CN116610036A - Track tracking optimization control method for disturbed mechanical arm system and storage medium - Google Patents
Track tracking optimization control method for disturbed mechanical arm system and storage medium Download PDFInfo
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Abstract
The invention discloses a disturbed mechanical arm system track tracking optimization control method and a storage medium. The method comprises the steps of constructing a dynamic model for a mechanical arm system consisting of n connecting rods, and converting the dynamic model into a space state form; designing an interference observer to estimate uncertainty contained in the robotic arm system; correcting steady-state signals of the system through systematic feedforward compensation design, so as to obtain a prediction model subjected to dynamic compensation; and obtaining a nominal system model based on the prediction model subjected to dynamic compensation, performing rolling optimization operation in generalized prediction control by using the obtained nominal system model, and obtaining a prediction control law of the generalized prediction controller by solving a performance index optimization function related to joint angle following errors. Compared with the traditional inverse dynamic control strategy, the method has obvious advantages in the aspects of track tracking precision and anti-interference capability, and has more accurate joint position response and stronger closed loop robustness.
Description
Technical Field
The invention relates to the technical field of mechanical arm track tracking optimization, in particular to a disturbed mechanical arm system track tracking optimization control method and a storage medium.
Background
The mechanical arm is usually composed of a kinematic chain formed by connecting joints, and is commonly used in various high-end application scenes such as intelligent manufacturing, aerospace and medical operation by virtue of the characteristics of high integration level, high flexibility and the like. In such applications, the mechanical arm is generally used to cooperate to complete more accurate and efficient engineering tasks, so that more urgent performance requirements are placed on high-precision trajectory tracking of the mechanical arm. However, in actual industrial scenes, a control method based on cascade PID is still more common, so as to complete various complex working condition tasks. However, the robot arm system is essentially a nonlinear control object with strong coupling and containing complex uncertainty, and it may be difficult to achieve better control expectations with only PID, even industrial accidents may occur. Therefore, the research on the advanced control algorithm for the mechanical arm has higher practical significance.
Numerous control schemes exist for robotic arm trajectory tracking control, which can be broadly categorized into the following: robust control, model predictive control (Model Predictive Control, MPC), adaptive neural network control, and sliding mode control, among others. Among them, MPC has been widely paid attention to engineering practitioners in recent years because of its simplicity and high trajectory tracking control performance, which has been considered by researchers as a control strategy with great development prospects. In general, MPC strategies can be subdivided into discrete-time optimized controls and continuous-time optimized controls. The former is widely applied by virtue of the fact that the optimization can be considered to solve the state constraint in the system, but the control effect is greatly influenced by the sampling control period, and the control performance is pursued uniformly, so that the problem of overlarge calculation load is further caused, and the real-time performance of the control system is further damaged. In order to alleviate the problem, yang proposes a generalized predictive control (Generalized Predictive Control, GPC) strategy, and the method does not need discretization processing on the model, but directly uses taylor approximation values of a system dynamics model to perform operation of optimizing performance indexes, so as to obtain a final display analysis solution.
However, the lumped uncertainty composed of parameter perturbation modeled by the mechanical arm system, the high-order dynamics state not modeled, external interference suffered by the system and the like is commonly existed in various engineering objects, the negative effect of the lumped uncertainty tends to cause the reduction of control performance, and even safety problems occur, namely, the completion of the established high-precision track tracking control of the mechanical arm system containing uncertainty is difficult to a certain extent. Also, the presence of uncertainty presents a significant challenge to conventional MPC designs. For this reason, uncertainty to the system needs to be taken into account in the controller design process, thereby improving various performances of the closed-loop system.
Disclosure of Invention
The invention aims to provide an optimized track tracking control method for a disturbed mechanical arm system and a storage medium for overcoming the defects in the prior art.
In order to achieve the above object, in a first aspect, the present invention provides a method for optimizing and controlling track tracking of a disturbed mechanical arm system, including:
step 1, constructing a dynamic model for a mechanical arm system consisting of n connecting rods, and converting the dynamic model into a space state form;
step 2, designing an interference observer to estimate uncertainty contained in the mechanical arm system;
step 3, correcting a steady-state signal of the system through systematic feedforward compensation design, so as to obtain a prediction model subjected to dynamic compensation;
and 4, obtaining a nominal system model based on the dynamic compensation prediction model, performing rolling optimization operation in generalized prediction control by using the obtained nominal system model, and obtaining a prediction control law of the generalized prediction controller by solving a performance index optimization function related to joint angle following errors.
