CN108279561B - Friction compensation based on disturbance bandwidth reduction and realization method and motion platform - Google Patents
Friction compensation based on disturbance bandwidth reduction and realization method and motion platform Download PDFInfo
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Abstract
The invention provides a friction compensation active disturbance rejection control method based on disturbance bandwidth reduction. In order to reduce the disturbance bandwidth of the active disturbance rejection controller at the speed zero crossing point of a motion platform, a design for reducing the system rigidity is provided, and the elastic restoring force ks is reduced, so that the disturbance which is low in the sensitivity of the motion of a friction force dead zone and difficult to eliminate is converted into the disturbance of limited rigidity elastic deformation; the invention also gives guidance to the inertia distribution of the rigid-flexible coupling platform, reduces the additional inertia as much as possible, leads the inertia of the core platform to be dominant, and leads the control rule of the friction dead zone to be similar to the rigid motion rule; in the movement process, the original friction force is used as the main disturbance and is changed into the composite disturbance of the friction force and elastic deformation, so that the bandwidth of the total disturbance is reduced, and the total disturbance elimination of the active disturbance rejection controller is facilitated.
Description
Technical Field
The invention relates to the technical field of high-speed precision motion control, in particular to a method for compensating and realizing the friction force based on reduction of disturbance bandwidth of an active disturbance rejection controller.
Background
In the field of high-speed precise motion control, a motion platform based on a mechanical guide rail has a friction dead zone, and the precision can only reach a micron level. In the occasions with higher precision requirements, the industry needs to adopt air flotation, magnetic suspension, hydrostatic guide rails and other modes to reduce or even eliminate the influence of friction, and the electronic manufacturing occasions have high cost, high requirements on use environment, and are not suitable for application and wide range of application. However, Moore's Law of electronics manufacturing (when the price is constant, the number of components that can be accommodated on an integrated circuit doubles approximately every 18-24 months, and performance doubles) places severe demands on both the precision and speed of packaging equipment. Conventional friction compensation schemes and control methods are difficult to meet with the ever-increasing demands of high-speed precision motion control. Scientific and technical personnel strive to find a control scheme capable of overcoming friction, an active disturbance rejection control algorithm is an effective method, model errors and external disturbance are considered uniformly, and disturbance information such as friction is well restrained. When the precision is in a micron order, the error can be rapidly and accurately eliminated without considering friction dead zone compensation. However, at the nanometer (<0.1um) level, there is a dynamic error at the velocity zero crossing. The main reason is that in a friction dead zone, although a motion platform does not overcome static friction to generate rigid motion, a driving force is applied, the motion platform generates tiny elastic deformation, the control rule is that a is (f-ks-cv)/M, and compared with the estimation of the overall motion, a is (f/M), the elastic deformation restoring force, the damping force and the accessory inertia all become disturbance terms, however, due to the common rigid design of the motion platform, the rigidity is too large, the prediction model accuracy of the extended observer of the active disturbance rejection controller is deteriorated, and the disturbance cannot be effectively eliminated.
The linearization and bandwidth concept is proposed in the text of 'control theory: model theory or control theory' of Mr. Han Jingqing 1989, and the introduction of the linearization and bandwidth concept provides a brand new visual angle for theoretical research and simultaneously reduces the research difficulty. However, in industry, bandwidth is cost. High bandwidth, while enabling increased tracking speed, also brings many problems: 1) the quality requirement on the actuating mechanism is improved; 2) exciting the high frequency dynamics of the object complicates the control problem; 3) the stability margin of the closed-loop system is reduced, and the closed-loop system is more sensitive to phase lag and time delay; 4) more sensitive to sensor noise.
Disclosure of Invention
The invention provides a design for reducing the system rigidity for reducing the disturbance bandwidth of an active disturbance rejection controller at the speed zero crossing point of a motion platform, and the elastic restoring force ks is reduced, so that the disturbance which is difficult to eliminate due to the deformation of a friction force dead zone is converted into the disturbance of limited rigidity elastic deformation; in the movement process, the original friction force is used as the main disturbance and is changed into the composite disturbance of the friction force and elastic deformation, so that the bandwidth of the total disturbance is reduced, and the total disturbance elimination of the active disturbance rejection controller is facilitated.
The technical scheme adopted by the invention is as follows.
