Dr. Hopkins in 2008.

E-Mail: mark.hopkins@rit.edu

This Quarter's schedule

This Quarter's Classes and Office Hours

Office: Gleason Bldg (09), Room 3021

Phone Number: (585) 475 - 6640

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Education and Interests

Publications, Patents, etc.

Education and Interests:

Degree:

Ph.D., 1988, Virginia Tech (Virginia Polytechnic Institute and State University), Blacksburg VA

Specialties:

System Identification

Control Systems

Research Interests:

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Model identification of flexible structures: Typically, the order of the model to be identified is at least 600, because the system it represents has considerably more than 300 (often closely-spaced) lightly-damped vibrational modes that are distributed over a frequency range of at least 4.5 orders-of-magnitude, with a dynamic range of about 120 dB. The identified model ideally has bode magnitude error less than 2 dB and bode phase error less than 10 degrees at every frequency over the full range of interest (when compared to the empirical data from the real system). This is a very tough problem, particularly the very wide bandwidth, not only in terms of system identification, but also in terms of numerical stability. I made very good progress on this modeling problem in the late 1990's in my work at Eastman Kodak Company, Commercial & Government Systems Division (currently ITT Space Systems Division), and developed a technique, called the Pick And Place Algorithm (P.A.P.A.), to create models this good.

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Extending the P.A.P.A. modeling technique to MIMO systems: During my professional development leave (2001-02) at C&GS, I successfully extended P.A.P.A. to multiple-input, multiple-output (MIMO) systems. The crux of this problem is converting a matrix of transfer functions into a state-space model in modal-canonic form, by way of partial fraction expansions. Getting this to work involved creating a new algorithm, called Residue Rank Reduction (R-cubed), that iteratively reduces the rank of all the MIMO Cauchy-residue-arrays to rank one. That is necessary in order to avoid having any multiple poles at the same location in the state-space model. The feasibility proof of the method is a two-input, two-output, 850-pole state-space model of a large flexible strucure. This model was created from four P.A.P.A. transfer functions, and has extremely good frequency response accuracy from 0.2 Hz to 10 kHz.

A more current challenge is a high-order six-input, nine-output model, which involves almost 15 times as much computation as the two-input, two-output model did. The algorithm was modified for distribution to a large number of processors, so as to keep computation time feasible, taking advantage of the Message Passing Interface (MPI) environment typically available on a supercomputer cluster. This is a current problem, not solved for very wide bandwidths (i.e., > 2.5 orders of magnitude).

More recently (March 2009), I essentially solved the problem of creating very high-order discrete-time MIMO state-space models that agree quite well with empirical data over a very broad range of frequencies ( > 4.5 orders-of-magnitude). Over the past two years I developed a method that successfully decouples individual modes, to the greatest extent possible, so that they can more easily be identified. This has led to a very successful new modeling technique that I call FORCASTER (Frequency Observability Range Context and Supramodal Topology to Estimate Residues). This new method relies on three fundamental tools, (1) The FORSE algorithm, published in 1996 by Liu, Jacques, and Miller in ASME JDSMC, (2) the mode-decoupling technique mentioned above, and (3) model components that, collectively, I call the "supramodal model", which models the effects of non-modal poles and of modes above the Nyquist frequency. These results will be published as soon as possible.

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Control of flexible structures: Apply advanced control techniques to high-order models generated by the model identification. This problem involves model-order reduction techniques, as there are significant numerical problems involved in designing a controller from models larger than 600-th order, and no possibility of implementing in hardware a real-time controller of that size and sample rate. In the past couple of years, I have been developing a method that tunes an initial LQR-based controller/observer design to achieve damping, isolation, and robustness goals, for the class of infinite-dimensional, reasonably linear, flexible structures that are my main interest. This method relies on having excellent high-order as well as reduced-order models, and uses the Nelder-Mead Simplex Method, and other similar algorithms, to tune the two feedback matrices. It also depends upon distributed computing to make it feasible to achieve good results in a reasonable amount of time. The work was funded by ITT Industries Space Systems Division.

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Courses Dr. Hopkins is Teaching in Winter Quarter, 2009-2010 (Nov 30, 2009 to Feb 26, 2010):

EE 453 Linear Systems I (11:00 - 11:50 am, M Tu Th F)

EE 453 Linear Systems I (2:00 - 2:50 pm, M Tu Th F)

EE 815 Multivariable Modeling (4:00 - 5:50 pm, Tu Th)

Office Hours in Winter Quarter, 2009-2010 (Nov 30, 2009 to Feb 26, 2010)

• Mondays       3:00 - 4:00 pm
• Tuesdays       12:45 - 1:45 pm
• Thursdays      12:45 - 1:45 pm
• Fridays          3:00 - 4:00 pm
•     or by appointment

Publications, Patents, etc.

