Application Of Optimal Control Theory Research Articles

Optimal control of fluid catalytic cracking processes

An investigation was made of the applicability of optimal control theory to the design of control systems for non-linear, multivariable chemical processes. A hypothetical fluid catalytic cracking process was selected as a typical representative of such a chemical process. Mathematical models describing the dynamic behavior of the process were developed from non-steady-state heat and material balances about the reactor and regenerator. The dynamic models were used to simulate the process on a digital computer. The simulations predicted most of the important dynamic characteristics that have been attributed to commercial units. A new approach to the design of control systems for highly non-linear multivariable chemical processes based on optimal feedback control theory was demonstrated. In the feedback control law which resulted, the regenerator temperature is controlled by the air rate and the oxygen level is controlled by the catalyst rate. This control scheme is quite different from that which is typically used in refinery operation where the reactor temperature is controlled by the catalyst rate and the oxygen level is controlled by the air rate. The performances of the resulted control scheme was demonstrated by dynamic simulation to be significantly better at controlling the hypothetical cracking process in the face of disturbances than was the conventional control scheme.

Application of optimal control theory to a scheduling theory problem using penalty functions

Application of optimal control theory to a scheduling theory problem using penalty functions

Application of Optimal Control Theory to the Crashworthiness of a Passenger Vehicle Model

Optimal control theory concepts are thought to be useful in understanding the problem of determining safe deceleration characteristics for a crashing vehicle. These deceleration waveforms are to be computed such that passenger belt forces are minimized. Using both a linear one-degree-of-freedom model and a nonlinear two-degree-of-freedom model for a frontal collision, this problem is shown to be equivalent to the minimization of a performance or cost function when the terminal time is not fixed a priori, but is determined by terminal constraints. While the maximum principle is applied directly to find the optimal deceleration waveform for the linear problem, the steepest ascent method is used to optimize iteratively the nonlinear problem. Passenger seatbelt forces which resulted from using these optimal waveforms were compared with those forces which resulted from using step and ramp functions. Results showed that the seat belt forces resulting from the optimally derived deceleration signals were considerably smaller than those using step and ramp functions. With further effort, these results could possibly be used as design guides.

Application of optimal control theory to problems of optimal programming

Application of optimal control theory to problems of optimal programming

Letter to the Editor—A Selected Bibliography on the Application of Optimal Control Theory to Economic and Business Systems, Management Science, and Operations Research

Free AccessAboutSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack CitationsPermissionsReprints ShareShare onFacebookTwitterLinked InEmail Go to SectionFree Access HomeOperations ResearchVol. 16, No. 1 Letter to the Editor—A Selected Bibliography on the Application of Optimal Control Theory to Economic and Business Systems, Management Science, and Operations ResearchG. S. TraczG. S. TraczPublished Online:1 Feb 1968https://doi.org/10.1287/opre.16.1.174 Previous Back to Top Next FiguresReferencesRelatedInformationCited byAnwendungen des Maximumprinzips im Operations Research, Teil 11 September 1982 | Operations-Research-Spektrum, Vol. 4, No. 3Chapter VII Theory of Optimal ControlOptimal SAM defense system: An application of optimal control concept to operations researchIEEE Transactions on Automatic Control, Vol. 18, No. 5Bibliography and References Volume 16, Issue 1January-February 1968Pages 1-225 Article Information Metrics Information Published Online:February 01, 1968 © 1968 INFORMSCite asG. S. Tracz, (1968) Letter to the Editor—A Selected Bibliography on the Application of Optimal Control Theory to Economic and Business Systems, Management Science, and Operations Research. Operations Research 16(1):174-186. https://doi.org/10.1287/opre.16.1.174 PDF download

An application of optimal control theory to the guided torpedo problem

An application of optimal control theory to the guided torpedo problem

The application of optimal control theory to cost effectiveness

The application of optimal control theory to cost effectiveness

Applications of optimal control theory in aerospace engineering.

