CN114815602A - Dynamic electromagnetic loading force multi-parameter optimization control system and control method for water lubricated bearing - Google Patents
Dynamic electromagnetic loading force multi-parameter optimization control system and control method for water lubricated bearing Download PDFInfo
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Abstract
The invention discloses a dynamic electromagnetic loading force control system of a water lubricated bearing, which comprises a pair of non-contact electromagnetic loading devices, a load device driver, an eddy current sensor, a torque and rotating speed sensor, a piezoresistive force transducer, a load controller and a current regulator, wherein the load controller is connected with a database stored in a server hard disk. The invention also discloses a dynamic electromagnetic loading force multi-parameter optimization control method for the water lubricated bearing, which is characterized in that data collected in actual operation are read, a path planning algorithm and a sliding mode control algorithm are applied, and an effective value of an output current is obtained by calculating a correction value of a coordinate and designing a form of a sliding mode surface, so that the overshoot is reduced and the dynamic performance of a load system is stabilized while the control precision is ensured.
Description
Technical Field
The invention belongs to the technical field of mechanical equipment state monitoring, and particularly relates to a dynamic electromagnetic loading force multi-parameter optimization control system for a water lubrication bearing, and further relates to a dynamic electromagnetic loading force multi-parameter optimization control method for the water lubrication bearing.
Background
Electromagnetic loading devices are increasingly used in monitoring the condition of mechanical equipment. The electromagnetic loading device can provide non-contact load, compared with a contact non-contact electromagnetic loading device, the electromagnetic loading device avoids the problems of friction, vibration and the like, and has better application effect. In the process of dynamically applying the electromagnetic loading force by the electromagnetic loading device, the loading force is unstable due to factors such as the rotating speed of a shaft system, the displacement of an axis, the change of a magnetic field and the like, so that the load simulation and even the bearing test are greatly influenced, and the problem is solved at present. Therefore, the method has important significance and engineering application value for implementing accurate control on the dynamic electromagnetic loading force.
The invention patent of application number CN201911147320.9 provides a control method and device for magnetic levitation huchdrop trajectory identification and resuspension, which proposes to identify trajectory response by detecting the radial displacement of the shafting and the expectation of instantaneous frequency obtained by hilbert transform.
The invention patent of application number CN201710471181.X provides a controller for controlling an active magnetic suspension bearing system and a control method thereof, and provides a method for controlling currents in two coils in a stack of active magnetic suspension bearings respectively by a three-section cascade control structure and introducing a single-layer neural network regulator.
The above patent proposes a method for stabilizing the shafting again when the shafting is subjected to radial displacement, but does not solve the problem of how to stabilize the loading force when the shafting is subjected to radial displacement in a certain direction.
Disclosure of Invention
The invention aims to provide a dynamic electromagnetic loading force control system of a water-lubricated bearing, which has a higher control effect in a long-time running situation and has shorter regulation time than a single control algorithm in different sudden change situations.
The invention also aims to provide a multi-parameter optimization control method for the dynamic electromagnetic loading force of the water lubrication bearing, which ensures the control precision, reduces the overshoot and stabilizes the dynamic performance of a load system.
The technical scheme adopted by the invention is that the dynamic electromagnetic loading force control system of the water lubricated bearing comprises a pair of non-contact electromagnetic loading devices respectively arranged at two ends of a bearing main shaft, wherein the non-contact electromagnetic loading devices are connected with a loading device driver, two ends of the bearing main shaft are respectively provided with an eddy current sensor, the end, close to a motor, of the bearing main shaft is provided with a torque and rotating speed sensor, the bottom of each non-contact electromagnetic loading device is provided with a piezoresistive force sensor, the eddy current sensors, the torque and rotating speed sensors and the piezoresistive force sensors are connected with a loading controller, the loading controller is connected with a database stored in a server hard disk, the loading controller is also connected with a current regulator, and the current regulator is further connected with the loading device driver.
The present invention is also 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.
The invention adopts another technical scheme that a dynamic electromagnetic loading force multi-parameter optimization control method for a water lubricated bearing is characterized in that a dynamic electromagnetic loading force control system for the water lubricated bearing is applied to carry out electromagnetic loading force control, target loading force is set, readings of a torque rotating speed sensor, a piezoresistive force transducer, two pairs of eddy current sensors and a load system controller are collected and transmitted to a load controller, the load controller reads the readings of the sensors and carries out mean value processing respectively to obtain the average value of the measured loading force of the signals of the piezoresistive force transducer
Excitation current measurement average of current sensor signal
Mean value of the rotational speed measurement of the torque rotational speed sensor signal
Judging whether the non-contact electromagnetic loading force is matched with a set value, if so, continuously repeating the process by each sensor, if not, preprocessing the database by taking the sensing signal after mean processing as a query condition to obtain a data block, reading the data block by a load controller by adopting a three-dimensional data path tracking algorithm optimized by a genetic algorithm, and calculating to obtain a reference current I r Will refer to the current I r Inputting the current into a current regulator, and calculating the current by adopting a sliding mode algorithm to obtain a control output current I smc And the electromagnetic loading force F is input into a load device driver to control the non-contact electromagnetic loading device of the water lubrication bearing, so that the purposes of improving the accuracy of the electromagnetic loading force and the robustness under different working conditions are achieved.
