CN113552796B - PID control performance comprehensive evaluation method considering uncertainty - Google Patents
PID control performance comprehensive evaluation method considering uncertainty Download PDFInfo
- Publication number
- CN113552796B CN113552796B CN202110817291.3A CN202110817291A CN113552796B CN 113552796 B CN113552796 B CN 113552796B CN 202110817291 A CN202110817291 A CN 202110817291A CN 113552796 B CN113552796 B CN 113552796B
- Authority
- CN
- China
- Prior art keywords
- engineering mechanical
- mechanical motion
- motion mechanism
- mechanism system
- comprehensive evaluation
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000011156 evaluation Methods 0.000 title claims abstract description 94
- 230000007246 mechanism Effects 0.000 claims abstract description 187
- 230000004044 response Effects 0.000 claims abstract description 61
- 238000000034 method Methods 0.000 claims abstract description 46
- 238000000342 Monte Carlo simulation Methods 0.000 claims abstract description 9
- 238000004519 manufacturing process Methods 0.000 claims abstract description 5
- 239000000463 material Substances 0.000 claims description 15
- 238000013461 design Methods 0.000 claims description 14
- 230000000694 effects Effects 0.000 claims description 13
- 238000005265 energy consumption Methods 0.000 claims description 13
- 238000010606 normalization Methods 0.000 claims description 11
- 238000005457 optimization Methods 0.000 claims description 11
- 238000012545 processing Methods 0.000 claims description 10
- 238000011158 quantitative evaluation Methods 0.000 claims description 8
- 230000008859 change Effects 0.000 claims description 6
- 230000008569 process Effects 0.000 claims description 5
- 238000004364 calculation method Methods 0.000 claims description 4
- 238000004088 simulation Methods 0.000 claims description 4
- 238000002474 experimental method Methods 0.000 claims description 2
- 238000012614 Monte-Carlo sampling Methods 0.000 description 3
- 238000005316 response function Methods 0.000 description 3
- 238000004458 analytical method Methods 0.000 description 2
- 238000009826 distribution Methods 0.000 description 2
- 238000013459 approach Methods 0.000 description 1
- 238000004422 calculation algorithm Methods 0.000 description 1
- 150000001875 compounds Chemical class 0.000 description 1
- 238000010276 construction Methods 0.000 description 1
- 239000006185 dispersion Substances 0.000 description 1
- 238000006073 displacement reaction Methods 0.000 description 1
- 238000012804 iterative process Methods 0.000 description 1
- 239000011159 matrix material Substances 0.000 description 1
- 230000008520 organization Effects 0.000 description 1
- 238000005381 potential energy Methods 0.000 description 1
- 238000003672 processing method Methods 0.000 description 1
- 238000005070 sampling Methods 0.000 description 1
- 230000009466 transformation Effects 0.000 description 1
- 230000000007 visual effect Effects 0.000 description 1
Images
Classifications
-
- 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
- G05B11/00—Automatic controllers
- G05B11/01—Automatic controllers electric
- G05B11/36—Automatic controllers electric with provision for obtaining particular characteristics, e.g. proportional, integral, differential
- G05B11/42—Automatic controllers electric with provision for obtaining particular characteristics, e.g. proportional, integral, differential for obtaining a characteristic which is both proportional and time-dependent, e.g. P. I., P. I. D.
Landscapes
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Engineering & Computer Science (AREA)
- Automation & Control Theory (AREA)
- Feedback Control In General (AREA)
Abstract
The invention discloses a PID control performance comprehensive evaluation method considering uncertainty, which comprehensively evaluates the control performance of an engineering mechanical motion mechanism system by considering a plurality of uncertainty parameters existing in the engineering mechanical motion mechanism system, optimizes the evaluation method according to the confidence coefficient of the comprehensive evaluation result and improves the evaluation result, firstly obtains an effective PID control system by optimizing according to a deterministic Lagrange dynamics model of the engineering mechanical motion mechanism system, and then determines various uncertainties such as manufacturing errors and control errors to establish a Lagrange dynamics model considering uncertainty; the method comprises the steps of calculating a response interval of the engineering machinery movement mechanism system by using a matching point method to obtain a comprehensive evaluation result of the control performance of the engineering machinery movement mechanism system, calculating the confidence coefficient of the evaluation result by using a Monte Carlo method, optimizing the comprehensive evaluation method according to the confidence level of the comprehensive evaluation result to obtain a comprehensive evaluation result of the mechanism control performance meeting the confidence coefficient, and effectively improving the confidence coefficient of the comprehensive evaluation result.
Description
Technical Field
The invention relates to the technical field of mechanism motion control performance evaluation, in particular to a PID control performance comprehensive evaluation method considering uncertainty.