Further, the dynamic model is described as:
wherein ,joint angle, angular velocity and acceleration vectors, respectively, < >>，/>For n-dimensional real number set, < >>For joint torque>，/>Is an inertial matrix->, and ，/>for centripetal and coriolis force matrices, +.>Is the gravity item of the mechanical arm, +.>，/>Is a lumped disturbance of parameterized uncertainty, unmodeled dynamics and external disturbances of the system.
Further, the mode of converting the dynamic model into the space state form is specifically as follows:
definition of the definition and />The robotic arm system is re-described as a state space form:
wherein ,、/>respectively-> and />First derivative of>To predict control law, ++>In order to integrate the interference into a set,a dynamic model is known for the system;
。
further, the interference observer is expressed as:
wherein ,to disturb the internal auxiliary state of the observer, +.>Is->First derivative of>For a positive gain matrix to be designed, +.>Is->Is used for estimating the vector of the vector;
defining estimation errors of an interference observerThe error equation of the interference observer is obtained to satisfy:
wherein ,is->Is a first derivative of (a).
Further, the step 3 specifically includes:
based on the estimated value of the interference observer, the steady-state reference signal is obtained by correcting the unknown uncertainty in the system、/>、/>：
wherein ,for a given trajectory desired by the robotic arm system, +.>Is->First derivative of>Is->Second derivative of>Dynamic models are known for systems->In steady state reference signal->、/>Numerical values at;
then, the following coordinate conversion is performed:
build up toA nonlinear system that is a new state variable, specifically as follows:
wherein ,representing the transpose of the matrix>Is an n-order identity matrix>Is->Is a first derivative of (a).
Further, the step 4 specifically includes:
the following optimization performance indexes are set:
wherein ,for prediction period +.>Is a time variable +.>Is an integral intermediate variable;
by ignoring the estimation error and nonlinear tracking error term in the nonlinear system, a nominal system model is obtained as follows:
will track deviationsIn one prediction period [0, T]Inner along the nominal system using taylor series expansion approximation:
wherein ,for factorial symbols, ++>A control order for a nominal system;
the optimization performance index is further calculated as:
for a pair ofAlong->Calculate the deviation and take +.>，/>At the same time at a known +.>On the premise of nonsingular, calculating to obtain predictive control law +.>The method comprises the following steps:
。
further, it willThe first column is the optimal predictive control law +.>This can further result in:
。
further, the control order is setSelecting 0, simplifying the optimal control law, and simplifying the optimal control law +.>The method comprises the following steps:
wherein ,respectively is->,/>Related constant matrix, < >>。
In a second aspect, the invention provides a storage medium storing a computer program which, when executed by a processor, implements the method described above.
The beneficial effects are that: the invention adopts the interference observer to reconstruct the uncertainty model of the mechanical arm system on line, designs a compensation loop along with the uncertainty model, corrects the unknown information of the uncertainty system, optimizes the nominal model of predictive control by utilizing the uncertainty estimation information, calculates the explicit form of the generalized predictive control law according to the set performance index containing joint tracking error, and has obvious advantages in the aspects of track tracking precision and anti-interference capability and has more accurate joint position response and stronger closed loop robust performance compared with the traditional inverse dynamic control strategy.
Drawings
FIG. 1 is a schematic diagram of a composite design framework based on a nonlinear disturbance observer and generalized predictive control;
Detailed Description
The invention will be further illustrated by the following drawings and specific examples, which are carried out on the basis of the technical solutions of the invention, it being understood that these examples are only intended to illustrate the invention and are not intended to limit the scope of the invention.
As shown in fig. 1, an embodiment of the present invention provides a method for tracking and optimizing a track of a disturbed mechanical arm system, including:
step 1, constructing a dynamic model for a mechanical arm system consisting of n connecting rods, and converting the dynamic model into a space state form. In particular, the dynamic model of the robotic arm system may be described as:
wherein ,joint angle, angular velocity and acceleration vectors, respectively, < >>，/>For n-dimensional real number set, < >>For joint torque>，/>Is an inertial matrix->, and ，/>for centripetal and coriolis force matrices, +.>Is the gravity item of the mechanical arm, +.>，/>Is a lumped disturbance of parameterized uncertainty, unmodeled dynamics and external disturbances of the system.