The present invention is also characterized in that,
calculating the average value of the axle center distance measurement of the eddy current sensor signal in the sampling period
The calculation formula of (c) is as follows:
in the formula (1), k is the number of points collected in a sampling period, x r (i) The value of the center distance in all horizontal directions, y, acquired by the eddy current sensor installed horizontally in one sampling period r (i) The values of the axial center distances in all vertical directions acquired by the eddy current sensor vertically installed in one sampling period are delta (i), and the values of all non-directional axial center distances acquired in one sampling period are delta (i);
calculating the average value of the loading force measurement of the piezoresistive force cell signal in the sampling period
The calculation formula of (a) is as follows:
in the formula (2), k is the number of points collected in one sampling period, and F (i) is the value of all loading forces collected in one sampling period;
calculating the average value of the excitation current measurement of the current sensor signal in the sampling period
The calculation formula of (a) is as follows:
in the formula (3), k is the number of points collected in a sampling period, I e (i) The values of all the exciting currents collected in a sampling period are obtained;
calculating torque in a sampling period&Mean value of the rotational speed measurement of the rotational speed sensor signal
The calculation formula of (a) is as follows:
in the formula (4), k is the number of points collected in one sampling period, and n (i) is the value of all the rotating speeds collected in one sampling period;
by averaging the measured electromagnetic loading force of the non-contact electromagnetic loading device over a sampling period
And a threshold value F 0 *ε 1 And comparing, and judging whether the non-contact electromagnetic loading force is matched with a set value, wherein the judgment formula is as follows:
The database is composed of a data storage end, a pre-calling data area, a plurality of processing processes, a user process, a server process and a backup log file, wherein the data storage end comprises: a data table space composed of actual test data, a parameter table space composed of optimized parameters and a shared pool composed of calling statements, table headers, table descriptions and the like;
the data table space formed by actual test data is composed of a test data table and a data index section, the test data table stores the actually measured test data of the electromagnetic loading force F under different axle center distances delta, different rotating speeds n and different exciting currents I, the test data table is divided into three-dimensional data tables under different axle center distances by taking the axle center distances delta as a primary query condition, and the three-dimensional data tables are all composed of three-dimensional data formed by the rotating speeds n, the exciting currents I and the electromagnetic loading force F;
the three-dimensional data table is subdivided into a plurality of data blocks by a rotating speed range, an exciting current range and a loading force range, wherein the axle center distance delta is a first-level query condition, the loading force interval is a second-level query condition, the rotating speed interval and the exciting current interval are third-level query conditions, a data index section is formed by index keywords, and the index keywords are formed by the first-level query condition, the second-level query condition and the third-level query condition;
the parameter table space is composed of an optimized parameter table and a parameter index segment, and the optimized parameter table stores various optimized parameters, such as maximum step length lambda max Maximum viewing distance s max Step gain factor K, curve path weight ζ 1 、ζ 2 、ζ 3 、η 1 、η 2 、η 3 The categories are used as primary query conditions and are respectively stored in a data table in a stack form.
The preprocessing of the database to obtain the data blocks is specifically,
sending out a call instruction, and averaging the values of the axle center distances
As a first-level query condition, designating a data table space; at average value of current loading force
As a secondary query condition, after a data area is designated, whether the value of the target coordinate point loading force F is located in the data area is queried, if so, the data area is a pre-calling data area, and if not, the target loading force F is called to the average value of the current loading force
All the data areas form a pre-calling data area; rotating speed according to current working condition
And an excitation current
And as a three-level query condition, designating a data segment in the pre-call data area, reading the data segment, putting the data segment and the index segment into local data in the pre-call data area together to obtain a preprocessed data block, and waiting for the load controller to read.
The three-dimensional data path tracking algorithm optimized by the load controller by adopting the genetic algorithm is composed of a global path planning layer, a local path planning layer, a path reconstruction layer and a behavior execution layer,
initializing load controller, waking up database, and reading axle center distance
Rotational speed of shaft
Exciting current
Loading force
Inputting a value, calling a data segment of local data stored in a pre-calling data area, entering a global path planning layer, establishing a three-dimensional graph, determining a current input value coordinate point and a target value coordinate point, and planning a global path; entering a local path planning layer, adding constraint conditions, and searching an optimal path in the global path; entering a behavior execution layer, reading an optimal path, judging and selecting a point-to-point tracking mode or a point-to-line tracking mode, respectively optimizing by using a simulated annealing algorithm and a particle swarm algorithm, and calculating a reference current I according to an excitation current coordinate change value r And reference current I r Outputting the current to a current controller;
meanwhile, the average value of the wheel center distances is judged in real time
If the path is changed, entering a path reconstruction layer, replacing a table space in a database, directly calling a specified data segment in the table space without indexing, entering a local path planning layer again, re-planning the path, adding a constraint condition, and searching an optimal path in the global path; entering a behavior execution layer, reading an optimal path, selecting the optimal path, determining a path tracking mode, and calculating a reference current I according to an excitation current coordinate change value r 。
The local path planning layer is used as a local planning part of a three-dimensional data path tracking algorithm, receives local map information generated by a global map and from an electromagnetic loading force three-dimensional coordinate to a target electromagnetic loading force three-dimensional coordinate under the current working condition, adds constraint conditions to select a local optimal path, stores the obtained optimal path in a specified data block of a database, is convenient to change in real time, and particularly,
invoking three low-order curve path weights ζ stored in a database 1 、ζ 2 、ζ 3 And three higher order curve path weights η 1 、η 2 、η 3 Reading the three-dimensional data graph, confirming the current coordinate and the target coordinate, calculating an electromagnetic loading force error e, and judging according to the error as follows:
determining whether the error e is within 30% of the target electromagnetic force, and if the error is less than 30% of the target electromagnetic force, determining the low-order curve path weight zeta 1 Is parameter 1; otherwise, determining the path weight eta of the high-order curve 1 Is parameter 1; whether a discontinuous point exists on the three-dimensional data graph is judged according to whether the derivative is continuous, and if the discontinuous point exists, the path weight zeta of the low-order curve is determined 2 Is parameter 2; otherwise, determining the path weight eta of the high-order curve 2 Is parameter 2; whether the small change of the working condition is allowed or not, the precision of the control system is within +/-2% - +/-5% of the target value, and if the rotation speed fluctuation is within the precision of the control system when the optimal path is allowed to be a low-order curve, the path weight eta of the low-order curve is determined 3 Is parameter 3; otherwise, determining the path weight eta of the high-order curve 3 Is parameter 3;
integrated path weight ζ 1 、ζ 2 、ζ 3 、η 1 、η 2 、η 3 The selected path weight is iteratively optimized through a genetic algorithm, parameters are adjusted, and the path weight zeta of the low-order curve 1 、ζ 2 、ζ 3 Summing to obtain total weight zeta of low-order curve path and weight eta of high-order curve path 1 、η 2 、η 3 Summing to obtain the total weight eta of the high-order curve path;
if zeta is larger than eta, the optimal low-order curve path set is judged to be searched, otherwise, the optimal high-order curve path set is judged to be searched, the weight difference value delta is calculated to be | eta-zeta |, and the weight difference value threshold delta is adjusted through a genetic algorithm * To determine whether to select a higher order or a lower order in the optimal curve group, the determination conditions are as follows:
the optimal high-order curve path group is selected by adopting a D × Lite path search algorithm, and the optimal low-order curve path group is selected by adopting a Dijkstra algorithm.