Background
In the field of engineering machinery motion mechanism design, visual evaluation of the motion performance level of the engineering machinery motion mechanism is often one of the keys of design work in order to master the motion performance level of the engineering machinery motion mechanism, however, the motion performance level of the engineering machinery motion mechanism is in dispersion on parameters such as engineering machinery motion mechanism structures or materials due to various uncertain factors in the actual operation process, and the situation of inconsistency with the design scheme is inevitable. Therefore, how to comprehensively and comprehensively evaluate the performance level of the engineering mechanical motion mechanism under the condition of considering the uncertainty of the engineering mechanical motion mechanism and ensure the confidence of the evaluation result is a problem to be solved urgently in the field of engineering mechanical motion mechanism design, and the method has important significance for guiding the mechanism design direction and accurately improving the mechanism performance level.
The uncertainty of the engineering machinery motion mechanism refers to the deviation of the motion condition of an actual mechanism and the motion condition of an ideal mechanism. Generally, at the beginning of the design of the engineering machinery movement mechanism, an ideal movement equation of the engineering machinery movement mechanism should be obtained. If a construction machine kinematic mechanism design can implement this equation of motion with complete accuracy, the mechanism is called an ideal mechanism. In practice, the ideal motion equation of the engineering mechanical motion mechanism is too complex to design, so that the engineering mechanical motion mechanism is usually designed according to the approximate equation of the ideal motion equation for simplifying the processing, and the error caused by the approximate design is called a structural error. The engineering mechanical motion mechanism has many original errors in the manufacturing, assembling and using processes, and the motion errors of the mechanism caused by the original errors are called mechanical errors. Combining the above two aspects, error generating factors can hardly be eliminated, and the motion situation of the actual mechanism can hardly completely accord with the motion situation of the ideal mechanism. The mechanical error is usually expressed in terms of a position error and a displacement error.
The inherent uncertainty of the engineering mechanical motion mechanism is a part which cannot be ignored in evaluating the mechanism performance, and the influence of the uncertainty is ignored by the traditional deterministic evaluation method. Meanwhile, the control performance of the engineering mechanical motion mechanism is generally comprehensively expressed by various different indexes, the control performance level of the mechanism is difficult to reflect by a single index, and meanwhile, the performance level of the engineering mechanical motion mechanism needs to be evaluated by mutually weighting different indexes, or the performance levels among the engineering mechanical motion mechanisms are compared, so that comprehensive evaluation has to be carried out from multiple aspects, and certain confidence coefficient needs to be ensured for the performance evaluation of the engineering mechanical motion mechanism.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the method is used for comprehensively evaluating the performance level of the mechanism aiming at the uncertain PID control system of the engineering mechanical motion mechanism containing interval variables according to the dynamic model response range of the engineering mechanical motion mechanism. The method can be used in an uncertain dynamics model with poor uncertain variable related information, comprehensively evaluates the control performance of the engineering mechanical motion mechanism, optimizes the comprehensive evaluation method according to the confidence level of the comprehensive evaluation result, obtains the comprehensive evaluation result of the mechanism control performance meeting the confidence level, and effectively improves the comprehensive evaluation result.
The technical scheme adopted by the invention is as follows: a comprehensive evaluation method for PID control performance considering uncertainty is characterized in that a Lagrange power model is established for an engineering mechanical motion mechanism system, an upper bound and a lower bound of dynamic response of the Lagrange power model are calculated by a point matching method, a comprehensive quantitative evaluation result of the motion control performance of the engineering mechanical motion mechanism system is obtained through a comprehensive evaluation function, the confidence of the quantitative evaluation result is further determined through a Monte Carlo method, the comprehensive evaluation method is optimized according to the confidence level, and the comprehensive evaluation result is effectively improved, and the comprehensive evaluation method specifically comprises the following steps:
the method comprises the following steps: according to the size structure and the material characteristic attribute of the engineering mechanical motion mechanism system, a Lagrange dynamics model of the engineering mechanical motion mechanism system is established, and based on the response result of the Lagrange dynamics model, the driving input value of the engineering mechanical motion mechanism system is calculated through a proportional, integral and differential controller, and a closed-loop control system of the engineering mechanical motion mechanism system is established;
step two: determining uncertain parameters in a Lagrange dynamics model of an engineering mechanical motion mechanism system, wherein the uncertain parameters comprise part length, mechanism material attributes, part-to-part contact relation parameters, connection pair gap parameters and corresponding change intervals thereof, so as to represent uncertainty caused by manufacturing errors and material errors;
