。1170· 北京科技大学学报 第29卷 Uniform Markovian jump model of netw orked control systems LIU Leiming,TONG Chaonan Irfomation Engineering School,University of Science and Technology Beijing,Beiing 100083,China ABSTRACI For the two different cases that the upper bound of network-induced delays is longer or less than one sampling period in a continuous-time netw orked control system (NCS),by discretizing the model of a con- tinuous-time system and applying the augmented state-space method to the model,a unifom discrete-time jump model governed by Markov chains was presented.The parameters of the model reflected both the length of the delays and computation precision,so this model had more widely adaptability.The existing theory of a jump lin- ear system was applied to analysis the necessary and sufficient conditions guaranteeing the sy stem's stability.An interior-point algorithm was applied to design stabilizing controllers,and an approach to get the feasible initial solution of the interior-point algorithm was proposed.This improved algorithm stated above was applied effec- tively to the netw orked control and design of a cart and inverted pendulum with random delays. KEY WORDS networked control system;delay;jump system;Markov chain:discretization;augmented state-space method (上接第1153页) [8 CapinteriA.Pugno N.A multifractal comminution approach for drilling scaling hws.Powder Technol.2003.131(1):93 [5]Feder J.Fractals.New York:Plenum Press,1988 9 Borodich F M.Some fractal models of fracture.J Mech Phys 【6杨志远，周安宁，曲建林.超细煤粉的颗粒分布分形与球磨工 Solids.1997.45(2):230 艺关系研究.煤炭科学技术，2004,32(1)：32 [10 Perfect E.Fractal models for the frgmentation of rocks and [7]Turcotte D L.Fractalsand fragmentation.J Geophys Res,1986. soils:a review.Eng Geol.1997,48:185 91(B2):1921 【1川张济忠.分形.北京：清华大学出版社，1995 Fractal model for particle-size distribution of coal grinding JIAO Honglei,XIA Dehong,ZHANG Shengxian,CHEN Yong Mechanical Engineering School,University of Science and Technology Beijing.Beijing 100083.China ABSTRACT By the fractal method,mathematical models for particle number variation,particle surface area profile and particle mass dist ribution were established to predict and control the particle-size distribution of coal grinding at any grinding time.The particle number variat ion can be used to describe the main range of particle diameter.The surface area profile can be used to predict the energy consumption in grinding process.The parti cle mass dist ribution could be used to calculate the specific stacking density of particles or the surry concentra- tion.These models were proved to be valid by comparison of the fractal particle-size distribution with practical measurement. KEY WORDS coal;grinding;particle-size distribution model;fractalUniform Markovian jump model of netw orked control systems LIU Leiming, TONG Chaonan Inf ormation Engineering School, Universit y of Science and Technology Beijing, Beijing 100083, China ABSTRACT Fo r the tw o different cases that the upper bound of netwo rk-induced delays is longer or less than one sampling period in a continuous-time netw orked control system ( NCS) , by discretizing the model of a con￾tinuous-time system and applying the augmented state-space method to the model, a unifo rm discrete-time jump model governed by Markov chains w as presented .The parameters of the model reflected both the leng th of the delay s and computatio n precision, so this model had more w idely adaptability .The existing theory of a jump lin￾ear sy stem w as applied to analysis the necessary and sufficient conditio ns guaranteeing the sy stem' s stability .An interior-point algo rithm was applied to design stabilizing controllers, and an approach to get the feasible initial solution of the interior-point algorithm was proposed .This improved algorithm stated above w as applied effec￾tively to the netw orked control and design of a cart and inverted pendulum w ith random delay s . KEY WORDS networked control system ;delay ;jump sy stem ;Markov chain ;discretization ;augmented state-space method ( 上接第 1153 页) [ 5] Feder J.Fractals.New York:Plenum Press, 1988 [ 6] 杨志远, 周安宁, 曲建林.超细煤粉的颗粒分布分形与球磨工 艺关系研究.煤炭科学技术, 2004, 32( 1) :32 [ 7] Turcotte D L .Fractals and fragmentation.J Geophys Res, 1986, 91 ( B2) :1921 [ 8] Capinteri A, Pugno N .A multi-fract al comminution approach for drilling scaling laws.Powder Technol, 2003, 131( 1) :93 [ 9] Borodich F M .Some fractal models of fracture.J Mech Phys Solids, 1997, 45( 2) :230 [ 10] Perfect E .Fract al models for the fragmentation of rock s and soils:a review .Eng Geol, 1997, 48:185 [ 11] 张济忠.分形.北京:清华大学出版社, 1995 Fractal model for particle-size distribution of coal g rinding J IAO Honglei, X IA Dehong, ZHANG Shengxian, CHEN Yong Mechanical Engineering School, University of Science and Technology Beijing, Beijing 100083, China ABSTRACT By the fractal method, mathematical models for particle number variation, particle surface area profile and particle mass distribution were established to predict and control the particle-size distribution of coal g rinding at any grinding time .The particle number variation can be used to describe the main range of particle diameter.The surface area profile can be used to predict the energy consumption in grinding process .The parti￾cle mass distribution could be used to calculate the specific stacking density of particles or the slurry concentra￾tion .These models were proved to be valid by comparison of the fractal particle-size distributio n with practical measurement . KEY WORDS coal ;g rinding ;particle-size distribution model ;fractal · 1170 · 北 京 科 技 大 学 学 报 第 29 卷