Estimation Of Initial Conditions Research Articles

Issues in the Application of Nonlinear Estimation for Improving Product Quality Control in Batch and Semi-Batch Processes

Inferential control techniques offer an attractive approach to overcome batch-to-batch variations in product quality, In order to calculate effective control moves, inferential techniques must have accurate on-line estimates of the key process states based on available secondary measurements. The focus of this paper is on the problem of nonlinear estimation of batch processes because of its importance to the inferential control approach. First, some of the important issues in applying nonlinear estimation techniques to batch and semi-batch processes are outlined. Then, methods for improving the estimation of initial batch conditions and the speed of convergence of the state estimates are considered. A practical example process, the nylon 6,6 autoclave reactor, is included to provide the physical motivations for many of the issues examined and to demonstrate the effectiveness of techniques proposed to address these issues. Finally, some areas where future research is needed to improve the effectiveness of the inferential approach are indicated.

Identification for Robust Control of an Unstable Plant

A new method for identification of continuous-time systems for robust control is presented, which allows incorporation of frequency dependent weighting functions in the minimization procedure. Parameter estimation and controller design are applied to a nontrivial double integral mechanical plant. The technique for parameter estimation profits by the properties of Hartley Modulating Functions (HMF), which make it easy to include frequency dependent weighting, so that only numerically significant spectral elements are used. Additionally, no estimation of initial conditions is neccessary when using HMF. The controller design for the task of closed loop data acquisition is performed by a discrete-time pole placement approach, whereas the final control strategy applies H∞ norm minimization utilizing the frequency weighted continuous-time model. Experimental studies demonstrate the results of parameter estimation and controller design. The real-time implementation illustrates the improved control performance obtained by the new approach.

Measurements and simulations of particle dispersion in a turbulent flow

A particle imaging technique has been used to collect droplet displacement statistics in a round turbulent jet of air. Droplets are injected on the jet axis, and a laser sheet and position-sensitive photomultiplier tube are used to track their radial displacement and time-of-flight. Dispersion statistics can be computed which are Lagrangian or Eulerian in nature. The experiments have been simulated numerically using a second-order closure scheme for the jet and a stochastic simulation for the particle trajectories. Results are presented for non-vaporizing droplets of sizes from 35 to 160 μm. The simulations have underscored the importance of initial conditions and early droplet displacement history on the droplet trajectory for droplets with large inertia relative to the turbulence. Estimates of initial conditions have been made and their effect on dispersion is quantified.

Phase reconstruction in the trispectrum domain

The phase reconstruction problem in the trispectrum domain is addressed in this correspondence. In particular, three different reconstruction algorithms are discussed and their performance is evaluated. The first two algorithms are recursive in nature and are shown to be sensitive to initial condition estimates.

On adaptive Kalman filtering for the Luenberger canonical form

This work reports on simulation results obtained from an adaptive filter for systems in Luenberger canonical form. In particular the effects of errors in estimation of innovations, autocorrelations and initial conditions are examined. The scheme proves to be more efficient than a similar one based on measurement autocorrelations. For a certain class of systems new formulae are given for calculating the structural indices required by the algorithm from the state and measurement dimensions. Extension is made to the more general problem of coloured measurement noise.

Techniques for initial condition estimation in linear systems†

Abstract Techniques for estimating the initial conditions of deterministic and stochastic linear systems are presented and investigated. Difficulties in implementation of existing and proposed algorithms for initial condition estimation are noted and methods for overcoming these difficulties are formulated.

Application of higher order variations of motion

The theoretical considerations developed in a previous paper (Kazantzis, 1973) are applied with the aid of the CDC-3300 computer and examples of new families of doubly symmetric solutions of the restricted three-dimensional problem obtained thereof are presented. Rough estimates of initial conditions of these families have been obtained by applying an extension of the scanning technique developed by Henon (1966).

An experimental evaluation of Kalman filtering

AbstractThe effectiveness of the stationary form of the discrete Kalman filter for state estimation in noisy process systems was demonstrated by simulated and experimental tests on a pilot plant evaporator. The filter was incorporated into a multivariable, computer control system and resulted in good control despite process and/or measurement noise levels of 10%. The results were significantly better than those obtained when the Kalman filter was omitted or replaced by conventional exponential filters. In this application the standard Kalman filter was reasonably insensitive to incorrect estimates of initial conditions or noise statistics and to errors in model parameters. The filter estimates were sensitive to unmeasured process disturbances. However this sensitivity could be reduced by treating the noise covariance matrices R and Q as design parameters rather than noise statistics and selecting values which result in increased weighting of the process measurements relative to the calculated model states.

A New Approach to Estimation of Initial Conditions and Smoothing Problems

A unified approach utilizing the Kalman-Bucy filtering technique istaken to solve the estimation problem of initial conditions and thesmoothing problem in linear dynamic systems. The equivalencebetween the forward integration method and the backward integrationmethod of the smoothing solution is proved. Complete analyticalsolutions of filtering and smoothing problems of rectilinear motion ofa randomly accelerated spacecraft are derived when the vehicle istracked by the ranging system at the ground station.

Estimation of pulse transfer function parameters by quasilinearization

An iterative algorithm for the identification of single-input single-output linear stationary discrete systems is developed using the method of quasilinearization. The resulting procedure is similar to mode 1 of the method of Steiglitz and McBride but has the advantage of the quadratic convergence property of quasilineariza-tion. It is shown that this algorithm becomes mode 1 if the measured plant output is used in the calculations in place of the model output. Consequently, the two methods are extremely compatible and it is a simple matter to combine them in a single program, which generates its own initial estimates has the wide range of convergence of mode 1, and possesses the quadratic convergence property of quasilineariza-tion for final convergence to a solution. The method also permits the estimation of plant initial conditions in those cases where they must be considered. Results of a few numerical applications are discussed.