step three: establishing a working condition scheme required for comprehensively evaluating the motion control performance of the engineering mechanical motion mechanism system, carrying out dimension-by-dimension propagation calculation on multiple uncertain parameters in a Lagrange dynamics model of the engineering mechanical motion mechanism system, namely the length of a part, the mechanism material attribute, the contact relation parameter between the parts and each uncertain parameter in a connecting pair gap, determining a response interval of the Lagrange dynamics model of the engineering mechanical motion mechanism system, and calculating the upper and lower bounds of response in each established industrial control scheme under the engineering mechanical motion mechanism system; responding to the representation of a simulation result of the engineering machinery movement mechanism system in a working condition scheme, wherein the simulation result comprises movement precision, energy consumption level, control effect and control time parameters;
step four: determining an evaluation index of the motion control performance of the engineering mechanical motion mechanism system, establishing a comprehensive evaluation function representing the control performance of the engineering mechanical motion mechanism system, and comprehensively evaluating to obtain a quantitative result of the control performance level of the engineering mechanical motion mechanism system based on the upper and lower response boundaries of a Lagrange dynamics model of the engineering mechanical motion mechanism system under each working condition scheme;
step five: according to the method, a path curve set of mechanism motion is generated through a stochastic method firstly according to multiple uncertain parameters in a Lagrange dynamics model of an engineering machinery motion mechanism system through a Monte Carlo simulation method, then a repeated stochastic experiment is carried out on the mechanism dynamics system according to the randomly generated mechanism motion path set by utilizing the Monte Carlo simulation method, a probability statistical result of a comprehensive evaluation function for representing the control performance of the mechanism dynamics system is solved, then the comprehensive evaluation result and the probability statistical result of the mechanism control performance are compared, the confidence coefficient of the comprehensive evaluation result is calculated, the comprehensive evaluation method is optimized according to the confidence level, finally the comprehensive evaluation result of the mechanism control performance meeting the confidence coefficient is obtained, and the comprehensive evaluation result is effectively improved.
In the first step, a method for optimizing a proportional gain parameter, an integral gain parameter and a differential gain parameter in a controller of an engineering mechanical motion mechanism system is used for firstly determining design parameters to be optimized, namely the proportional gain parameter, the integral gain parameter and the differential gain parameter in each controller, respectively determining value intervals of the gain parameters, then determining an optimization target, namely a response of the engineering mechanical motion mechanism containing motion precision, energy consumption level, control effect and control time parameters, and finally optimizing the controller design parameters by taking the response of a Lagrange dynamics model of the engineering mechanical motion mechanism system as the optimization target through a sequence quadratic programming method to obtain values of each control parameter of the Lagrange dynamics model controller of the engineering mechanical motion mechanism system.
And in the third step, under the condition that the uncertainty of the length of the part, the material property of the mechanism, the contact relation parameter between the parts and the clearance parameter of the connecting pair in the engineering mechanical motion mechanism system is considered, calculating the change interval of the engineering mechanical motion mechanism system for the motion precision, the energy consumption level, the control effect and the control time parameter response by adopting a point matching method. Firstly, carrying out normalization processing on uncertain parameters in an engineering mechanical motion mechanism system, calculating model responses corresponding to each group of uncertain parameters of the engineering mechanical motion mechanism system in a standardized interval by using a collocation method, and returning the normalized uncertain parameters of the corresponding dynamic response extreme points of the engineering mechanical motion mechanism system to an original parameter interval so as to solve each group of uncertain parameters one by one and obtain a response interval of the engineering mechanical motion mechanism system.
In the fourth step, the comprehensive evaluation function considers a plurality of different evaluation indexes related to the mechanism control performance, including the motion precision, the energy consumption level, the control effect and the control time of the engineering machinery motion mechanism system. And calculating according to the weight of each index to obtain a comprehensive quantitative evaluation result of the control performance of the engineering mechanical movement mechanism system. The method comprises the steps of firstly obtaining the extreme value of each response parameter from a response interval of an engineering mechanical motion mechanism system comprising a motion precision, an energy consumption level, a control effect and a control time parameter response interval, then carrying out normalization processing on the extreme values of the response parameters in different orders of magnitude to obtain the normalized extreme value of the response parameter in the same order of magnitude, and finally obtaining the comprehensive quantitative evaluation result of the control performance of the engineering mechanical motion mechanism system according to the weight coefficient corresponding to the mechanism control performance evaluation index of the normalized extreme value of the response parameter.
Compared with the prior art, the invention has the advantages that:
(1) The invention solves the response interval of the mechanism dynamic system by adopting a coordinate method, has small requirement on the distribution information of uncertain parameters in the dynamic system, only needs to determine the change interval of the uncertain parameters, solves the response interval of the mechanism dynamic system under the condition of not determining the complex distribution of the uncertain parameters, and accurately and comprehensively evaluates the motion performance of the engineering mechanical motion mechanism according to the response interval.
