Control Engineering Problems Research Articles

On the application of singular perturbation techniques to nuclear engineering control problems

Using a linear state regulator problem for the control of xenon-induced spatial flux oscillations in a nuclear reactor it is shown that model simplifications may cause the system equations to behave like singularly perturbed ones. An example illustrates that an attempt to transform the system equations to standard singular perturbation form also transforms the performance index and raises the possibility of cheap control, which is physically not possible with mechanical control systems in a nuclear reactor. Another example demonstrates that the stiffness of the system equations is improved dramatically by making the model less approximate. It is concluded that care must, therefore, be exercised while applying singular perturbation techniques to problems which are ill-conditioned as a result of model simplification. >

Design and Application of the Portable Simulator PSI

Digital simulation is an effective and important tool for the stages of design, test and operation of multivariable control systems. The common block-oriented simulation languages are only partially qualified for these purposes on account of their great demand of memory and calculation time. Therefore, a digital simulation system has been developed, which is based on a capable PC and macro assembler programming. This Portable Simulator PSI is reasonable in price, modular structured and very user-friendly, since it has a dialogue in menu technique, graphic display of simulation results and a modular program library. PSI is well qualified for the simulation of control engineering problems during the trial runs of controlled systems in industrial plants, because simulation of linear or nonlinear dynamic systems with complex structures as well as interactive optimization and adjustment of controller parameters can be achieved. The application of PSI is demonstrated by two examples.

Trigonometric approximation of optimal periodic control problems for distributed-parameter systems

The optimal periodic control problem for a system described by first order partial differential equations is approximated by a sequence of discretized optimization problems. Trigonometric polynomials in two variables are used in the latter problems to approximate the state trajectory, the control and functions appearing in differential equations and in the criterion of the basic problem. The state equations and the instantaneous constraints on the state and the control are taken into account by the mixed exterior-interior penalty function. Sufficient conditions are given for the convergence of solutions of discretized problems to the optimal solution of the basic problem. The possibility of applying the method to a class of optimal periodic control problems in chemical engineering is emphasized.

Trigonometric approximation of optimal periodic control problems

Trigonometric polynomials are used to approximate the state trajectory, the control and the functions in differential equations and in the criterion of the constrained optimal periodic control problem. Several discretized problems using such polynomials are proposed to approximate the problem considered. Sufficient conditions for the convergence of solutions of approximating problems to the optimal solution of the basic problem are given. The application to a class of optimal periodic control problems in chemical engineering is discussed.

Restarting techniques in nonlinear programming algorithms applied to the optimal control of chemical plants

A convenient way for solving many optimal control problems in chemical engineering is to cast them into the form of nonlinear programming. While this transcription is formally straightforward, its implementation can give rise to some peculiar problems, most of which are connected with the high dimensionality resulting from this transformation. One of the crucial problems is how to continue the minimization procedure when the current step does not coincide with a descent direction. As a matter of fact this drawback is common to most minimization problems, but its frequency and importance increase with increasing dimensionality. Hence its significance in optimal control. Consequently robust methods are expected to be able to deal with these situations in which ordinary algorithms often get stuck. Restarting techniques are meant to overcome this difficulty with the choice of a new direction and/or of a new step length. Typically steps are computed according to the expression Δx_n=x_n−x_n-1=−αHn-1-1gn-1 where gn is the gradient vector and Hn a convenient approximation to the hessian matrix of the objective function f at the point x_n-1 and α an opportune real number (0,1] such that dfxn-1+αHn-1-1gn-1dα=0 We define Hn-1-1gn-1 an ascent direction if there is no such α or (which is computationally the same) it is zero to machine precision. In this case restarting techniques serve the purpose of modifying Δx_n either by improving (or even eliminating) approximations or by rejecting false assumptions. The following cases have been considered A) The expression for the computation of the steps is adequate, but the approximation to the hessian matrix is poor B) The objective function is far from being locally quadratic and descent directions lie in a narrow region along the gradient direction C) The objective function is "numerically" discontinuous, i.e. derivatives are very large and highly oscillating or are approximated badly by means of finite differences. The difficulty that arises in case A) can sometimes be removed by reduction of efficiency in favour of robustness (such as a more frequent updating in quasi-Newton algorithms). More often a different approximation has to be used (such as from Gauss-Newton to variable metric methods). The latter case is discussed in this paper. Case B) is generally more serious. It is frequently tackled by means of strategies that combine Newton-like and steepest descent steps , such as the dog-1eg algorithm. The Marquardt procedure and the pseudo-inverse method can also be regarded as belonging to this class, since the Marquardt parameter and the number of eigenvalues retained in the pseudo inverse method indicate the weight attached to each of the two components of the global step. A point that is discussed thorougly in this paper is whether the algorithm should vary the parameter that determines the contribution of each component continuously from iteration to iteration or whether this parameter should be a local property.Furthermore the convenience of adopting pure strategies (i.e. one always uses Newton-like directions and takes a few steepest descent steps only to overcome regions where Newton-like steps do not correspond to descent directions)is examined. A direct search has to be started in a situation like the one described in the case C) . In fact the gradient vector is either ill computed or does not provide much information. Sometimes a minimum has already been well located in spite of large values of derivatives, which are to be regarded as noise. Deterministic and random methods are compared as to the effectiveness of this procedure. A general algorithm, which can cope with the difficulties mentioned in A), B) and C) is proposed in this paper and applied to the optimal control of a chemical reactor.

