CN101510072A - Servo system controller with self-adapting fuzzy frictional compensation - Google Patents
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Abstract
The invention discloses a servo system controller with self-adaptive fuzzy friction compensation. The servo system controller is used for improving the output tracking precision and fast response of a motor servo system, and is particularly applicable to a precision motor servo system which requires high precision and fast response. The invention comprises a parameter self-adaptive adjustment module, a fuzzy friction compensator and a robust control module. By adopting a fuzzy model to approximate a friction force model, the online assessment of the friction force value is realized by a self-adaptive adjustment of the fuzzy model parameters, and then a friction compensation is carried out so as to eliminate the adverse effects of the friction force on the output tracking precision and fast response of the servo system; and the adjustment of the fuzzy model parameters adopts a composite self-adaptive law and simultaneously uses the information relative to the system output error and the parameter evaluation error for carrying out the parameter adjustment so as to improve the parameter convergence speed. As the controller can realize fast and accurate friction model evaluation and friction compensation, the output tracking precision and fast response of the servo system can be greatly improved.
Description
Technical Field
The invention relates to a servo system controller with self-adaptive fuzzy friction compensation, which is used for improving the output tracking precision and quick response of a motor servo system and is particularly suitable for a precise motor servo system with high required precision and quick response.
Background
For servo systems with contact motion, friction is an important factor affecting its accuracy and response speed. Because of the influence of friction, the output speed of the servo system is often unstable when the servo system moves at low speed, and even the phenomenon of sliding is generated. Another important factor affecting servo systems is external disturbances. The accuracy of the servo system may be degraded by the disturbance. Therefore, in order to improve the accuracy and rapidity of the servo system, the controller needs to compensate the friction and overcome the influence of external disturbance on the system.
In order to eliminate the influence of friction and disturbance on the motor performance, a heuristic fuzzy logic controller is designed in the literature (A novel fuzzy logic compensation approach to improve the performance of a DC motor control system [ J ]. IEEE Trans on Industrial Electronics, 1996, 43 (1): 113 and 120.) by Teeter J T et al, so as to improve the control performance of the DC motor. However, this method employs a fixed fuzzy model, lacks adaptive capability, and is effective only for a specific object. In order to adapt the controller to different motor servo systems and reduce the dependence on the prior knowledge of the friction model, patent CN1974325A proposes an adaptive friction compensation controller based on least square estimation. The method adopts a discrete least square algorithm to carry out on-line identification on a friction model, and compensates the friction force according to the on-line identification. However, this method does not take into account the closed loop stability of the servo system, and the system will suffer from unstable oscillation when the parameter setting does not match the actual object.
Existing friction compensation modules for servo system controllers typically employ a simplified non-linear friction model, such as: coulomb friction model, coulomb plus sliding friction model, Stribeck model, etc. However, the actual friction has more complicated non-linear characteristics, and it is difficult to describe the real friction characteristics by using a simplified friction model, so that it is difficult to accurately compensate the friction force of the motor servo system. Furthermore, typical servo system controllers cannot guarantee the control performance of the system in the presence of bounded disturbances. Therefore, the current servo system controller often cannot meet the requirements of high precision and quick response of the servo system.
Disclosure of Invention
It is an object of the present invention to provide a servo system controller with adaptive fuzzy friction compensation. The controller estimates and compensates friction by using a self-adaptive algorithm according to the change of a friction model under different working environments (such as lubrication conditions, temperature, air pressure difference and the like), and inhibits the influence of external disturbance on the system performance, thereby improving the output tracking precision and the response rapidity of a servo system.
The purpose of the invention is realized by the following technical scheme.
The invention provides a servo system controller with self-adaptive fuzzy friction compensation, which comprises a parameter self-adaptive adjusting module, a fuzzy friction compensator and a robust control module. The parameter self-adaptive adjusting module comprises a regression vector generating module and a composite self-adaptive law module; the fuzzy friction compensator comprises a fuzzy model compensation module and a basic friction compensation module. The parameter self-adaptive adjusting module adjusts parameters in the fuzzy friction compensator according to the acquired speed signal and the angle tracking error amount of the servo system, wherein the regression vector generating module is used for calculating regression vectors required by the composite self-adaptive law module, and the composite self-adaptive law module executes a composite self-adaptive algorithm to realize the online adjustment of the parameters; the fuzzy friction compensator has different parameters for different friction models so as to adapt to different working environments, wherein the fuzzy model compensation module compensates continuous parts in the friction models, and the basic friction compensation module is used for compensating discontinuous parts in the friction models and viscous friction.