(2) Compared with an evaluation method of a single evaluation index, the comprehensive evaluation function adopted by the invention can carry out comprehensive evaluation according to a plurality of evaluation indexes related to the mechanism motion control performance and different weights, and comprehensively and accurately analyze the performance level of the mechanism dynamics control system.
(3) According to the method, the confidence coefficient analysis is carried out on the comprehensive evaluation result of the mechanism motion control performance, on the basis of obtaining the comprehensive evaluation result, the confidence coefficient analysis is further carried out on the evaluation result, the comprehensive evaluation method is optimized according to the confidence level, the comprehensive evaluation result meeting the confidence coefficient is further obtained, and the confidence coefficient of the comprehensive evaluation of the mechanism motion control performance is effectively improved.
Drawings
FIG. 1 is a flow chart of a method implementation of the present invention;
FIG. 2 is a schematic view of a single degree of freedom four-bar linkage mechanism according to embodiment 1 of the present invention;
FIG. 3 is a graph of angular response time history of a single degree of freedom four-bar linkage mechanism according to embodiment 1 of the present invention;
fig. 4 is a graph showing the monte carlo sampling result of the single-degree-of-freedom four-bar linkage in embodiment 1 of the method of the present invention.
Detailed Description
The invention is further described with reference to the following figures and specific examples.
As shown in FIG. 1, the comprehensive evaluation method for PID control performance considering uncertainty of the invention comprises the following steps:
the method comprises the following steps: according to the dimension structure and material property of the engineering mechanical movement mechanism system, establishing a Lagrange dynamics model of the engineering mechanical movement mechanism system,
wherein theta is 1 The rotation angle of an input rod of a mechanism system of the mechanism system is used as a generalized coordinate for describing the motion of the system;
is the kinetic energy of the mechanism system, V ix 、V iy 、J i The speed of the mass center of the ith part in the x direction, the speed of the mass center in the y direction and the moment of inertia are respectively; p = { m 1 r 1 sin(θ 1 )+m 2 [L 1 sin(θ 1 )+r 2 sin(θ 2 )]+m 3 [L 4 sin(θ 4 )+r 3 sin(θ 3 )]G is the potential energy of the mechanism system, where m i Is the mass of the ith part, L i The distance from the ith part centroid to the generalized coordinate origin; τ is the driving force or torque input externally to the mechanism system. Based on the response result of the Lagrange dynamics model, the driving input value of the engineering mechanical motion mechanism system is calculated through a proportional controller, an integral controller and a differential controller, and the engineering mechanical motion mechanism system is establishedA closed loop control system of the system.
Determining design parameters to be optimized, namely proportional gain parameters, integral gain parameters and differential gain parameters in each controller, respectively determining value intervals of the gain parameters, and determining optimal proportional, integral and differential gain parameters, namely K, of the dynamic system in a preset range c ＝[K P K I K D ]Then, determining an optimization target, namely the response of the engineering machinery movement mechanism containing movement precision, energy consumption level, control effect and control time parameters, so as to obtain a response error e = | d-d i I is the minimum optimization objective, where d and d i Optimization of gain parameters in the mechanism PID control parameters for target and actual response values, respectively, is shown below:
find K P ,K I ,K D
min e＝|d-d i |
0≤K P ≤K Pmax
s.t.0≤K I ≤K Imax
0≤K D ≤K Dmax
for an engineering machinery motion mechanism system, an optimization problem is usually a nonlinear problem, and the optimization problem of gain parameters can be solved iteratively by a sequential quadratic programming method, wherein the iterative process is shown by the following expression:
s.t.C i (x)＝0,i＝1,…,r,
C i (x)≥0,i＝r+1,…,s,
wherein f (x) and C i (x) (i =1, \8230;, s) is R n The real function above respectively represents a response function and a constraint function of the mechanism dynamic system, n is the number of independent variables in the response function of the mechanism dynamic system and represents the structural parameters of the engineering machinery movement structure system, and r and s are positive integers and are the number of the constraint functions of the mechanism dynamic system respectively.
Solving the nonlinear optimization problem by iteration by using an SQP method, and solving the QP in the k-th iteration process k ，QP k The solution formula of (c) is as follows:
in the formula (I), the compound is shown in the specification,
the gradient of the function of the constraint is represented,
representing the gradient of the response function, M = {1, \8230;, r }, S = { r +1, \8230;, S }, the number of the constraint function, H, respectively k Is a lagrange function Hessian matrix approximation of the mechanism dynamics system response.
