitation current coordinates .

8. The water-lubricated bearing dynamic electromagnetic loading force multi-parameter optimization control method according to claim 7, Characterized in that, The local path planning layer, as the local planning part of the three-dimensional data path tracking algorithm, receives the map information from the global map generated from the three-dimensional coordinates of the electromagnetic loading force under the current working condition to the local three-dimensional coordinates of the target electromagnetic loading force, adds constraint conditions to select the local optimal path, and the obtained optimal path is stored in the specified data block of the database for convenient real-time update. Specifically, Call three low-order curve path weights stored in the database and three high-order curve path weights , read the three-dimensional data map, confirm the current coordinates and target coordinates, and calculate the electromagnetic loading force error , and make the following judgments based on this error: Error Whether it is within 30% of the target electromagnetic force. If the error is less than 30% of the target electromagnetic force, determine the low-order curve path weight as Parameter 1; Conversely, determine the weight of the high-order curve path is parameter 1; whether there are discontinuous points on the three-dimensional data graph is determined by whether the derivative is continuous. If there are discontinuous points, determine the weight of the low-order curve path is parameter 2; conversely, determine the weight of the high-order curve path is parameter 2; whether a slight change in the working condition is allowed, and the control system accuracy is within the range of ±2% to ±5% of the target value. If the rotational speed fluctuation is within the control system accuracy when the optimal path is a low-order curve, determine the weight of the low-order curve path is parameter 3; Otherwise, determine the high-order curve path weight is parameter 3; Integrated path weight The selected path weights are iteratively optimized by a genetic algorithm, adjusting the parameters, and the low-order curve path weights are summed to obtain the total weight of the low-order curve path The high-order curve path weights are summed to obtain the total weight of the high-order curve path ; If greater than , it is determined to be searching for the optimal low-order curve path; otherwise, it is determined to be searching for the optimal high-order curve path group, and the weight difference is adjusted through the genetic algorithm to obtain the weight difference threshold to determine whether to select the relatively higher-order or relatively lower-order one in the optimal curve group. The judgment conditions are as follows: ； The optimal high-order curve path group is selected by using the D*Lite path search algorithm, and the optimal low-order curve path group is selected by using the Dijkstra algorithm.

9. The water-lubricated bearing dynamic electromagnetic loading force multi-parameter optimization control method according to claim 7, Characterized in that, The entering behavior execution layer reads the optimal path, determines whether to use the point-to-point tracking method or the point-to-line tracking method, and optimizes them using the simulated annealing algorithm and the particle swarm algorithm respectively, and calculates the reference current according to the change value of the excitation current coordinates Specifically, Read the line-of-sight distance from the database , the maximum line-of-sight distance , the step size , the maximum step size and the step size gain coefficient , and the optimal path obtained by the local path planning layer , determine the order of the optimal path whether it is greater than 2; If , the dot-line tracking method is selected, and the process of this method is as follows: judge the relationship between the current signal error and the maximum line-of-sight distance ; if , select the forward point on the optimal path with the maximum step size ; if , that is, the target point can be "seen" at this time. At this time, the step gain coefficient is corrected according to the size of the error through the particle swarm optimization algorithm, and the product of the corrected step gain coefficient and the maximum step size is calculated to obtain the step size , so as to select the forward point on the optimal path. When reaching the point before the target point, the step size should be 0; if there are discontinuous points in the step size , use the discontinuous points as the forward points and perform path tracking in segments; obtain the excitation current coordinates of each step, and calculate the respective reference currents for each step, and gradually reach the final reference current ; If , the dot-by-dot tracking method is selected, and the process of this method is as follows: According to the magnitude of the current signal error , the number of segmentation points is adjusted by the particle swarm optimization algorithm ; According to the number of segmentation points , the optimal low-order curve is segmented into the current point , the intermediate point , and the target point ; The intermediate point is set as the next target point, the correction value of the excitation current coordinate is confirmed, and the reference current is calculated; Point by point, the reference current is obtained respectively , and finally the reference current of the target point is obtained .

10. The multi-parameter optimization control method for the dynamic electromagnetic loading force of a water-lubricated bearing according to claim 9, characterized in that, the current controller is a sliding mode controller and is designed based on the following mathematical model: （5） In formula (5), , , , is the outer radius of the loading disk, is the thickness of the loading disk, is the vacuum permeability, is the number of turns of the coil, is the exciting current, is the air-gap length, is the harmonic order, is the linear velocity of the loading disk; Sliding mode variable of the sliding mode controller s is selected as: （6） In formula (6), c is the speed of adjusting the error, and the current signal error , ; the sliding mode controller is designed by using the reaching law, and the reaching law is: （7） In formula (7), and are both normal constants, is the sign function; The calculated control output current of the sliding mode controller is as follows: （8）。

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