THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

1. Introduction 2. Reference kinematics 3. Analytical techniques 4. Mechanics of deformable bodies 5. Floating frame of reference formulation 6. Finite element formulation 7. Large deformation problem Appendix: Linear algebra References Index.

Dynamics of multibody systems

Differential-Difference Equations. By Richard Bellman and Kenneth L. Cooke. Pp. xvi, 465. 1963. (Academic Press)

Dynamic analysis of flexible manipulators, a literature review

Survey of advanced suspension developments and related optimal control applications

During recent decades, controllability and observability of linear time delay systems have been studied, including various definitions and corresponding criteria. However, the lack of an analytical solution approach has limited the applicability of the existing theory. Recently, the solution to systems of linear delay differential equations has been derived in the form of an infinite series of modes written in terms of the matrix Lambert W function. The solution form enables one to put the results for point-wise controllability and observability of systems of delay differential equations to practical use. We derive the criteria for point-wise controllability and observability, obtain the analytical expressions for their Gramians in terms of the parameters of the system, and develop a method to approximate them for the first time using the matrix Lambert W function-based solution form.

Controllability and Observability of Systems of Linear Delay Differential Equations Via the Matrix Lambert W Function

This paper addresses the coupling between the plant and control optimization problems for a suspension comprising both passive and active components. Suspension dynamics are modeled using a two degree-of-freedom, linear and time-invariant quarter-car model whose ability to capture the influence of the passive stiffness on rattle space depends on the ground disturbance's spectral density. Nested optimization, a strategy that guarantees system optimality, is presented and used to find the optimal suspension system design. The design exhibits superior performance compared to its passive, active and sequentially optimized passive/active counterparts because it accounts for the coupling between the passive and active suspension optimization problems.

Nested plant/controller optimization with application to combined passive/active automotive suspensions

System performance can significantly benefit from optimally integrating the design and control of engineering systems. To improve the robustness properties of systems, this paper introduces an approach that combines robust design with robust control and investigates the coupling between them. However, the computational cost of improving this robustness can often be high due to the need to solve a resulting minimax design and control optimization problem. To reduce this cost, sequential and iterative strategies are proposed and compared to an all-in-one (Aio) strategy for solving the minimax problem. These strategies are then illustrated for a case study: Robust design and robust control (RDRC) of a dc motor. Results show that the resulting strategies can improve the robustness properties of the dc motor. In addition, the coupling strength between the robust design and robust control tends to increase as the applied level of uncertainty increases.

Combined Robust Design and Robust Control of an Electric DC Motor

In this paper, we consider the problem of feedback controller design via eigenvalue assignment for linear time-invariant systems of linear delay differential equations (DDEs) with a single delay. Unlike ordinary differential equations (ODEs), DDEs have an infinite eigenspectrum, and it is not feasible to assign all closed-loop eigenvalues. However, we can assign a critical subset of them using a solution to linear systems of DDEs in terms of the matrix Lambert W function. The solution has an analytical form expressed in terms of the parameters of the DDE, and is similar to the state transition matrix in linear ODEs. Hence, one can extend controller design methods developed based upon the solution form of systems of ODEs to systems of DDEs, including the design of feedback controllers via eigenvalue assignment. We present such an approach here, illustrate it using some examples, and compare with other existing methods.

Ali Galip. Ulsoy

Papers

Controllability and Observability of Systems of Linear Delay Differential Equations Via the Matrix Lambert W Function

Nested plant/controller optimization with application to combined passive/active automotive suspensions

Combined Robust Design and Robust Control of an Electric DC Motor

Eigenvalue Assignment via the Lambert W Function for Control of Time-delay Systems

Dynamic state model for on-line tool wear estimation in turning.