Step two: introducing actual interval variable parameters and a change interval thereof into the engineering mechanical motion mechanism:
and epsilon represents the variation interval comprising the length of the part, the material property of the mechanism, the contact relation parameter between the parts, the gap parameter of the connecting pair and the corresponding variation interval so as to represent the uncertainty caused by manufacturing errors and material errors.
Step three: establishing a working condition scheme required by comprehensively evaluating the motion control performance of a mechanism, carrying out dimension-by-dimension propagation calculation on the uncertainty in the engineering mechanical motion mechanism by adopting a point matching method for multiple uncertainty parameters in a Lagrange dynamics model of an engineering mechanical motion mechanism system, namely the length of a part, the material attribute of the mechanism, the contact relation parameters between the parts and each uncertainty parameter in a connecting pair gap, carrying out normalization processing on the uncertainty parameters in the engineering mechanical motion mechanism, calculating the model response corresponding to each group of uncertainty parameters in the engineering mechanical motion mechanism in a standardized interval by using the point matching method, and carrying out the normalization processing on the corresponding mechanismThe normalized uncertain parameters of the dynamic response extreme points are regressed to the original parameter interval, so that each group of uncertain parameters is solved dimension by dimension to obtain the response interval of the engineering mechanical movement mechanism
Further calculating the upper and lower response limits of the mechanical movement mechanism under each working condition scheme
Step four: and comprehensively evaluating the performance level of the mechanism according to the upper and lower limits of the response of the engineering mechanical motion mechanism. Determining an evaluation index of the motion control performance of the engineering mechanical motion mechanism system, establishing a comprehensive evaluation function representing the control performance of the engineering mechanical motion mechanism system, and establishing an upper and a lower response bounds of a Lagrange dynamics model of the engineering mechanical motion mechanism system under each working condition scheme. Establishing a comprehensive function for evaluating the performance of an organization
Wherein
Is an evaluation index value after normalization, p i The weight coefficient of each evaluation index, and the normalization processing method of the evaluation index is as follows:
k n ＝max(x n1 ,x n2 ,...)
wherein x n1 ,x n2 For the parameter value, k, of the n-th structural parameter of the mechanical dynamics system n In order to normalize the coefficients of the coefficients,
the structural parameters of the mechanism dynamics system after normalization processing are the parameter values.
The comprehensive evaluation function considers a plurality of different evaluation indexes related to the control performance of the mechanism, including the motion precision, the energy consumption level, the control effect and the control time of the mechanism system. And calculating according to the weight of each index to obtain a comprehensive quantitative evaluation result of the control performance of the mechanism. Firstly, obtaining the extreme value of each response parameter from the response interval of the mechanism dynamics model dynamics including the motion precision, the energy consumption level, the control effect and the control time parameter response interval, then carrying out normalization processing on the extreme values of each response parameter in different orders of magnitude to obtain the normalized extreme value of the response parameter in the same order of magnitude, and finally obtaining the comprehensive quantitative evaluation result of the engineering mechanical movement mechanism according to the weight coefficient corresponding to the control performance evaluation index of the mechanism dynamics model of the normalized extreme value of the response parameter.
Step five: firstly, generating a path curve set of mechanism motion by a random method according to a multivariate uncertainty parameter in a Lagrange dynamics model of an engineering machinery motion mechanism system by a Monte Carlo simulation method, and solving a probability statistical result of mechanism control performance according to the randomly generated mechanism motion path set by the Monte Carlo simulation method, wherein a sample mean value and a sample variance can be calculated by the following formula:
Example 1:
as shown in FIG. 2, the single degree of freedom planar four-bar mechanism is provided, wherein a shaft 1 is a driving shaft, a driving moment is applied to the driving shaft, the lengths of connecting bars are respectively 55mm, 73mm, 135mm and 145mm, the mass m =1kg of each connecting bar, and the inertia moment is 0.01kgm 2 . The operation condition is that the shaft 1 rotates 90 degrees, the angle response of the mechanism shaft 1 is shown in fig. 3, the motion error of the plane four-bar mechanism gradually becomes smaller along with the motion process, the angle of the plane four-bar mechanism shaft 1 gradually approaches to a target value, and the gain coefficient in the system controller is obtained through iterative optimization calculation of a sequence quadratic programming algorithm: k is P ＝5.13，K I ＝1.81，K D ＝0.83。
Further introducing uncertainty in the mechanical system, 5% uncertainty was introduced in the length and mass of each rod in the mechanical system. Solving the response upper and lower bounds of the engineering mechanical motion mechanism considering uncertainty through a point matching method, carrying out normalization processing on the result, and substituting the result into a comprehensive evaluation function, wherein the evaluation indexes considered by the evaluation function comprise: the total time consumption, the total work load, the average maximum overshoot and the average endpoint error are the same, and the weight of each evaluation index is the same.
