nextupprevious
Next:About this document ...Up:Experiences with an ExperimentalPrevious:Acknowledgments

Bibliography

1
G. J. Balas, J. C. Doyle, K. Glover, A. Packard, and R. Smith.

$\mu$-Analysis and Synthesis Toolbox User's Guide.
The Mathworks, Natick, MA, 1995.
2
K. H. Johansson and J. L. R. Nunes.

A multivariable laboratory process with an adjustable zero.
In Proc. American Control Conf., 1998.
3
N. A. Kheir, K. J. Åstrom, D. Auslander, K. C. Cheok, G. F. Franklin, M. M. Masten, and M. Rabins.

Control systems engineering education.
Automatica, 51(8):147-166, 1995.
4
S. Skogestad and I. Postlethwaite.

Multivariable Feedback Control.
John Wiley & Sons, New York, NY, 1996.
5
R. Vadigepalli, E. P. Gatzke, and F. J. Doyle III.

Robust $H_\infty$ control of an experimental 4-tank system.
in preparation, 1999.
 
Ed Gatzke received his B.S.ChE. from the Georgia Institute of Technology in 1995. After two years of graduate study at Purdue University, he moved to the University of Delaware Chemical Engineering Department for completion of his Ph.D. Ed has held internships with Teledyne Brown Engineering, Mead Paper, and Honeywell. His interests include: process control, optimization, and artificial intelligence.

Raj Vadigepalli received his B.Tech. in Chemical Engineering from the Indian Institute of Technology, Madras, India, in 1996, and began his Ph.D. research in chemical engineering at Purdue University, West Lafayette, IN, in the fall of 1996 under Prof. Francis J. Doyle III. In September 1997, he moved with professor Doyle to the University of Delaware to complete his doctoral degree. His research focus includes modeling and analysis of control mechanisms in biological systems and distributed hierarchical methods for control of large-scale process systems.

Edward S. Meadows is a postdoctoral fellow at the University of Delaware, working in the areas of modeling and control of polymerization reactors as part of a broader research program in optimization and control of chemical processes. Dr. Meadows received the Ph.D. degree from the University of Texas in 1994.

Frank Doyle received his B.S.E. from Princeton (1985), C.P.G.S. from Cambridge (1986), and Ph.D. from Caltech (1991), all in Chemical Engineering. After graduate school, he worked at DuPont as a Visiting Scientist in the Strategic Process Technology Group (1991-1992), then started as an Assistant Professor at Purdue University in 1992. He moved to the University of Delaware as an Associate Professor in the fall of 1997. His research interests are in the areas of process and biosystems analysis and control.

Table 1: Steps in control design 
\fbox{ \centering \begin{tabular}{cp{2.3 in}}1& Study the system (plant) to be...... control system, and tune thecontroller on-line, if necessary.\end{tabular}}

 
Table 2: Nonlinear model equations
\( \frac{dh_{1}}{dt}=-\frac{a_{1}}{A_{1}}\sqrt{2gh_{1}}+\frac{a_{3}}{A_{1}}\sqrt{2gh_{3}}+\frac{\gamma _{1}k_{1}}{A_{1}}\nu _{1} \)
\( \frac{dh_{2}}{dt}=-\frac{a_{2}}{A_{2}}\sqrt{2gh_{2}}+\frac{a_{4}}{A_{2}}\sqrt{2gh_{4}}+\frac{\gamma _{2}k_{2}}{A_{2}}\nu _{2} \)
\( \frac{dh_{3}}{dt}=-\frac{a_{3}}{A_{3}}\sqrt{2gh_{3}}+\frac{(1-\gamma _{2})k_{2}}{A_{3}}\nu _{2}-\frac{k_{d_{1}}d_{1}}{A_{3}} \)
\( \frac{dh_{4}}{dt}=-\frac{a_{4}}{A_{4}}\sqrt{2gh_{4}}+\frac{(1-\gamma _{1})k_{1}}{A_{4}}\nu _{1}-\frac{k_{d_{2}}d_{2}}{A_{4}} \)

 
Table 3: Linearized model equations
\({{dx} \over {dt}}=\left[ {\matrix{{-{1 \over {T_1}}}&0&0&0\cr0&{-{1 \over......-{{k_{d_1}} \over {A_3}}}&0\cr0&{-{{k_{d_2}} \over {A_4}}}\cr}} \right]d\)

 
 
\( T_{i}=\frac{A_{i}}{a_{i}}\sqrt{\frac{2h_{i}(0)}{g}} \)

 
Table 4: Model parameters
a1,a2 \( 2.3\, cm^{2} \) k1 \( 5.51\, cm^3/s \)
a3,a4 \( 2.3\, cm^{2} \) k2 \( 6.58\, cm^3/s \)
A1,A2,A3,A4 \( 730\, cm^{2} \) g \( 981\, \frac{cm}{s^{2}} \)
\( \nu _{1}(0) \) \( 60\% \) \( \gamma _{1} \) 0.333
\( \nu _{2}(0) \) \( 60\% \) \( \gamma _{2} \) 0.307
T1 \( 53.8\, sec \) h1(0) \( 14.1\, cm \)
T2 \( 48.0\, sec \) h2(0) \( 11.2\, cm \)
T3 \( 38.5\, sec \) h3(0) \( 7.2\, cm \)
T4 \( 31.1\, sec \) h4(0) \( 4.7\, cm \)

 
Figure 1: Schematic of the four tank system
\resizebox*{5in}{!}{\includegraphics{4tank.ps}}

 
Figure 2: Laboratory apparatus
\resizebox*{5in}{!}{\includegraphics{Doylebw2.eps}}

 
Figure 3: Schematic of the control system
\resizebox*{5in}{!}{\includegraphics{comps.ps}}

 
Figure 4: Screenshot of Freelance four tank schematic
\resizebox*{5in}{!}{\includegraphics{tank1.ps}}

 
Figure 5: Screenshot of Freelance tank level trends
\resizebox*{5in}{!}{\includegraphics{tank2.ps}}

 
Figure 6: Screenshot of the Matlab Interface
\resizebox*{5in}{!}{\includegraphics{sim.ps}}

 
Figure 7: Disturbance rejection using robust controller
\resizebox*{5in}{!}{\includegraphics{distrej2.ps}}

 
Figure 8: Reference tracking using robust controller
\resizebox*{5in}{!}{\includegraphics{reftrack2.ps}}


Figure Captions: Figure 1: Schematic of the four tank system Figure 2: Laboratory apparatus Figure 3: Schematic of the control system Figure 4: Screenshot of Freelance four tank schematic Figure 5: Screenshot of Freelance tank level trends Figure 6: Screenshot of the Matlab Interface Figure 7: Disturbance rejection using robust controller Figure 8: Reference tracking using robust controller 

nextupprevious
Next:About this document ...Up:Experiences with an ExperimentalPrevious:Acknowledgments
Edward Price Gatzke

1999-07-20