Distributed Parameter Observer Research Articles

State estimation of the time–space propagation of COVID-19 using a distributed parameter observer based on a SEIR-type model

The real-time prediction and estimation of the spread of diseases, such as COVID-19 is of paramount importance as evidenced by the recent pandemic. This work is concerned with the distributed parameter estimation of the time–space propagation of such diseases using a diffusion–reaction epidemiological model of the susceptible–exposed–infected–recovered (SEIR) type. State estimation is based on continuous measurements of the number of infections and deaths per unit of time and of the host spatial domain. The observer design method is based on positive definite matrices to parameterize a class of Lyapunov functionals, in order to stabilize the estimation error dynamics. Thus, the stability conditions can be expressed as a set of matrix inequality constraints which can be solved numerically using sum of squares (SOS) and standard semi-definite programming (SDP) tools. The observer performance is analyzed based on a simplified case study corresponding to the situation in France in March 2020 and shows promising results.

Optimization of DTC algorithm based on distributed parameter modelling of PMSM

Accurate mathematical model is the basis and precondition of electric motor control. The existing motor model under concentrated parameters is difficult to describe the harmonic and nonlinear characteristics of the motor, while the motor model under distributed parameters can accurately describe the torque and flux characteristics of the motor precisely at all working points, which provides the foundation for model-based motor control. The stator flux and torque observer have an essential influence on the performance of direct torque control (DTC) for PMSM. The concentrated parameter model of PMSM considering only the fundamental wave vector of the magnetic field for DTC will have obvious deficiencies in the performance such as torque ripple. This paper therefore uses the reconstructed magnetic co-energy (MCE) model to establish a torque and flux observer based on distributed parameters, which is introduced into the DTC algorithm of PMSM as an observer. The optimized DTC algorithm makes full use of the flux and torque harmonic description capabilities of the distributed parameter model, which improves control performance. The superiority of the distributed parameter observer is verified by simulation and bench test.

Backstepping-based extended Luenberger observer design for a Burgers-type PDE for multi-agent deployment * *Financial support by the German Research Council (DFG) in the project ME 3231/2-1 is gratefully acknowledged.

Abstract An extended Luenberger state observer is presented for a Burgers-type PDE. For this, pointwise boundary and an additional in-domain measurement are considered, which allows to split the observer setup into two subsystems. The observer gains are determined by utilizing the backstepping technique, which enables to stabilize the distributed parameter observer error dynamics. The concept is integrated into a motion planning and feedback control strategy and is applied to achieve the deployment of multi-agent continuum into desired spatial-temporal formation profiles. For the evaluation of the observer strategy the transfer to a finite-dimensional discrete multi-agent system in leader-follower configuration is obtained by means of a finite difference discretization. This in addition imposes the required communication topology for the interconnected agents.

Observer-based output feedback linearizing control applied to a denitrification reactor

In this work a late lumping approach is used in order to design a state feedback linearizing controller for influent disturbance attenuation and regulating the nitrogen concentration at the output of a denitrification biofilter. This controller is associated to a distributed parameter observer to estimate all the states needed to compute the controlled input. It results in an output feedback nonlinear controller with stable closed-loop dynamics.

State estimation of a stratified storage tank

Two approaches for the state estimation of the spatial temperature profile in a stratified storage tank, i.e. the state of the art domestic hot water storage system, are presented. There are a distributed parameter observer as a late lumping and an Unscented Kalman filter (UKF) as an early lumping approach which are investigated with respect to applicability and reconstruction convergence. Both, the distributed parameter observer and the UKF are designed based on a hybrid distributed parameter model of the stratified storage tank. The hybrid model is composed of a finite state automaton interacting with an underlying thermal heat conduction–convection system described by a quasi-linear partial differential equation. The performance of the estimation algorithms is illustrated by simulation studies and measurement data, showing excellent convergence results.

State Profile Estimation for a Nonisothermal Adsorption Process by a Nonlinear Distributed Parameter Observer

A major dynamical characteristic of pressure swing adsorption plants are nonlinear wave propagation phenomena travelling forwards and backwards within the fixed beds due to the change in flow direction. The control of product purity by an advanced process control strategy requires knowledge of the spatial concentration profiles. In this paper, the reconstruction of the spatial profiles of a single fixed bed of an oxygen production plant with a nonlinear distributed parameter observer is examined as a contribution to the design and the realization of a model based process control strategy. Assuming a binary mixture, the distributed parameter model describing the nonisothermal adsorption process comprises six space and time dependent states: temperature, pressure, oxygen mole fraction in the gaseous phase, the adsorbed amounts of oxygen and nitrogen, and the molar flux. The location of sensors is examined and discussed with respect to observer convergence and a nonlinear distributed parameter observer is designed for the adsorption process injecting correction terms in selected balance equations. The placement of the injected correction terms as well as their tuning parameters are of major importance concerning the convergence properties of the observer. The observer is implemented with the simulation environment DIVA and examined with respect to its convergence behavior.