Coordination: a vector-matrix description of transformations of overcomplete CNS coordinates and a tensorial solution using the Moore-Penrose generalized inverse

Neuronal organisms express their function, such as a movement, by multicomponental actions. Thus, the problem of how the central nervous system (CNS) coordinates the elements of a single action is fundamental to our understanding of brain function. Coordinated activation of multijointed "limbs" has also become an acute problem in modern multivariable control theory and engineering, such as robotics. Thus, a coherent interdisciplinary approach is expected, one that arrives at concepts and formalisms applicable to this problem both in living and man-made organisms. By treating coordination with coordinates, tensor network theory of the CNS, which explains transformations through the neuronal networks of natural non-orthogonal coordinates that are intrinsic to living organisms, may successfully integrate the diverse approaches to this general problem. A link between tensor network theory of the CNS and multivariable control engineering can be established if the latter is formulated in generalized non-orthogonal coordinates, rather than in conventional Cartesian expressions. In general terms, the problem of coordinating an overcomplete (more than necessary) number of components of an action can be resolved by a three-step tensorial scheme. A key operation is a covariant-to-contravariant transformation executed by the Moore-Penrose generalized inverse when, in an overcomplete manifold, the covariant metric tensor is singular. In the neuronal organization of the CNS, it is assumed that the cerebellum plays this role of acting as a contravariant metric. A quantitative example is also provided, in order to demonstrate the viability of the numerical and network-implementations.

Recursive Estimation in Diffusion Model

This paper is concerned with the nonlinear identification of dynamical systems disturbed by white noise, an important problem in control engineering. A nonparametric identification procedure for such systems which are usually described by a diffusion model is given in Banon (1977), (1978), where weak consistency of estimators has been obtained and simulation study has been carried out successfully. In this paper, we prove a stronger result concerning asymptotic properties of the estimators of the drift term, namely, strong consistency, and also related results.

The Dynamic Finite Element and Nonlinear Programming Method in Control of Transient Differential Systems

By combining the finite element method with dynamic programming, the dynamic finite element & nonlinear programming method (the dynamic FE&NLP method, i.e. the finite element & dynamic programming method (the FE&DP method) is developed and systematized in order to control transient differential equation systems with both equality or inequality constraints and a nonlinear objective function. Such systems are frequently encountered in various engineering and scientific problems of control and optimal design. The dynamic FE&NLP method (the FE&DP method) is applied to optimal control in thermal diffusion phenomena. The tractability in the initial or final condition, the boundary conditions and the equality or inequality constraints makes sure that the method becomes a powerful technique for several new types of boundary value problems with nonlinear objective function.

Noise control on offshore installations : Postlethweite, B.C.Noise Control, Vibration and Insulation, Aug/Sep 1977, 8..7, 231–234; abstr in CIS Abstracts (CIS 78–85)

Noise control must be considered on offshore installations to reduce the risk of hearing damage and allow adequate communication, rest and recreation facilities. Consideration of the problem of noise should commence at the inception of the design and continue through to the platform commissioning stage. Experience gained from existing installations will assist operators in overcoming some of the associated engineering problems of noise control and generally help to provide a better working and sleeping environment for future generations of platforms.

