O. Beker

University of Massachusetts Amherst, Amherst Center, Massachusetts, United States

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Publications (11)8.61 Total impact

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    ABSTRACT: Reset controllers are linear controllers that reset some of their states to zero when their inputs reach a threshold. We are interested in their feedback connection with linear plants, and in this context, the objective of this paper is twofold. First, to motivate the use of reset control through theory, simulations and experiments, and secondly, to summarize some of our recent results which establish classic performance properties ranging from quadratic and BIBO stability to steady-state and transient performance.
    10/2007: pages 123-147;
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    Orhan Beker, C.V. Hollot, Y. Chait, H. Han
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    ABSTRACT: Reset controllers are linear controllers that reset some of their states to zero when their input is zero. We are interested in their feedback connection with linear plants, and in this paper we establish fundamental closed-loop properties including stability and asymptotic tracking. This paper considers more general reset structures than previously considered, allowing for higher-order controllers and partial-state resetting. It gives a testable necessary and sufficient condition for quadratic stability and links it to both uniform bounded-input bounded-state stability and steady-state performance. Unlike previous related research, which includes the study of impulsive differential equations, our stability results require no assumptions on the evolution of reset times.
    Automatica 01/2004; · 2.92 Impact Factor
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    ABSTRACT: This paper develops a compensation algorithm based on Linear–Quadratic–Gaussian (LQG) control system design whose parameters are determined (in part) by a model of the atmosphere. The model for the atmosphere is based on the open-loop statistics of the atmosphere as observed by the wavefront sensor, and is identified from these using an auto-regressive, moving average (ARMA) model. The (LQG) control design is compared with an existing compensation algorithm for a simulation developed at ESO that represents the operation of MACAO adaptive optics system on the 8.2 m telescopes at Paranal, Chile.
    Experimental Astronomy 01/2003; 15(2):67-88. · 2.97 Impact Factor
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    O. Beker, C.V. Hollot, Y. Chait
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    ABSTRACT: The purpose of this paper is twofold: 1) to give conditions under which linear feedback control of a plant containing integrator must overshoot; and 2) to give an example of reset control that does not overshoot under such constraints
    IEEE Transactions on Automatic Control 12/2001; · 2.72 Impact Factor
  • O. Beker, C.V. Hollot, Y. Chait
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    ABSTRACT: In this paper, the authors continue their work on establishing the properties of reset control systems. Here, they focus on the local stability of limit-cycles induced under sinusoidal sensor excitation
    American Control Conference, 2001. Proceedings of the 2001; 02/2001
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    ABSTRACT: Reset control has the potential of providing better trade-offs among competing specifications compared to LTI control. We consider a specific class of reset control systems consisting of a feedback interconnection between a linear second-order system and a so-called first-order reset element. Despite the simplicity of this feedback system, few theoretical results are available to quantify stability and performance. The paper develops a necessary and sufficient condition for asymptotic stability and a sufficient condition for BIBO stability. We also characterize steady-state response, overshoot, rise time and settling time to step input
    American Control Conference, 2000. Proceedings of the 2000; 10/2000
  • O. Beker, C.V. Hollot, Y. Chait
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    ABSTRACT: Reset controllers are linear systems that reset some or all of their states to zero based on a given reset law. We (1999) previously established asymptotic stability results for reset control systems under constant inputs. The bounded-input bounded-output stability of reset systems was addressed by Chen et al. (2000). In this paper, we study their response to sinusoidal inputs and analyze oscillations forced by sinusoidal sensor noise. Our motivation is to establish reset control system response to (sinusoidal) sensor noise
    Decision and Control, 2000. Proceedings of the 39th IEEE Conference on; 02/2000
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    ABSTRACT: Develops a compensation algorithm based on optimal control system design. The optimal control design is compared with the existing classical compensation algorithm using a simulation that represents the ALFA adaptive optics system at the Calar Alto Observatory
    Decision and Control, 1999. Proceedings of the 38th IEEE Conference on; 02/1999
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    ABSTRACT: Reset controllers are standard linear compensators equipped with mechanism to instantaneously reset their states. With respect to pure linear control, there is evidence that this reset action is capable of improving control system tradeoffs. This paper's objective is to analyze the stability of a particular example of reset control system when excited by constant inputs. Our main result shows that the equilibrium point of the closed-loop dynamics is asymptotically stable
    American Control Conference, 1999. Proceedings of the 1999; 02/1999
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    ABSTRACT: Presents the existing compensation designs for the ALFA adaptive optics system that is implemented on the 3.5 m telescope at the Calar Alto observatory (operated by the Max-Planck Institut f¨ur Astronomie (MPIA) in Spain). The ALFA system uses a modal compensation architecture. This architecture is presented with the objective of highlighting the modal compensation design problem. The compensator design is developed. The paper presents both comparative-and scientific results obtained with the compensator designs
    Control Applications, 1999. Proceedings of the 1999 IEEE International Conference on; 02/1999
  • O. Beker, C.V. Hollot, Y. Chait
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    ABSTRACT: Reset controllers are standard linear compensators equipped with a mechanism to instantaneously reset their states. With respect to pure linear control, there is evidence that this reset action is capable of improving control system tradeoffs. In Beker et al. (1999) we established stability conditions for SISO reset control systems and this paper extends these results to the MIMO case. The paper's objective is to analyze the stability of such reset control systems when excited by constant inputs. Our main result gives conditions under which the equilibrium point of the closed-loop dynamic is asymptotically stable
    Decision and Control, 1999. Proceedings of the 38th IEEE Conference on; 02/1999