Nonlinear inferential control of an autonomous periodic fixed-bed reactor

Abstract This paper deals with the control of an autonomous periodic fixed-bed reactor, which is called circulation loop reactor (CLR). This process can be described by a distributed parameter system with sustained oscillations. The state variables at some positions of such a process, e.g. the conversion at the reactor exit, may be required to vary in a smooth fashion, which in general is a difficult task due to the process's inherent complex behavior. Here, a straightforward control strategy of the CLR based on direct exit concentration regulation is presented. A relay feedback controller is found to be effective for achieving overall conversion while using relatively small external heating. In order to implement the control scheme without on-line concentration measurement, a nonlinear inferential control concept is adopted. A newly-developed nonlinear distributed parameter observer is used to infer the exit concentration from the temperature measurements at only a few positions. Moreover, an approach based on integrating a disturbance estimator is presented for improving the performance of the observer in the case of unmeasured inlet concentration. It is found that there exist simple determinate relations between the inlet variables or the model parameters and the maximum amplitude or the period of the oscillatory temperature at an axial position for the considered cases. By employing the oscillatory feature of the CLR, a method of estimating the inlet concentration is proposed, and a parameter estimation method based on the least square technique is given to update offline model parameters. It is shown that substantial benefits could be realized using the proposed nonlinear inferential control scheme for the CLR because it can provide excellent disturbance rejection capabilities and strong robustness.

State profile estimation of an autothermal periodic fixed-bed reactor

In this paper, the state profile estimation of a novel autothermal fixed-bed reactor (called circulation loop reactor, CLR), which can be operated as an autonomous periodic system, is studied. Since in autothermal operation the reactor shows sustained large oscillations, its dynamics have to be modelled as a strongly nonlinear distributed parameter system. The generally used lumping techniques (e.g. the orthogonal collocation method) for designing the state estimator of fixed-bed reactors are not applicable in this case. An approach for estimating the state profiles of the CLR based on a nonlinear distributed parameter observer is presented. To decrease the computational effort of the observer in real-time applications, the reduction of the detailed model of the CLR is investigated. In order to achieve asymptotic stability and fast convergence of the observer, the observability of the CLR is analysed, and use of features of the sustained oscillatory system and physical insight are made. A method based on exponential weighting functions is proposed to approximate the observation error profile. The temperature and concentration profiles are estimated from a small number of temperature measurements. The obtained observer was successfully tested with the dynamic simulator DIVA in the cases of errors in the initial condition and the model parameters, random noisy measurements, and unknown disturbances, also including the different choice of sensor locations, and different observer parameters. It shows excellent dynamic tracking of the reactor profiles, strong robustness, and easy tuning. It forms a basis for developing appropriate control strategies of the CLR.

State Estimation of a Distributed Parameter Fixed-Bed Reactor with Oscillations

Abstract In this paper, the state estimation of a novel autothermal fixed-bed reactor (called circulation loop reactor, CLR) is studied. Since in autothermal operation the reactor shows sustained large oscillations and has to be modelled as a strongly nonlinear distributed parameter system, the generally used linearization and lumping techniques (e.g. the orthogonal collocation method) for designing the state estimator of fixed-bed reactors are not applicable. An approach for estimating the state profiles of the CLR based on a nonlinear distributed parameter observer is presented. A simplified model for the CLR is derived, which reduces the computational effort of the observer in realtime applications. In order to achieve asymptotic stability and fast convergence of the observer, the observability of the CLR is analysed. Features of the sustained oscillatory system as well as physical insight are used for the observer design. A method based on exponential weighting functions is proposed for the approximation of the observation error profile. The temperature and concentration profiles are estimated from a limited number of temperature measurements. The obtained observer was successfully tested with the dynamic simulator DIVA in the cases of errors in the initial condition, random noisy measurement, and different sensor locations. It shows excellent dynamic tracking of the reactor profiles, strong robustness, and easy tuning. It forms a basis for the development of control strategies for the CLR.

An observer-based solution of inverse heat conduction problems

An inverse heat conduction problem arises when temperature measurements are taken in the interior of a body, and the temperature and heat flux on the surface are desired. A new approach to the solution of this class of problems is introduced. It relies on the concept of state and disturbance observers which is well-known from systems theory. The complete temperature profile in the heat conducting body as well as the surface heat flux and temperature can be computed from one or several interior temperature measurements by means of a non-linear distributed parameter observer. The technique is introduced and analysed theoretically by means of a simple tutorial example. The approach is finally applied to a difficult inverse problem of technical significance. The time history of local heat flux and temperature oscillations at the inner surface of an evaporator tube are estimated during transition boiling conditions. Experimental results with boiling refrigerant R114 flowing upward in an electrically heated tube are presented.

An Observer-based Solution of an Inverse Heat Transfer Problem in Transition Boiling

An inverse heat conduction problem arises when temperature measurements are taken in the interiour of a body, and the temperature and heat flux on the surface are desired. A new approach to the solution of this class of problems is introduced. It is based on the concept of state and disturbance observers which is well-known from systems theory. The complete temperature profile in the heat conducting body as well as the surface heat flux and temperature can be computed from one or several interior temperature measurements by means of a nonlinear distributed parameter observer. The technique is applied to the estimation of the time history of local heat flux and temperature oscillations at the inner surface of a tube during transition boiling conditions. After discussion of the design methodology and evaluation of the observer scheme, experimental results with boiling refrigerant R114 flowing upward in an electrically heated nickel tube are given.

Reconstruction of atmospheric pollutant concentrations from remote sensing data--An application of distributed parameter observer theory

The reconstruction of a concentration distribution from spatially averaged and noise-corrupted data is a central problem in processing atmospheric remote sensing data. Distributed parameter observer theory is used to develop reconstructibility conditions for distributed parameter systems having measurements typical of those in remote sensing. The relation of the reconstructibility condition to the stability of the distributed parameter observer is demonstrated. The theory is applied to a variety of remote sensing situations, and it is found that those in which concentrations are measured as a function of altitude satisfy the conditions of distributed state reconstructibility.