The control method of the controller adopts a composite self-adaptive law, and utilizes the relevant information of system output errors and parameter estimation errors to carry out parameter adjustment so as to improve the speed of parameter convergence of a fuzzy model and ensure that parameter estimation values are converged to optimal values; the fuzzy friction compensator compensates the friction according to the parameter estimation value, inhibits the adverse effect of the friction on the output tracking precision and the response speed of the motor servo system, and improves the control performance of the motor servo system.
The method adopts a fuzzy model to approximate a continuous nonlinear part in a friction model; the discontinuous part can be approximated by the product of a sign function and a pending parameter; thus, a friction model F is obtainedfIn the form of a linear parameterization of:
wherein
The vector is a regression vector, theta is a parameter vector of the fuzzy friction compensator, and omega is an approximation error of the fuzzy model; according to the linear parameterization form of the friction model, the approximation error of the fuzzy model can be regarded as the external disturbance of the system according to a self-adaptive robust control method, and a robust control law is designed; the robust control law enables a motor servo system to have closed-loop stability and expected transient response performance under any self-adaptive law.
The principle of the invention is as follows: friction is a non-linear characteristic of discontinuity at zero. The discontinuous part can be extracted and the continuous part is left, so that the friction model can be decomposed into continuous non-linear characteristic and zero pointA discontinuous characteristic. Since the fuzzy model can approximate continuous nonlinearity with an arbitrary accuracy, the fuzzy model can be used to approximate the continuous nonlinear portion in the friction model. While the discontinuity portion may be approximated by the product of a sign function and a pending parameter. Thus, a friction model F is obtainedfIn the form of a linear parameterization of:
wherein
The regression vector is shown as theta, the parameter vector of the fuzzy friction compensator is shown as theta, and the approximation error of the fuzzy model is shown as omega. According to the linear parameterization form of the friction model, the approximation error omega of the fuzzy model can be regarded as the external disturbance of the system according to the self-adaptive robust control method, and a robust control law is designed. The robust control law is executed in a robust control module, and can ensure that a servo system has closed-loop stability and expected transient response performance under any self-adaptive law. Design of robust control laws can be found in the literature (LIX, YAO B. adaptive robust prediction control of linear motors with negligiblelectric dynamics: the same and experiments [ J].IEEE Trans on Mechatronics，2001，6(4)：444-452.)。
Advantageous effects
1. The invention adopts a fuzzy model to approximate the nonlinear characteristic of friction. The fuzzy model has stronger nonlinear approximation capability than a simplified friction nonlinear model (such as a Coulomb friction model, a Coulomb plus sliding friction model or a Stribeck model) so as to describe the friction characteristic with higher precision. Therefore, on one hand, the invention can ensure that a more accurate friction model can be identified on line, and on the other hand, the friction compensation has better effect, namely: and unknown friction is offset more accurately, and the precision of a control system is improved.
2. The invention carries out friction compensation under the framework of the adaptive robust control method, and can ensure the closed loop stability and the expected transient response performance of the servo system. The friction compensation module of the conventional servo system controller does not consider the closed loop stability of the system, so the parameters of the friction compensation module need to be adjusted to avoid the oscillation phenomenon of the system. The invention can ensure the closed loop stability of the system, thereby greatly reducing the workload of parameter adjustment. In addition, the invention can enable the system to have expected transient response performance, thereby effectively improving the response speed of the motor servo system.
3. Most servo system controllers adopt a gradient method or a least square method to realize self-adaptive friction compensation. The invention adopts a composite adaptive law, and the method has faster parameter convergence speed and higher parameter estimation precision than the adaptive law, so that the friction model identification speed and the friction model identification precision are higher than those of a common servo system controller with friction compensation.
4. The composite adaptive law adopted by the invention has stronger anti-interference capability than the conventional adaptive law, so that the method can still ensure good online identification effect on friction under the influence of sensor noise or external disturbance. Therefore, the invention has stronger robustness.
