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ABSTRACT: This paper presents a general framework for the design of linear controllers
for linear systems subject to time-domain constraints. The design framework
exploits sums-of-squares techniques to incorporate the time-domain constraints
on closed-loop signals and leads to conditions in terms of linear matrix
inequalities (LMIs). This control design framework offers, in addition to
constraint satisfaction, also the possibility of including an optimization
objective that can be used to minimize steady state (tracking) errors, to
decrease the settling time, to reduce overshoot and so on. The effectiveness of
the framework is shown via a numerical example.
10/2011;
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ABSTRACT: In this paper we present a general linear matrix inequality-based analysis method to determine the performance of a SISO reset control system in both the ℒ2 gain and ℋ2 sense. In particular, we derive convex optimization problems in terms of LMIs to compute an upperbound on the ℒ2 gain performance and the ℋ2 norm, using dissipativity theory with piecewise quadratic Lyapunov functions. The results are applicable to for all LTI plants and linear-based reset controllers, thereby generalizing the available results in the literature. Furthermore, we provide simple though convincing examples to illustrate the accuracy of our proposed ℒ2 gain and ℋ2 norm calculations and show that, for an input constrained ℋ2 problem, reset control can outperform a linear controller designed by a common nonlinear optimization method. Copyright © 2009 John Wiley & Sons, Ltd.
International Journal of Robust and Nonlinear Control 07/2010; 20(11):1213 - 1233. · 1.55 Impact Factor
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ABSTRACT: Recent results on the control of linear systems subject to time-domain constraints could only handle the case of closed-loop poles that are situated on the real axis. As most closed-loop systems in practice contain also complex poles, there is a strong need for a general framework encompassing all cases. In this paper such a framework is presented based on sums-of-squares techniques and we show indeed that time-domain constraints on closed-loop signals of linear systems can be incorporated as linear matrix inequalities, even when complex conjugate poles are assigned. The effectiveness of this complete design method is evaluated by means of a simulation example.
Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009. Proceedings of the 48th IEEE Conference on; 01/2010
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ABSTRACT: Non-stationary disturbances in motion systems generally limit the closed-loop performance. If these disturbance can be measured, this measurement can be used to enable a linear parameter varying (LPV) controller to adapt itself to the current operating condition, resulting in a closed-loop system with an overall increased performance. In this paper, this idea is applied to an active vibration isolation system.
American Control Conference, 2009. ACC '09.; 07/2009
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ABSTRACT: In this paper we present a general LMI-based analysis method to determine an upperbound on the L<sub>2</sub> gain performance of a reset control system. These computable sufficient conditions for L<sub>2</sub> stability, based on piecewise quadratic Lyapunov functions, are suitable for all LTI plants and linear-based reset controllers, thereby generalizing the results available in literature. Our results furthermore extend the existing literature by including tracking and measurement noise problems by using strictly proper input filters. We illustrate the approach by a numerical example.
American Control Conference, 2008; 07/2008
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ABSTRACT: To overcome fundamental limitations of linear controllers, reset controllers were proposed in literature. Since the closed loop system including such a reset controller is of a hybrid nature, it is difficult to determine its performance. The focus in this paper is to determine the performance of a SISO reset control system in H<sub>2</sub> sense. The method is generally applicable in the sense that it is valid for any proper LTI plant and linear-based reset controller. We derive convex optimization problems in terms of LMIs to compute an upperbound on the H<sub>2</sub> norm, using dissipativity theory with piecewise quadratic Lyapunov functions. Finally, by means of a simple multiobjective tracking example, we show that reset control can outperform a linear controller obtained via a standard multiobjective control design method.
Decision and Control, 2007 46th IEEE Conference on; 01/2008