A method for compensating and realizing disturbance bandwidth friction based on reduction of active disturbance rejection controller is characterized by comprising the following steps: s1, setting a rigid platform of a motion platform as a rigid-flexible coupling platform; the motion platform includes: frame, linear guide, rigid-flexible coupling motion platform, rigid-flexible coupling platform includes: a rigid frame, a flexible hinge and a core motion platform; wherein the core motion platform is connected to the rigid frame by the flexible hinge; s2, constructing an actuator and a displacement detection closed-loop system, inputting the total inertia M of the rigid-flexible coupling motion platform, and the equivalent rigidity k, mass M and damping c of the elastic vibration response of the rigid-flexible coupling motion platform supported by a guide rail, wherein the displacement, speed and acceleration of the rigid-flexible coupling motion platform are respectively expressed by s, v and a, the inertia influence coefficient is expressed by alpha, and the driving force is expressed by f; establishing an active disturbance rejection control algorithm, and setting a prediction model of an extended observer as a ═ f/[ M + alpha (M-M) ]; when the response of the process is emphasized, the value of alpha is 1; when the tail end response is emphasized, the value of alpha is 0; when both are considered, the value of alpha is between 0 and 1; when the rigid body moves, alpha is 1, the control model is a f/[ M + alpha (M-M) ], and the disturbance is friction; when rubbing the dead zone, the platform produces elastic vibration, and the control model should be the elastic vibration response of the rigidity of platform this moment: and f, setting alpha to 0, setting a control model to a to f/m, and disturbing to obtain an elastic deformation restoring force ks damping force cv.
Further, by reducing the elastic stiffness of the platform, and thus the elastic restoring force ks, the flexible hinge is made of a low damping metal material, so cv can also be regarded as a disturbance control model of approximately a ═ f/m.
Furthermore, the frame is made of light materials, the mass M of the core platform accounts for the main component, and M is approximately equal to M, so that the approximate model a of the friction dead zone is f/M and is approximate to the motion law of rigid motion.
Further, the core motion platform of the rigid-flexible coupling platform is located at the upper part of the rigid frame, and the core motion platform and the rigid frame are connected through the flexible hinge.
Further, the flexible hinges between the core motion platform and the rigid frame of the rigid-flexible coupled platform are symmetrically arranged.
A motion platform, comprising: frame, linear guide, rigid-flexible coupling motion platform, rigid-flexible coupling platform includes: a rigid frame, a flexible hinge and a core motion platform; wherein the core motion platform is connected to the rigid frame by the flexible hinge; the rigid-flexible coupling platform adopts the following control method: constructing an actuator and a displacement detection closed-loop system, inputting the total inertia M of a rigid-flexible coupling motion platform, and the equivalent rigidity k, mass M and damping c of the elastic vibration response of the rigid-flexible coupling motion platform under the support of a guide rail, wherein the displacement, speed and acceleration of the rigid-flexible coupling motion platform are respectively expressed by s, v and a, the inertia influence coefficient is expressed by alpha, and the driving force is expressed by f; establishing an active disturbance rejection control algorithm, and setting a prediction model of an extended observer as a ═ f/[ M + alpha (M-M) ]; when the response of the process is emphasized, the value of alpha is 1; when the tail end response is emphasized, the value of alpha is 0; when both are considered, the value of alpha is between 0 and 1; when the rigid body moves, alpha is 1, the control model is a f/M, and the disturbance is friction force; when rubbing the dead zone, the platform produces elastic vibration, and the control model should be the elastic vibration response of the rigidity of platform this moment: and f, setting alpha to 0, setting a control model to a to f/m, and disturbing to obtain an elastic deformation restoring force ks damping force cv.
Further, by reducing the elastic stiffness of the platform, and thus the elastic restoring force ks, the flexible hinge is made of a low damping metal material, so cv can also be regarded as a disturbance control model of approximately a ═ f/m.
Furthermore, the frame is made of light materials, the mass M of the platform accounts for the main component, and M is approximately equal to M, so that the approximate model a of the friction dead zone is f/M and is approximate to the motion law of rigid motion
Further, the core motion platform of the rigid-flexible coupling platform is located at the upper part of the rigid frame, and the core motion platform and the rigid frame are connected through the flexible hinge.
