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Research Papers

Time-Optimal Output Transition for Minimum-Phase Systems

[+] Author and Article Information
Jennifer Haggerty

e-mail: jrh6@buffalo.edu

Tarunraj Singh

Professor
Fellow of ASME
e-mail: tsingh@buffalo.edu
Department of Mechanical
and Aerospace Engineering,
University at Buffalo,
Buffalo, NY 14260

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received December 3, 2012; final manuscript received July 10, 2013; published online August 23, 2013. Assoc. Editor: Won-jong Kim.

J. Dyn. Sys., Meas., Control 135(6), 061014 (Aug 23, 2013) (11 pages) Paper No: DS-12-1398; doi: 10.1115/1.4025032 History: Received December 03, 2012; Revised July 10, 2013

The time-optimal output transition control problem for stable or marginally stable systems with minimum-phase zeros is discussed in this paper. A double integrator system with a real left-half plane zero is used to illustrate the development of the time-optimal output transition controller. It is shown that an exponentially decaying postactuation control profile is necessary to maintain the output at the desired final location. It is shown that the resulting solution to the output transition time-optimal control profile can be generated by a time-delay filter whose zeros and poles cancels the poles and zeros of the system to be controlled. The design of the time-optimal output transition problem is generalized and illustrated on the benchmark floating oscillator problem.

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References

Devasia, S., 2012, “Time-Optimal Control With Pre/Post Actuation for Dual-Stage Systems,” IEEE Trans. Control Syst. Technol., 20(2), pp. 323–334. [CrossRef]
Stearns, H., Yu, S., Fine, B., Mishra, S., and Tomizuka, M., 2008, “A Comparative Study of Feedforward Tuning Methods for Wafer Scanning Systems,” ASME Conf. Proc., 2008(43352), pp. 669–676.
Singhose, W., and Vaughan, J., 2011, “Reducing Vibration by Digital Filtering and Input Shaping,” IEEE Trans. Control Syst. Technol., 19(6), pp. 1410–1420. [CrossRef]
Singh, T., and Vadali, S. R., 1993, “Input-Shaped Control of Three-Dimensional Maneuvers of Flexible Spacecraft,” J. Guid. Control Dyn., 16(6), pp. 1061–1068. [CrossRef]
Singer, N., and Seering, W. P., 1990, “Pre-Shaping Command Inputs to Reduce System Vibration,” ASME J. Dyn. Syst., Meas. Control, 112(1), pp. 76–82. [CrossRef]
Singh, T., and Vadali, S. R., 1993, “Robust Time Delay Control,” ASME J. Dyn. Syst., Meas. Control, 115(2), pp. 303–306. [CrossRef]
Singhose, W., Derezinski, S., and Singer, N., 1996, “Extra-Insensitive Input Shapers for Controlling Flexible Spacecraft,” J. Guid. Control Dyn., 19(2), pp. 385–391. [CrossRef]
Singh, T., 2002, “Minimax Design of Robust Controllers for Flexible Systems,” J. Guid. Control Dyn., 25(5), pp. 868–875. [CrossRef]
Singh, T., 2004, “Jerk Limited Input Shapers,” ASME J. Dyn. Syst., Meas. Control, 126(1), pp. 215–219. [CrossRef]
Junkins, J. L., Rahman, Z. H., and Bang, H., 1991, “Near-Minimum-Time Maneuvers of Flexible Structures by Parameter Optimization,” J. Guid. Control Dyn., 14(2), pp. 406–415. [CrossRef]
Dijkstra, B., and Bosgra, O., 2003, “Exploiting Iterative Learning Control for Input Shaping, With Application to a Wafer Stage,” American Control Conference, Proceedings of the 2003, Vol. 6, pp. 4811–4815.
Bodson, M., 1997, “An Adaptive Algorithm for the Tuning of Two Input Shaping Methods,” American Control Conference, Proceedings of the 1997, Vol. 3, pp. 1340–1344.
Singh, G., Kabamba, P. T., and McClamroch, N. H., 1989, “Planar Time-Optimal Control, Rest-to-Rest Slewing of Flexible Spacecraft,” J. Guid. Control Dynamics, 12(1), pp. 71–81. [CrossRef]
Ben-Asher, J., Burns, J. A., and Cliff, E. M., 1992, “Time-Optimal Slewing of Flexible Spacecraft,” J. Guid. Control Dyn., 15(2), pp. 360–367. [CrossRef]
Singh, T., and Vadali, S. R., 1994, “Robust Time-Optimal Control: Frequency Domain Approach,” J. Guid. Control Dyn., 17(2), pp. 346–353. [CrossRef]
Wie, B., Sinha, R., Sunkel, J., and Cox, K., 1993, “Robust Fuel- and Time-Optimal Control of Uncertain Flexible Space Strcutures,” Guidance, Dynamics and Control Conference.
Singh, T., 1995, “Fuel/Time Optimal Control of the Benchmark Problem,” J. Guid. Control Dyn., 18(6), pp. 1225–1231. [CrossRef]
Muenchhof, M., and Singh, T., 2003, “Jerk Limited Time Optimal Control of Flexible Structures,” ASME J. Dyn. Syst., Meas. Control, 125(1), pp. 139–142. [CrossRef]
Ben-Itzak, S., and Karniel, A., 2008, “Minimum Acceleration Criterion With Constraints Implies Bang-Bang Control as an Underlying Principle for Optimal Trajectories of Arm Reaching Movements,” Neural Comput., 20, pp. 779–812. [CrossRef] [PubMed]
Iamratanakul, D., Jordan, B., Leang, K., and Devasia, S., 2008, “Optimal Output Transitions for Dual-Stage Systems,” IEEE Trans. Control Syst. Technol., 16(5), pp. 869–881. [CrossRef]
Iamratanakul, D., and Devasia, S., 2008, “Feedforward Input Design for Minimum-Time/Energy, Output Transitions for Dual-Stage Systems,” American Control Conference, pp. 3263–3268.
Devasia, S., 2012, “Time-Optimal Control With Pre/Post Actuation for Dual-Stage Systems,” IEEE Trans. Control Syst. Technol., 20(2), pp. 323–334. [CrossRef]
Singh, T., 1996, “Effect of Damping on the Structure of Time-Optimal Controllers,” J. Guid. Control Dyn., 19(5), pp. 1182–1184. [CrossRef]

Figures

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Fig. 1

Variation of maneuver and switch time

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Fig. 2

Output constraint for postactuation

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Fig. 3

Variation of maneuver and switch time

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Fig. 4

Floating oscillator

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Fig. 5

Three-switch postactuation control profile

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Fig. 6

Large maneuver three-switch postactuation

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Fig. 7

Switch and maneuver time

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Fig. 8

Single-switch postactuation control profile

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Fig. 9

Small maneuver single-switch postactuation

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Fig. 10

Comparison of maneuver times

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