The mechanical system with backlash is distinguished between a＂backlash mode＂and a＂contact mode＂.The inherent switching between the two operating modes makes the system a prime example of hybrid system.For elimina...The mechanical system with backlash is distinguished between a＂backlash mode＂and a＂contact mode＂.The inherent switching between the two operating modes makes the system a prime example of hybrid system.For eliminating the bad effect of backlash, a piecewise affine（PWA） model of the mechanical servo system with backlash is built.The optimal control of constrained PWA system is obtained by taking advantage of model predictive control（MPC） method, and the explicit solution of MPC in a look-up table form is figured out by combining the dynamic programming and multi-parametric quadratic programming, thereby establishing an explicit hybrid model predictive controller.Furthermore, a piecewise quadratic（PWQ） function for guaranteeing the stability of closed-loop control is found by formulating the search of PWQ function as a semi-definite programming problem.In the tracking experiments, it is demonstrated that the explicit hybrid model predictive controller has a good traction control effect on the mechanical system with backlash.The error meets the demands of real system.Further, compared to the direct on-line computation, the computation burden is reduced by the explicit solution, thereby being suitable for real-time control of system with short sampling time.展开更多
This paper aims to investigate the nonlinear dynamic behaviors of an NGW planetary gear train with multi-clearances and manufacturing/assembling errors. For this purpose, an analytical translational- torsional coupled...This paper aims to investigate the nonlinear dynamic behaviors of an NGW planetary gear train with multi-clearances and manufacturing/assembling errors. For this purpose, an analytical translational- torsional coupled dynamic model is developed considering the effects of time-varying stiffness, gear backlashes and component errors. Based on the proposed model, the nonlinear differential equations of motion are derived and solved iteratively by the Runge-Kutta method. An NGW planetary gear reducer with three planets is taken as an example to analyze the effects of nonlinear factors. The results indicate that the backlashes induce complicated nonlinear dynamic behaviors in the gear train. With the increment of the backlashes, the gear system has experienced periodic responses, quasi-periodic response and chaos responses in sequence. When the planetary gear system is in a chaotic motion state, the vibration amplitude increases sharply, causing severe vibration and noise. The present study provides a fundamental basis for design and parameter optimization of NGW planetary gear trains.展开更多
Electro-hydraulic control systems are nonlinear in nature and their mathematic models have unknown parameters. Existing research of modeling and identification of the electro-hydraulic control system is mainly based o...Electro-hydraulic control systems are nonlinear in nature and their mathematic models have unknown parameters. Existing research of modeling and identification of the electro-hydraulic control system is mainly based on theoretical state space model, and the parameters identification is hard due to its demand on internal states measurement. Moreover, there are also some hard-to-model nonlinearities in theoretical model, which needs to be overcome. Modeling and identification of the electro-hydraulic control system of an excavator arm based on block-oriented nonlinear（BONL） models is investigated. The nonlinear state space model of the system is built first, and field tests are carried out to reveal the nonlinear characteristics of the system. Based on the physic insight into the system, three BONL models are adopted to describe the highly nonlinear system. The Hammerstein model is composed of a two-segment polynomial nonlinearity followed by a linear dynamic subsystem. The Hammerstein-Wiener（H-W） model is represented by the Hammerstein model in cascade with another single polynomial nonlinearity. A novel Pseudo-Hammerstein-Wiener（P-H-W） model is developed by replacing the single polynomial of the H-W model by a non-smooth backlash function. The key term separation principle is applied to simplify the BONL models into linear-in-parameters struc^tres. Then, a modified recursive least square algorithm（MRLSA） with iterative estimation of internal variables is developed to identify the all the parameters simultaneously. The identification results demonstrate that the BONL models with two-segment polynomial nonlinearities are able to capture the system behavior, and the P-H-W model has the best prediction accuracy. Comparison experiments show that the velocity prediction error of the P-H-W model is reduced by 14%, 30% and 75% to the H-W model, Hammerstein model, and extended auto-regressive （ARX） model, respectively. This research is helpful in controller design, system monitoring and diagnosis.展开更多
The position errors in the axis direction of a vertical machine center have been measured by means of the VM101 linear encored measurement system. The character of the backlash error is discussed;results show that the...The position errors in the axis direction of a vertical machine center have been measured by means of the VM101 linear encored measurement system. The character of the backlash error is discussed;results show that the backlash error has great influence on the position error. The position accuracy is enhanced after the backlash errors are compensated.展开更多
基金supported by the Beijing Education Committee Cooperation Building Foundation Project (XK100070532)
文摘The mechanical system with backlash is distinguished between a＂backlash mode＂and a＂contact mode＂.The inherent switching between the two operating modes makes the system a prime example of hybrid system.For eliminating the bad effect of backlash, a piecewise affine（PWA） model of the mechanical servo system with backlash is built.The optimal control of constrained PWA system is obtained by taking advantage of model predictive control（MPC） method, and the explicit solution of MPC in a look-up table form is figured out by combining the dynamic programming and multi-parametric quadratic programming, thereby establishing an explicit hybrid model predictive controller.Furthermore, a piecewise quadratic（PWQ） function for guaranteeing the stability of closed-loop control is found by formulating the search of PWQ function as a semi-definite programming problem.In the tracking experiments, it is demonstrated that the explicit hybrid model predictive controller has a good traction control effect on the mechanical system with backlash.The error meets the demands of real system.Further, compared to the direct on-line computation, the computation burden is reduced by the explicit solution, thereby being suitable for real-time control of system with short sampling time.