Further, the flexible hinges between the core motion platform and the rigid frame of the rigid-flexible coupled platform are symmetrically arranged.
Compared with the prior art, the beneficial effects are: when the observer bandwidth is more than 10 times of the natural frequency (disturbance bandwidth) and a prediction model is arranged during black box control (without a model), the observer bandwidth only needs to be higher than 3 times of the natural frequency and is higher, the control cost is higher, the platform natural frequency is reduced, and the observer bandwidth can be reduced by matching with the prediction model, so that the control cost is reduced.
Drawings
Fig. 1 is a rigid motion model of a conventional motion platform.
Fig. 2 is a motion model considering elastic deformation of the platform.
Fig. 3 shows a single-sided flexible hinge scheme for reducing the disturbance bandwidth according to the present invention.
FIG. 4 is a diagram of a symmetrical compliant hinge for reducing the bandwidth of a perturbation according to the present invention.
Detailed Description
The drawings are for illustrative purposes only and are not to be construed as limiting the patent; for the purpose of better illustrating the embodiments, certain features of the drawings may be omitted, enlarged or reduced, and do not represent the size of an actual product; it will be understood by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted. The positional relationships depicted in the drawings are for illustrative purposes only and are not to be construed as limiting the present patent.
The traditional PID control directly takes the difference between reference given and output feedback as a control signal, so that the contradiction between response rapidity and overshoot occurs. The active disturbance rejection controller evolves from a PID controller, and a core idea of PID error feedback control is adopted.
The active disturbance rejection controller mainly comprises three parts: a tracking differentiator (tracking differentiator), an extended state observer (extended state observer) and a nonlinear state error feedback control law (nonlinear state error feedback law).
The tracking differentiator is used for arranging a transition process and giving a reasonable control signal, so that the contradiction between the response speed and the overshoot is solved. The extended state observer is used for solving the influence of the unknown part of the model and the unknown disturbance integration on the control object. Although called an extended state observer, it is different from a general state observer. The extended state observer designs an extended state quantity to track the effects of unknown parts of the model and external unknown disturbances. A control quantity is then given to compensate for these disturbances. The control object is changed to a general integral cascade type control object. The purpose of designing the extended state observer is to observe the extended state variables, estimate unknown disturbance and the unmodeled part of the control object, realize the feedback linearization of a dynamic system and change the control object into an integral series type. And the nonlinear error feedback control law gives a control strategy of the controlled object.
Designing an extended state photodetector becomes the most important link for ADRC applications. When the object model is not completely unknown, the bandwidth of the state photodetector needs to be set above 10 times the disturbance bandwidth. With a relatively accurate model, the observer bandwidth can be only required to be 3 times of the disturbance bandwidth. The higher the observer bandwidth, the higher the acquisition frequency and the shorter the servo period, which is costly.
The friction compensation active disturbance rejection control method based on disturbance bandwidth reduction comprises the following steps:
1) the original rigid platform of the motion platform is changed into a rigid-flexible coupling platform as shown in figure 2.
The motion platform includes: the device comprises a base, a linear guide rail and a rigid-flexible coupling motion platform.
The rigid-flexible coupling platform comprises: a rigid frame, a flexible hinge and a core motion platform; the core motion platform is connected with the rigid frame through a flexible hinge.
Preferably, as shown in fig. 3, the flexible coupling platform may adopt a single-sided flexible hinge scheme, and the core motion platform is located at the upper part of the rigid frame, and the core motion platform and the rigid frame are connected through a flexible hinge. The advantage of using a single-sided flexible hinge scheme is lower cost.
Because the unilateral flexible hinge can cause height change in the working process, when the height is required, the scheme of symmetrically arranged flexible hinges shown in figure 4 can be adopted, and the flexible hinges between the core motion platform and the rigid frame of the rigid-flexible coupling platform are symmetrically arranged. The adoption of the symmetrically arranged flexible hinge scheme can well avoid the height change.
2) Constructing an actuator and a displacement detection closed-loop system, inputting the total inertia M of a rigid-flexible coupling motion platform, and the equivalent rigidity k, mass M and damping c of the elastic vibration response of the rigid-flexible coupling motion platform under the support of a guide rail, wherein the displacement, speed and acceleration of the rigid-flexible coupling motion platform are respectively expressed by s, v and a, the inertia influence coefficient is expressed by alpha, and the driving force is expressed by f; and establishing an active disturbance rejection control algorithm, and setting a prediction model of the extended observer as a ═ f/[ M + alpha (M-M) ].
