This paper discusses the design problem of distributed H-infinity Luenberger-type partial differential equation (PDE) observer for state estimation of a linear unstable parabolic distributed parameter system (DPS) wit...
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This paper discusses the design problem of distributed H-infinity Luenberger-type partial differential equation (PDE) observer for state estimation of a linear unstable parabolic distributed parameter system (DPS) with external disturbance and measurement disturbance. Both pointwise measurement in space and local piecewise uniform measurement in space are considered;that is, sensors are only active at some specified points or applied at part thereof of the spatial domain. The spatial domain is decomposed into multiple subdomains according to the location of the sensors such that only one sensor is located at each subdomain. By using Lyapunov technique, Wirtinger's inequality at each subdomain, and integration by parts, a Lyapunov-based design of Luenberger-type PDE observer is developed such that the resulting estimation error system is exponentially stable with an H-infinity performance constraint, and presented in terms of standard linear matrix inequalities (LMIs). For the case of local piecewise uniform measurement in space, the first mean value theorem for integrals is utilised in the observer design development. Moreover, the problem of optimal H-infinity observer design is also addressed in the sense of minimising the attenuation level. Numerical simulation results are presented to show the satisfactory performance of the proposed design method.
In this paper, stabilization of the distributed parameter system (DPS) with time delay is studied using Galerkin's method and fuzzy control. With the help of Galerkin's method, the dynamics of DPS with time de...
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In this paper, stabilization of the distributed parameter system (DPS) with time delay is studied using Galerkin's method and fuzzy control. With the help of Galerkin's method, the dynamics of DPS with time delay can be first converted into a group of low-order functional ordinary differential equations, which will be used for design of the robust fuzzy controller. The fuzzy controller designed can guarantee exponential stability of the closed-loop DPS. Some sufficient conditions are derived for the stabilization together with the linear matrix inequality design approach. The effectiveness of the proposed control design methodology is demonstrated in numerical simulations.
In this paper, partial synchronization of the distributed parameter system (DPS) with time delay is considered via Galerkin's method and the fuzzy control. First, based on Galerkin's method, the dynamics of ma...
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In this paper, partial synchronization of the distributed parameter system (DPS) with time delay is considered via Galerkin's method and the fuzzy control. First, based on Galerkin's method, the dynamics of master DPS and slave DPS can be described by low-order ordinary differential equations (ODEs). Then the low-order functional ODEs are used as the basis for the design of the fuzzy controller to ensure the synchronization between the two low-order ODEs;moreover, when the slow system of master DPS and the slow system of slave DPS are synchronized, the error between master DPS and slave DPS is bounded. Some criteria are derived for stabilization and linear matrix inequality design approach is developed. The effectiveness of the proposed controller design methodology is finally demonstrated through numerical simulation.
In this paper, we present a numerical solution for an inverse heat problem to estimate 2D space-wise coefficient in a parabolic system describing heat transfer. The inverse problem is recast into an optimization probl...
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In this paper, we present a numerical solution for an inverse heat problem to estimate 2D space-wise coefficient in a parabolic system describing heat transfer. The inverse problem is recast into an optimization problem solved with a conjugate gradient method. This approach use the non linear optimization formulation by minimizing a cost function taking into account both the measured outputs of the system and the outputs calculated by means of the model. The solution is performed by using the free finite element software FreeFem. Numerical example is carried out to check the validity of the proposed method.
In this work, a dynamic switching based fuzzy controller combined with spectral method is proposed to control a class of nonlinear distributed parameter systems (DPSs). Spectral method can transform infinite-dimension...
