Discontinuous feedback stabilization of minimum-phase semilinear infinite-dimensional systems with application to chemical tubular reactor
Tóm tắt
This paper develops discontinuous control methods for minimum-phase semilinear infinite-dimensional systems driven in a Hilbert space. The control algorithms presented ensure asymptotic stability, global or local accordingly, as state feedback or output feedback is available, as well as robustness of the closed-loop system against external disturbances with the a priori known norm bounds. The theory is applied to stabilization of chemical processes around prespecified steady-state temperature and concentration profiles corresponding to a desired coolant temperature. Two specific cases, a plug flow reactor and an axial dispersion reactor, governed by hyperbolic and parabolic partial differential equations of first and second order, respectively, are under consideration. To achieve a regional temperature feedback stabilization around the desired profiles, with the region of attraction, containing a prescribed set of interest, a component concentration observer is constructed and included into the closed-loop system so that there is no need for measuring the process component concentration which is normally unavailable in practice. Performance issues of the discontinuous feedback design are illustrated in a simulation study of the plug flow reactor.
Từ khóa
#Chemical reactors #Inductors #Temperature #Control systems #Plugs #Hilbert space #Asymptotic stability #State feedback #Output feedback #Robust controlTài liệu tham khảo
foias, 1996, Robust Control of Infinite Dimensional Systems Frequency Domain Methods
10.1007/BFb0027563
10.1252/jcej.2.95
friedman, 1969, Partial Differential Equations
10.1007/978-1-4612-0347-6
khalil, 1996, Nonlinear Systems
10.1007/978-94-010-1542-4
10.1016/S0167-6911(00)00088-8
laabissi, 2001, multiple equilibrium profiles for a nonisothermal tubular reactor nonlinear model
10.1109/9.855545
10.1137/1.9780898717525.ch6
10.1109/9.90226
deimling, 1970, Nonlinear Functional Analysis
curtain, 1995, An Introduction to Infinite Dimensional Linear Systems Theory, 10.1007/978-1-4612-4224-6
10.1007/978-3-642-87643-1
10.1002/acs.691
10.1109/9.661074
fjeld, 1971, approximate lumped models of a tubular chemical reactor, and their use in feedback and feedforward control, Proc 2nd IFAC Symp Multivariable Technical Control Systems, 1
10.1109/CDC.1997.657586
pazy, 1983, Semigroups of Linear Operators and Applications to Partial Differential Equations, 10.1007/978-1-4612-5561-1
10.1007/978-3-642-84379-2
10.1109/9.75101
10.1002/aic.690160318
varma, 1977, stirred pots and empty tubes, Chemical Reactor Theory, 79
10.1016/S0005-1098(99)00170-3