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Parametric models of a one-dimensional heat diffusion process are determined using the maximum likelihood method. The process is a linear, infinite dimensional system. Statistical teats indicate that the appropriate orders of the models obtained are relatively low. It is found empirically that successive terms in the modal expansion of the transfer function of the process, having gain factors of t
Finite-difference methods are used to derive lumped state-space models of a diffusion process. The accuracy of the lumped models is primarily determined by the number of intervals used. A refinement of the approximations to the partial derivatives only improves this accuracy to a certain extent. The study also shows that it is important to use smaller intervals near the ends of the rod.
Connections between dead-beat control strategies and optimal control policies for linear, time-invariant, discrete-time systems are established. The performance index of the system is quadratic and only the terminal state of the system is penalized. An explicit solution to the singular Riccati equation, associated with this optimization problem, is given. Properties of the time-variable gain matri
The purpose of this study is to compare three different methods for determining the thermal diffusivity of a one dimensional heat diffusion process. A modifiedA˚ngstro¨m's method, an on-line least squares method and a maximum likelihood method have been applied to data obtained from experiments on a long copper rod. The accuracy, the amount of computation, the storage capacity and in general the a
The problem of forcing the state of a linear, multivariable, sampled-data system to zero in a minimum number of time steps is discussed. The solution to the posed problem is given as linear state feedbacks. Numerical aspects of the algorithms for computing these feedbacks are presented. The methods are successfully used to control the temperature profile of a diffusion process in the laboratory.
The problem of forcing the output of a multivariate sampled-data system to zero in a minimum number of time steps is discussed. The solution to the posed problem is given as a linear state feedback. The zeros of the system are contained among the poles of the closed-loop system. The performance of the closed-loop system will be unsatisfactory if any of these zeros are located close to or outside t
Examples are given that modify some oversimplified statements usually made about the motion of robots in singular configurations. A robot may be controlled in an arbitrary direction from a singular configuration if the velocity profiles are shaped in a proper way. The observations on possible motions open a number of questions, since a wider class of motions is possible that at first sight. Hence,
Hemicellulose is a promising renewable raw material for the production of hydrogels. This polysaccharide exists in large amounts in various waste streams, in which they are usually impure and heavily diluted. Several downstream processing methods can be combined to concentrate and purify the hemicellulose. However, such an approach can be costly; hence, the effect of impurities on the formation an
Based on various approaches, several different solutions to the smoothing problem have been given. The relationships between these solutions are not immediate, although they solve the same problem. Making use of a certain framework from scattering theory, we derive two families of solutions, with equations evolving forwards and backwards in time, respectively. Within these families three major pre
The possibility of estimating process parameters using input-output data collected when the system operates in closed loop is discussed in this paper. Concepts that are useful for a systematic treatment of the problem are introduced. The results refer to the case where the regulator is a linear feedback law or alternates between several such laws. It is shown that a straightforwardly applied ident
The ever-increasing consumption of natural resources required for the production of consumer electronics, and the growing amount of electronic waste, underline the importance and urgency of extending the lifespan and use of such products. Information and Communication Technology (ICT) remanufacturing is a growing industry, which nonetheless faces several barriers. Consumers often have a perception
A recursive algorithm for parametric identification of discrete-time systems known as Panuska's method, the approximate maximum likelihood method or the extended matrix method, is analyzed. Making use of recently developed theory for asymptotic analysis of recursive stochastic algorithms, dynamic systems, and autoregressive moving average (ARMA) processes are constructed for which this algorithm d
The convergence of a proposed method for state estimation in power systems is analysed for a case with constant state vector. In particular, a set into which estimates obtained by two versions of the SCI method converge is determined.
The Riccati equation plays as important a role in scattering theory as it does in linear least squares estimation theory. However, in the scattering literature, a somewhat different framework of treating the Riccati equation has been developed. This framework is shown to be appropriate for estimation problems and makes possible simple derivations of known results as well as leading to several new
A certain "star-product" formalism in scattering theory as developed by Redheffer is shown to also be naturally applicable to discrete-time linear least-squares estimation problems. The formalism seems to provide a nice way of handling some of the well-known algebraic complications of the discrete-time case, e.g., the distinctions between time and measurement updates, predicted and filtered estima