The mode of converting the dynamic model into the space state form is specifically as follows:
definition of the definition and />The robotic arm system is re-described as a state space form:
wherein ,、/>respectively-> and />First derivative of>To predict control law, ++>In order to integrate the interference into a set,a dynamic model is known for the system;
。
and 2, designing an interference observer to estimate uncertainty contained in the mechanical arm system. Specifically, the above-mentioned interference observer may be expressed as:
wherein ,to disturb the internal auxiliary state of the observer, +.>Is->First derivative of>For a positive gain matrix to be designed, +.>Is->Is used for estimating the vector of the vector;
defining estimation errors of an interference observerThe error equation of the interference observer is obtained to satisfy:
wherein ,is->Is a first derivative of (a).
And step 3, correcting a steady-state signal of the system through systematic feedforward compensation design, so as to obtain a prediction model subjected to dynamic compensation. The method comprises the following steps:
based on the estimated value of the interference observer, the steady-state reference signal is obtained by correcting the unknown uncertainty in the system、/>、/>：
wherein ,for a given trajectory desired by the robotic arm system, +.>Is->First derivative of>Is->Second derivative of>Dynamic models are known for systems->In steady state reference signal->、/>Numerical values at;
then, the following coordinate conversion is performed:
build up toA nonlinear system that is a new state variable, specifically as follows:
wherein ,for disturbing the estimation error of the observer, +.>，/>Representing the transpose of the matrix>Is an n-order identity matrix>Is->Is a first derivative of (a).
And 4, obtaining a nominal system model based on the dynamic compensation prediction model, performing rolling optimization operation in generalized prediction control by using the obtained nominal system model, and obtaining a prediction control law of the generalized prediction controller by solving a performance index optimization function related to joint angle following errors. The method comprises the following steps:
the following optimization performance indexes are set:
wherein ,for prediction period +.>Is a time variable +.>Is an integral intermediate variable;
by ignoring the estimation error and nonlinear tracking error term in the nonlinear system, a nominal system model is obtained as follows:
will track deviationsIn one prediction period [0, T]Inner along the nominal system using taylor series expansion approximation:
wherein ,for factorial symbols, ++>A control order for a nominal system;
the optimization performance index is further calculated as:
for a pair ofAlong->Calculate the deviation and take +.>，/>At the same time at a known +.>On the premise of nonsingular, calculating to obtain predictive control law +.>The method comprises the following steps:
。
preferably willThe first column is the optimal predictive control law +.>This can further result in:
。
it is also preferable to control the orderSelecting 0, simplifying the optimal control law, and adding ∈0 into the simplified optimal control law>The method comprises the following steps:
wherein ,respectively is->,/>Related constant matrix, < >>。
To verify the effectiveness of the present invention, the present invention was tested on a six degree of freedom welding robot platform. The experimental platform consists of a motion control unit, a joint PMSM servo driving unit and a robot body structure. Simulation verification is performed in MATLAB/Simulink, and algorithm module generation is performed by using a model-based design method (Model Based Design, MBD). The motion control unit is realized by a double-Fu controller, a TE1400 plug-in is adopted to import a C++ file generated by MBD, and the algorithm module is invoked and verified in TwainCAT software. In addition, the expected track required to be executed by the mechanical arm is planned by a cubic polynomial curve; each dynamic parameter matrix in a robotic arm systemObtained by modeling and identification methods.
The feasibility and effectiveness of the proposed control strategy is verified in terms of interference suppression capability and closed loop system steady state performance. For comparison, three schemes of reference inverse dynamics control (Inverse Dynamic Control, IDC), inverse dynamics control (idc+ndo) of integrated nonlinear disturbance observer and control method (gpc+ndo) proposed by the present invention are respectively designed. Wherein, the control law of the joint torque based on IDC is designed as follows:
wherein ：the location and velocity gain matrices, respectively.
Based on the above embodiments, it will be readily appreciated by a person skilled in the art that the present invention also provides a storage medium storing a computer program which, when executed by a processor, implements the above-described method.
The foregoing is merely a preferred embodiment of the present invention, and it should be noted that other parts not specifically described are within the prior art or common general knowledge to a person of ordinary skill in the art. Modifications and alterations may be made without departing from the principles of this invention, and such modifications and alterations should also be considered as being within the scope of the invention.