When the response of the process is emphasized, the value of alpha is 1; when the tail end response is emphasized, the value of alpha is 0; when both are considered, the value of alpha is between 0 and 1.
When the rigid body moves, alpha is 1, the control model is a f/[ M + alpha (M-M) ], and the disturbance is friction.
When rubbing the dead zone, the platform produces elastic vibration, and the control model should be the elastic vibration response of the rigidity of platform this moment: and f, setting alpha to 0, setting a control model to a to f/m, and disturbing to obtain an elastic deformation restoring force ks damping force cv.
The frame is made of light materials, the mass M of the platform accounts for the main component, and M is approximately equal to M, so that an approximate model a of a friction dead zone is f/M and is approximate to a motion rule during rigid motion.
The existing rigid platform has high rigidity, the disturbance quantity can be eliminated only by needing very high control bandwidth, and the implementation cost is very high. The invention provides a design scheme for reducing disturbance bandwidth, reduces rigidity, thereby reducing the disturbance bandwidth, obviously reducing the elastic restoring force ks term, and having displacement output even under a small control force, thereby avoiding the problem that the expansion state observer cannot work due to zero displacement output under a small driving force when the traditional rigidity is too large. The invention also gives guidance to the inertia distribution of the rigid-flexible coupling platform, reduces the additional inertia as much as possible, leads the inertia of the core platform to be dominant, leads the control law of the friction dead zone to be similar to the rigid motion law a as f/M, and improves the stability of active disturbance rejection.
The friction compensation active disturbance rejection control method based on disturbance bandwidth reduction has the following working principle:
the traditional rigid body motion model (figure 1) is changed into a model (figure 2) considering the elastic vibration of the platform, and when the driving force is insufficient to overcome static friction at the zero crossing point of speed (starting and stopping), the platform generates elastic deformation, and the control rule at the moment is that a is (f-ks-cv)/m. Because the existing platform design is too rigid, the deformation is below the micron level. When the positioning accuracy of the platform is required to be in the micron order, the elastic deformation can be not considered. However, if the positioning accuracy is submicron or even nanometer, the control of the elastic deformation must be considered. The active disturbance rejection control is difficult to eliminate errors with small sensitivity, so that the rigidity of the platform is reduced, and the flexible hinge is used for connecting the moving platform and the sliding block, so that the rigidity of the platform is reduced (figure 3). Because the unilateral flexible hinge can cause height change in the working process, when the height requirement exists, the flexible hinge which is symmetrically arranged can be adopted (figure 4).
It should be understood that the above-described embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. And are neither required nor exhaustive of all embodiments. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be included in the protection scope of the claims of the present invention.
Claims (10)
1. A friction force compensation and realization method based on disturbance bandwidth reduction is characterized by comprising the following steps:
s1, setting a rigid platform of a motion platform as a rigid-flexible coupling platform;
the motion platform includes: a base, a linear guide rail and a rigid-flexible coupling platform,
the rigid-flexible coupling platform comprises: a rigid frame, a flexible hinge and a core motion platform; wherein the core motion platform is connected to the rigid frame by the flexible hinge;
s2, constructing an actuator and a displacement detection closed-loop system, inputting the total inertia M of the rigid-flexible coupling platform, the equivalent rigidity k, the mass M and the damping c of the elastic vibration response of the rigid-flexible coupling platform supported by a guide rail, respectively representing the displacement, the speed and the acceleration of the rigid-flexible coupling platform by s, v and a, representing the inertia influence coefficient by alpha and representing the driving force by f;
establishing an active disturbance rejection control algorithm, and setting a predicted control model of an extended observer as a ═ f/[ M + alpha (M-M) ];
when the response of the process is emphasized, the value of alpha is 1; when the tail end response is emphasized, the value of alpha is 0; when both are considered, the value of alpha is between 0 and 1;
when the rigid body moves, alpha is 1, the control model is a f/[ M + alpha (M-M) ], and the disturbance is friction;
when rubbing the dead zone, the platform produces elastic vibration, and the control model should be the elastic vibration response of the rigidity of platform this moment: and f, setting alpha to 0, setting the control model to a to f/m, and disturbing the control model to elastic deformation restoring force ks and damping force cv.
