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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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Sampled-data H∞ˆž-control for time-varying hybrid systems
- 2001
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Ingår i: Dynamics of continuous, discrete and impulsive systems. - 1201-3390 .- 1918-2538. ; 8:4b, s. 427-444
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Tidskriftsartikel (refereegranskat)abstract
- This paper presents sampled-data H∞ˆž-control of linear mixed continuous-time and discrete-time systems, including a mix of continuous-time and discrete-time performance signals and disturbances. However, neither continuous-time control signals nor continuous-time measurements are included. The sampling may well be multirate, i.e. different signals may be sampled by different rates, as long as a periodic pattern is repeated over the period, consisting of a number of sampling steps. In fact, the results are applicable even to arbitrary linear time-varying systems. The sampled-data system is discretised such that the continuous-time performance is reflected in the discretised or "lifted" system. This lifted system is combined with discrete-time updates at the sampling instants to achieve the sampled-data controller. The "hold-states" case is presented as a special application, when there is also a hold circuit at the controller output. The continuous-time Riccati equations with discrete-time updates then can be replaced by one discrete-time static feedback and filter Riccati equation respectively, which also reflect the intersample behaviour. Furthermore, convergence results between the discretised Riccati solutions and the corresponding continuous-time solutions are shown, when the sampling interval decreases towards zero. Simulations are shown when the results are applied to the control of a MIMO jet-engine model.
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- Christiansson, Anna-Karin, 1947, et al.
(författare)
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Sampled-Data H-infinity-Control for Time-Varying Hybrid Systems
- 2001
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Ingår i: Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms. - 1492-8760. ; 8:4, s. 427-444
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Tidskriftsartikel (refereegranskat)abstract
- This paper presents sampled-data H-infinity-control of linear mixed continuous-time and discrete-time systems, including a mix of continuous-time and discrete-time performance signals and disturbances. However, neither continuous-time control signals nor continuous-time measurements are included. The sampling may well be multirate, i.e. different signals may be sampled by different rates, as long as a periodic pattern is repeated over the period, consisting of a number of sampling steps. In fact, the results are applicable even to arbitrary linear time-varying systems.The sampled-data system is discretised such that the continuous-time performance is reflected in the discretised or "lifted" system. This lifted system is combined with discrete-time updates at the sampling instants to achieve the sampled-data controller. The "hold-states" case is presented as a special application, when there is also a hold circuit at the controller output. The continuous-time Riccati equations with discrete-time updates then can be replaced by one discrete-time static feedback and filter Riccati equation respectively, which also reflect the intersample behaviour.Furthermore, convergence results between the discretised Riccati solutions and the corresponding continuous-time solutions are shown, when the sampling interval decreases towards zero, Simulations are shown when the results are applied to the control of a MIMO jet-engine model.
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