| 1. |
- Jirstrand, Mats, et al.
(författare)
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A Linear Programming Approach to the Design of Thermostat Controllers of Interconnected Thermal Systems
- 1998
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Ingår i: Proceedings of the 37th IEEE Conference on Decision and Control. - Linköping : Linköping University Electronic Press. - 0780343948 ; , s. 449-454, s. 47-54
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Konferensbidrag (refereegranskat)abstract
- We investigate how to tune the thermostat hysteresis for a system of interconnected thermal processes. Using linear programming techniques and the worst-case analysis we compute switch levels for the controller to make the system stay close to the desired temperature levels. Both the cases with and without amplitude bounded disturbances are treated. The same technique can also be applied to a system of interconnected tanks despite the fact that such a system is nonlinear.
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| 2. |
- Jirstrand, Mats, et al.
(författare)
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A Negative Result on Piecewise Quadratic Lyapunov Functions for Decay Rate Analysis
- 1999
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Ingår i: Proceedings of the 38th IEEE Conference on Decision and Control. - 0780352505 ; , s. 2312-2313 vol.3
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Konferensbidrag (refereegranskat)abstract
- In recent years, the advent of efficient methods for solving linear matrix inequality (LMI) problems has yielded a new interesting class of Lyapunov functions, the piecewise quadratic Lyapunov functions, subject to efficient computation. This class has shown promise, e.g. in the stability analysis of hybrid systems. In this paper, we describe one example that we have analyzed in order to investigate how LMI methods and piecewise quadratic Lyapunov functions can be used to iteratively synthesize a switched control law in order to obtain an improved decay rate. The example shows that piecewise quadratic Lyapunov functions are not sufficient to analyze the decay rate of a piecewise affine system, given that the partitioning used in the Lyapunov function is the same as in the piecewise affine system. As noted in other performance analysis examples, a finer partitioning is needed
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| 3. |
- Pogromsky, A. Yu., et al.
(författare)
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On Stability and Passivity of a Class of Hybrid Systems
- 1998
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Ingår i: Proceedings of the 37th IEEE Conference on Decision and Control. - Linköping : Linköping University Electronic Press. - 0780343948 ; , s. 3705-3710 vol.4
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The paper deals with the stabilizability and passifiability properties of a class of hybrid dynamical systems. The systems under consideration are composed of a continuous time invariant plant and discrete event controller. An algebraic criterion for existence of a Lyapunov function for a piecewise linear system is given. Based on these results some passifiability issues are considered.
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| 4. |
- Spångéus, Per, et al.
(författare)
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An LMI based Method for Safety Controller Design
- 1999
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Ingår i: Proceedings of the 38th IEEE Conference on Decision and Control. - 0780352505 ; , s. 3633-3638 vol.4
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Konferensbidrag (refereegranskat)abstract
- A common problem in industry is the issue of safety controllers. Usually there is a basic controller that works well for normal conditions, but when certain state variables get too large we need to switch to a safety controller in order to get the state back to a normal level. The design of the safety controller such that it works well together with the basic controller is the topic of the paper. In practice, the design is often done in an ad hoc manner. The paper describes an approach to extending a given static output feedback control law with a safety controller. The safety controller is activated when the state gets close to the forbidden region in state space. It pushes the state to a safe distance from the forbidden region within a maximum prescribed time despite disturbances. It does this with a prescribed bound on the input and in a manner that guarantees stability of the overall system. The switching between the two controllers takes place through hysteresis, this helps to avoid chattering. The method is based on LMIs which ensures scalability to large systems. However, the LMI approach imposes some conservatism on the results. Also, the method is as at present limited to systems with a relative degree one from the input to a specific output of the system
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