TABLE 1 comprehensive evaluation results of the organization system
The confidence of the evaluation result is verified by a Monte Carlo method, as shown in FIG. 4, wherein the average error between the Monte Carlo sampling result and the comprehensive evaluation result is only 0.051, and the confidence is 96% when the comprehensive evaluation result is credible under the condition that the absolute value of the error between the sampling result and the comprehensive evaluation result is less than 1, thus the comprehensive evaluation method is accurate and effective.
From the results, the invention can calculate the response limit of the mechanism more accurately under the condition of considering uncertainty, and can make accurate evaluation on the control performance of the mechanism.
The invention has not been described in detail and is part of the common general knowledge of a person skilled in the art.
The above are only the specific steps of the present invention, and the protection scope of the present invention is not limited in any way; the method can be expanded and applied to the fields of mechanism dynamics response interval solution and mechanism motion function evaluation, and all technical schemes formed by adopting equivalent transformation or equivalent replacement fall within the protection scope of the invention.
Claims (4)
1. A comprehensive evaluation method for PID control performance considering uncertainty is characterized by comprising the following steps:
the method comprises the following steps: according to the size structure and the material characteristic attribute of the engineering mechanical motion mechanism system, a Lagrange dynamics model of the engineering mechanical motion mechanism system is established, based on the response result of the Lagrange dynamics model, the driving input value of the engineering mechanical motion mechanism system is calculated through a proportional, integral and differential controller, and a closed-loop control system of the engineering mechanical motion mechanism system is established;
step two: determining uncertain parameters in a Lagrange dynamics model of an engineering mechanical motion mechanism system, wherein the uncertain parameters comprise part length, mechanism material attributes, part-to-part contact relation parameters, connection pair gap parameters and corresponding change intervals thereof, so as to represent uncertainty caused by manufacturing errors and material errors;
step three: establishing a working condition scheme required for comprehensively evaluating the motion control performance of the engineering mechanical motion mechanism system, carrying out one-dimensional propagation calculation on multiple uncertain parameters in a Lagrange dynamics model of the engineering mechanical motion mechanism system, namely the length of a part, the mechanism material attribute, the contact relation parameter between the parts and each uncertain parameter in a connecting pair gap, determining the response interval of the Lagrange dynamics model of the engineering mechanical motion mechanism system, and calculating the upper and lower bounds of the response of the engineering mechanical motion mechanism system in each established industrial control scheme; responding to the representation of a simulation result of the engineering mechanical movement mechanism system in a working condition scheme, wherein the simulation result comprises movement precision, an energy consumption level, a control effect and a control time parameter;
step four: determining an evaluation index of the motion control performance of the engineering mechanical motion mechanism system, establishing a comprehensive evaluation function representing the control performance of the engineering mechanical motion mechanism system, and comprehensively evaluating to obtain a quantitative result of the control performance level of the engineering mechanical motion mechanism system based on the upper and lower response boundaries of a Lagrange dynamics model of the engineering mechanical motion mechanism system under each working condition scheme;
step five: according to the method, firstly, a path curve set of mechanism motion is generated through a random method according to multivariate uncertainty parameters in a Lagrange dynamics model of an engineering machinery motion mechanism system through a Monte Carlo simulation method, then, a repeated random experiment is carried out on the mechanism dynamics system according to the randomly generated mechanism motion path set through the Monte Carlo simulation method, a probability statistical result of a comprehensive evaluation function for representing the control performance of the mechanism dynamics system is solved, then, the comprehensive evaluation result and the probability statistical result of the mechanism control performance are compared, the confidence coefficient of the comprehensive evaluation result is calculated, the comprehensive evaluation method is optimized according to the confidence level, and finally, the comprehensive evaluation result of the mechanism control performance meeting the confidence coefficient is obtained.
2. The comprehensive evaluation method for PID control performance considering uncertainty according to claim 1, characterized in that: in the first step, the method for optimizing the proportional gain parameter, the integral gain parameter and the differential gain parameter in the engineering mechanical motion mechanism system controller comprises the following steps: firstly, determining design parameters to be optimized, namely a proportional gain parameter, an integral gain parameter and a differential gain parameter in each controller, respectively determining value intervals of the gain parameters, then determining an optimization target, namely a response of an engineering mechanical motion mechanism comprising motion precision, energy consumption level, control effect and control time parameters, and finally optimizing the controller design parameters by taking the response of a Lagrange dynamics model of the engineering mechanical motion mechanism system as the optimization target through a sequential quadratic programming method to obtain values of each control parameter of the Lagrange dynamics model controller of the engineering mechanical motion mechanism system.
