On control of nonlinear system dynamics at unstable steady state
TL;DR: In this paper, two effective strategies for shifting an oscillatory or chaotic trajectory to the unstable steady state of a nonlinear system in the presence of stochastic or deterministic load disturbances are presented.
About: This article is published in Chemical Engineering Journal.The article was published on 1997-05-01. It has received 3 citations till now. The article focuses on the topics: Control of chaos & Variable structure control.
Citations
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01 Jan 2009
TL;DR: The results evaluated for stabilizing the reactor for different conditions including deterministic and stochastic disturbances show the better performance of the soft sensor based nonlinear control strategy over that of a PID controller with modified feedback mechanism.
Abstract: Control of nonlinear systems exhibiting complex dynamic behavior is a challenging task because such systems present a variety of behavioral patterns depending on the values of physical parameters and intrinsic features. Understanding the behavior of the nonlinear dynamic systems and controlling them at the desired conditions is important to enhance their performance. In this work, a soft sensor based nonlinear controller strategy is presented and applied to control a chemical reactor that exhibit multi-stationary unstable behavior, oscillations and chaos. In this strategy, an extended kalman filter is designed to serve as a soft sensor that provides the estimates of unmeasured process states. These states are used as inferential measurements to the nonlinear controller that is designed in the framework of globally linearizing control. The results evaluated for stabilizing the reactor for different conditions including deterministic and stochastic disturbances show the better performance of the soft sensor based nonlinear control strategy over that of a PID controller with modified feedback mechanism.
22 citations
01 Mar 2013
TL;DR: In this paper, a nonlinear internal model control (NIMC) strategy that incorporates the nonlinear model structure and the estimator dynamics in the control law is presented for the control of complex dynamical systems characterized by input-output multiplicities, nonlinear oscillations and chaos.
Abstract: A nonlinear internal model control (NIMC) strategy that incorporates the nonlinear model structure and the estimator dynamics in the control law is presented for the control of complex dynamical systems characterized by input-output multiplicities, nonlinear oscillations and chaos. A model based estimator is designed to provide the unmeasured process states that capture the fast changing nonlinear dynamics of the process to incorporate in the controller. The estimator uses the mathematical model of the process in conjunction with the known process measurements to estimate the states. The design and implementation of the estimator supported NIMC strategy is studied by choosing two typical continuous non-isothermal nonlinear processes, a chemical reactor and a polymerization reactor, which show rich dynamical behavior ranging from stable situations to chaos. The results evaluated under different conditions show the superior performance of the estimator based NIMC strategy over the conventional controllers for the control of complex nonlinear processes.
6 citations
01 Jan 2022
TL;DR: In this article , a nonlinear internal model control (NIMC) strategy that incorporates the nonlinear model structure and the estimator dynamics in the control law is presented for the control of nonlinear dynamical systems.
Abstract: Optimal state estimation has received considerable significance in the control of complex nonlinear dynamical systems that are characterized by input–output multiplicities, parametric sensitivity, nonlinear oscillations, and chaos. In this study, a nonlinear internal model control (NIMC) strategy that incorporates the nonlinear model structure and the estimator dynamics in the control law is presented for the control of nonlinear dynamical systems. The state estimator is designed to provide the unmeasured process states that capture the fast-changing nonlinear dynamics of the process to incorporate in the controller. The performance of the estimator-supported NIMC strategy is evaluated by applying it for the control of a nonisothermal nonlinear chemical reactor and a homopolymerization reactor, which exhibit rich dynamical behavior ranging from stable situations to chaos. The results evaluated under different conditions show the better performance of the estimator-based NIMC strategy over the conventional controllers.
References
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TL;DR: In this paper, the stabilization of unstable periodic orbits of a chaotic system is achieved either by combined feedback with the use of a specially designed external oscillator, or by delayed self-controlling feedback without using of any external force.
2,957 citations
TL;DR: In this article, the chaotic dynamics found in the diode resonator have been converted into stable orbits with periods up to 23 drive cycles long, using a modification of that of Ott, Grebogi, and Yorke.
Abstract: The chaotic dynamics found in the diode resonator has been converted into stable orbits with periods up to 23 drive cycles long. The method used is a modification of that of Ott, Grebogi, and Yorke [Phys. Rev. Lett. 64, 1196 (1990)]. In addition to stabilizing existing low-period orbits, the method allows making small alterations in the attractor permitting previously nonexistent periodic orbits to be stabilized. It is an analog technique and therefore can be very fast, making it applicable to a wide variety of systems.
461 citations
TL;DR: A method is developed which uses the exponential sensitivity of a chaotic system to tiny perturbations to direct the system to a desired accessible state in a short time by applying a small, judiciously chosen, perturbation to an available system parameter.
Abstract: A method is developed which uses the exponential sensitivity of a chaotic system to tiny perturbations to direct the system to a desired accessible state in a short time. This is done by applying a small, judiciously chosen, perturbation to an available system parameter. An expression for the time required to reach an accessible state by applying such a perturbation is derived and confirmed by numerical experiment. The method introduced is shown to be effective even in the presence of small-amplitude noise or small modeling errors.
345 citations
TL;DR: Using both experimental and theoretical results, this Letter describes how low-energy, feedback control signals can be successfully utilized to suppress (laminarize) chaotic flow in a thermal convection loop.
Abstract: Using both experimental and theoretical results, this Letter describes how low-energy, feedback control signals can be successfully utilized to suppress (laminarize) chaotic flow in a thermal convection loop. Disciplines Engineering | Mechanical Engineering Comments Suggested Citation: Singer, Jonathan, Y-Z Wang, and Haim H. Bau. (1991) Controlling a Chaotic System. Physical Review Letters. Vol. 66(9). Copyright 1991 American Physical Society. This article may also be viewed at http://prl.aps.org/pdf/PRL/ v66/i9/p1123_1 This journal article is available at ScholarlyCommons: http://repository.upenn.edu/meam_papers/201
262 citations
TL;DR: This chapter discusses controlling chaos using time delay coordinates, a new method of controlling a chaotic dynamical system by stabilizing one of the many unstable periodic orbits embedded in a chaotic attractor through only small time dependent perturbations in some accessible system parameter.
Abstract: This chapter discusses controlling chaos using time delay coordinates. The Ott-Grebogi-Yorke (OGY) control method is analyzed in the case that the attractor is reconstructed from a time series using time delay coordinates. It turns out that the control formula of Ott, Grebogi and Yorke should be modified in order to apply to experimental systems if time delay coordinates are used. The chapter reveals that the experimental surface of section map depends not only on the actual parameter but also on the preceding one. In order to meet this dependence two modifications are introduced which lead to a better performance of the control. To compare their control abilities they are applied to simulations of a Duffing oscillator. OGY proposed a new method of controlling a chaotic dynamical system by stabilizing one of the many unstable periodic orbits embedded in a chaotic attractor, through only small time dependent perturbations in some accessible system parameter. This makes OGY's approach quite different from other previously published methods on controlling chaos. OGY's method has attracted the attention of many physicists interested in applications of nonlinear dynamics.
208 citations