Pth Approximation Research Articles

Operating cost optimisation of speed-changing induction motors

A computer program is developed for the optimisation of single-winding, dual speed induction motors using least pth approximation method combined with Rosenbrock technique. The overall economy in designing the motors for minimum operating cost is brought out with examples. Optimisation results show that the performance values, as well as manufacturing cost, are essentially the same for a dual-speed motor of a given kW rating and pole combination designed for various duty cycles. The treatment of independent variables, and constraint specifications and the logic incorporated in the program are discussed.

Worst Case Network Tolerance Optimization

The theory and its implementation in a new user oriented computer program package is described for solving continuous or discrete worst case tolerance assignment problems simultaneously with the selection of the most favorable nominal design. Basically, the tolerance problem is to ensure that a design subject to specified tolerances will meet performance or other specifications. Our approach, which is believed to be new to the microwave design area, can solve a variety of tolerance and related problems. Dakin's tree search, a new quasi-Newton minimization method, and least pth approximation are used. The program itself is organized such that future additions and deletions of performance specifications and constraints, and replacement of cost functions and optimization methods are readily realized. Options and default values are used to enhance flexibility. The full Fortran listing of the program and documentation will be made available.

General programmes for least pth and near minimax approximation

User-oriented computer programmes in FORTRAN IV for discrete least pth approximation with a single specified function, and more generalized discrete least pth approximation with various specifications, which may also be used for non-linear programming, are presented. Values of p up to 10 can be used successfully in conjunction with efficient gradient minimization algorithms such as the Fletcher-Powell method and a method due to Fletcher. It has been demonstrated how efficiently extremely near minimax results can be achieved on a discrete sot of sample points using this approach and the programmes written verify this. The programmes may be applied to a wide variety of design problems with a wide range of specifications. They are suitable for electrical network and system design and such problems as filter design.

A General Program for Discrete Least pth Approximation (Computer Program Descriptions)

To minimize an objective function of k variables defined as the generalized discrete least pth objective using gradient methods.

A Special Program for Least pth Approximation Including Interpolation (Computer Program Descriptions)

Minimization of a least pth objective function of k variables using gradient methods. Interpolation brings the discrete problem closer to the continuous minimax approximation problem.

Gradient minimax techniques for system modelling

Some recently proposed gradient methods for minimax or near minimax approximation are applied to producing optimal second-order and third-order models of a high-order system. The Fletcher-Powell method, a more recent method by Fletcher and o. method by Jacobson and Oksman are employed with least pth approximation, using large values of p, as proposed by Bandler and Charalambous and critically compared with the grazer search technique of minimax approximation by Bandler et al. The solutions obtained are shown to satisfy the necessary conditions for a minimax optimum.

On conditions for optimality in least pth approximation withp → ∞

This paper presents a theoretical discussion of the necessary and sufficient conditions for optimality in generalized nonlinear leastpth approximation problems forp → ∞. In the limit, the conditions for a minimax approximation are derived, as is to be expected. Numerical examples involving the modeling of a linear time-invariant fourth-order system by a second-order model and the design of quarter-wave transmission-line transformers illustrate the results.

Practical Least pth Optimization of Networks

A new and practical approach to computer-aided design optimization is presented. Central to the process is the application of least pth approximation using extremely large values of p, typically 1000 to 1 000 000. It is shown how suitable and reasonably well conditioned objective functions can be formulated, giving particular emphasis to more general approximation problems as, for example, in filter design. It is demonstrated how easily and efficiently extremely near minimax results can be achieved on a discrete set of sample points. Highly efficient gradient methods can be employed and, in network design problems, the use of the adjoint network approach for evaluating gradients results in greater savings in computer effort. A comparison between the Fletcher-Powell method and the more recent Fletcher method is made on the application of least pth approximation, using a range of values of p up to 1 000 000 000 000 on transmission-line transformer problems for which optimal minimax solutions are known. This is followed by filter design examples subject to certain constraints.

Theory of generalized least pth approximation

A unified discussion of least p th approximation as it relates to optimal computer-aided design of networks and systems is presented. General objective functions are proposed and their properties discussed. The main result is that a wider variety of design problems and a wider range of specifications than appear to have been considered previously from the least pth point of view should now be tractable.