Periodic Event triggered Control of Singularly Perturbed systems
01 Dec 2019-
TL;DR: In this paper, the authors proposed a periodic event-triggered control of singularly perturbed systems, where state variables are sampled at their natural frequency avoiding oversampling of slow variables.
Abstract: This paper proposes periodic event-triggered control of singularly perturbed systems. The proposed triggering strategy allows periodic evaluation of triggering rule. Continuous state measurements are no longer required, instead, the states are measured periodically and are transmitted to controller only if certain condition based on the system performance is satisfied. Another advantage of this triggering mechanism is that there exists a uniform positive lower bound on the inter-event time which is equal to one sampling period at least. In this work, we use independent event-triggering mechanism for the slow and fast variables of the system. This allows state variables to be sampled at their natural frequency avoiding oversampling of slow variables. The proposed strategy ensures bounded stability of the closed-loop system. Simulation results are included to show the efficacy of the proposed method.
Citations
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01 Jan 2002
TL;DR: In this article, it is shown that Lebesgue sampling gives better performance for some simple systems than traditional Riemann sampling, which is an analog of integration theory and is called event-based sampling.
Abstract: The normal approach to digital control is to sample periodically in time. Using an analog of integration theory we can call this Riemann sampling. Lebesgue sampling or event based sampling is an alternative to Riemann sampling. It means that signals are sampled only when measurements pass certain limits. In this paper it is shown that Lebesgue sampling gives better performance for some simple systems.
77 citations
01 Jan 1984
TL;DR: In this paper, the design of stabilizing feedback control of singularly perturbed diserete-time systems is decomposed into slow and fast controllers which are combined to form the composite control.
Abstract: The design of stabilizing feedback control of singularly perturbed diserete-time systems is decomposed into the design of slow and fast controllers which are combined to form the composite control. Composite control strategies are developed for the case of single rate measurements (all variables are measured at the same rate) as well as for the case of multirate measurements (slow variables are measured at a rate slower than that of fast variables).
23 citations
References
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TL;DR: In this paper, the control of a two-time-scale plant, where the sensor is connected to a linear controller/actuator via a network, is addressed, and it is shown that the whole systems via the network control are generally asymptotically stable as long as their slow and fast systems are both stable.
Abstract: In this paper, the control of a two-time-scale plant, where the sensor is connected to a linear controller/actuator via a network is addressed. The slow and fast systems of singularly perturbed systems are used to produce an estimate of the plant state behavior between transmission times, by which one can reduce the usage of the network. The approximate solutions of the whole systems are derived and it is shown that the whole systems via the network control are generally asymptotically stable as long as their slow and fast systems are both stable. These results are also extended to the case of network delay.
13 citations
01 Dec 2009
TL;DR: It is shown by this Tikhonov-like result that there exists a bound of the small parameter to guarantee global exponential stability of the overall hybrid system on the time interval if the eigenvalues of a lower order slow test matrix are strictly inside its unit circles.
Abstract: In this paper, a robust stabilization of the uncertain singularly perturbed system via a networked state feedback with the transmission time-delay is addressed. Taking its nominal system as a model plant, propagation unit and overall states chosen to overcome the difficulty of communication delay, the characterization of singular perturbation for the overall hybrid system is still preserved on each sampling interval. Since the traditional two-time-scale technique is not applicable for the overall hybrid system, its approximated slow and fast subsystems are constructed. Based on the decomposition, the approximated slow and fast test matrix for the stability is established. Then, Tikhonov-like limit process of the stability test matrix for the overall hybrid system is proved. It is shown by this Tikhonov-like result that there exists a bound of the small parameter to guarantee global exponential stability of the overall hybrid system on the time interval if the eigenvalues of a lower order slow test matrix are strictly inside its unit circles. Further, a structure analysis of the approximated slow test matrix is developed. Finally, a numerical simulation is presented to illustrate the main results.
12 citations
TL;DR: In this article, the authors considered the problem of finite-time H∞-optimal control of linear, singularly perturbed, discrete-time systems from the game theoretic approach and showed that the attenuation level achieved by the singular perturbation method, compared to the full-order solution, depends on the order of approximation.
Abstract: In this paper, we consider the problem of finite-time H∞-optimal control of linear, singularly perturbed, discrete-time systems. The problem is addressed from the game theoretic approach. This leads to a singularly perturbed, matrix Riccati difference equation, the solution of which is given in terms of an outer series solution, and a boundary-layer correction series solution. We show that the disturbance attenuation level achieved by the singular perturbation method, compared to the full-order solution, depends on the order of approximation. The theory is illustrated by considering two examples. © 1998 John Wiley & Sons, Ltd.
10 citations
"Periodic Event triggered Control of..." refers methods in this paper
...Finally, an example of an atomic reactor mood [22] is considered to illustrate the application of the proposed PETC....
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...SIMULATION RESULTS In this section, the proposed PETC approach is applied to an example of a nuclear reactor mood [22], [30]....
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05 Nov 2007
TL;DR: In this paper, the control of two-time-scale plant, where the sensor is connected to a linear controller and actuator via a network, is addressed, and the slow and fast systems of singularly perturbed systems are used to produce an estimation of the plant state between transmission instants, by which one can reduce the use of network.
Abstract: In this paper the control of two-time-scale plant, where the sensor is connected to a linear controller and actuator via a network, is addressed. The slow and fast systems of singularly perturbed systems are used to produce an estimation of the plant state between transmission instants, by which one can reduce the use of network. The approximate solutions of the systems are derived and it is globally shown that the whole systems via the network control are asymptotically stable as long as their slow and fast systems are both stable.
8 citations
"Periodic Event triggered Control of..." refers background in this paper
...To increase the sampling period of periodic transmissions for a networked SPS, the model-based network control has been studied in [14]–[17]....
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6 citations
"Periodic Event triggered Control of..." refers background in this paper
...Since slow and fast dynamics co-exist in a SPS, we can either choose a slow sampling period Ts = [ 1 ε ]T (where [ 1 ε ] is the largest integer < 1 ε ) or a sufficiently short sampling period Tf = εT as in [26], [27] for the sample data control of the SPS....
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