Selection of Deterministic Models for Adaptive Regulation of Industrial Time-Delay Processes

Performance of adaptive regulation systems has been analysed for different forms of linear deterministic model of a single-input/single-output time-delay process. In particular, the ordinary difference equation, weighting sequence, Wittenmark and, to some extent, state-space models have been investigated. It is possible for open-loop stable minimum phase systems only to be minimum variance controlled, no matter what kind of input-output model quoted is initially used. On the contrary, it has been shown that there are quite different conditions for different input-output models to optimum controlling open-loop unstable and/or nonminimum phase systems. Specifically, different performance Indices must be used for different models to gain equivalent, favourable control performance and, as a result, different control strategies are obtained, with different numbers of weighting coefficients to be Together with some computational aspects of both identification and control stages, this forms a basis for a new aptive-control-oriented classification of linear deterministic to be hopefully utilized especially in computer control engineering problems. Surprisingly, a common difference equation model has appeared to be most advisable.

Production Flow System Evaluation of Within-tree Populations of Dendroctonus frontalis (Coleoptera: Scolytidae)

Production flow system methodologies, originally developed for use in industrial quality control and electrical engineering problem solving, were adopted for use in describing the partial within-tree population system of Dendroctonus frontalis . The spatial and statistical distribution of D. frontalis life stages were defined by 2 and 3 parameter non-linear mathematical models. By integrating under the curves generated by the models for the various life stages it was possible to quantitatively define within-tree populations of the various life stages. For each year of study, transition probabilities between life stages were calculated using standard production flow system techniques. These transition probabilities were cast into a production flowgraph format. Each of the production flow models was evaluated using an algebraic solution technique and the similarities and differences between populations occuring in the 3 yr of study were contrasted. The production flow system technique was suggested as an alternative to the traditional life table format. Several advantages of the production flow system format over the life table were suggested. The most important advantage was that the variables are tied together mathematically and cast into a formalized engineering methodology.

The wired-up society - A problem for control engineers

The wired-up society - A problem for control engineers

Engineering problems of control of an unstable power distribution of a nuclear reactor

Engineering problems of control of an unstable power distribution of a nuclear reactor

Foundations of Optimal Control Theory.

Abstract : This complete and authoritative presentation of the current status of control theory offers a useful foundation for both study and research. With emphasis on general nonlinear differential systems, the book is carefully and systematically developed from elementary motivating examples, through the most comprehensive theory, to the final numerical solution of serious scientific and engineering control problems. The book features reviews of the most recent researches on processes described by partial differential equations, functional- differential, and delay-differential equations; the most recent treatment of impulse controllers, bounded rate controllers, feedback controllers, and bounded phase problems; and many unpublished new research results of the authors. In addition to an exhaustive treatment of the quantitative problems of optimal control, the qualitative concepts of stability, controllability, observability, and plant recognition receive a complete exposition. (Author)

Non-linear vibrations and non-linear problems in control engineering, Part I. (in Dutch) : R. G. Boiten. De Ingenieur, 74, (14) (1962) O1–O13; 25 figs.

Non-linear vibrations and non-linear problems in control engineering, Part I. (in Dutch) : R. G. Boiten. De Ingenieur, 74, (14) (1962) O1–O13; 25 figs.

A Novel Type of Isograph (Algebraic Equation Solver)

Polynomial equations occur quite often in physical and mathematical problems and require an exact solution. Several problems in control engineering, aerodynamics, and many other fields require the formulation and exact solution of algebraic equations of quite a high order. In the past, several mechanical and electrical machines for the determination of the roots of polynomials have been developed, but all of them suffer from the serious disadvantage that they are very expensive and are incapable of high accuracy and rapidity of operation. This paper describes the development, design, and construction of an inexpensive and portable isograph which is capable of locating the roots of a polynomial with fairly high accuracy. This isograph can serve as a valuable aid to large-scale computing machinery, for which the roots of a polynomial must be isolated before further calculations can be performed. It can also serve as a very useful adjunct to other mathematical processes such as complementary solution of differential equations, determination of latent roots of a matrix, and similar other applications. It is hoped that this inexpensive and portable instrument will prove extremely useful in the design of servosystems and in other fields where the problem may be presented as a polynomial and that theoretical studies of engineering problems will be greatly augmented by its use.

Analog computer control for compound aircraft machining

ELECTRICAL ENGINEERING techniques are constantly providing the solution to control engineering problems which previously were insurmountable. One of the more recent applications of electrical engineering to the mechanical control field has been the design of electric analog computers for industrial machine tool control.