Entering a behavior execution layer, reading an optimal path, judging and selecting a point-to-point tracking mode or a point-to-line tracking mode, respectively optimizing by using a simulated annealing algorithm and a particle swarm algorithm, and calculating a reference current I according to an excitation current coordinate change value r In particular to a method for preparing a high-performance nano-silver alloy,
reading the sight distance s and the maximum sight distance s from the database max Step length lambda, maximum step length lambda max Judging whether the order m of the optimal path L is greater than 2 or not according to the step gain coefficient K and the optimal path L obtained by the local path planning layer;
if m>2, selecting a point-line tracking mode, wherein the flow of the mode is as follows: judging the current signal error e and the maximum visual range s max The relationship of (1); if e<s max At the maximum step size λ max Selecting a forward point on the optimal path; if e>s max That is, the target point can be seen, the step gain coefficient K is corrected according to the error e by the particle swarm optimization algorithm, and the corrected step gain coefficient and the maximum step lambda are calculated max Obtaining the step length lambda by multiplication, so that a forward point is selected on the optimal path, and when the forward point of the target point is reached, the step length lambda is 0; if a discontinuous point exists in the step length lambda, the discontinuous point is taken as a forward point, and path tracking is carried out in a segmented mode; obtaining the excitation current coordinate of each step, and calculating each step to obtain respective reference current I rn Gradually reach the final reference current I r ；
If m<2, selecting a point-point tracking mode, wherein the flow of the mode is as follows: adjusting the number q of the segmentation points by a particle swarm optimization algorithm according to the magnitude of the current signal error e; according to the number q of the division points, the optimal low-order curve is divided into a current point A and an intermediate point A 1 、A 2 、…、A q A target point B; the intermediate point A 1 Setting as the next target point, confirming the correction value of the excitation current coordinate, and calculating to obtain the reference current I r1 (ii) a The reference current I is obtained respectively by performing point by point r2 、I r3 、…、I rq Finally, the target point reference current I is obtained r 。
The current controller is a sliding mode controller and is designed based on the following mathematical model:
in the formula (5), the reaction mixture is,
r is the excircle radius of the loading disc, the thickness of the loading disc and mu 0 Is vacuum magnetic conductivity, N is coil turn number, I is exciting current, l is air gap length, N is harmonic frequency, v x Is the loading disc linear velocity;
the sliding mode variable s of the sliding mode controller is selected as follows:
in the formula (6), c is the speed of the adjustment error, and the current signal error e is equal to I r -I e ，
The sliding mode controller is designed in an approach rate mode, and the approach rate is as follows:
in the formula (7), the reaction mixture is,k s and gamma are both normal numbers, sgn(s) is a sign function;
calculating to obtain the control output current I of the sliding mode controller smc Comprises the following steps:
I smc ＝ce+k s +γsgn(s) (8)。
the invention has the beneficial effects that:
compared with a traditional control system with a single control algorithm, the dynamic electromagnetic loading force control system for the water-lubricated bearing has the advantages that the control effect is higher in precision under the condition of long-time running, and the adjustment time is shorter than that of the single control algorithm under different mutation conditions; the database is used for storing massive test data and optimized parameters, so that not only can historical data be checked, but also the non-contact electromagnetic loading devices with different structures can be corrected, and the application range is expanded; the query mode of the tablespace is designed to directly call the specified data segment when the tablespace is switched, so that the query step is simplified, and the time and the memory are saved; the air gap of the shafting is changed uninterruptedly in the motion process, and the design of the database ensures the sensitivity and the response speed of the control system in the dynamic operation process of the shafting; and the database adopts an Oracle form, one of the characteristics lies in a locking mechanism strategy, namely, the read operation cannot be blocked by the write operation of the parameters, which means that in the real-time running process, the parameters in the database can be reasonably corrected through an optimization algorithm, and further, the control precision, the robustness under the complex working condition and the adaptability to the sudden change working condition are continuously improved.
The dynamic electromagnetic loading force multi-parameter optimization control method for the water lubricated bearing adopts decentralized control, drives different excitation currents aiming at different non-contact electromagnetic loading devices, has more accurate control effect than centralized control under the condition of axle center deviation caused by complex working conditions and heavy load conditions, and improves the rigidity of a shafting; the problems of difficult decoupling and the like are avoided, the data collected under actual operation are read, the effective value of the output current is obtained by calculating the correction value of the coordinate and designing the form of the slide film surface by using a path planning algorithm and a sliding mode control algorithm, the decoupling on mathematical modeling among the rotating speed, the current and the electromagnetic loading force is not needed, the static loss and the dynamic loss under the current working condition are contained in the data, and further compensation is not needed. The method simplifies the control difficulty while effectively ensuring the control effect; three parameters of 'line of sight', step length and step gain are designed, and a higher 'speed' is ensured at the initial stage of the change process, so that the overall lower adjusting time is ensured; meanwhile, in the process of reducing the sight distance, the step length gain parameter is also reduced, so that the overshoot is reduced while the control precision is ensured, and the dynamic performance of a load system is stabilized.
Drawings
FIG. 1 is a block diagram of a dynamic electromagnetic loading force control system for a water lubricated bearing according to the present invention;
FIG. 2 is a control flow chart of the dynamic electromagnetic loading force multi-parameter optimization control method for the water lubricated bearing of the invention;
FIG. 3 is a diagram of an Oracle database structure;
FIG. 4 is a diagram of a data table space structure;
FIG. 5 is a database call flow diagram;
FIG. 6 is a pre-call data area structure;
FIG. 7 is a flow chart of a three-dimensional data path tracking algorithm;
FIG. 8 is a flow chart of a local path planning algorithm;
FIG. 9 is a flow chart of a behavior execution layer algorithm;
FIG. 10 is a global three-dimensional diagram of an embodiment;
FIG. 11 is a partial three-dimensional view of an embodiment.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
The dynamic electromagnetic loading force control system of the water-lubricated bearing comprises a pair of non-contact electromagnetic loading devices respectively arranged at two ends of a bearing main shaft, wherein the non-contact electromagnetic loading devices are connected with a loading device driver, a loading controller is a three-dimensional path tracking controller, two ends of the bearing main shaft are respectively provided with an eddy current sensor, and a torque rotating speed sensor is arranged at the end of the bearing main shaft close to the motor, a piezoresistive force measuring sensor is arranged at the bottom of the non-contact type electromagnetic loading device, the eddy current sensor, the torque rotating speed sensor and the piezoresistive force measuring sensor are connected with a load controller through an acquisition card and an analog-to-digital converter, the load controller is connected with an Oracle database stored in a 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 connected with a load device driver.