3. The comprehensive evaluation method for PID control performance considering uncertainty according to claim 1, characterized in that: in the third step, under the condition that uncertainty of part length, mechanism material attributes, contact relation parameters between parts and connection pair gap parameters of the engineering mechanical motion mechanism system is considered, the method for calculating the change interval of the engineering mechanical motion mechanism system for motion precision, energy consumption level, control effect and control time parameter response by adopting a point matching method comprises the following steps: firstly, carrying out normalization processing on uncertain parameters in an engineering mechanical motion mechanism system, calculating model responses corresponding to each group of uncertain parameters of the engineering mechanical motion mechanism system in a standardized interval by using a coordinate method, and returning the normalized uncertain parameters of the corresponding dynamic response extreme points of the engineering mechanical motion mechanism system to an original parameter interval so as to solve each group of uncertain parameters in a dimension-by-dimension manner and obtain a response interval of the engineering mechanical motion mechanism system.
4. The comprehensive evaluation method for the PID control performance considering the uncertainty according to claim 1, characterized in that: in the fourth step, the comprehensive evaluation function considers a plurality of different evaluation indexes related to the mechanism control performance, including the motion precision, the energy consumption level, the control effect and the control time of the engineering mechanical motion mechanism system, and the process of calculating the comprehensive quantitative evaluation result of the engineering mechanical motion mechanism system control performance according to the weight of each index is as follows: the method comprises the steps of firstly obtaining the extreme value of each response parameter from a response interval of an engineering mechanical motion mechanism system comprising a motion precision, an energy consumption level, a control effect and a control time parameter response interval, then carrying out normalization processing on the extreme values of the response parameters in different orders of magnitude to obtain the normalized extreme value of the response parameter in the same order of magnitude, and finally obtaining the comprehensive quantitative evaluation result of the control performance of the engineering mechanical motion mechanism system according to the weight coefficient corresponding to the mechanism control performance evaluation index of the normalized extreme value of the response parameter.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202110817291.3A CN113552796B (en) | 2021-07-20 | 2021-07-20 | PID control performance comprehensive evaluation method considering uncertainty |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202110817291.3A CN113552796B (en) | 2021-07-20 | 2021-07-20 | PID control performance comprehensive evaluation method considering uncertainty |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN113552796A CN113552796A (en) | 2021-10-26 |
| CN113552796B true CN113552796B (en) | 2023-01-10 |
Family
ID=78103451
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202110817291.3A Active CN113552796B (en) | 2021-07-20 | 2021-07-20 | PID control performance comprehensive evaluation method considering uncertainty |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN113552796B (en) |
Families Citing this family (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN114707291B (en) * | 2022-01-11 | 2024-06-28 | 同济大学 | Statics calculation method based on novel grid-free stable distribution points |
Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105893699A (en) * | 2016-04-25 | 2016-08-24 | 北京航空航天大学 | Connecting rod mechanism robust synthesis method containing mixed uncertainty parameter |
| KR101668788B1 (en) * | 2016-03-15 | 2016-10-25 | 연세대학교 산학협력단 | Structural health assessment method and system based on rigid rink |
| CN107832493A (en) * | 2017-10-12 | 2018-03-23 | 天津大学 | A kind of parallel institution multi-objective optimization design of power method for considering parameter uncertainty |
| CN110450156A (en) * | 2019-07-30 | 2019-11-15 | 洛阳润信机械制造有限公司 | The optimum design method of multi-freedom Mechanism adaptive fuzzy controller |
| CN110456632A (en) * | 2019-09-12 | 2019-11-15 | 北京航空航天大学 | A kind of time-dependent ability appraisal procedure for uncertain PID control system |
| CN111352340A (en) * | 2020-04-27 | 2020-06-30 | 北京航空航天大学 | Uncertainty system PID controller design method based on time-varying reliability |
| CN112632699A (en) * | 2020-12-21 | 2021-04-09 | 华南理工大学 | Method for optimizing performance of dual-mass flywheel based on uncertain parameters |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US10309059B2 (en) * | 2016-09-23 | 2019-06-04 | Honeywell International Inc. | Method of designing model predictive control for cross directional flat sheet manufacturing processes to guarantee temporal robust stability and performance |
