Dynamic mode decomposition with control (DMDc) is a modal decomposition method that extracts dynamically relevant spatial structures disambiguating between the underlying dynamics and the effects of actuation. In this...
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Dynamic mode decomposition with control (DMDc) is a modal decomposition method that extracts dynamically relevant spatial structures disambiguating between the underlying dynamics and the effects of actuation. In this work, we extend the concepts of DMDc to better capture the local dynamics associated with highly nonlinear processes and develop temporally-local reduced-order models that accurately describe the fully-resolved data. In this context, we first partition the data into clusters using a Mixed Integer Nonlinear Programming based optimization algorithm, the Global Optimum Search, which incorporates an added feature of predicting the optimal number of clusters. Next, we compute the reduced-order models tailored to each cluster by applying DMDc within each cluster. The developed models are subsequently used to compute approximate solutions to the original high-dimensional system and to design a feedback control system of hydraulic fracturing processes for the computation of optimal pumping schedules. Published by Elsevier Ltd.
This paper discusses a cooperative control problem by two one-link flexible Timoshenko arms. The goal is to control a grasping force to collect an object with the two flexible arms, and to simultaneously suppress the ...
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This paper discusses a cooperative control problem by two one-link flexible Timoshenko arms. The goal is to control a grasping force to collect an object with the two flexible arms, and to simultaneously suppress the vibrations of the arms. To solve this problem, we propose a boundary controller that is based on a dynamic model represented by a hybrid PDE-ODE model;the exponential stability of the closed-loop system is then proven by the frequency domain method. Finally, several numerical simulations are carried out to investigate the validity of the proposed boundary cooperative controller. (C) 2017 Elsevier Ltd. All rights reserved.
Improving mixing is one of the important goals in flow control, e.g., to decrease concentration polarization in membrane systems to reduce fouling. As with many distributed parameter systems, fluid flow can be control...
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Improving mixing is one of the important goals in flow control, e.g., to decrease concentration polarization in membrane systems to reduce fouling. As with many distributed parameter systems, fluid flow can be controlled using boundary value manipulation. Fluid manipulation using electro-osmosis is studied in this work, where several cylindrical electrodes are used to create multiple spatially non-uniform time-varying electric fields. The proposed approach converts the distributedparameter system into an infinite-dimensional system by spatial and spectral discretization. A virtual output variable is constructed to allow the optimization of a mixing objective function to be conducted using frequency response analysis, with consideration of the constraints of conservation of charge. The solution obtained in this paper is the input profile that provides the greatest achievable ratio of time-average dissipation function to time-average input energy satisfying the input constraints. (C) 2016 Elsevier Ltd. All rights reserved.
Rapid thermal processing (RTP) is very important for semiconductor manufacturing. The RTP is actually a spatially distributed dynamical system (SDDS) with multiple control sources. Due to its highly nonlinear and spat...
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Rapid thermal processing (RTP) is very important for semiconductor manufacturing. The RTP is actually a spatially distributed dynamical system (SDDS) with multiple control sources. Due to its highly nonlinear and spatiotemporal dynamics, it would be difficult to maintain the temperature uniformity inside the RTP. In this paper, a hierarchical intelligent methodology is proposed for the spatiotemporal control of RTP. The control scheme consists of three different levels. At the lower level, the decomposition strategy is taken to divide the SDDS into several relatively simple subsystems;each of them is handled by one control source. At the mid-level, 3-D fuzzy logic controllers (3-D-FLCs) are designed, which have inherent capability to process spatiotemporal dynamics, to maintain the temperature uniformity of each subsystem. At the upper level, a local coordination strategy will be designed to adjust 3-D-FLCs to overcome interactions between the adjacent subsystems. The proposed scheme is applied to the temperature uniformity control of a rapid thermal chemical vapor deposition system, and better temperature uniformity can be achieved.
This technical note discusses a contact-force control problem of a one-link flexible arm. This flexible arm includes a Timoshenko beam, and thus we call it the flexible Timoshenko arm. The primary aim is to control th...
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This technical note discusses a contact-force control problem of a one-link flexible arm. This flexible arm includes a Timoshenko beam, and thus we call it the flexible Timoshenko arm. The primary aim is to control the contact force at the contact point. To do so, we first apply our previously proposed force controller, which exponentially stabilizes the closed-loop system of a flexible Euler-Bernoulli arm, to the force-control problem of the flexible Timoshenko arm. We then show that our previously proposed force controller cannot exponentially stabilize the flexible Timoshenko arm. Next, we consider the flexible Timoshenko arm, which is making contact with a soft environment. By utilizing the damping force in the soft environment, as well as the controller, we try to overcome the problem. We then prove the exponential stability of the closed-loop system. Finally, we provide simulation results, and consider the validity of our force controller.
In the present paper, an adaptive parameter estimation algorithm applicable to linear systems with transfer functions of arbitrary structure is proposed. The approach can be applied to a wide class of linear processes...
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In the present paper, an adaptive parameter estimation algorithm applicable to linear systems with transfer functions of arbitrary structure is proposed. The approach can be applied to a wide class of linear processes, including non-linearly parameterized ones. The proposed method is applicable to fractional-order systems, distributed-parameter and delayed systems, and other classes of systems described by irrational transfer functions. In the first stage of the proposed procedure, values of the transfer function at specific frequencies are pinpointed by means of the Recursive Least Square algorithm with forgetting factor. In the second stage, the unknown parameters are found by numerically inverting complex non-linear relations linking them to the quantities estimated in the first stage. The inversion is performed by means of an iterative, gradient-based scheme. The method is illustrated by several detailedly explained numerical examples. (C) 2017 Elsevier GmbH. All rights reserved.
We present an optimization-based framework for analysis and control of linear parabolic partial differential equations (PDEs) with spatially varying coefficients without discretization or numerical approximation. For ...
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We present an optimization-based framework for analysis and control of linear parabolic partial differential equations (PDEs) with spatially varying coefficients without discretization or numerical approximation. For controller synthesis, we consider both full-state feedback and point observation (output feedback). The input occurs at the boundary (point actuation). We use positive-definite matrices to parameterize positive Lyapunov functions and polynomials to parameterize controller and observer gains. We use duality and an invertible state variable transformation to convexify the controller synthesis problem. Finally, we combine our synthesis condition with the Luenberger observer framework to express the output feedback controller synthesis problem as a set of LMI/SDP constraints. We perform an extensive set of numerical experiments to demonstrate the accuracy of the conditions and to prove the necessity of the Lyapunov structures chosen. We provide numerical and analytical comparisons with alternative approaches to control, including Sturm-Liouville theory and backstepping. Finally, we use numerical tests to show that the method retains its accuracy for alternative boundary conditions.
We consider a vector reaction-advection-diffusion equation on a hypercube. The measurements are weighted averages of the state over different subdomains. These measurements are asynchronously sampled in time. Subject ...
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We consider a vector reaction-advection-diffusion equation on a hypercube. The measurements are weighted averages of the state over different subdomains. These measurements are asynchronously sampled in time. Subject to matched disturbances, the discrete control signals are applied through shape functions and zero-order holds. The feature of this work is that we consider generalized relay control: the control signals take their values in a finite set. This allows for networked control through low capacity communication channels. First, we derive linear matrix inequalities (LMIs) whose feasibility guarantees the ultimate boundedness with a limit bound proportional to the sampling period. Then we construct a switching procedure for the controller parameters that ensures semi-global practical stability: for an arbitrarily large domain of initial conditions the trajectories converge to a set whose size does not depend on the domain size. For the disturbance-free system this procedure guarantees exponential convergence to the origin. The results are demonstrated by two examples: 2D catalytic slab and a chemical reactor. (C) 2017 Elsevier Ltd. All rights reserved.
Recently, the problem of boundary stabilization for unstable linear constant-coefficient coupled reaction-diffusion systems was solved by means of the back-stepping method. The extension of this result to systems with...
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Recently, the problem of boundary stabilization for unstable linear constant-coefficient coupled reaction-diffusion systems was solved by means of the back-stepping method. The extension of this result to systems with advection terms and spatially-varying coefficients is challenging due to complex boundary conditions that appear in the equations verified by the control kernels. In this technical note we address this issue by showing that these equations are essentially equivalent to those verified by the control kernels for first-order hyperbolic coupled systems, which were recently found to be well-posed. The result therefore applies in this case, allowing us to prove H-1 stability for the closed-loop system. It also unveils a previously unknown connection between backstepping kernels for coupled parabolic and hyperbolic problems.
This technical note discusses a contact-force control problem for a flexible arm. This flexible arm includes a Timoshenko beam, and thus we call it the flexible Timoshenko arm. The aim of the force control is to contr...
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This technical note discusses a contact-force control problem for a flexible arm. This flexible arm includes a Timoshenko beam, and thus we call it the flexible Timoshenko arm. The aim of the force control is to control the contact force at the contact point. To solve this problem, we propose a simple boundary controller and show the exponential stability of the closed-loop system by the frequency domain method. Finally, we describe simulation results carried out to investigate the validity of the proposed controller for the force control problem.
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