2. The method for friction force compensation and realization based on reduction of disturbance bandwidth according to claim 1 is characterized in that the elastic stiffness of the rigid-flexible coupling platform is reduced, thereby reducing the elastic deformation restoring force ks, the flexible hinge is made of low damping metal material, and the control model is approximately a ═ f/m.
3. The method for friction force compensation and realization based on reduction of disturbance bandwidth according to claim 1 or 2, characterized in that the rigid frame is made of light material, the mass M of the core motion platform is the main component, M is approximately equal to M, so the approximate control model of the friction dead zone is a ═ f/M, which is approximate to the motion law of rigid motion.
4. The reduced disturbance bandwidth friction force compensation and implementation method according to claim 3, wherein the core motion platform of the rigid-flexible coupling platform is located at an upper part of the rigid frame, and the core motion platform and the rigid frame are connected through the flexible hinge.
5. The reduced disturbance bandwidth based friction force compensation and implementation method according to claim 3, wherein the flexible hinges between the core motion platform and the rigid frame of the rigid-flexible coupled platform are symmetrically arranged.
6. A motion platform, comprising: frame, linear guide, rigid-flexible coupling platform includes: a rigid frame, a flexible hinge and a core motion platform; wherein the core motion platform is connected to the rigid frame by the flexible hinge;
the rigid-flexible coupling platform adopts the following control method:
constructing an actuator and a displacement detection closed-loop system, inputting the total inertia M of a rigid-flexible coupling platform, and the equivalent rigidity k, mass M and damping c of the elastic vibration response of the rigid-flexible coupling platform under the support of a guide rail, wherein the displacement, speed and acceleration of the rigid-flexible coupling platform are respectively expressed by s, v and a, the inertia influence coefficient is expressed by alpha, and the driving force is expressed by f;
establishing an active disturbance rejection control algorithm, and setting a prediction model of an extended observer as a ═ f/[ M + alpha (M-M) ];
when the response of the process is emphasized, the value of alpha is 1; when the tail end response is emphasized, the value of alpha is 0; when both are considered, the value of alpha is between 0 and 1;
when the rigid body moves, alpha is 1, the control model is a f/M, and the disturbance is friction force;
when rubbing the dead zone, the platform produces elastic vibration, and the control model should be the elastic vibration response of the rigidity of platform this moment: and f, setting alpha to 0, setting the control model to a to f/m, and disturbing the control model to elastic deformation restoring force ks and damping force cv.
7. The motion platform of claim 6, wherein the elastic stiffness of the rigid-flexible coupling platform is reduced to reduce the elastic deformation restoring force ks, and the flexible hinge is made of a low damping metal material, approximately with a control model of a ═ f/m.
8. The motion platform according to claim 6 or 7, wherein the rigid frame is made of light materials, the mass M of the core motion platform is a main component, and M is approximately equal to M, so that the approximation of the friction dead zone adopts a control model a ═ f/M, which approximates the motion law of rigid motion.
9. The motion platform of claim 8, wherein the core motion platform of the rigid-flex coupled platform is located on an upper portion of the rigid frame, the core motion platform and the rigid frame being connected by the flexible hinge.
10. The motion platform of claim 8, wherein the flexible hinges between the core motion platform and the rigid frame of the rigid-flex coupled platform are symmetrically arranged.
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| CN109129479B (en) * | 2018-08-23 | 2021-03-09 | 广东工业大学 | Rigid-flexible coupling motion platform control method based on disturbance force compensation |
| CN109581862B (en) * | 2018-11-22 | 2021-09-03 | 广东工业大学 | Driver embedded with disturbance estimation compensation algorithm |
| CN109407511B (en) * | 2018-11-22 | 2021-07-09 | 广东工业大学 | Double-channel feedback rigid-flexible coupling platform control method |
| CN109617497B (en) * | 2018-11-22 | 2021-01-05 | 广东工业大学 | Dual-channel feedback disturbance estimation compensation driver |
| US11626815B2 (en) * | 2019-10-23 | 2023-04-11 | Guangdong University Of Technology | High-precision rigid-flexible coupling rotating platform and control method thereof |
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