O the past 25 years a great body of knowledge has been built up on the subject of feedback control of linear, time-invariant dynamic systems. This knowledge plays an important role in our technology, and engineering schools recognize this fact by teaching courses in this area. However, many dynamic systems, particularly aerospace systems, are nonlinear and/or time-varying, and the techniques for analysis and design of linear, time-invariant control systems are, in general, not applicable to these more complicated systems. The appearance of practical, high-speed digital computers in the 1950's provided an essential tool for dealing with nonlinear and time-varying systems. Engineers were quick to take advantage of them to do extensive cut-and-try design work on paper instead of doing it in the development laboratory or on the test range. In many instances, particularly when designing guidance and control systems, it became clear that a more systematic approach was desirable. This led to a renewed interest in an old subject, the calculus of variations, and to the discovery of an interesting extension of this subject, dynamic programming.' The application of these techniques to deterministic, nonlinear, and timevarying systems forms the first part of this lecture. The computer also made possible rapid data-processing, sometimes almost simultaneous with the generation of the data. This stimulated a re-assessment of techniques for filtering and smoothing noisy measurements. An idea that seems to have been used by Gauss in determining orbits of the planets was rediscovered about 1960 and is now gaining wide acceptance, namely recursive maximum likelihood filtering.The increased cost of testing complicated control systems also led to a requirement for better predictions of reliability and accuracy. This requirement is strongly related to the response of the control system to random fluctuations in the environment and random errors in the measurement system. The second part of this paper is concerned with these latter topics, culminating in a discussion of the design of optimum logical structures for guid-

On the application of optimal control theory in problems of heat conduction

On the application of optimal control theory in problems of heat conduction

The minimum miss distance problem

I. In the statement of most extant theorems concerning optimal control, a fundamental hypothesis is that of the existence of a control function which drives the controlled system from a given initial state to a specified target. Thus the utility of these theorems is contingent upon the solution of what is itself a fundamental and difficult problem of the mathematical theory of control: the so-called controllability problem. One thus is led to ask if it is possible, through suitable reformulation of the basic problem of optimal control, to prove analogues of existing theorems with a weaker hypothesis than that of controllability. That it may be possible in some cases is suggested by the comments in [1 ] concerning the minimum miss distance problem. Stated loosely, the minimum miss distance problem is that of controlling the motion of an object (interceptor) in such a way as to minimize its distance of closest approach (miss distance) to another moving object (target). In [1], a mathematical formulation of this problem was presented for the case in which the interceptor is described mathematically by a system of ordinary differential equations involving a number of more or less arbitrary (control) functions and the target is described in mathematical generality sufficient to include most cases of interest in applications of optimal control theory. In this paper we present a detailed analysis of the minimum miss distance problem as formulated in [1]. We show that: (i) if there is a control which moves the interceptor closer to the target (a weakening of the controllability hypothesis) then the conditions of Filippov's existence theorem [2 ] are sufficient to ensure the existence of a control which not only minimizes miss distance but does so in minimum time; (ii) among other topological properties, the set Bx of initial data from which it is possible for the interceptor to get closer to the target possesses the property of being open (a property of substantial utility in the solution of optimal feedback control problems). Finally, we establish a simple criterion, in the case of a fixed point target, for the nonemptiness of the set B., the nonemptiness of this set being equivalent

Matrix analysis of dynamic stability in synchronous multimachine systems

The design of synchronous-generator automatic regulating equipment by linearisation techniques is now firmly established. The paper presents an obvious extension of one method, where, by means of matrix algebra, a set of general coefficients related to the well known Heffron and Phillips constants is derived, which allows complex impedance terms to be included in the analysis. In keeping with modern practice, these constants are incorporated in equations which are formulated as sets of first-order differential equations. This form provides a basis for future applications of optimal control theory, and, in addition, may be scaled more easily in both time and amplitude for analogue-simulation studies. A detailed example of a multiloop a.v.r. connected to a 30MW machine is given for reference purposes. The matrix methods, used in conjunction with the matrix iterative techniques of load-flow analysis, extend naturally to multimachine systems, allowing the dynamic operating and stability problem to be investigated with respect to possible future multimachine co-ordinated control schemes.