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In this work, a dynamic switching based fuzzy controller combined with spectral method is proposed to control a class of nonlinear distributed parameter systems (DPSs). Spectral method can transform infinite-dimensional DPS into finite ordinary differential equations (ODEs). A dynamic switching based fuzzy controller is constructed to track reference values for the multi-inputs multi-outputs (MIMO) ODEs. Only a traditional fuzzy logic system (FLS) and a rule base are used in the controller, and membership functions (MFs) for different ODEs are adjusted by scaling factors. Analytical models of the dynamic switching based fuzzy controller are deduced to design the scaling factors and analyze stability of the control system. In order to obtain a good control performance, particle swarm optimization (PSO) is adopted to design the scaling factors. Moreover, stability of fuzzy control system is analyzed by using the analytical models, definition of the stability and Lyapunov stability theory. Finally, a nonlinear rod catalytic reaction process is used as an illustrated example for demonstration. The simulation results show that performance of proposed dynamic switching based fuzzy control strategy is better than a multi-variable fuzzy logic controller. (C) 2013 Elsevier Ltd. All rights reserved.
This paper proposes a recursive least squares algorithm for a distributed parameter system with missing observations. By using the finite difference method, the distributed parameter system can be turned into a lumped...
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This paper proposes a recursive least squares algorithm for a distributed parameter system with missing observations. By using the finite difference method, the distributed parameter system can be turned into a lumped parametersystem. Then a missing output identification model based recursive least squares algorithm is derived to estimate the unknown parameters of the lumped parametersystem. Furthermore, the parameters of the distributed parameter system can be computed by the estimated parameters of the lumped parametersystem. The simulation results indicate that the proposed method is effective.
This paper studies the application of reduced models of a distributed parameter system for robust process control and state estimation. We take the approach of integrating model reduction, parameter identification, an...
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This paper studies the application of reduced models of a distributed parameter system for robust process control and state estimation. We take the approach of integrating model reduction, parameter identification, and model uncertainty analysis, in purpose to find an appropriate trade-off between complexity and robust performance. The application example is the temperature system in a continuous paper pulp digester. Physical modeling of this process results in coupled linearized partial differential equations which are then reduced into low-order nominal process models using an orthogonal collocation approximation method. Two different approaches to obtaining it model uncertainty description are adapted for use on a distributed parameter system with low-order nominal model and shown to produce similar results when tested with measurement data. It is also demonstrated how this uncertainty description, in combination with the reduced model, may be used for robust control design and verification of the control performance on the distributed parameter system. Finally, the possibility of estimating the distributed process state using a state observer for the reduced process is demonstrated. Measurements of the process state in a certain position is available and is shown to agree with the estimated state at the same position. (C) 2008 Elsevier Ltd. All rights reserved.
This paper considers the state observation for a class of distributed parameter systems(DPSs)with moving boundaries modelled by parabolic partial differential equations(PDEs).The method of mobile observation is presen...
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This paper considers the state observation for a class of distributed parameter systems(DPSs)with moving boundaries modelled by parabolic partial differential equations(PDEs).The method of mobile observation is presented to improve the observation performance of the systems and to eliminate the influence of moving boundaries on system observation with the aids of mobile sensor networks(MSNs).The MSNs which can move throughout the time-dependent spatial domain are used to provide the spatially averaged observations of the *** using the abstract evolution equation theory of parabolic PDEs and the Lyapunov stability arguments,a centralised observer is designed and a mobile control scheme for each of the mobile sensors is presented while taking account of the dynamics of the MSNs.A numerical example is finally presented to illustrate the effectiveness and the advantages of the proposed approach.
The control of the distributed parameter system(DPS) has some problems like as that 1)the construction of the mathematical model of the DPS is difficult and 2) the allocation of control equipments must be optimized. F...
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The control of the distributed parameter system(DPS) has some problems like as that 1)the construction of the mathematical model of the DPS is difficult and 2) the allocation of control equipments must be optimized. For the former problem, we applied the fuzzy technique to the control of the DPS because it has dominance of that one can construct the control system with the experience rules but without the mathematical model. For the latter problem, the genetic algorithm(GA) was used because one can optimize the controller allocation with low calculation time by using it. Simulation experiments were performed for the temperature control problem on a finite length stick. As the result, effectiveness of the proposed method was confirmed.
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