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There is considered a mean square convergence of a stochastic approximation algorithm, are derived, formelas of the asimptotical variances of the solution estimations, which are right for dependent observations as well, is defined optimal consequence of coefficients.
Some representative results from modeling and identification experiments on the Halden boiling water reactor (HBWR) in Norway are presented in this chapter. Linear input–output models, as well as time invariant and time variable linear state models, have been used as model structures. The chapter describes the different phases of identification and modeling of a complex dynamical system. Different
Control of activated sludge process based on measurement of the dissolved oxygen profile has the distinct advantage of using sensors of proven reliability. These measurements, when coupled with the power of an on-line computer, permit the calculation of important variables which cannot be measured directly. The features of the profile which are of major significance are the position of the maximum
Process dynamics and control in biological waste water treatment operations are considered. Particular emphasis has been put on the control of dissolved oxygen and its spatial distribution in activated sludge aerators. It is demonstrated how dissolved oxygen profiles can be used for the estimation of the biodegradable load. Aspects of the control of chemical precipitation are discussed as well.
Research was conducted to examine the transient performance of a final settler. Dynamical models of minimal order were derived based on effluent data collected from a pilot scale settler. Parameter values for the models were adjusted until satisfactory fits to the observed data were obtained. Results were compared to select those models with the simplest structures and the ability to predict the m
Research has been performed model the dynamics of different kinds of wastewater treatment systems. Plant models are built up from standard modules of subprocesses. Available model knowledge has been packaged into suitable software modules and a library of simulation models has been created. The paper describes this library and the kind of simulations that can be performed.
The control of an activated sludge process is considered. It is discussed how the organism activity is a crucial information for the control. It is shown, how the concentration profile of dissolved oxygen (DO) in the biological reactor is related to the sludge activity. As a result the DO profile is a useful measurement information for control purposes
Objective Based on clinical experience gained over many years, the maximal haemostatic effect following administration of local anaesthetics containing epinephrine is generally believed to occur within 10 minutes. Surprisingly, it was found in a recent study, in which bleeding was quantified intraoperatively, that maximal haemostasis did not occur until 30 minutes. If this is indeed the case, the
In this survey the state of the art of wastewater treatment system control is presented. Instrumentation, dynamical models, and identification applications are reviewed. Current practice in control is described, and computerization of wastewater treatment plants is discussed. Biological treatment systems have been emphasized. The interactions between unit processes and between the sewage treatment
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,