Claims (9)
1. The track tracking optimization control method for the disturbed mechanical arm system is characterized by comprising the following steps of:
step 1, constructing a dynamic model for a mechanical arm system consisting of n connecting rods, and converting the dynamic model into a space state form;
step 2, designing an interference observer to estimate uncertainty contained in the mechanical arm system;
step 3, correcting a steady-state signal of the system through systematic feedforward compensation design, so as to obtain a prediction model subjected to dynamic compensation;
and 4, obtaining a nominal system model based on the dynamic compensation prediction model, performing rolling optimization operation in generalized prediction control by using the obtained nominal system model, and obtaining a prediction control law of the generalized prediction controller by solving a performance index optimization function related to joint angle following errors.
2. The method for optimizing control of trajectory tracking of a disturbed mechanical arm system according to claim 1, wherein the dynamic model is described as:
；
wherein ,joint angle, angular velocity and acceleration vectors, respectively, < >>，/>For n-dimensional real number set, < >>For joint torque>，/>Is an inertial matrix->, and />，For centripetal and coriolis force matrices, +.>Is the gravity item of the mechanical arm, +.>，/>Is a lumped disturbance of parameterized uncertainty, unmodeled dynamics and external disturbances of the system.
3. The method for optimizing track following control of a disturbed mechanical arm system according to claim 2, wherein the mode of converting the dynamic model into a space state form is specifically as follows:
definition of the definition and />The robotic arm system is re-described as a state space form:
；
wherein ,、/>respectively-> and />First derivative of>To predict control law, ++>For lumped interference +.>A dynamic model is known for the system;
；
。
4. a disturbed mechanical arm system trajectory tracking optimization control method according to claim 3, characterized in that the disturbance observer is expressed as:
；
wherein ,to disturb the internal auxiliary state of the observer, +.>Is->First derivative of>For a positive gain matrix to be designed, +.>Is->Is used for estimating the vector of the vector;
defining estimation errors of an interference observerThe error equation of the interference observer is obtained to satisfy:
；
wherein ,is->Is a first derivative of (a).
5. The method for optimizing and controlling track following of a disturbed mechanical arm system according to claim 4, wherein the step 3 specifically comprises:
based on the estimated value of the interference observer, the steady-state reference signal is obtained by correcting the unknown uncertainty in the system、、/>：
；
wherein ,for a given trajectory desired by the robotic arm system, +.>Is->First derivative of>Is->Is used for the first derivative of (c),dynamic models are known for systems->In steady state reference signal->、/>The numerical value of the position is calculated,representing the desired angular value of the j-th joint, j=1, 2, … …, n;
then, the following coordinate conversion is performed:
；
build up toA nonlinear system that is a new state variable, specifically as follows:
；
；
wherein ,representing the transpose of the matrix>Is an n-order identity matrix>Is->Is a first derivative of (a).
6. The method for optimizing and controlling track following of a disturbed mechanical arm system according to claim 5, wherein the step 4 specifically comprises:
the following optimization performance indexes are set:
；
wherein ,for prediction period +.>Is a time variable +.>Is an integral intermediate variable;
by ignoring the estimation error and nonlinear tracking error term in the nonlinear system, a nominal system model is obtained as follows:
；
will track deviationsIn one prediction period [0, T]Inner along the nominal system using taylor series expansion approximation:
；
wherein ,for the order ofMultiplication symbol, & lt>A control order for a nominal system;
the optimization performance index is further calculated as:
；
；
；
；
for a pair ofAlong->Calculate the deviation and take +.>，/>At the same time, at a known timeOn the premise of nonsingular, calculating to obtain predictive control law +.>The method comprises the following steps:
。
7. the method for optimizing trajectory tracking control of a disturbed mechanical arm system according to claim 6, whereinThe first column is the optimal predictive control law +.>This can further result in:
；
。
8. the optimized control method for tracking the track of the disturbed mechanical arm system according to claim 7, wherein the control order isSelecting 0, simplifying the optimal control law, and simplifying the optimal control law +.>The method comprises the following steps:
；
wherein ,respectively is->,/>Related constant matrix, < >>。
9. A storage medium storing a computer program, which when executed by a processor implements the method of any one of claims 1-8.
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