Showing papers on "Optimal design published in 1969"

Optimal and Efficient Designs of Experiments

Abstract: This paper consists of new results continuing the series of papers on optimal design theory by Kiefer (1959), (1960), (1961), Kiefer and Wolfowitz (1959), (1960), Farrell, Kiefer and Walbran (1965) and Karlin and Studden (1966a). After disposing of the necessary preliminaries in Section 1, we show in Section 2 that in several classes of problems an optimal design for estimating all the parameters is supported only on certain points of symmetry. This is applied to the problem (introduced by Scheffe (1958)) of multilinear regression on the simplex. In Section 3 we consider optimality when nuisance parameters are present. A new sufficient condition for optimality is given. A corrected version is given to the condition which Karlin and Studden (1966a) state as equivalent to optimality, and we prove the natural invariance theorem involving this condition. These results are applied to the problem of multilinear regression on the simplex when estimating only some of the parameters. Section 4 consists primarily of a number of bounds on the efficiency of designs; these are summarized at the beginning of that section.

Learning Control Systems

Abstract: In designing an optimal control system, if all the a priori information about the controlled process (plant-environment) is known and can be described deterministically, the optimal controller is usually designed by deterministic optimization techniques. If all or a part of the a priori information can only be described statistically—for example, in terms of probability distribution or density functions—then stochastic or statistical design techniques will be used. However, if the a priori information required is unknown or incompletely known, in general an optimal design cannot be achieved. Two different approaches have been taken to solve this class of problems. One approach is to design a controller based only upon the amount of information available. In that case the unknown information is either ignored or is assumed to take on some known values chosen according to the designer’s best guess. The second approach is to design a controller which is capable of estimating the unknown information during its operation and of determining an optimal control action on the basis of the estimated information. In the first case a rather conservative design criterion (for example, the minimax criterion) is often used; the systems designed are in general inefficient and suboptimal. In the second case, if the estimated information gradually approaches the true information as time proceeds, then the controller thus designed will approach to the optimal controller.

Sensitivity Analysis of Power Systems

Abstract: Modern control theory is being used more and more in regulator design of synchronous generator automatic regulating equipment. Making use of the well-established linearized equations of the synchronous machine and its control equipment, the characteristic equation of the system is developed from which the eigenvalues of the system are found. The sensitivities of these eigenvalues to the various parameters of the control system are calculated. This approach can provide a basis for optimal design of the system. A detailed sensitivity analysis is made of a particular system under various operating conditions, and results are tabulated, making it possible to obtain a clear idea about the effect of any parameter on the system performance and dynamic stability limit.

Optimum design of spatial structures

Abstract: : A systematic approach is presented to the optimal design of spatial frames for minimum weight subject to constraints on stress and geometry. The optimization procedures discussed are general and may be applied to structures which can be analyzed by matrix displacement or finite element methods. Two methods of mathematical programming are applied to obtain a minimum weight design. Both of these techniques require derivatives of the objective and constraint functions to improve estimates of the optimum design. In order to take full advantage of existing analysis capability, the programming techniques in this research have been assuming that such derivatives are not available.

Physically Realizable Filtering for Data Transmission Systems

Abstract: In this paper, the design of physically realizable rational fuction transmitting or receiving filters for use in pulse transmission systems operating in the presence of Gaussian noise and intersymbol interference is explored. For the design, the three iteria considered are 1) mean-square error (MSE), 2) error probability, and 3) a weighted sum of the squares of the signal-to-noise ratios corresponding to all possible received signal patterns (MSSN). Expressions are obtained for the various error criteria in terms of the transnmission system poles and residues (coefficients of a partial fraction expansion), assuming that the transmitting and receiving filters and the transmission medium are given by physically realizable rational function forms. It is shown that optimization of the MSE criterion under a received signal amplitude constraint with respect to the receiving filter residues, for a fixed set of poles, leads to a set of linear equations readily solvable for the optimal residues. A suboptimal technique is used to specify "reasonable" pole values, thereby the poles are constrained to belong to some "standard" set of all-pole transmission functions, as for example, maximally flat delay or maximally flat magnitude. The bandwidth of the given pole configuration is determined to optimize the given error criterion. Numemical examples are presented to illustrate the filter design techniques developed. The results indicate that, in many cases, filter design under the MSE or MSSN error criteria leads to optimal or near optimal design under an error-probability criterion. A brief discussion is also given of the filter sensitivity to parameter variations.

