CN116339177A - Robot control method based on dynamic friction compensation - Google Patents
Robot control method based on dynamic friction compensation Download PDFInfo
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- CN116339177A CN116339177A CN202111588964.9A CN202111588964A CN116339177A CN 116339177 A CN116339177 A CN 116339177A CN 202111588964 A CN202111588964 A CN 202111588964A CN 116339177 A CN116339177 A CN 116339177A
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- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B19/00—Programme-control systems
- G05B19/02—Programme-control systems electric
- G05B19/04—Programme control other than numerical control, i.e. in sequence controllers or logic controllers
- G05B19/042—Programme control other than numerical control, i.e. in sequence controllers or logic controllers using digital processors
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B2219/00—Program-control systems
- G05B2219/20—Pc systems
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Abstract
The invention relates to a robot control method based on dynamic friction compensation, in particular to a robot control method which is mainly based on high-precision measurement and compensation of dynamic friction force when a robot runs under various complex working conditions. The technical means is that firstly, a dynamic friction moment compensation model is built for a robot servo system, a forward compensator is constructed, secondly, dynamic friction moment is calculated according to the expected movement angular speed of the servo system and is used as interference moment needing to be counteracted, and finally, the dynamic friction counteracting moment is counteracted with the actual friction of the servo system, so that the interference moment is reduced or even completely counteracted. In the construction of the dynamic friction moment compensation model, the dynamic friction moment equation of the servo system in different working areas needs to be considered to obtain the disturbance moment equation.
Description
Technical Field
The invention relates to a method for controlling high-precision motion of a robot. Particularly, the invention is mainly based on a robot control method for measuring dynamic friction force with high precision and compensating when the robot runs under various complex working conditions.
Background
When each joint of the robot runs, the system is easy to generate unstable or unstable motion, namely low-speed crawling phenomenon, also called stick-slip motion, which is mainly caused by disturbance torque with friction torque as a main component; meanwhile, the existence of friction can cause dead zone nonlinearity of a robot servo system for low-speed operation, so that resolution and system repetition rate are reduced, and steady-state errors are caused. The reduction of friction moment is limited by the conditions of the process level, the test expense and the like. It is therefore necessary to analyze and compensate for the effect of friction torque on the servo system.
At the same time, the influence of motor cogging torque on the low-speed performance of the robot servo system is also a non-negligible part. The cogging torque of the motor can generate speed fluctuation of a robot servo system, so that the low-speed stability of the system is affected to a certain extent. Secondly, the low-speed stability of the robot servo system is also affected by the quantization effect of the code wheel in the feedback link. Under the condition of ultra-low speed operation, due to the influence of quantization noise, a robot position signal jumps up and down on a command signal, and the low-speed stability of a robot servo system is influenced.
In summary, a better rate evaluation method is obtained, and the factors affecting the low-speed performance of the robot servo system are analyzed and compensated to improve the high-speed performance and the low-speed performance of the robot servo system.
In order to overcome the harm of friction to a servo system and improve the performance of the servo system, a static friction model is widely used in engineering technology for friction compensation, but with the continuous improvement of requirements, the defects that the dynamic friction characteristics cannot be reflected are more and more obvious. This is because there is a disadvantage in the static friction model, firstly, there is a sudden change in friction at zero speed, and secondly, in the boundary friction state, the model does not completely fit the actual friction curve. A method for measuring dynamic friction force with high precision and compensating when a robot operates under various complex working conditions is provided.
Disclosure of Invention
In the prior art, a static friction model is widely used for friction compensation, but with the continuous increase of requirements, the defect that the static friction model cannot reflect dynamic friction characteristics is more and more obvious. This is because there is a disadvantage in the static friction model, firstly, there is a sudden change in friction at zero speed, and secondly, in the boundary friction state, the model does not completely fit the actual friction curve. Accordingly, a method for measuring and compensating dynamic friction with high precision when the robot operates under various complex working conditions is provided.
A robot control method based on dynamic friction compensation comprises the following steps:
step one: establishing a dynamic friction moment compensation mathematical model for the friction moment of a robot motor to form a forward compensator, wherein the forward compensator is used for acquiring interference moment of a motor rotor at different expected rotating speeds;
step two: obtaining dynamic friction torque according to the expected rotating speed of the robot motor, and taking the dynamic friction torque as interference torque to be counteracted by the forward compensator;
step three: and the disturbance moment is counteracted by the forward compensator, so as to control the motor to act.
The robot motor friction force comprises a static friction force, a dynamic friction force and a viscous friction force, wherein the viscous friction force is directly proportional to motor rotation speed, only the static friction force exists when the motor does not move, and the dynamic friction force and the viscous friction force exist simultaneously after the motor moves.
