On the derivative constraints of input shaping control

Conventionally, derivative constraints have been added to the input shaper to increase robustness to modeling error in natural frequency and damping ratio, and the robustness of input shaping has been evaluated from the ratio of residual vibration amplitude with input shaping to that without input shaping. However, the derivative constraints used for the ZVD shaper and the derivative of the ratio of residual vibration amplitude are mathematically confused in the previous literatures, even if the conceptual explanation for both derivatives therein is generally acceptable. In this paper, the relationship of the derivative constraints used for ZVD shaper and the zero derivative of the ratio of residual vibration amplitude are derived and clarified mathematically, and the relationship between them is demonstrated using an example.

[1]  William Singhose,et al.  Reference Command Shaping Using Specified-Negative-Amplitude Input Shapers for Vibration Reduction , 2004 .

[2]  William Singhose,et al.  Input shaping/time delay control of maneuvering flexible structures , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[3]  Sırrı Sunay Gürleyük.  Optimal unity-magnitude input shaper duration analysis , 2006 .

[4]  William Singhose,et al.  Concurrent Design of Vibration Absorbers and Input Shapers , 2005 .

[5]  Warren P. Seering,et al.  Preshaping Command Inputs to Reduce System Vibration , 1990 .

[6]  Otto J. M. Smith.  Posicast Control of Damped Oscillatory Systems , 1957, Proceedings of the IRE.

[7]  Keum-Shik Hong,et al.  Adaptive control of an axially moving system , 2009 .

[8]  S. S. Gürleyük,et al.  Robust Three-impulse Sequence Input Shaper Design , 2007 .

[9]  William Singhose,et al.  Comparison of robust input shapers , 2008 .

[10]  William E. Singhose,et al.  Finite-State Input Shaping , 2010, IEEE Transactions on Control Systems Technology.

[11]  Rifat Hacioglu,et al.  Three-step input shaper for damping tubular step motor vibrations , 2007 .

[12]  William Singhose,et al.  Performance Measures For Input Shaping and Command Generation , 2006 .

[13]  William Singhose,et al.  EXTRA-INSENSITIVE INPUT SHAPERS FOR CONTROLLING FLEXIBLE SPACECRAFT , 1996 .

[14]  Warren P. Seering,et al.  Convolved and simultaneous two-mode input shapers , 1997 .

[15]  William Singhose,et al.  A controller enabling precise positioning and sway reduction in bridge and gantry cranes , 2007 .

[16]  A. Galip Ulsoy,et al.  An Approach to Control Input Shaping With Application to Coordinate Measuring Machines , 1999 .

[17]  Juyi Park,et al.  Design of learning input shaping technique for residual vibration suppression in an industrial robot , 2006, IEEE/ASME Transactions on Mechatronics.

[18]  Warren P. Seering,et al.  Time-Optimal Negative Input Shapers , 1997 .

[19]  Hirohisa Kojima,et al.  Adaptive Deflection-Limiting Control for Slewing Flexible Space Structures , 2007 .

[20]  Sadettin Kapucu,et al.  Residual swing/vibration reduction using a hybrid input shaping method , 2001 .

[21]  George Vukovich,et al.  Nonlinear Input Shaping Control of Flexible Spacecraft Reorientation Maneuver , 1998 .

[22]  William E. Singhose,et al.  Effects of input shaping on two-dimensional trajectory following , 1996, IEEE Trans. Robotics Autom..

[23]  Sırrı Sunay Gürleyük,et al.  Improved three-step input shaping control of crane system , 2008 .

[24]  Sungsoo Rhim,et al.  Experiments of optimal delay extraction algorithm using adaptive time-delay filter for improved vibration suppression , 2009 .

[25]  Neil C. Singer,et al.  Residual Vibration Reduction in Computer controlled Machines , 1989 .

[26]  Warren P. Seering,et al.  Residual Vibration Reduction Using Vector Diagrams to Generate Shaped Inputs , 1994 .

[27]  M. A. Ahmad,et al.  Robust input shaping for anti-sway control of rotary crane , 2009, TENCON 2009 - 2009 IEEE Region 10 Conference.

[28]  William Singhose,et al.  Verifying Robust Time-Optimal Commands for Multimode Flexible Spacecraft , 1997 .

[29]  Lucy Y. Pao,et al.  Robust Input Shaper Control Design for Parameter Variations in Flexible Structures , 2000 .

[30]  William Singhose,et al.  Command generation for flexible systems , 1997 .

[31]  William Singhose,et al.  Robust Negative Input Shapers for Vibration Suppression , 2009 .