The invention relates to a dynamic electromagnetic loading force multi-parameter optimization control method for a water lubricated bearing, which is characterized in that a dynamic electromagnetic loading force control system for the water lubricated bearing is applied to control the electromagnetic loading force, as shown in figure 2, after the system is initialized, a target loading force is set, readings of a torque rotating speed sensor, a piezoresistive force transducer, two pairs of eddy current sensors and a load system controller are collected and transmitted to a load controller, the load controller reads the readings of the sensors and carries out mean value processing respectively to obtain the loading force measurement mean value of the signals of the piezoresistive force transducer
Excitation current measurement average of current sensor signal
Mean value of the rotational speed measurement of the torque rotational speed sensor signal
Judging whether the non-contact electromagnetic loading force is matched with a set value, if so, continuously repeating the process by each sensor, if not, preprocessing the database by taking the sensing signal after mean processing as a query condition to obtain a data block, reading the data block by a load controller by adopting a three-dimensional data path tracking algorithm optimized by a genetic algorithm, and calculating to obtain a reference current I r Will refer to the current I r Inputting the current into a current regulator, and calculating the current by adopting a sliding mode algorithm to obtain a control output current I smc Input into the drive of the load device to control the non-contact of the water-lubricated bearingThe electromagnetic loading force F of the electromagnetic loading device achieves the purposes of improving the accuracy of the electromagnetic loading force and the robustness under different working conditions.
Calculating the average value of the axle center distance measurement of the eddy current sensor signal in the sampling period
The calculation formula of (a) is as follows:
in the formula (1), k is the number of points collected in a sampling period, x r (i) The value of the center distance in all horizontal directions, y, acquired by the eddy current sensor installed horizontally in one sampling period r (i) The values of the axial center distances in all vertical directions acquired by the eddy current sensor vertically installed in one sampling period are delta (i), and the values of all non-directional axial center distances acquired in one sampling period are delta (i);
calculating the average value of the loading force measurement of the piezoresistive force cell signal in the sampling period
The calculation formula of (a) is as follows:
in the formula (2), k is the number of points collected in one sampling period, and F (i) is the value of all loading forces collected in one sampling period;
calculating the average value of the excitation current measurement of the current sensor signal in the sampling period
The calculation formula of (a) is as follows:
in the formula (3), k is the number of points collected in a sampling period, I e (i) The values of all the exciting currents collected in a sampling period are obtained;
calculating torque in a sampling period&Mean value of the rotational speed measurement of the rotational speed sensor signal
The calculation formula of (a) is as follows:
in the formula (4), k is the number of points acquired in a sampling period, and n (i) is the value of all the rotating speeds acquired in the sampling period;
by averaging the measured electromagnetic loading force of the non-contact electromagnetic loading device over a sampling period
And a threshold value F 0 *ε 1 And comparing, and judging whether the non-contact electromagnetic loading force is matched with a set value, wherein the judgment formula is as follows:
The Oracle database is stored in a server hard disk, and waits for the upper computer to send a user instruction at any time for calling, the structure of the Oracle database is shown in figure 3, and the Oracle database consists of a data storage end, a pre-calling data area, a plurality of processing processes, a user process, a server process and a backup log file. Wherein, the data storage end stores complete data table space, complete parameter table space and corresponding index file; calling parameters, data blocks obtained after preprocessing, library name files, mirror image files and the like are stored in a pre-calling data area to wait for calling instructions; the processing process comprises a CKPT process, an SMON process, an LGWR process, a DBWN process, an ARCN process and a PMON process and is respectively responsible for functions of checking, calling, recording, deleting and the like; the user process is a calling instruction or a modifying instruction sent by the upper computer, and then the database is modified after the server process.
The data storage end comprises: a data table space composed of actual test data, a parameter table space composed of optimized parameters and a shared pool composed of calling statements, table headers, table descriptions and the like;
the data table space formed by actual test data is composed of a test data table and a data index section, the test data table stores the actually measured test data of loading force F under different axial center distances delta, different rotating speeds n and different exciting currents I, the test data table is divided into three-dimensional data tables under different axial center distances by taking the axial center distances delta as a primary query condition, and the three-dimensional data tables are composed of three-dimensional data formed by the rotating speeds n, the exciting currents I and the electromagnetic loading force F;
the spatial structure of the data table is shown in fig. 4, the three-dimensional data table is subdivided into a plurality of data blocks by a rotating speed range, an exciting current range and a loading force range, wherein a shaft center distance delta is a primary query condition, a loading force interval is a secondary query condition, the rotating speed interval and the exciting current interval are tertiary query conditions, a data index section is formed by index keywords, and the index keywords are formed by the primary query condition, the secondary query condition and the tertiary query condition;
the parameter table space is composed of an optimized parameter table and a parameter index segment, and the optimized parameter table stores various optimized parameters, such as maximum step length lambda max Maximum viewing distance s max Step gain factor K, curve path weight ζ 1 、ζ 2 、ζ 3 、η 1 、η 2 、η 3 The categories are used as primary query conditions and are respectively stored in a data table in a stack form.
Each process plays different roles in the three-dimensional database reading process, and after the CKPT process checks the integrity of the database at the data storage end, the SMON process clears the temporary time period which is not used any more, so that the database is ensured to have enough data space record modification records. During operation, the DBWR process saves the old parameters generated during optimization in the modification record, and if there is data modification in the data table space, the old parameters are also saved in the modification record. The database is limited, and the modified record and the modified data are respectively sent back to the data storage end through the LGWR process and the DBWN process to be respectively stored. The modified record is time-efficient, and in order to ensure that a long-time change curve of the parameter can be generated, the ARCN process calls the modified record in the database to be stored additionally.
The calling flow chart is shown in FIG. 5, and in combination with FIG. 4, the user process sends out a calling instruction, and first inquires the average value of the wheelbase, which is the primary inquiry condition
Specifying a data table space; at average value of current loading force
Confirming a secondary query condition, after a data area is appointed, querying whether the value of the target coordinate point loading force F is located in the data area, if not, calling the target loading force F to the average value of the current loading force
All the data areas of (2) constitute a pre-call data area, the structure of which is shown in fig. 6; by current operating mode-speed of rotation
And an excitation current
Confirming three-stage query conditions, specifying a data segment in the pre-call data area, reading the data segment and placing it with the index segment into local data located in the pre-call data area, etcTo be read.