Minimal design of sandwich axisymmetric cylindrical shells obeying Mises' criterion

Abstract: The solution is presented of the problem of minimum volume design of the circular cylindrical sandwich shell obeying theMises yield criterion and carrying loads transverse to the lateral surface and symmetric about the axis of the cylinder. Detailed conditions are established, which are necessary and sufficient for the determination of the minimal stress both bounded and unbounded. In the case of one-directional loads the minimal and optimal designs corresponding to the above minimal stresses are specified up to the point from which only routine calculations are required. It is shown that for such loads the characteristic features of the minimal and optimal designs are independent of the peculiarities of the loading. All six possible combinations of edge support are considered. The results are compared with those of the only previous investigation of the same structure but underTresca's criterion. Some significant discrepancies between the results of the two papers are pointed out.

Optimal Synthesis of Distributed Parameter Systems

Abstract: A technique is developed for the synthesis and design of a distributed parameter system guiding waves from one point in space to another. The parameter distributions are assumed to be nonrestricted except for the upper and lower bounds resulting from the imposition of physical realizability. The problem is similar to the "sensitivity" problem encountered in the optimal control of the systems. An improved version of the first-order gradient technique is used to obtain the optimal distributions of the parameters. The first-order gradient technique is sensitive to the form of the arbitrary distributions assumed at the start of the iterations. This technique has serious convergence problems associated with it. The problem is particularly severe and is encountered in "singular" optimal control problems. The algorithm devised here improves the first-order gradient technique so that it becomes less sensitive to the initial assumed distributions and virtually eliminates the convergence problems generated because of the bounds on the parameter distributions. A transmission line with distributed series r, l and shunt c is a particular case of the distributed parameter system. The optimal design of a notched filter employing a thin film circuit is a successful example of the application of the improved gradient technique. These distributions have been obtained by the use of a hybrid computer.

Optimal Control Theory due to Parameter Optimization Method and its Application to The Design of Optimal Control Equipment for Aircraft

Abstract: For the design procedure of control system, the method to choose the value of parameters of controller so that the characteristics of the system will pass thle prescribed specification has been generally used, and Root Loci method has been preferred to the design of aircraft controller among many existing design techniques. Such a design method as to derive the closed loop characteristics into the domain of prescribed specifications has a defect that some ambiguity remains in the resulting closed loop system. On the other hand, the notion of optimal control gives us thevery definite design procedure and The PONTRYAGIN's Maximum Principle has contributed much to the design of optimal control system. Although optimal control aims to construct a control system so that some criterion function assumes the minimum value, the strongly damped system usually results from the optimal control technique on the contrary to the expectation of the designer. The reason is such that although the designer has some expectation about the characteristics of the control system to be constructed, he exclusively relies on the result from the optimal control technique without any reference to his expectation.Then the authors has endeavored to solve the optimization problem such that the value of the prescribed criterion function must be the minimum under the constraint that some characteristics of the system to be constructed is given. That kind of problem cannot be solved through Maximum Principle but can be solved only through Parmeter Optimization Method which has been developed by the authors.Parameter optimization technique and the optimal design based on it under the condition that some characteristics of the system to be constructed is prescribed are presented in this paper. How the airplane controller can be designed with satistactory rationality is also presented.

OPTIMAL FRACTIONAL FACTORIAL PLANS FOR MAIN EFFECTS ORTHOGONAL TO TWO- FACTOR INTERACTIONS: 2 TO THE mth POWER SERIES

Abstract: : A general theory of balanced 2 to the mth power fractional factorial designs are developed which permit estimation of main effects orthogonally to 2- factor interactions and the general mean, whose size N is desirably small, and which are optimal with respect to various standard criteria involving the variance-covariance matrix of the estimates. For various practical values of m and N, a method is given by which such optimal designs can be easily obtained from known balanced incomplete block designs.

Optimal design of elastic structural elements.

Abstract: : The class of problems treated falls into the rapidly developing field of optimal structural design. A structure is initially laid out with its geometry fixed but with the distribution of material in the elements left to the designer's choice. The amount and distribution of material is chosen so that the structure performs some function and is best in some sense. The examples treated in this report take minimum weight as their optimality criterion. A broad class of optimal design problems is first formulated as an optimal control problem. Two methods of solving this class of problems are then presented and their application to optimal design problems is discussed. Three optimal design problems are formulated and solved in detail. These problems contain many of the features expected of real-world problems and illustrate the power of computational methods which can be applied for their solution. (Author)