When the motor working point is in a motor constant-speed operation interval, the interference moment and the dynamic friction moment are equal in magnitude and opposite in direction and can be expressed by the following equation:
T f linearity ＝T c sgn(ω) (7)
Wherein T is f linearity T is the interference moment of the motor in a constant-speed operation interval c For dynamic friction torque, sgn () is a sign function, the positive and negative values of which representOmega represents the angular speed of the motor rotor in different motion directions; t (T) c Is a dynamic friction torque, i.e. a friction torque under steady state operating conditions; the motor is obtained by measuring the actual running torque of the motor when the motor stably runs.
When the motor is in the acceleration range of the starting process, the motor interferes with the torque T f low speed As the motor rotor speed increases, the static friction torque decreases exponentially to the dynamic friction torque T c The value can be expressed by the following equation:
T f low speed ＝ΔTe -α|ω| sgn(ω) (8)
Wherein T is f low speed Representing the disturbance moment when the motor is in the acceleration interval of the starting process.
The friction torque compensation mathematical model is as follows:
T f ＝T c sgn(ω)+ΔTe -α|ω| sgn(ω) (9)
wherein T is f To interfere with the moment, T c For dynamic friction torque, deltaT represents static friction torque T s And dynamic friction moment T c Alpha represents the curvature of the friction curve of the acceleration section during the starting process, sgn () is a sign function, the positive and negative values thereof represent different directions of movement, and ω represents the angular speed of the motor rotor.
The Δt calculation method is as follows:
ΔT＝T s -T c (10)
wherein T is s T is the static friction torque of the motor rotor at the speed of 0 c Is a dynamic friction moment.
Static friction moment T when the motor rotor speed is 0 s The method comprises inputting a ramp moment into the motor, and inputting an instantaneous moment when the motor rotor suddenly changes from a zero speed state to a non-zero speed state, namely, a static friction moment T when the motor rotor speed is 0 s 。
For disturbance moment T f By interfering with the torque T of the motor f The equation is obtained by simulation experiments, wherein the simulation experiment method comprises the following steps:
inputting a slope moment to the motor, wherein the instantaneous input moment when the motor rotor is suddenly changed from a zero speed state to a non-zero speed state, namely, the static friction moment when the motor rotor speed is 0 is T s ；
After the motor runs stably, the dynamic friction torque is a constant value, and the running torque is measured when the motor runs stably, so that a friction characteristic curve is obtained and fitted, and the parameter alpha is obtained.
The dynamic friction moment T c The method comprises the following steps of:
T c for dynamic friction torque, i.e. friction torque under steady state operating conditions of FIG. 2
The third step is specifically as follows:
the expected rotating speed omega of the motor rotor is converted into expected input torque, and meanwhile the expected rotating speed omega of the motor rotor is input to the forward compensator, so that the motor interference torque T is obtained f Disturbance moment T obtained by forward compensator f For counteracting the actual friction with the motor, and controlling the motor action through the expected input moment. The actual output torque acts on the motor, the actual friction feedback is obtained in the form of torque, the feedback is the angular speed of the motor, one of the two closed-loop feedback is torque and the other is speed, and the method is a method for closed-loop control of the motor. The invention has the following beneficial effects and advantages:
1. the situation that the measurement cannot be carried out under the condition that the friction force is suddenly changed at the position of zero speed is avoided;
2. in the boundary friction state, a method for measuring dynamic friction force with high precision and compensating when the robot operates under various complex working conditions is ensured by setting a friction curve which is completely fit with reality. Therefore, the influence of friction on the system performance can be eliminated, and the purpose of counteracting or reducing the influence of friction links on the system is achieved.
Drawings
FIG. 1 is a block diagram of dynamic friction compensation of a robot provided by the invention;
FIG. 2 is a schematic diagram of an actual dynamic friction torque model provided by the present invention.
Detailed Description
As shown in fig. 1, the invention is realized by the following technical scheme:
the method comprises the steps of firstly adopting a forward compensator to dynamically compensate the robot system, wherein the forward compensator can be approximately equivalent to a feedforward compensation method, namely, firstly establishing a dynamic compensation mathematical model for a friction link in the system, so that the model and state variable information in the system are obtained, then estimating friction moment, and then identifying friction parameters through analyzing the state information of the system to estimate the friction moment. And finally, adding a compensation moment for balancing the friction moment into the control system to offset or reduce the friction link.