-
2021
- 2021-07-20 CN CN202110817291.3A patent/CN113552796B/en active Active
Patent Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| KR101668788B1 (en) * | 2016-03-15 | 2016-10-25 | 연세대학교 산학협력단 | Structural health assessment method and system based on rigid rink |
| CN105893699A (en) * | 2016-04-25 | 2016-08-24 | 北京航空航天大学 | Connecting rod mechanism robust synthesis method containing mixed uncertainty parameter |
| CN107832493A (en) * | 2017-10-12 | 2018-03-23 | 天津大学 | A kind of parallel institution multi-objective optimization design of power method for considering parameter uncertainty |
| CN110450156A (en) * | 2019-07-30 | 2019-11-15 | 洛阳润信机械制造有限公司 | The optimum design method of multi-freedom Mechanism adaptive fuzzy controller |
| CN110456632A (en) * | 2019-09-12 | 2019-11-15 | 北京航空航天大学 | A kind of time-dependent ability appraisal procedure for uncertain PID control system |
| CN111352340A (en) * | 2020-04-27 | 2020-06-30 | 北京航空航天大学 | Uncertainty system PID controller design method based on time-varying reliability |
| CN112632699A (en) * | 2020-12-21 | 2021-04-09 | 华南理工大学 | Method for optimizing performance of dual-mass flywheel based on uncertain parameters |
Non-Patent Citations (4)
| Title |
|---|
| Performance evaluation of complex systems using evidential reasoning approach with uncertain parameters;Leiyu Chen;《Chinese Journal of Aeronautics》;20201016;全文 * |
| 不确定非线性结构动力响应的区间分析方法;邱志平 等;《力学学报》;20060930;全文 * |
| 代理模型在复杂机电系统全局敏感度分析中的应用;李洁翎 等;《机械设计与制造》;20170908;全文 * |
| 考虑相关性的机械结构不确定性传播分析;杨超;《工程科技Ⅱ辑》;20170215;全文 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN113552796A (en) | 2021-10-26 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Li et al. | Modeling and multi-objective optimization of cutting parameters in the high-speed milling using RSM and improved TLBO algorithm | |
| Marie et al. | Elasto-geometrical modeling and calibration of robot manipulators: Application to machining and forming applications | |
| Villarreal-Cervantes et al. | Off-line PID control tuning for a planar parallel robot using DE variants | |
| CN110936382B (en) | Data-driven industrial robot energy consumption optimization method | |
| US8332057B2 (en) | Method of multi-dimensional nonlinear control | |
| Chen et al. | Posture optimization in robotic machining based on comprehensive deformation index considering spindle weight and cutting force | |
| Singh et al. | Real-time control of ball balancer using neural integrated fuzzy controller | |
| Qi et al. | Multi-objective optimization of parallel tracking mechanism considering parameter uncertainty | |
| CN112926152B (en) | Digital twin-driven thin-wall part clamping force precise control and optimization method | |
| CN115648228B (en) | Industrial robot multi-source error compensation method, device, equipment and storage medium | |
| CN113552796B (en) | PID control performance comprehensive evaluation method considering uncertainty | |
| Shang et al. | Vibration suppression for two-inertia system with variable-length flexible load based on neural network compensation sliding mode controller and angle-independent method | |
| Li et al. | A new calibration method for hybrid machine tools using virtual tool center point position constraint | |
| Chen et al. | Convex polytopic modeling for flexible joints industrial robot using TP-model transformation | |
| CN106292290A (en) | A kind of wheeled mobile robot point is calmed rolling optimization control method | |
| Delchev | Iterative learning control for robotic manipulators: A bounded‐error algorithm | |
| Chen et al. | Indirect iterative learning control for robot manipulator with non‐Gaussian disturbances | |
| Høifødt | Dynamic modeling and simulation of robot manipulators: the Newton-Euler formulation | |
| Akkar et al. | Design Stable Controller for PUMA 560 Robot with PID and Sliding Mode Controller Based on PSO Algorithm. | |
| US6785624B2 (en) | Method for calibrating of machine units located in machine tools or robotic devices | |
| CN111624872B (en) | PID controller parameter setting method and system based on adaptive dynamic programming | |
| CN112318511A (en) | Mechanical arm trajectory tracking control method based on data driving | |
| Høifødt | Dynamic modeling and simulation of robot manipulators | |
| Zhou et al. | A Semi-linearized Approach for Dynamic Identification of Manipulator Based on Nonlinear Friction Model | |
| CN103345556B (en) | Based on the welding cantilever beam Optimization Design of the double-stranded quantum genetic algorithm of self-regulation |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| TA01 | Transfer of patent application right |
Effective date of registration: 20220525 Address after: 100191 No. 37, Haidian District, Beijing, Xueyuan Road Applicant after: BEIHANG University Applicant after: Ningbo Institute of innovation Beijing University of Aeronautics and Astronautics Address before: 100191 No. 37, Haidian District, Beijing, Xueyuan Road Applicant before: BEIHANG University |
|
| TA01 | Transfer of patent application right | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |