http://iet.metastore.ingenta.com
1887

Closed-form smoothers and shapers with distributed delay for damped oscillatory modes

Closed-form smoothers and shapers with distributed delay for damped oscillatory modes

For access to this article, please select a purchase option:

Buy article PDF
$19.95
(plus tax if applicable)
Buy Knowledge Pack
10 articles for $120.00
(plus taxes if applicable)

IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.

Learn more about IET membership 

Recommend Title Publication to library

You must fill out fields marked with: *

Librarian details
Name:*
Email:*
Your details
Name:*
Email:*
Department:*
Why are you recommending this title?
Select reason:
 
 
 
 
 
IET Control Theory & Applications — Recommend this title to your library

Thank you

Your recommendation has been sent to your librarian.

The study deals with parametrisation of input shapers and smoothers with distributed delays, which are a common tool used for pre-compensating oscillatory modes of flexible systems. These filtering structures can be easily parametrised, if the oscillatory mode is undamped, leading to fully analytical formulas. For the damped case, however, the parametrisation needs to be done numerically as a rule. Utilising a straightforward complex domain transformation, as the main results, the structure of the filters is turned to the closed-form that can be parametrised analytically for the damped case too. The adjusted smoothers and shapers accommodate the reference and the system output signals without vibration at the same time lengths like the pre-forms for the undamped case. This methodology is applied to Trapezoidal, S-curve and Trigonometric smoothers, Jerk Limited shaper and recently proposed Zero Vibration shaper with a distributed delay. The proposed new types of smoothers and shapers, which are essentially based on exponential distribution of delays, are investigated in time and frequency domains. Subsequently, the basic properties, i.e. response performances, spectrum distribution and robustness analysis, are demonstrated and cross-compared in a case study example.

References

    1. 1)
      • 1. Smith, O.J.M.: ‘Feedback control systems’ (ser. McGraw-Hill Series in Control Systems Engineering) (McGraw-Hill, New York, 1958).
    2. 2)
      • 2. Singer, N.C., Seering, W.P.: ‘Preshaping command input to reduce system vibration’, J. Dyn. Syst., Meas. Control, 1990, 112, pp. 7682.
    3. 3)
      • 3. Singhose, W.E., Seering, W., Singer, N.C.: ‘Residual vibration reduction using vector diagrams to generate shaped inputs’, J. Mech. Des., 1994, 116, pp. 654659.
    4. 4)
      • 4. Singhose, W.E., Porter, L.J., Singer, N.C.: ‘Vibration reduction using multi-hump input shapers’, J. Dyn. Syst. Meas. Control, 1997, 119, (2), pp. 320326.
    5. 5)
      • 5. Singh, T., Heppler, G.R.: ‘Shaped inputs for a multimode system’, ASME J. Dyn. Syst. Meas. Control, 1993, 115, pp. 341347.
    6. 6)
      • 6. Singh, T., Vadali, S.R.: ‘Robust time-delay control of multimode systems’, Int. J. Control, 1995, 62, (6), pp. 13191339.
    7. 7)
      • 7. Singhose, W., Crain, E., Seering, W.: ‘Convolved and simultaneous two-mode input shapers’, IEE Proc. – Control Theory Appl., 1997, 144, (6), pp. 515520.
    8. 8)
      • 8. Singhose, W.E., Sung, Y.G.: ‘Robustness analysis of input shaping commands for two-modes flexible systems’, IET Control Theory Appl., 2009, 3, (6), pp. 722730.
    9. 9)
      • 9. Tuttle, T.D., Seering, W.P.: ‘A zero-placement technique for designing shaped inputs to suppress multiple-mode vibration’. Proc. American Control Conf., Baltimore, MA, June 1994, pp. 25332537.
    10. 10)
      • 10. Cole, M.O.T.: ‘A discrete-time approach to impulse-based adaptive input shaping for motion control without residual vibration’, Automatica, 2011, 47, (11), pp. 25042510.
    11. 11)
      • 11. Singh, T.: ‘Jerk limited input shapers’, ASME J. Dyn. Syst., Meas. Control, 2004, 121, (1), pp. 215219.
    12. 12)
      • 12. Béarée, R.: ‘New damped-jerk trajectory for vibration reduction’, Control Eng. Pract., 2014, 28, (1), pp. 112120.
    13. 13)
      • 13. Vyhlídal, T., Kučera, V., Hromčík, M.: ‘Signal shapers with distributed delays: spectral analysis and design’, Automatica, 2013, 48, (9), pp. 22072212.
    14. 14)
      • 14. Vyhlídal, T., Hromčík, M.: ‘Parametrization of input shapers with delays of various distribution’, Automatica, 2015, 59, pp. 256263.
    15. 15)
      • 15. Vyhlídal, T., Hromčík, M., Kučera, V., Anderle, M., et al: ‘On Feedback Architectures with Zero-Vibration Signal Shapers’, IEEE Trans. Autom. Control, 2016, 61, (8), pp. 20492064.
    16. 16)
      • 16. Eloundou, R., Singhose, W.E.: ‘Interpretation of smooth reference commands as input-shaped functions’. Proc. American Control Conf., Anchorage, AK, May 2002, pp. 49484953.
    17. 17)
      • 17. Singhose, W., Eloundou, R., Lawrence, J.: ‘Command generation for flexible systems by input shaping and command smoothing’, AIAA J. Guid., Control, Dyn., 2010, 33, (6), pp. 16971707.
    18. 18)
      • 18. Meckl, P.H., Arestides, P.B., Woods, M.C.: ‘Optimized S-curve motion profiles for minimum residual vibration’. Proc. American Control Conf., Philadelphia, PA, June 1998, pp. 26272631.
    19. 19)
      • 19. Singhose, W.: ‘Command shaping for flexible systems: a review of the first 50 years’, Int. J. Precis. Eng. Manuf., 2009, 10, (4), pp. 153168.
    20. 20)
      • 20. Singh, T., Muenchhof, M.: ‘Closed-form minimax time-delay filters for underdamped systems’, Optim. Control Appl. Methods, 2007, 28, (3), pp. 157173.
    21. 21)
      • 21. Biagiotti, L., Melchiorri, C., Moriello, L.: ‘Optimal trajectories for vibration reduction based on exponential filters’, IEEE Trans. Control Syst. Technol., 2016, 24, (2), pp. 609622.
    22. 22)
      • 22. Vyhlídal, T., Kučera, V., Hromčík, M.Design, analysis and implementation of smoothed input shapers with distributed delays’, in Witrant, E., Fridman, E., Sename, O., Dugard, L. (eds.): ‘Advances in delays and dynamics: recent results on time-delay systems analysis and control’ (Springer, 2016), vol. 5, pp. 229248.
    23. 23)
      • 23. Brown, J.W., Churchill, R.V.: ‘Complex variables and applications’ (McGraw-Hill, New York, NY, 2009, 8th edn.).
    24. 24)
      • 24. Huey, J.R., Singhose, W.: ‘Trends in the stability properties of CLSS controllers: a root-locus analysis’, IEEE Trans. Control Syst. Technol., 2010, 18, (5), pp. 10441056.
    25. 25)
      • 25. Vyhlídal, T., , Zítek, P.QPmR – quasi-polynomial root-finder: algorithm update and examples’, in Vyhlídal, T, Lafay, J.F., Sipahi, R. (eds.): ‘Advances in delays and dynamics: delay systems: from theory to numerics and applications’ (Springer, 2013), vol. 1, pp. 299312.
    26. 26)
      • 26. Cole, M.O.T., Wongratanaphisan, T.: ‘Optimal FIR input shaper designs for motion control with zero residual vibration’, J. Dyn. Syst., Meas. Control, 2011, 133, (2), pp. 0210080.
    27. 27)
      • 27. Cole, M.O.T.: ‘A class of low-pass FIR input shaping filters achieving exact residual vibration cancelation’, Automatica, 2012, 48, (9), pp. 23772380.
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2015.1337
Loading

Related content

content/journals/10.1049/iet-cta.2015.1337
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading
This is a required field
Please enter a valid email address