And secondly, according to the compensation mechanism, a dynamic friction model of the robot joint is established to describe a friction link in the system, then a friction parameter is identified by analyzing state information of the system to estimate friction moment, and finally a dynamic compensation moment with balanced friction moment is added into a control system, so that a control effect can be exerted in the system to offset each instant friction force, thus the influence of friction on the system performance can be eliminated, and the aim of offset or reduction of the influence of the friction link on the system is fulfilled.
1. Firstly, a mathematical model of a permanent magnet synchronous motor used by the robot is established, and a motor equation of the permanent magnet synchronous motor under a rotating d-q coordinate system is as follows:
stator flux linkage equation:
stator voltage equation:
bringing the stator flux linkage equation into the stator voltage equation can be obtained:
the electromagnetic torque 0 of the motor is as follows:
wherein the method comprises the steps of
D, q-axis stator flux linkage; l (L) d ，L q D, q-axis stator inductance; i.e d ，i q D, q-axis stator current; u (u) d ，u q D, q-axis stator voltage; r is stator resistance; p (P) n Is the pole pair number; omega r Is the mechanical angular velocity of the rotor; />
Is a coupling flux linkage on the stator windings. T (T) e Is the electromagnetic torque of the motor.
Since the motor control is performed by vector control, the current component i is caused to d 0, and d, q-axis stator inductances of the motor are equal, whereby:
the motor equation of motion is:
wherein J is rotor rotational inertia, B is viscous friction coefficient, T f Is a disturbance torque.
2. Thereby creating a dynamic friction model as shown in fig. 2. The friction force in the robot system consists of static friction force, dynamic friction force and viscous friction force, wherein the viscous friction force is in direct proportion to the speed of the system, namely is a linear function of the speed, and the viscous friction force and the linear system modeling are integrated into a whole to form a part of the linear system model. Separating viscous frictionStatic and dynamic friction torque T f Which act as interference in the system and are desirably cancelled. The static friction moment exists only at the initial starting moment of the robot system, and the amplitude of the static friction moment is always larger than the dynamic friction moment. Once the system is started, only dynamic friction torque acts on the actuator, which has a value T c The direction of the force is always opposite to the direction of movement, and when the working point is in the linear region, the following equation holds:
T f ＝T c sgn(ω) (7)
where sgn (ω) is a sign function, positive and negative values representing different directions of motion.
Disturbance moment T f At low speed, the static friction moment gradually and exponentially drops to the dynamic friction moment T along with the increase of the speed c Values. Based on this, disturbance moment T f The mathematical model of (2) can be given by:
T f ＝T c sgn(ω)+ΔTe -α|ω| sgn(ω) (8)
where ω represents the motor rotor angular velocity and α represents the curvature of the friction curve of the acceleration interval during start-up.
3. According to the above deduction, the forward compensator is adopted to dynamically compensate the friction of the robot system, and the forward compensator can be approximately equivalent to a feedforward compensation method, namely, a dynamic compensation mathematical model is firstly established for the friction links in the system, so that the model and state variable information in the system are obtained, then the friction moment is estimated, and then the friction parameters are identified through analyzing the state information of the system to estimate the friction moment. And finally, adding a compensation moment for balancing the friction moment into the control system to offset or reduce the friction link.
As shown in FIG. 1, the system reference input is a torque command T in The friction interference moment is T f The given instruction of the forward compensator is that the friction interference moment is T f By system reference input T in Given instruction T with forward compensator f Coacting to counteract the effects of nonlinear friction torque.
When a forward compensator is used to act on the robotic system, dynamic compensation is performed for the nonlinear friction torque, Δt=t in equation 8 s -T c ，T s The static friction torque at the speed equal to 0 can be obtained by the static characteristic of the motor, and when a slope torque is input, the instantaneous input torque of the motor from zero speed to non-zero speed is corresponding to T s Values. And then, performing simulation experiments on the system obtained by adding the friction force model to the linear system model to obtain the value of alpha, thereby obtaining an accurate friction moment compensation model. Once the friction model is built, the robot servo system presents linear characteristics, and can be controlled by adopting a conventional control strategy, so that satisfactory control effects can be obtained in different speed intervals. Therefore, the dynamic friction force is measured with high precision and compensated, so that the influence of friction on the system performance can be eliminated, and the aim of counteracting or reducing the influence of friction links on the system is fulfilled.
Claims (9)
1. The robot control method based on dynamic friction compensation is characterized by comprising the following steps:
step one: establishing a dynamic friction moment compensation mathematical model for the friction moment of a robot motor to form a forward compensator, wherein the forward compensator is used for acquiring interference moment of a motor rotor at different expected rotating speeds;
step two: obtaining dynamic friction torque according to the expected rotating speed of the robot motor, and taking the dynamic friction torque as interference torque to be counteracted by the forward compensator;
step three: and the disturbance moment is counteracted by the forward compensator, so as to control the motor to act.