The preprocessing of the database to obtain the data blocks is specifically,
sending out a call command, averaging the wheel center distances
As a first-level query condition, designating a data table space; at average value of current loading force
As a secondary query condition, after a data area is designated, whether the value of the target coordinate point loading force F is located in the data area is queried, if so, the data area is a pre-calling data area, and if not, the target loading force F is called to the average value of the current loading force
All the data areas form a pre-calling data area; rotating speed according to current working condition
And an excitation current
And as a three-level query condition, designating a data segment in the pre-call data area, reading the data segment, putting the data segment and the index segment into local data in the pre-call data area together to obtain a preprocessed data block, and waiting for the load controller to read.
The three-dimensional data path tracking algorithm optimized by the load controller through the genetic algorithm is composed of a global path planning layer, a local path planning layer, a path reconstruction layer and a behavior execution layer, and is shown in fig. 7. In particular to a method for preparing a high-performance nano-silver alloy,
initializing load controller, waking up database, reading axle center distance
Rotational speed of shaft
Exciting current
Loading force
Inputting a value, calling a data segment of local data stored in a pre-calling data area, entering a global path planning layer, establishing a three-dimensional graph, determining a current input value coordinate point and a target value coordinate point, and planning a global path; entering a local path planning layer, adding constraint conditions, and searching an optimal path in the global path; entering a behavior execution layer, reading an optimal path, judging and selecting a point-to-point tracking mode or a point-to-line tracking mode, respectively optimizing by using a simulated annealing algorithm and a particle swarm algorithm, and calculating a reference current I according to an excitation current coordinate change value r And reference current I r Outputting the current to a current controller;
meanwhile, the average value of the wheel center distances is judged in real time
If the path is changed, entering a path reconstruction layer, replacing a table space in a database, directly calling a specified data segment in the table space without indexing, entering a local path planning layer again, re-planning the path, adding a constraint condition, and searching an optimal path in the global path; entering a behavior execution layer, reading an optimal path, selecting the optimal path, determining a path tracking mode, and calculating a reference current I according to an excitation current coordinate change value r 。
The local path planning layer is used as a local planning part of a three-dimensional data path tracking algorithm, receives local map information generated by a global map and from an electromagnetic loading force three-dimensional coordinate to a target electromagnetic force three-dimensional coordinate under the current working condition, adds constraint conditions to select a local optimal path, and stores the obtained optimal path in a specified data block of a database, so that real-time alternation is facilitated, as shown in figure 8, specifically,
calling three stored in the databaseLow order curve path weight ζ 1 、ζ 2 、ζ 3 And three higher order curve path weights η 1 、η 2 、η 3 Reading the three-dimensional data graph, confirming the current coordinate and the target coordinate, calculating an electromagnetic loading force error e, and judging according to the error as follows:
determining whether the error e is within 30% of the target electromagnetic force, and if the error is less than 30% of the target electromagnetic force, determining the low-order curve path weight zeta 1 Is parameter 1; otherwise, determining the path weight eta of the high-order curve 1 Is parameter 1; whether a discontinuous point exists on the three-dimensional data graph is judged according to whether the derivative is continuous, and if the discontinuous point exists, the path weight zeta of the low-order curve is determined 2 Is parameter 2; otherwise, determining the path weight eta of the high-order curve 2 Is parameter 2; whether the small change of the working condition is allowed or not, the precision of the control system is within +/-2% - +/-5% of the target value, and if the rotation speed fluctuation is within the precision of the control system when the optimal path is allowed to be a low-order curve, the path weight eta of the low-order curve is determined 3 Is parameter 3; otherwise, determining the path weight eta of the high-order curve 3 Is parameter 3;
integrated path weight ζ 1 、ζ 2 、ζ 3 、η 1 、η 2 、η 3 The selected path weight is iteratively optimized through a genetic algorithm, parameters are adjusted, and the path weight zeta of the low-order curve 1 、ζ 2 、ζ 3 Summing to obtain total weight zeta of low-order curve path and weight eta of high-order curve path 1 、η 2 、η 3 Summing to obtain the total weight eta of the high-order curve path;
if zeta is larger than eta, the optimal low-order curve path set is judged to be searched, otherwise, the optimal high-order curve path set is judged to be searched, the weight difference value delta is calculated to be | eta-zeta |, and the weight difference value threshold delta is adjusted through a genetic algorithm * To determine whether to select a higher order or a lower order in the optimal curve group, the determination conditions are as follows:
the optimal high-order curve path group is selected by adopting a D × Lite path search algorithm, and the optimal low-order curve path group is selected by adopting a Dijkstra algorithm.