Drawings
FIG. 1 is a block diagram of a servo system controller with adaptive fuzzy friction compensation;
FIG. 2 is a diagram of a servo system controller with adaptive fuzzy friction compensation and a controlled object;
FIG. 3 is a schematic diagram of the interior of the parameter adaptive adjustment module;
FIG. 4 is an internal schematic diagram of a fuzzy friction compensator;
FIG. 5 is a graph of membership functions for a fuzzy model;
FIG. 6 is a schematic diagram of an experimental platform of a motor servo system;
FIG. 7 is an output error plot of a comparative experiment of a servo controller with adaptive fuzzy friction compensation and a fixed model friction compensation controller, wherein (a) is the output error plot of the servo controller with adaptive fuzzy friction compensation; (b) an output error curve of the fixed model friction compensation controller;
FIG. 8 is a plot of a friction model obtained 40 seconds after the adaptive fuzzy friction compensator starts.
Detailed Description
The invention provides a self-adaptive fuzzy friction compensation method for a motor servo system. Embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
FIG. 1 is a block diagram of a servo system controller with adaptive fuzzy friction compensation. A servo system controller with adaptive fuzzy friction compensation comprising: the system comprises a robust control module, a parameter self-adaptive adjusting module and a fuzzy friction compensator. The servo system controller with the self-adaptive fuzzy friction compensation can be realized by embedded processors such as digital signal processors (such as TMS320F2812 and TMS320LF2407), 8051 single-chip microcomputers and the like and peripheral circuits thereof. Because the algorithm provided by the invention is a continuous time algorithm, the software implementation in the embedded processor needs to convert the continuous time algorithm into a discrete algorithm by using numerical methods such as a Runge-Kutta method, an Eulerian method and the like. The embedded processor and the peripheral circuit thereof are used for acquiring the measurement values of the speed measuring motor and the angle sensor in real time, and the output angular velocity value, the output angular value and the given angle of the servo system are all available for the servo system controller with self-adaptive fuzzy friction compensation. The embedded processor can calculate the output tracking error of the system according to the given angle and the measured system output angle value. The parameter self-adaptive adjusting module can adjust the parameters of the fuzzy friction compensator in real time according to the output tracking error, the output angular speed of the system and the total control quantity in the controller part, so that the fuzzy friction compensator can output accurate friction compensation quantity. The friction compensation quantity is superposed with the robust control quantity output by the robust control module to generate a total control quantity and input the total control quantity into the drive circuit, and the drive circuit generates drive current to enable the servo motor to operate.
FIG. 2 is a diagram of a servo system controller and controlled object with adaptive fuzzy friction compensation. The whole servo system consists of a servo system controller with adaptive fuzzy friction compensation and a controlled object, wherein the controlled object comprises: drive circuit, servo motor, tacho motor, angle sensor. Since the output of the servo system controller with adaptive fuzzy friction is received by the driving circuit and converted into driving current, the servo motor will generate a torque for offsetting friction to inhibit the adverse effect of friction on the accuracy and response rapidity of the motor servo system.
Fig. 3 is a schematic diagram of the inside of the parameter adaptive adjustment module. The parameter adaptive adjusting module comprises: a regression vector generation module and a composite adaptive law module. The regression vector generation module calculates a regression vector according to the output tracking error, the measured speed value and the master control quantity, and inputs the regression vector to the composite adaptive law module. And the composite adaptive law module internally runs an algorithm of the composite adaptive law to adjust the parameters of the fuzzy friction compensator. The known regression vector isThe algorithm of the composite adaptation law is as follows:
wherein
Gamma is any positive number, gamma is positive definite matrix, J is total inertia of servo system load and motor rotor, KfIs motor moment coefficient, u is total control quantity, e is system output tracking error, k1Is the feedback gain.
Projection operator, which is a vector, is defined as: <math> <mrow> <msub> <mi>Proj</mi> <mover> <mi>θ</mi> <mo>^</mo> </mover> </msub> <mrow> <mo>(</mo> <mo>·</mo> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mrow> <mo>[</mo> <msub> <mi>Proj</mi> <msub> <mover> <mi>θ</mi> <mo>^</mo> </mover> <mn>1</mn> </msub> </msub> <mrow> <mo>(</mo> <msub> <mo>·</mo> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mo>,</mo> <mo>·</mo> <mo>·</mo> <mo>·</mo> <mo>,</mo> <msub> <mi>Proj</mi> <msub> <mover> <mi>θ</mi> <mo>^</mo> </mover> <mi>p</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mo>·</mo> <mi>p</mi> </msub> <mo>)</mo> </mrow> <mo>]</mo> </mrow> <mi>T</mi> </msup> <mo>.</mo> </mrow></math>
where p is the dimension of the unknown parameter vector θ.
Is defined as follows:
in the above formula θiminAnd thetaimaxAre each thetaiThe minimum and maximum values of the value range.
Fig. 4 is an internal schematic diagram of the fuzzy friction compensator. The fuzzy friction compensator includes: a fuzzy model compensation module and a basic friction compensation module. According to the parameters and the measured speed value of the fuzzy friction compensator provided by the parameter self-adaptive adjusting module, the fuzzy model compensation module calculates and generates fuzzy model compensation quantityθ G T μ F(ii) a The basic friction compensation module calculates the compensation quantity of the discontinuous part and the viscous friction
Wherein
Is an estimate of the coefficient of viscous friction,
is an estimate of the maximum coulomb friction. The friction compensation quantity is the sum of the fuzzy model compensation quantity and the discontinuous part and the viscous friction compensation quantity, and the sum is as follows:
FIG. 5 is a graph of membership functions for a fuzzy model. The design process is as follows: taking an input ambiguity variable as
The domain of discourse is the real number domain R. Define 7 fuzzy sets on R: f1, F2.., F7. Corresponding membership function of μF1，μF2，...，μF7The definition is as follows:
wherein eiThe variable scale represents the size of the region of the fuzzy basis function peak points cluster where the fuzzy model can effectively approximate an arbitrary function, and outside this region only a constant function. For the output fuzzy variable, only one fuzzy set G is defined, and the corresponding membership function is muGAnd assume muG1. Because the fuzzy system is a single-input single-output system, the front piece and the back piece of the fuzzy rule only correspond to one fuzzy set. The 7 rules for this fuzzy system are as follows:
r1: if it is not
Is F1, then FfconIs G.
R2: if it is not
Is F2, then FfconIs G.
…，…
R7: if it is not
Is F7, then FfconIs G.
By adopting a product reasoning, central average defuzzification method and a single-value fuzzy generator, the obtained fuzzy system output has the following form:
wherein, thetaGiIs muFiF corresponding to maximum pointfconThe value is obtained. Easy to prove <math> <mrow> <munderover> <mi>Σ</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>7</mn> </munderover> <msub> <mi>μ</mi> <mi>Fi</mi> </msub> <mrow> <mo>(</mo> <mover> <mi>y</mi> <mo>.</mo> </mover> <mo>)</mo> </mrow> <mo>=</mo> <mn>1</mn> <mo>,</mo> </mrow></math>
The output of the fuzzy system can thus be expressed as: <math> <mrow> <msub> <mover> <mi>F</mi> <mo>^</mo> </mover> <mi>fcon</mi> </msub> <mrow> <mo>(</mo> <mover> <mi>y</mi> <mo>.</mo> </mover> <mo>|</mo> <msub> <munder> <mi>θ</mi> <mo>‾</mo> </munder> <mi>G</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>Σ</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>7</mn> </munderover> <msub> <mi>θ</mi> <mi>Gi</mi> </msub> <mo>·</mo> <msub> <mi>μ</mi> <mi>Fi</mi> </msub> <mrow> <mo>(</mo> <mover> <mi>y</mi> <mo>.</mo> </mover> <mo>)</mo> </mrow> <mo>=</mo> <msup> <msub> <munder> <mi>θ</mi> <mo>‾</mo> </munder> <mi>G</mi> </msub> <mi>T</mi> </msup> <msub> <munder> <mi>μ</mi> <mo>‾</mo> </munder> <mi>F</mi> </msub> <mo>.</mo> </mrow></math>
wherein,θ G＝[θG1，θG2，…，θG7]Tparameters for online adjustment;μ F＝[μF1，μF2，...，μF7]Tis a vector consisting of fuzzy basis functions. Defining a parameter vector
Comprises the following steps: <math> <mrow> <msubsup> <munder> <mi>θ</mi> <mo>‾</mo> </munder> <mi>G</mi> <mo>*</mo> </msubsup> <mo>=</mo> <mi>arg</mi> <msub> <mi>min</mi> <mrow> <msub> <munder> <mi>θ</mi> <mo>‾</mo> </munder> <mi>G</mi> </msub> <mo>∈</mo> <msub> <mi>Ω</mi> <mi>G</mi> </msub> </mrow> </msub> <mrow> <mo>[</mo> <msub> <mi>sup</mi> <mrow> <mover> <mi>y</mi> <mo>.</mo> </mover> <mo>∈</mo> <mi>R</mi> </mrow> </msub> <mrow> <mo>|</mo> <msub> <mover> <mi>F</mi> <mo>^</mo> </mover> <mi>fcon</mi> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>|</mo> <msub> <munder> <mi>θ</mi> <mo>‾</mo> </munder> <mi>G</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>F</mi> <mi>fcon</mi> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>|</mo> </mrow> <mo>]</mo> </mrow> <mo>.</mo> </mrow></math>
then when <math> <mrow> <msub> <munder> <mi>θ</mi> <mo>‾</mo> </munder> <mi>G</mi> </msub> <mo>=</mo> <msubsup> <munder> <mi>θ</mi> <mo>‾</mo> </munder> <mi>G</mi> <mo>*</mo> </msubsup> </mrow></math>
In time, the fuzzy model can realize the optimal approximation to the friction model. The invention designs the self-adaptive law so thatθ GCan approach to the ground on lineThereby obtaining an optimum estimate of friction
And compensation is performed.
Fig. 6 is a schematic diagram of an experimental platform of the motor servo system. Motor servo system experiment platform includes: servo controller, response synchronous ware, speed measuring motor, drive circuit, motor, load, servo controller includes: analog-to-digital conversion circuit, digital signal processor TMS320F2812, digital-to-analog conversion circuit. The induction synchronizer and the speed measuring motor are connected with a motor output shaft, the angle and the angular speed of the motor output shaft are converted into analog electric signals respectively, and then the analog electric signals are connected to an analog-to-digital conversion circuit and converted into digital signals which can be received by a digital signal processor TMS320F 2812. According to the digital signal, the digital signal processor TMS320F2812 calculates a control quantity by adopting the self-adaptive fuzzy friction compensation method provided by the invention, transmits the control quantity to the digital-to-analog conversion circuit, converts the control quantity into an analog signal, and then accesses the analog signal to the driving circuit to generate a current for driving the motor so as to enable the motor to run.
FIG. 7 is a graph of the output error of a comparison experiment of a servo controller with adaptive fuzzy friction compensation and a fixed model friction compensation controller. In the comparison experiment, a direct current motor servo system needs to track a sine angle signal with the amplitude of 1 degree and the frequency of 0.5 Hz, the two controllers are respectively used for carrying out experiments, and the output response angle is subtracted from a given angle signal to obtain output error curves of the two methods. The parameter self-adaptive adjusting module continuously adjusts the parameters of the fuzzy friction compensator in the running process of the motor servo system, so that the online identified friction model continuously approaches the actual friction characteristic, and more accurate friction compensation can be realized. The effect of the decrease in output angle error with time (maximum output tracking error less than 0.02 degrees when the start-up time is greater than 5 seconds) can be seen from the corresponding output error curve (a) for the servo controller with adaptive fuzzy friction compensation. As can be seen from the output error curve (b) corresponding to the fixed model friction compensation controller, the output angle error of the method is fixed (the maximum tracking error is 0.085 degrees) along with the increase of time, and the output angle error is obviously larger than that of the servo system controller with the adaptive fuzzy friction compensation. As can be seen from the output error curves obtained from the above comparative experiments, the servo system controller with adaptive fuzzy friction compensation has higher output tracking accuracy than the fixed model friction compensation controller.
FIG. 8 is a plot of a friction model obtained 40 seconds after the adaptive fuzzy friction compensator starts. Therefore, the friction model can embody the Stribeck effect and the viscous friction effect in actual friction, so that the servo system controller with the self-adaptive fuzzy friction compensation has good online identification capability of the friction model and can realize accurate friction compensation.
The present invention is not limited to the above-described embodiments, and various modifications, equivalent substitutions, improvements and the like made within the spirit and principle of the present invention are included in the scope of the present invention.
Claims (3)
1. Servo system controller with adaptive fuzzy friction compensation, its characterized in that: the robust adaptive control system comprises a parameter adaptive adjusting module, a fuzzy friction compensator and a robust control module, wherein the parameter adaptive adjusting module comprises a regression vector generating module and a composite adaptive law module; the fuzzy friction compensator comprises a fuzzy model compensation module and a basic friction compensation module; the parameter self-adaptive adjusting module adjusts parameters in the fuzzy friction compensator according to the acquired speed signal and the angle tracking error amount of the servo system, wherein the regression vector generating module is used for calculating regression vectors required by the composite self-adaptive law module, and the composite self-adaptive law module executes a composite self-adaptive algorithm to realize the online adjustment of the parameters; the fuzzy friction compensator has different parameters for different friction models so as to adapt to different working environments, wherein the fuzzy model compensation module compensates continuous parts in the friction models, and the basic friction compensation module compensates discontinuous parts in the friction models and viscous friction.
2. The servo system controller with adaptive fuzzy friction compensation of claim 1 wherein: the control method of the controller adopts a composite self-adaptive law, and utilizes the relevant information of system output errors and parameter estimation errors to carry out parameter adjustment so as to improve the speed of parameter convergence of a fuzzy model and ensure that parameter estimation values converge to optimal values; the fuzzy friction compensator compensates the friction according to the parameter estimation value, inhibits the adverse effect of the friction on the output tracking precision and the response speed of the motor servo system, and improves the control performance of the motor servo system.
3. The servo controller with adaptive fuzzy friction compensation of claim 1 wherein: the design method of the controller is to use a fuzzy model to approximate a continuous nonlinear part in a friction model; the discontinuous part can be approximated by the product of a sign function and a pending parameter; this results in a linear parameterized form of the friction model Ff, namely:wherein
The vector is a regression vector, theta is a parameter vector of the fuzzy friction compensator, and omega is an approximation error of the fuzzy model; according to the linear parameterization form of the friction model, the approximation error of the fuzzy model can be regarded as the external disturbance of the system according to a self-adaptive robust control method, and a robust control law is designed; the motor servo system of the robust control law has closed loop stability and expectation under any self-adaptive lawTransient response performance.
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| CN101846975A (en) * | 2010-05-28 | 2010-09-29 | 北京理工大学 | Servo system self-adaptive robust controller with dynamic frictional compensation |
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| CN101846975A (en) * | 2010-05-28 | 2010-09-29 | 北京理工大学 | Servo system self-adaptive robust controller with dynamic frictional compensation |
| CN102063061B (en) * | 2010-11-24 | 2012-07-04 | 西安理工大学 | Adaptive compensation method of friction in pneumatic servo system |
| CN102063061A (en) * | 2010-11-24 | 2011-05-18 | 西安理工大学 | Adaptive compensation method of friction in pneumatic servo system |
| CN102654775A (en) * | 2011-03-04 | 2012-09-05 | 富士机械制造株式会社 | Disturbing force compensating control device |
| CN102393639B (en) * | 2011-10-18 | 2015-04-22 | 河海大学常州校区 | Micro-gyroscope tracking control method based on adaptive fuzzy sliding mode |
| CN102393639A (en) * | 2011-10-18 | 2012-03-28 | 河海大学常州校区 | Micro-gyroscope tracking control method based on adaptive fuzzy sliding mode |
| CN102501251A (en) * | 2011-11-08 | 2012-06-20 | 北京邮电大学 | Mechanical shoulder joint position control method with dynamic friction compensation |
| CN103197562B (en) * | 2013-04-11 | 2015-04-22 | 浙江工业大学 | Rotary-table servo system neural network control method |
| CN103197562A (en) * | 2013-04-11 | 2013-07-10 | 浙江工业大学 | Rotary-table servo system neural network control method |
| CN104166346B (en) * | 2014-08-06 | 2016-08-24 | 东北大学 | A kind of servo system control method based on friciton compensation |
| CN104166346A (en) * | 2014-08-06 | 2014-11-26 | 东北大学 | Servo system control method based on friction compensation |
| CN104647379A (en) * | 2015-01-19 | 2015-05-27 | 广东工业大学 | Dual-arm robot movement control method under non-linear condition of driver |
| CN108646549A (en) * | 2018-03-31 | 2018-10-12 | 西南石油大学 | A kind of compensating control method improving servo-drive system tracking accuracy |
| CN108880357A (en) * | 2018-07-30 | 2018-11-23 | 福建工程学院 | The adaptive Non-smooth surface curren tracing control method of permanent magnet synchronous motor |
| CN108880357B (en) * | 2018-07-30 | 2020-10-27 | 福建工程学院 | Self-adaptive non-smooth current tracking control method of permanent magnet synchronous motor |
| CN112904720A (en) * | 2021-01-18 | 2021-06-04 | 中国船舶重工集团公司第七二四研究所 | Servo system friction nonlinear self-adaptive control method |
| CN113341702A (en) * | 2021-06-25 | 2021-09-03 | 中国民航大学 | Composite control method for electric servo system of airplane steering engine |
| CN113341702B (en) * | 2021-06-25 | 2023-02-03 | 中国民航大学 | Composite control method for electric servo system of airplane steering engine |
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