Internal model based tracking and disturbance rejection for stable well-posed systems

Automatica

Volumn 39, Issue 9, 2003, Pages 1555-1569

  Rebarber, Richard ^a   Weiss, George ^b  

^a UNIVERSITY OF NEBRASKA LINCOLN   (United States)

^b IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

Coupled beams; Dynamic stabilization; Exponential stability; Input output stability; Internal model principle; Optimizability; Positive transfer function; Structural acoustics; Tracking; Well posed linear system

Indexed keywords

ACOUSTIC NOISE; GAIN CONTROL; OPTIMIZATION; PARTIAL DIFFERENTIAL EQUATIONS; SYSTEM STABILITY; TRANSFER FUNCTIONS;

DYNAMIC STABILIZATION;

LINEAR SYSTEMS;

EID: 0041591136     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0005-1098(03)00192-4     Document Type: Article

References (38)

1. Ammari K., Liu Z., Tucsnak M. Decay rates for a beam with pointwise force and moment feedback. Mathematics of Control, Signals, and Systems. 15:2002;229-255.
2. ∞ feedback control in a structural acoustic model with periodic excitation International Journal of Robust and Nonlinear Control. 6:1996;453-478.
3. Banks H.T., Smith R.C. Feedback control of noise in a 2-D nonlinear structural acoustics model. Discrete and Continuous Dynamical Systems. 1:1995;119-149.
4. Chen G., Krantz S.G., Russell D.L., Wayne C.E., West H.H., Coleman M.P. Analysis, designs, and behavior of dissipative joints for coupled beams. SIAM Journal on Control and Optimization. 49:1989;1665-1693.
5. Curtain, R., & Weiss, G. Stabilization of essentially skew-adjoint systems by collocated feedback. Submitted, available at www.ee.ic.ac.uk/CAP/.
6. Davison E.J. The robust control of a servomechanism problem for linear time invariant multivariable systems. IEEE Transactions on Automatic Control. 21:1976;25-34.
7. Davison E.J. Multivariable tuning regulators: the feedforward and robust control of a general servomechanism problem. IEEE Transactions on Automatic Control. 21:1976;35-47.
8. Francis B.A., Wonham W.M. The internal model principle for linear multivariable regulators. Applied Mathematics and Optimization. 2:1975;170-194.
9. Hämäläinen T., Pohjolainen S. Robust control and tuning problem for distributed parameter systems. International Journal of Robust and Nonlinear Control. 6:1996;479-500.
10. Hämäläinen T., Pohjolainen S. A finite dimensional robust controller for systems in the CD-algebra. IEEE Transactions on Automatic Control. 45:2000;421-431.
11. Ho L.F., Russell D.L. Admissible input elements for systems in Hilbert space and a Carleson measure criterion. SIAM Journal on Control and Optimization. 21:1983;614-640.
12. Krein, S. G. (1971). In J. M. Danskin (Trans.), Linear differential equations in Banach space. Translations of Mathematical Monographs, Providence, RI: American Mathematical Society (in Russian).
13. Lasiecka, I. (2002). Mathematical control theory of coupled PDEs. CBMS-NSF Regional Conference Series in Applied Mathematics. Philadelphia: SIAM.
14. Logemann H., Bontsema J., Owens D.H. Low-gain control of distributed parameter systems with unbounded control and observation. Control Theory and Advanced Technology. 4:1988;429-446.
15. Logemann, H., & Curtain, R. F. (2000). Absolute stability results for infinite-dimensional well-posed systems with applications to low-gain control. ESAIM: Control, Optimisation and Calculus of Variations, 5, 395-424, http://www.edpsciences.com/articles/cocv/abs/2000/01/cocvVol5-16.
16. Logemann, H., & Mawby, A. D. (2001). Low-gain integral control of infinite dimensional regular linear systems subject to input hysteresis. In F. Colonius et al. (Eds.), Advances in math. systems theory (pp. 255-293). Boston: Birkhäuser.
17. Logemann H., Owens D.H. Low-gain control of unknown infinite-dimensional systems. A frequency-domain approach Dynamics and Stability of Systems. 4:1989;13-29.
18. Logemann H., Ryan E.P., Townley S. Integral control of infinite-dimensional linear systems subject to input saturation. SIAM Journal on Control and Optimization. 36:1998;1940-1961.
19. Logemann H., Townley S. Low-gain control of uncertain regular linear systems. SIAM Journal on Control and Optimization. 35:1997;78-116.
20. Logemann H., Townley S. Discrete-time low-gain control of uncertain infinite-dimensional system. IEEE Transactions on Automatic Control. 42:1997;22-37.
21. Morgul O. Stabilization and disturbance rejection for the beam equation. IEEE Transactions on Automatic Control. 46:2001;1913-1918.
22. Pohjolainen S. Robust multivariable PI-controllers for infinite dimensional systems. IEEE Transactions on Automatic Control. 27:1982;17-30.
23. Pohjolainen S. Robust controllers for systems with exponentially stable strongly continuous semigroups. Journal of Mathematical Analysis and Applications. 111:1985;622-636.
24. Pohjolainen S., Lätti I. Robust controller for boundary control systems. International Journal of Control. 38:1983;1189-1197.
25. Rebarber R. Exponential stability of coupled beams with dissipative joints. a frequency domain approach SIAM Journal on Control and Optimization. 33:1995;1-28.
26. Rebarber R., Weiss G. Necessary conditions for exact controllability with a finite-dimensional input space. Systems & Control Letters. 40:2000;217-227.
27. Salamon D. Infinite dimensional systems with unbounded control and observation: a functional analytic approach. Transactions of the American Mathematical Society. 300:1987;383-431.
28. Salamon D. Realization theory in Hilbert space. Mathematical Systems Theory. 21:1989;147-164.
29. Staffans O.J. Quadratic optimal control of stable well-posed linear systems. Transactions of the American Mathematical Society. 349:1997;3679-3715.
30. Staffans O.J. Coprime factorizations and well-posed linear systems. SIAM Journal on Control and Optimization. 38:1998;1268-1292.
31. Staffans O.J. Admissible factorizations of Hankel operators induce well-posed linear systems. Systems and Control Letters. 37:1999;301-307.
32. Staffans O.J., Weiss G. Transfer functions of regular linear systems, Part II. The system operator and the Lax-Phillips semigroup Transactions of the American Mathematical Society. 354:2002;3229-3262.
33. Weiss G. Admissibility of unbounded control operators. SIAM Journal on Control and Optimization. 27:1989;527-545.
34. Weiss G. Admissible observation operators for linear semigroups. Israel J. Math. 65:1989;17-43.
35. Weiss G. Transfer functions of regular linear systems, Part I. Characterizations of regularity Transactions of the American Mathematical Society. 342:1994;827-854.
36. Weiss G. Regular linear systems with feedback. Mathematics of Control, Signals, and Systems. 7:1994;23-57.
37. Weiss G., Curtain R.F. Dynamic stabilization of regular linear systems. IEEE Transactions on Automatic Control. 42:1997;4-21.
38. Weiss G., Rebarber R. Optimizability and estimatability for infinite-dimensional linear systems. SIAM Journal on Control and Optimization. 39:2001;1204-1232.