基金Funded by the National Natural Science Foundation of China(Grant No.51375013)the Anhui Provincial Natural Science Foundation(Grant No.1208085ME64)
文摘This paper aims to investigate the nonlinear dynamic behaviors of an NGW planetary gear train with multi-clearances and manufacturing/assembling errors. For this purpose, an analytical translational- torsional coupled dynamic model is developed considering the effects of time-varying stiffness, gear backlashes and component errors. Based on the proposed model, the nonlinear differential equations of motion are derived and solved iteratively by the Runge-Kutta method. An NGW planetary gear reducer with three planets is taken as an example to analyze the effects of nonlinear factors. The results indicate that the backlashes induce complicated nonlinear dynamic behaviors in the gear train. With the increment of the backlashes, the gear system has experienced periodic responses, quasi-periodic response and chaos responses in sequence. When the planetary gear system is in a chaotic motion state, the vibration amplitude increases sharply, causing severe vibration and noise. The present study provides a fundamental basis for design and parameter optimization of NGW planetary gear trains.
基金supported by National Natural Science Foundation of China(Grant No.51175511)
文摘Electro-hydraulic control systems are nonlinear in nature and their mathematic models have unknown parameters. Existing research of modeling and identification of the electro-hydraulic control system is mainly based on theoretical state space model, and the parameters identification is hard due to its demand on internal states measurement. Moreover, there are also some hard-to-model nonlinearities in theoretical model, which needs to be overcome. Modeling and identification of the electro-hydraulic control system of an excavator arm based on block-oriented nonlinear（BONL） models is investigated. The nonlinear state space model of the system is built first, and field tests are carried out to reveal the nonlinear characteristics of the system. Based on the physic insight into the system, three BONL models are adopted to describe the highly nonlinear system. The Hammerstein model is composed of a two-segment polynomial nonlinearity followed by a linear dynamic subsystem. The Hammerstein-Wiener（H-W） model is represented by the Hammerstein model in cascade with another single polynomial nonlinearity. A novel Pseudo-Hammerstein-Wiener（P-H-W） model is developed by replacing the single polynomial of the H-W model by a non-smooth backlash function. The key term separation principle is applied to simplify the BONL models into linear-in-parameters struc^tres. Then, a modified recursive least square algorithm（MRLSA） with iterative estimation of internal variables is developed to identify the all the parameters simultaneously. The identification results demonstrate that the BONL models with two-segment polynomial nonlinearities are able to capture the system behavior, and the P-H-W model has the best prediction accuracy. Comparison experiments show that the velocity prediction error of the P-H-W model is reduced by 14%, 30% and 75% to the H-W model, Hammerstein model, and extended auto-regressive （ARX） model, respectively. This research is helpful in controller design, system monitoring and diagnosis.
文摘The position errors in the axis direction of a vertical machine center have been measured by means of the VM101 linear encored measurement system. The character of the backlash error is discussed;results show that the backlash error has great influence on the position error. The position accuracy is enhanced after the backlash errors are compensated.
