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- Christiansson, Anna-Karin, 1947-, et al.
(författare)
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Continuous-, discrete- and sampled-data- H∞ˆž control - a unified framework
- 2000
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Ingår i: IEEE Proceedings. - 0191-2216. ; 2, s. 1936-1941
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Tidskriftsartikel (refereegranskat)abstract
- We present a unified and general framework for H∞-control in both continuous time, discrete time and combinations of these. The general result is a hybrid continuous-/discrete-time H∞ˆž-controller. Using a compact hybrid notation, the work shows a close relationship between the continuous-and discrete-time solutions. In fact, the pure continuous and discrete time equations may be obtained as two similar interpretations of the general result. There are no assumptions made on certain system matrices being zero or normalised, e.g. D11 = 0. The method is Riccati equation (RE) based, and it is shown how the continuous REs can be "lifted" into discrete ones reflecting the system behaviour during the period. Typical applications are control of continuous-time or discrete-time periodic systems, as well as multirate and sampled-data control, including mixed continuous and sampled-data measurements.
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- Christiansson, Anna-Karin, 1947-, et al.
(författare)
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Low order sampled-data H∞ control
- 2003
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Ingår i: Decision and Control, 2003. Proceedings. 42nd IEEE Conference on. ; 3, s. 2308 - 2313
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Konferensbidrag (refereegranskat)abstract
- A method for obtaining low order sampled-data H∞ controllers is presented. The method is mainly based on a parametric static feedback controller for a plant that is augmented with the controller dynamics. The design of a full-order controller is a convex problem, while the optimisation problem for lower order controllers is non convex. The proposed method starts with design of a full-order sampled-data controller using Riccati equations. Then this controller is reduced by an ordinary model reduction technique, and the reduced controller is used as an initial value for an iterative procedure using linear matrix inequalities (LMIs) in the search for an optimal controller. The matrix inequalities are in fact linear in either the Lyapunov matrix or the static controller matrix, why the solution to the non convex problem fundamentally is given by a bilinear matrix inequality (BMI). The order of the controller is reduced until the closed loop performance degrades too much. Simulations are shown for the control of a time delayed SISO-plant where the controller order can be reduced from 8th to 3rd order. Results are also shown from control of a MIMO-model of a jet engine where the reduction is successful from 15th to 4th order. It is argued that the non convexity is handled efficiently since the procedure uses a model reduction of the full-order controller as initial value.
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- Christiansson, Anna-Karin, 1947-, et al.
(författare)
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Mixed continuous/discrete-time output feedback H∞ control : A unified approach
- 1999
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Ingår i: European Control Conference, ECC 1999 - Conference Proceedings. - 9783952417355 ; , s. 4077-4082
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Konferensbidrag (refereegranskat)abstract
- A Riccati equation (RE) based solution to the H∞ optimal control problem for mixed continuous/discrete-time systems is presented. The results unify a number of recently penetrated H∞ control problems. In the infinite-horizon case a periodic behaviour is assumed, and it is shown how the related continuous RE with jumps can be replaced by an equivalent discrete periodic RE. A related algebraic RE, which involves the system behaviour during one period, then can be formulated and solved by standard methods. Typical applications are control of continuous-time or discrete-time periodic systems, as well as multirate and sampled-data control, including mixed continuous and sampled-data measurements. © 1999 EUCA.
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