P/H-cascade controlled servo axes sometimes provide insufficient damping of structural vibrations, especially for high dynamic machine tools or robots. The axis performance can be improved significantly by state space...P/H-cascade controlled servo axes sometimes provide insufficient damping of structural vibrations, especially for high dynamic machine tools or robots. The axis performance can be improved significantly by state space control extensions that are meanwhile available for commercial machine tool control systems. This contribution explains the state space control extension application with effective commissioning rules of thumb for benefit is elucidated by exemplary machine tool axes. typical machine tool axes as well as robot joint drives. The achievable展开更多
Commissioning of P/PI-cascade controlled servo axes with flexible load can be quite time consuming, if the step response based setup procedures are applied for the velocity controller as indicated by the automation sy...Commissioning of P/PI-cascade controlled servo axes with flexible load can be quite time consuming, if the step response based setup procedures are applied for the velocity controller as indicated by the automation systems manufacturers. Based on the drive frequency response, suitable rules of thumb with optimum velocity control damping performance are derived in this contribution that turned out to be very efficient in several dozen machine tool servo axis applications of different industrial partners in Switzerland and southern Germany. Anyway, single feedback loop velocity control sometimes provides insufficient damping of structural vibrations, especially for high dynamic machine tools or robots. The axis performance can be improved significantly by state space control extensions that are meanwhile available for commercial machine tool control systems. This contribution explains the state space control extension application with effective commissioning rules of thumb for typical machine tool axes as well as robot joint drives. The achievable benefit is elucidated by exemplary machine tool axes.展开更多
Let Ro be a Noetherian local ring and R a standard graded R0-algebra with maximal ideal ra and residue class field K = Rim. For a graded ideal I in R we show that for k 〉〉 0： （1） the Artin-Rees number of the syzy...Let Ro be a Noetherian local ring and R a standard graded R0-algebra with maximal ideal ra and residue class field K = Rim. For a graded ideal I in R we show that for k 〉〉 0： （1） the Artin-Rees number of the syzygy modules of Ik as submodules of the free modules from a free resolution is constant, and thereby the Artin-Rees number can be presented as a proper replacement of regularity in the local situation; and （2） R is a polynomial ring over the regular Ro, the ring R/Ik is Golod, its Poincar4-Betti series is rational and the Betti numbers of the free resolution of K over R/I^k are polynomials in k of a specific degree. The first result is an extension of the work by Swanson on the regularity of I^k for k 〉〉 0 from the graded situation to the local situation. The polynomiality consequence of the second result is an analog of the work by Kodiyalam on the behaviour of Betti numbers of the minimal free resolution of R/Ik over R.展开更多
文摘P/H-cascade controlled servo axes sometimes provide insufficient damping of structural vibrations, especially for high dynamic machine tools or robots. The axis performance can be improved significantly by state space control extensions that are meanwhile available for commercial machine tool control systems. This contribution explains the state space control extension application with effective commissioning rules of thumb for benefit is elucidated by exemplary machine tool axes. typical machine tool axes as well as robot joint drives. The achievable
文摘Commissioning of P/PI-cascade controlled servo axes with flexible load can be quite time consuming, if the step response based setup procedures are applied for the velocity controller as indicated by the automation systems manufacturers. Based on the drive frequency response, suitable rules of thumb with optimum velocity control damping performance are derived in this contribution that turned out to be very efficient in several dozen machine tool servo axis applications of different industrial partners in Switzerland and southern Germany. Anyway, single feedback loop velocity control sometimes provides insufficient damping of structural vibrations, especially for high dynamic machine tools or robots. The axis performance can be improved significantly by state space control extensions that are meanwhile available for commercial machine tool control systems. This contribution explains the state space control extension application with effective commissioning rules of thumb for typical machine tool axes as well as robot joint drives. The achievable benefit is elucidated by exemplary machine tool axes.
文摘Let Ro be a Noetherian local ring and R a standard graded R0-algebra with maximal ideal ra and residue class field K = Rim. For a graded ideal I in R we show that for k 〉〉 0： （1） the Artin-Rees number of the syzygy modules of Ik as submodules of the free modules from a free resolution is constant, and thereby the Artin-Rees number can be presented as a proper replacement of regularity in the local situation; and （2） R is a polynomial ring over the regular Ro, the ring R/Ik is Golod, its Poincar4-Betti series is rational and the Betti numbers of the free resolution of K over R/I^k are polynomials in k of a specific degree. The first result is an extension of the work by Swanson on the regularity of I^k for k 〉〉 0 from the graded situation to the local situation. The polynomiality consequence of the second result is an analog of the work by Kodiyalam on the behaviour of Betti numbers of the minimal free resolution of R/Ik over R.