Entering a behavior execution layer, reading an optimal path, judging and selecting a point-to-point tracking mode or a point-to-line tracking mode, respectively optimizing by using a simulated annealing algorithm and a particle swarm algorithm, and calculating a reference current I according to an excitation current coordinate change value r As shown in fig. 9, specifically,
reading the sight distance s and the maximum sight distance s from the database max Step length lambda, maximum step length lambda max Judging whether the order m of the optimal path L is larger than 2 or not according to the step gain coefficient K and the optimal path L obtained by the local path planning layer;
if m>2, selecting a point-line tracking mode, wherein the flow of the mode is as follows: judging the current signal error e and the maximum visual range s max The relationship of (1); if e<s max At the maximum step size λ max Selecting a forward point on the optimal path; if e>s max That is, the target point can be seen, the step gain coefficient K is corrected according to the error e by the particle swarm optimization algorithm, and the corrected step gain coefficient and the maximum step lambda are calculated max Obtaining the step length lambda by multiplication, so that a forward point is selected on the optimal path, and when the forward point of the target point is reached, the step length lambda is 0; if a discontinuous point exists in the step length lambda, the discontinuous point is taken as a forward point, and path tracking is carried out in a segmented mode; obtaining the excitation current coordinate of each step, and calculating each step to obtain respective reference current I rn Gradually reach the final reference current I r ；
If m<2, selecting a point-point tracking mode, wherein the flow of the mode is as follows: adjusting the number q of the segmentation points by a particle swarm optimization algorithm according to the magnitude of the current signal error e; according to the number q of the division points, the optimal low-order curve is divided into a current point A and an intermediate point A 1 、A 2 、…、A q A target point B; the intermediate point A 1 Setting as the next target point, confirming the correction value of the excitation current coordinate, and calculating to obtain the parameterTest current I r1 (ii) a The reference current I is obtained respectively by performing point by point r2 、I r3 、…、I rq Finally, the target point reference current I is obtained r 。
The current controller is a sliding mode controller and is designed based on the following mathematical model:
in the formula (5), the reaction mixture is,
r is the excircle radius of the loading disc, the thickness of the loading disc, mu 0 Is vacuum magnetic conductivity, N is coil turn number, I is exciting current, l is air gap length, N is harmonic frequency, v x Is the loading disc linear velocity;
the sliding mode variable s of the sliding mode controller is selected as follows:
in the formula (6), the sliding mode variable s is designed through the sliding mode surface
Obtain, where x is the state vector and C is the matrix [ C ] 1 …c n-1 1] T In sliding mode control, parameter c 1 c 2 …c n-1 Should satisfy 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 the formula, n is 2, x 2 Is composed of
The magnitude of the adjustment c can be adjusted at the speed that the adjustment state approaches zero, the larger the c is, the higher the speed of the adjustment error is, and the current signal error e is equal to I r -I e ，
The sliding mode controller is designed in an approach rate mode, and the approach rate is as follows:
in the formula (7), k s And gamma are both normal numbers, sgn(s) is a sign function;
calculating to obtain the control output current I of the sliding mode controller smc Comprises the following steps:
I smc ＝ce+k s +γsgn(s) (8)。
examples
In this embodiment, according to the dynamic electromagnetic loading force multi-parameter optimization control method for the water lubricated bearing, a target loading force is set, readings of a torque rotating speed sensor, a piezoresistive force transducer, two pairs of eddy current sensors and a load system controller are collected and transmitted to a load controller, the readings of the sensors are read by the load controller and are respectively subjected to mean value processing, and a loading force measurement average value of signals of the piezoresistive force transducer is obtained
Excitation current measurement average of current sensor signal
Mean value of the rotational speed measurement of the torque rotational speed sensor signal
Determining non-contact electromagnetic loadingWhether the force is matched with a set value or not, if so, continuously repeating the process by each sensor; if not, preprocessing the database by taking the sensing signals after mean processing as query conditions to obtain data blocks, reading the data blocks by the load controller by adopting a three-dimensional data path tracking algorithm optimized by a genetic algorithm, and calculating to obtain a reference current I r Will refer to the current I r Inputting the current into a current regulator, and calculating to obtain a control output current I of the current regulator by adopting a sliding mode algorithm smc And the electromagnetic loading force F is input into a load device driver to control the non-contact electromagnetic loading device of the water lubrication bearing, so that the purposes of improving the accuracy of the electromagnetic loading force and the robustness under different working conditions are achieved.
As shown in fig. 10, the three-dimensional map is obtained by converting the table space data composed of the exciting current, the rotating speed and the electromagnetic loading force in a certain air gap, and the coordinate form of all points on the three-dimensional map is as follows: (I) e N, F), the formation of the three-dimensional graph comprises two steps of calling a database and a global path planning layer. Assuming that the current working condition coordinate is a point A and the target working condition coordinate is a point B, the current working condition coordinate point needs to be moved to the point B in a form of changing a horizontal coordinate by constructing an optimal path on the three-dimensional graph. First, entering the local path planning layer, the data segment from point a to point B is extracted, as shown in fig. 11.
FIG. 11 shows the optimal path L that may be selected by 3 path planning layers 1 、L e 、L 3 Wherein L is 1 、L 2 Is a high-order curve path passing through the surface of the three-dimensional graph; l is a radical of an alcohol 3 Is a path of a low-order curve passing through the inside of the three-dimensional graph, and L 3 And L 1 There is a turning point. The path planning layer starts to judge according to the following conditions:
1) whether the error e is within 30% of the target electromagnetic force;
2) whether a discontinuity exists on the three-dimensional data map;
3) whether minor changes in operating conditions are permitted;
assume that the current selections are:
1) the error e is within 30% of the target electromagnetic force;
2) there are no discontinuities on the three-dimensional data map;
3) allowing minor changes in operating conditions;
at this time, the path weight is selected as:
1) low-order curve path weight 1-zeta 1
2) High order curve path weight 2-eta 2 ；
3) Low order curve path weight 3-zeta 3 ；
After the total weight zeta of the low-order curve path and the total weight eta of the high-order curve path are obtained through iteration and summation of the genetic algorithm, the size of the zeta and the eta are judged, and at the moment, the eta is>ζ and Δ>Δ * Selecting L 2 And storing the curve path as an optimal curve path in a specified data block in a database, and waiting for the calling of a behavior execution layer.
The behavior execution layer calls the optimal curve L 2 Then, first, a judgment L is made 2 The order of (a). Obviously, L 2 The order is more than 2, so the point-line type tracking mode is adopted. Reading the sight distance s and the maximum sight distance s from the database max Step length lambda, maximum step length lambda max And step gain coefficient K, starting from starting point A, using point A as centre of circle, maximum visual distance s max Forming a line-of-sight circle O for the radius s Looking for the eye distance circle O s L from the optimum curve 2 And the intersection point is taken as a middle target point, and multi-step advancing is carried out through the step length lambda corresponding to the sight distance s.
Since there is an inflection point in the line of sight circle, point a is taken as the inflection point 1 Advancing as a target point to ensure a coordinate point (I) A ,n A ,F A ) Change to
In the process, only the exciting current I or the rotating speed n is changed, so that the instability of the shafting caused by the simultaneous change is avoided. From the k-th advancing point A as shown in FIG. 9 k To the (k + 1) th advance point A k+1 When there is no inflection or discontinuity in the path, therefore | A k ,A k+1 |＝ s max Step size is maximumLarge step size lambda max . At the advancing point A n To the target point B, due to | A n ,B|<s max Thus, the step λ ═ K λ max Selecting a forward point on the optimal path to obtain an excitation current coordinate of each step, and calculating each step to obtain respective reference current I rn Gradually reach the final reference current I r 。
Claims (10)
1. The dynamic electromagnetic loading force control system of the water lubricated bearing is characterized by comprising a pair of non-contact electromagnetic loading devices arranged at two ends of a bearing main shaft respectively, wherein the non-contact electromagnetic loading devices are connected with a loading device driver, two ends of the bearing main shaft are provided with eddy current sensors respectively, a torque and rotating speed sensor is arranged at the end, close to a motor, of the bearing main shaft, a piezoresistive force measuring sensor is arranged at the bottom of each non-contact electromagnetic loading device, the eddy current sensors, the torque and rotating speed sensors and the piezoresistive force measuring sensors are connected with a loading controller, the loading controller is connected with a database stored in a hard disk of a server, the loading controller is further connected with a current regulator, and the current regulator is connected with the loading device driver.
2. The dynamic electromagnetic loading force control system for water lubricated bearings of claim 1 wherein said load controller is a three dimensional path tracking controller;
the current regulator is a sliding mode controller;
the database is an Oracle database.
3. A dynamic electromagnetic loading force multi-parameter optimization control method for a water lubricated bearing, which is used for controlling electromagnetic loading force by applying the dynamic electromagnetic loading force control system for the water lubricated bearing as claimed in claim 1, and is characterized in that target loading force is set, readings of a torque rotating speed sensor, a piezoresistive force measuring sensor, two pairs of eddy current sensors and a load system controller are collected and signals are transmitted to the load controller, the load controller reads the readings of the sensors and performs mean value processing respectively to obtainMean value of the load force measurement of piezoresistive force sensor signals
Excitation current measurement average of current sensor signal
Mean value of the rotational speed measurement of the torque rotational speed sensor signal
Judging whether the non-contact electromagnetic loading force is matched with a set value, if so, continuously repeating the process by each sensor, if not, preprocessing the database by taking the sensing signal after mean processing as a query condition to obtain a data block, reading the data block by a load controller by adopting a three-dimensional data path tracking algorithm optimized by a genetic algorithm, and calculating to obtain a reference current I r Will refer to the current I r Inputting the current into a current regulator, and calculating the current by adopting a sliding mode algorithm to obtain a control output current I smc And the electromagnetic loading force F is input into a load device driver to control the non-contact electromagnetic loading device of the water lubrication bearing, so that the purposes of improving the accuracy of the electromagnetic loading force and the robustness under different working conditions are achieved.
4. The dynamic electromagnetic loading force multiparameter optimization control method for the water-lubricated bearing according to claim 3, wherein the mean value of the axle center distance measurements of the eddy current sensor signals in the sampling period is calculated
The calculation formula of (a) is as follows:
in the formula (1), k is the number of points collected in a sampling period, x r (i) Is oneValues of the axial distance in all horizontal directions, y, acquired by the eddy current sensor mounted horizontally in the sampling period r (i) The values of the axial center distances in all vertical directions acquired by the eddy current sensor vertically installed in one sampling period are delta (i), and the values of all non-directional axial center distances acquired in one sampling period are delta (i);
calculating the average value of the loading force measurement of the piezoresistive force cell signal in the sampling period
The calculation formula of (a) is as follows:
in the formula (2), k is the number of points collected in one sampling period, and F (i) is the value of all loading forces collected in one sampling period;
calculating the average value of the excitation current measurement of the current sensor signal during the sampling period
The calculation formula of (a) is as follows:
in the formula (3), k is the number of points collected in a sampling period, I e (i) The values of all the exciting currents collected in a sampling period are obtained;
calculating torque in a sampling period&Mean value of the rotational speed measurement of the rotational speed sensor signal
The calculation formula of (a) is as follows:
in the formula (4), k is the number of points collected in one sampling period, and n (i) is the value of all the rotating speeds collected in one sampling period;
by averaging the measured electromagnetic loading force of the non-contact electromagnetic loading device over a sampling period
And a threshold value F 0 *ε 1 And comparing, and judging whether the non-contact electromagnetic loading force is matched with a set value, wherein the judgment formula is as follows:
5. The dynamic electromagnetic loading force multi-parameter optimization control method for the water lubricated bearing according to claim 3, wherein the database is composed of a data storage end, a pre-call data area, a plurality of processing processes, a user process, a server process and a backup log file, and the data storage end comprises: a data table space composed of actual test data, a parameter table space composed of optimized parameters and a shared pool composed of calling statements, table headers, table descriptions and the like;
the data table space formed by the actual test data is composed of a test data table and a data index section, the test data table stores the actually measured test data of the electromagnetic loading force F under different axial center distances delta, different rotating speeds n and different exciting currents I, the test data table is divided into three-dimensional data tables under different axial center distances by taking the axial center distances delta as a primary query condition, and the three-dimensional data tables are composed of three-dimensional data formed by the rotating speeds n, the exciting currents I and the electromagnetic loading force F;
the three-dimensional data table is subdivided into a plurality of data blocks by a rotating speed range, an exciting current range and a loading force range, wherein the axle center distance delta is a first-level query condition, the loading force interval is a second-level query condition, the rotating speed interval and the exciting current interval are third-level query conditions, a data index section is formed by index keywords, and the index keywords are formed by the first-level query condition, the second-level query condition and the third-level query condition;
the parameter table space is composed of an optimized parameter table and a parameter index segment, and the optimized parameter table stores various optimized parameters, such as maximum step length lambda max Maximum viewing distance s max Step gain factor K, curve path weight ζ 1 、ζ 2 、ζ 3 、η 1 、η 2 、η 3 The categories are used as primary query conditions and are respectively stored in a data table in a stack form.
6. The dynamic electromagnetic loading force multi-parameter optimization control method for the water-lubricated bearing according to claim 3, wherein the data block obtained by preprocessing the database is specifically,
sending out a call instruction, and averaging the values of the axle center distances
As a first-level query condition, designating a data table space; at average value of current loading force
As a secondary query condition, after a data area is designated, whether the value of the target coordinate point loading force F is located in the data area is queried, if so, the data area is a pre-calling data area, and if not, the target loading force F is called to the average value of the current loading force
All the data areas form a pre-calling data area; rotating speed according to current working condition
And an excitation current
And as a three-level query condition, designating a data segment in the pre-call data area, reading the data segment, putting the data segment and the index segment into local data in the pre-call data area together to obtain a preprocessed data block, and waiting for the load controller to read.