2. The robot control method based on dynamic friction compensation according to claim 1, characterized in that:
the robot motor friction force comprises a static friction force, a dynamic friction force and a viscous friction force, wherein the viscous friction force is directly proportional to motor rotation speed, only the static friction force exists when the motor does not move, and the dynamic friction force and the viscous friction force exist simultaneously after the motor moves.
3. The robot control method based on dynamic friction compensation according to claim 1, characterized in that:
when the motor working point is in a motor constant-speed operation interval, the interference moment and the dynamic friction moment are equal in magnitude and opposite in direction and can be expressed by the following equation:
T f linearity ＝T c sgn(ω) (7)
Wherein T is f linearity T is the interference moment of the motor in a constant-speed operation interval c For dynamic friction moment, sgn () is a sign function, positive and negative values of the sgn () represent different motion directions, and omega represents the angular speed of a motor rotor; t (T) c Is a dynamic friction torque, i.e. a friction torque under steady state operating conditions; the motor is obtained by measuring the actual running torque of the motor when the motor stably runs.
4. The robot control method based on dynamic friction compensation according to claim 1, characterized in that:
when the motor is in the acceleration range of the starting process, the motor interferes with the torque T f low speed As the motor rotor speed increases, the static friction torque decreases exponentially to the dynamic friction torque T c The value can be expressed by the following equation:
T f low speed ＝ΔTe -α|ω| sgn(ω) (8)
Wherein T is f low speed Representing the disturbance moment when the motor is in the acceleration interval of the starting process.
5. The robot control method based on dynamic friction compensation according to claim 1, wherein the friction torque compensation mathematical model is as follows:
T f ＝T c sgn(ω)+ΔTe -α|ω| sgn(ω) (9)
wherein T is f To interfere with the moment, T c For dynamic friction torque, deltaT represents static friction torque T s And dynamic friction moment T c Alpha represents the curvature of the friction curve of the acceleration section of the starting processSgn () is a sign function whose positive and negative values represent different directions of motion, ω represents the motor rotor angular speed.
The Δt calculation method is as follows:
ΔT＝T s -T c (10)
wherein T is s T is the static friction torque of the motor rotor at the speed of 0 c Is a dynamic friction moment.
6. The robot control method based on dynamic friction compensation according to claim 5, wherein:
static friction moment T when the motor rotor speed is 0 s The method comprises inputting a ramp moment into the motor, and inputting an instantaneous moment when the motor rotor suddenly changes from a zero speed state to a non-zero speed state, namely, a static friction moment T when the motor rotor speed is 0 s 。
7. The robot control method based on dynamic friction compensation according to claim 5, wherein:
for disturbance moment T f By interfering with the torque T of the motor f The equation is obtained by simulation experiments, wherein the simulation experiment method comprises the following steps:
inputting a slope moment to the motor, wherein the instantaneous input moment when the motor rotor is suddenly changed from a zero speed state to a non-zero speed state, namely, the static friction moment when the motor rotor speed is 0 is T s ；
After the motor runs stably, the dynamic friction torque is a constant value, and the running torque is measured when the motor runs stably, so that a friction characteristic curve is obtained and fitted, and the parameter alpha is obtained.
8. The robot control method based on dynamic friction compensation according to claim 5, wherein: the dynamic friction moment T c The method comprises the following steps of:
T c is a dynamic friction torque, i.e., a friction torque under steady state operating conditions of fig. 2.
9. The robot control method based on dynamic friction compensation according to claim 1, characterized in that:
the third step is specifically as follows:
the expected rotating speed omega of the motor rotor is converted into expected input torque, and meanwhile the expected rotating speed omega of the motor rotor is input to the forward compensator, so that the motor interference torque T is obtained f Disturbance moment T obtained by forward compensator f For counteracting the actual friction with the motor, and controlling the motor action through the expected input moment. The actual output torque acts on the motor, the actual friction feedback is obtained in the form of torque, the feedback is the angular speed of the motor, one of the two closed-loop feedback is torque and the other is speed, and the method is a method for closed-loop control of the motor.
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN117400268A (en) * | 2023-12-13 | 2024-01-16 | 苏州康多机器人有限公司 | Nonlinear friction force compensation method and device, electronic equipment and storage medium |
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117400268A (en) * | 2023-12-13 | 2024-01-16 | 苏州康多机器人有限公司 | Nonlinear friction force compensation method and device, electronic equipment and storage medium |
| CN117400268B (en) * | 2023-12-13 | 2024-03-15 | 苏州康多机器人有限公司 | Nonlinear friction force compensation method and device, electronic equipment and storage medium |
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