Publications:

• Hopkins, Mark A., "Relating continuous-time and discrete-time in the classroom," Proceedings of ASEE 2008 Annual Conference and Exposition, AC-2008-2741, Pittsburgh PA, June 22-25, 2008.
• Hopkins, Mark A., "Improved selection of state-weighting matrices for LQR MIMO-controller design," Proceedings of IASTED, 10th International Conference on Intelligent Systems and Control, L. M. Sztandera, ed., Vol. 592-800, Cambridge MA, November, 2007.
• Hopkins, Mark A., "Demonstrating in the classroom the ideas of frequency response," Proceedings of ASEE Engineering Teaching and Learning Practices, Joan Dannenhoffer, ed., Toronto ONT, October, 2007.
• Rowen, D., and M.A.Hopkins, "H-infinity controller design for structural damping," Proceedings of SPIE, 13th International Symposium on Smart Structures and Materials, Damping and Isolation Conference, Volume 6169, pp. 22-33, February 26 - March 3, 2006.
• Hopkins, M.A., D.A. Smith, P. Vallone, and R. Sandor, "Hybrid multivariable controller architecture," Proceedings of SPIE Vol. 5760, 12th International Symposium on Smart Structures and Materials, Damping and Isolation Conference, March 6-10, 2005, pages 390-401.
• Hopkins, M.A., and H.F. VanLandingham, "Optimal Nonlinear Estimation of Linear Stochastic Systems: The Multivariable Extension," ASME Journal of Dynamic Systems, Measurement and Control, Vol. 118, No. 2, June 1996, pp. 350-353.
• Vallone, Phillip, and Mark Hopkins, "Experimental Verification of a Novel System ID Technique Called PLID using a 3-D Flexible Structure," Proc. of the SPIE North American Conf. on Smart Structures and Materials, San Diego CA, February 1995.
• Hopkins, M.A., and H.F. VanLandingham, "Optimal Nonlinear Estimation of Linear Stochastic Systems," ASME Journal of Dynamic Systems, Measurement and Control, Vol. 116, No. 3, September 1994, pp. 529-536.
• Lyon, Bruce, and Mark Hopkins, Genetic Algorithm Design of a Fuzzy Logic TRC Controller, Xerox/WRC Monograph, January 1994.
• Hopkins, Mark A., Report on a Three-Input, Three-Output Fuzzy Logic Tone Reproduction Curve (TRC) Controller, Xerox/WRC Monograph, May 1993.
• Hopkins, Mark A., Report on an Adaptive Fuzzy Logic Controller, Xerox/WRC Monograph, November 1992.
• Hopkins, Mark A., A New Method to Predict Photoreceptor Dark Decay Voltage Transients, Xerox/WRC Monograph, August 1991.
• Hopkins, Mark A., Photoreceptor Dark Decay Potential Control in a Prototype Color Printer, Xerox/WRC Monograph, July 1990.
• Hopkins, M.A., and H.F. VanLandingham, "Optimal Joint Parameter and State Estimation of Linear Stochastic MIMO Systems," Proceedings of the 1988 American Control Conference, Atlanta, GA.

Patents:

• U.S. Patent # 5,760,812, Two-Input, Two-Output Fuzzy Logic Print Quality Controller for an Electrophotographic Printer, Inventor: Mark A. Hopkins, Assignee: Xerox Corp., issued June 2, 1998.
• U.S. Patent # 5,390,004, Three-Input, Three-Output Fuzzy Logic Print Quality Controller for an Electrophotographic Printer, Inventor: Mark A. Hopkins, Assignee: Xerox Corp., issued February 14, 1995.
• U.S. Patent # 5,355,197, Method and Apparatus for Predicting the Cycle-Down Behavior of a Photoreceptor, Inventor: Mark A. Hopkins, Assignee: Xerox Corp., issued October 11, 1994.

Professional Affiliations:

• Senior Member Institute of Electrical and Electronics Engineers (IEEE)
• Member American Society for Engineering Education
(ASEE)
• Member Tau Beta Pi
• Member Society for Industrial and Applied Mathematics
(SIAM)
• Technical reviewer for the ASME Journal of Dynamic Systems, Measurement and Control
• Technical reviewer for the ASME Journal of Vibration and Acoustics

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