7. The dynamic electromagnetic loading force multi-parameter optimization control method for the water lubricated bearing according to claim 6, wherein the load controller adopts a three-dimensional data path tracking algorithm optimized by a genetic algorithm and is composed of a global path planning layer, a local path planning layer, a path reconstruction layer and a behavior execution layer, in particular,
initializing load controller, waking up database, and reading axle center distance
Rotational speed of shaft
Exciting current
Loading force
Inputting a value, calling a data segment of local data stored in a pre-calling data area, entering a global path planning layer, establishing a three-dimensional graph, determining a current input value coordinate point and a target value coordinate point, and planning a global path; entering a local path planning layer, adding constraint conditions, and searching an optimal path in the global path; entering a behavior execution layer, reading an optimal path, judging whether a point-to-point tracking mode or a point-to-line tracking mode is selected, and respectively optimizing by using a simulated annealing algorithm and a particle swarm algorithmCalculating reference current I according to the variation value of exciting current coordinate r And reference current I r Outputting the current to a current controller;
meanwhile, the average value of the wheel center distances is judged in real time
If the path is changed, entering a path reconstruction layer, replacing a table space in a database, directly calling a specified data segment in the table space without indexing, entering a local path planning layer again, re-planning the path, adding a constraint condition, and searching an optimal path in the global path; entering a behavior execution layer, reading an optimal path, selecting the optimal path, determining a path tracking mode, and calculating a reference current I according to an excitation current coordinate change value r 。
8. The dynamic electromagnetic loading force multiparameter optimization control method for the water lubricated bearing according to claim 7, wherein the local path planning layer, as a local planning part of a three-dimensional data path tracking algorithm, receives map information generated from a global map and from an electromagnetic loading force three-dimensional coordinate under a current working condition to a target electromagnetic loading force three-dimensional coordinate, adds constraint conditions to select a local optimal path, and stores the obtained optimal path in a specified data block of a database, thereby facilitating real-time alternation,
invoking three low-order curve path weights ζ stored in a database 1 、ζ 2 、ζ 3 And three higher order curve path weights η 1 、η 2 、η 3 Reading the three-dimensional data graph, confirming the current coordinate and the target coordinate, calculating an electromagnetic loading force error e, and judging according to the error as follows:
determining whether the error e is within 30% of the target electromagnetic force, and if the error is less than 30% of the target electromagnetic force, determining the low-order curve path weight zeta 1 Is parameter 1; otherwise, determining the path weight eta of the high-order curve 1 Is parameter 1; whether a discontinuous point exists on the three-dimensional data graph is judged according to whether the derivative is continuous or not, if the discontinuous point exists,determining a low-order curve path weight ζ 2 Is parameter 2; otherwise, determining the path weight eta of the high-order curve 2 Is parameter 2; whether the small change of the working condition is allowed or not, the precision of the control system is within +/-2% - +/-5% of the target value, and if the rotation speed fluctuation is within the precision of the control system when the optimal path is allowed to be a low-order curve, the path weight eta of the low-order curve is determined 3 Is parameter 3; otherwise, determining the path weight eta of the high-order curve 3 Is parameter 3;
integrated path weight ζ 1 、ζ 2 、ζ 3 、η 1 、η 2 、η 3 The selected path weight is iteratively optimized through a genetic algorithm, parameters are adjusted, and the path weight zeta of the low-order curve 1 、ζ 2 、ζ 3 Summing to obtain total weight zeta of low-order curve path and weight eta of high-order curve path 1 、η 2 、η 3 Summing to obtain the total weight eta of the high-order curve path;
if zeta is larger than eta, the optimal low-order curve path is judged to be searched, otherwise, the optimal high-order curve path group is judged to be searched, the weight difference value delta is calculated to be | eta-zeta |, and the weight difference value threshold delta is adjusted through a genetic algorithm * To determine whether to select a higher order or a lower order in the optimal curve group, the determination conditions are as follows:
the optimal high-order curve path group is selected by adopting a D × Lite path search algorithm, and the optimal low-order curve path group is selected by adopting a Dijkstra algorithm.
9. The dynamic electromagnetic loading force multiparameter optimization control method for the water-lubricated bearing according to claim 7, wherein the entering action execution layer reads an optimal path, judges whether a point-to-point tracking mode or a point-to-line tracking mode is selected, optimizes the optimal path by using a simulated annealing algorithm and a particle swarm algorithm respectively, and calculates a reference current I according to a coordinate change value of an excitation current r In particular to a method for preparing a high-performance nano-silver alloy,
reading the sight distance s and the maximum sight distance s from the database max Step length lambda, maximum step length lambda max Judging whether the order m of the optimal path L is greater than 2 or not according to the step gain coefficient K and the optimal path L obtained by the local path planning layer;
if m is greater than 2, selecting a point-line type tracking mode, wherein the flow of the mode is as follows: judging the current signal error e and the maximum visual range s max The relationship of (1); if e < s max At the maximum step size λ max Selecting a forward point on the optimal path; if e > s max That is, the target point can be seen, the step gain coefficient K is corrected according to the error e by the particle swarm optimization algorithm, and the corrected step gain coefficient and the maximum step lambda are calculated max Obtaining the step length lambda by multiplication, so that a forward point is selected on the optimal path, and when the forward point of the target point is reached, the step length lambda is 0; if a discontinuous point exists in the step length lambda, the discontinuous point is taken as a forward point, and path tracking is carried out in a segmented mode; obtaining the excitation current coordinate of each step, and calculating each step to obtain respective reference current I rn Gradually reach the final reference current I r ；
If m is less than 2, selecting a point-point tracking mode, wherein the flow of the mode is as follows: adjusting the number q of the segmentation points by a particle swarm optimization algorithm according to the magnitude of the current signal error e; according to the number q of the division points, the optimal low-order curve is divided into a current point A and an intermediate point A 1 、A 2 、…、A q A target point B; the intermediate point A 1 Setting as the next target point, confirming the correction value of the excitation current coordinate, and calculating to obtain the reference current I r1 (ii) a The reference current I is obtained respectively by performing point by point r2 、I r3 、…、I rq Finally, the target point reference current I is obtained r 。
10. The dynamic electromagnetic loading force multi-parameter optimization control method for the water-lubricated bearing according to claim 9, wherein the current controller is a sliding mode controller and is designed based on the following mathematical model:
in the formula (5), the reaction mixture is,
r is the excircle radius of the loading disc, h is the thickness of the loading disc, mu 0 Is vacuum magnetic conductivity, N is coil turn number, I is exciting current, l is air gap length, N is harmonic frequency, v x Is the loading disc linear velocity;
the sliding mode variable s of the sliding mode controller is selected as follows:
in the formula (6), c is the speed of the adjustment error, and the current signal error e is equal to I r -I e ，
The sliding mode controller is designed in an approach rate mode, and the approach rate is as follows:
in the formula (7), k s And gamma are both normal numbers, sgn(s) is a sign function;
calculating to obtain the control output current I of the sliding mode controller smc Comprises the following steps:
I smc ＝ce+k s +γsgn(s) (8)。
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