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Stabilisation of Linear Time-Invariant Systems subject to Output Saturation

Hilhorst, Gijs (2011) Stabilisation of Linear Time-Invariant Systems subject to Output Saturation.

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Abstract:Nowadays we heavily rely on all kinds of control systems, ranging from boilers and thermostats to airplanes and GPS satellites. By means of measurement devices, useful information about a dynamical system can be obtained. Using the measurement data, a control law generating an input may be designed to meet specific demands of the closedloop dynamics. Output saturation, describing range limitations of measurement devices, has not received much attention yet. Since output saturation is present in many automatic control systems, controllers coping with this measurement limitation are desired. The main difficulty with output saturation is that the magnitude of a saturated measurement is unknown. To be able to control the system, the output must be steered towards the region where it does not saturate. If this can be achieved, well-known observation techniques can be applied locally. We specialise to the class of controllable and observable linear time-invariant systems with saturated output. We show that, if such a system is stable, a controller global asymptotically stabilising the system can be designed by means of a quadratic Lyapunov function. LaSalle’s invariance principle is necessary to prove this result. First continuous-time systems are treated. Since implementability is the major issue, we expand the results to discrete-time systems. Furthermore, we discuss how a continuoustime system can be discretised, and under which conditions an implementable controller design can be achieved.
Item Type:Essay (Master)
Faculty:EEMCS: Electrical Engineering, Mathematics and Computer Science
Subject:31 mathematics
Programme:Applied Mathematics MSc (60348)
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