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RESEARCH PAPERS

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1961;83(1):10-14. doi:10.1115/1.3658878.

An experiment is described in which the strain energy at the critical location for fatigue failure is maintained constant while the stresses on a given plane of the material at the same location are caused to fluctuate. Apparatus developed to produce this condition consisted of a circular disk with a wide flanged rim which was loaded along a diameter by means of pivot-pad bearings. The disk was then rotated under a constant load to produce the desired fluctuation in stresses at the center of the disk while maintaining a constant strain energy at the center. The fact that fatigue cracks were developed in the region of constant strain energy was considered to indicate that a concept of a fluctuating strain energy as a basic theory of failure by fatigue under combined stresses is not tenable.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1961;83(1):15-22. doi:10.1115/1.3658884.

In this paper an energy criterion for fatigue failure is postulated. Microplastic strain hysteresis energy is considered to be an index for fatigue damage. On this basis, a relation is developed between stress amplitude and the number of cycles to failure which utilizes only material properties obtained from the static true stress-strain tension test. The analysis is found to compare well with an experimentally determined S-N curve for SAE 4340 steel.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1961;83(1):23-31. doi:10.1115/1.3658886.

An experimental and analytical investigation was undertaken to study the fundamental factors of crack propagation in a thin metal sheet under repeated axial loading. Sheet specimens of 2024-T3 aluminum alloy containing a central hole were used in the experimental investigation. Stress range and mean stress were the controlled parameters. An expression for crack length was derived, based on the concept of geometric similarity of crack configuration, for a semi-infinite sheet subjected to repeated loads consisting of a constant stress and mean stress. The expression is in terms of a stress dependent propagation factor and an exponential function of the number of cycles of loading. The expression for a semi-infinite sheet was modified for crack propagation in a specimen of finite width. Accurate predictions of the propagation life was possible using the modified equation. Photomicrographic observations of the crack tips were made.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1961;83(1):32-38. doi:10.1115/1.3658887.

The mode of crack propagation and failure in relatively large 2024-T3 aluminum sheets reinforced with stiffeners parallel to the crack direction has been investigated. Curved specimens with a 69-in. radius of curvature as well as flat panels were subjected to uniaxial tension perpendicular to a simulated crack to study the effects of curvature, crack location, and stiffener spacing. Increase in strength due to stiffening particularly in the curved panels was observed although these specimens exhibited considerable lower crack strength than flat ones. For the specimens tested, crack location as well as variations of stiffener spacing from 3 to 12 in. had no appreciable effect on either critical crack length or failure stress.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1961;83(1):39-44. doi:10.1115/1.3658888.

Experimental data are presented for a cast nodular iron and for high-silicon cast iron materials which represent limiting conditions of ductility in a test of fracture theories. Data of other pertinent investigations are reviewed and various failure theories are discussed with regard to their applicability. It is concluded that failure under combined stresses of brittle materials can be predicted adequately by applying a notch modified distortion energy criterion. However, other criteria are also applicable. Since criteria for the failure of brittle materials are conspicuously phenomenological, the application of solid state and dislocation theory, to explain the initiation and growth of a crack in a heterogeneous structure under combined stresses, has been discussed.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1961;83(1):45-52. doi:10.1115/1.3658889.

A new technique for the synthesis of optimum switching criteria for higher-order saturating systems is investigated in this paper. Basically, the technique consists of generating a linear switching criterion that is equivalent to the optimum switching criterion for each state of the system. Thus as a trajectory of the system is traced out, the optimum forcing function is determined point by point, resulting in the optimum trajectory for the system. The synthesis procedure has been proved experimentally by simulation of a third-order system on an IBM 797 digital computer.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1961;83(1):53-58. doi:10.1115/1.3658890.

In this paper, we study the control of the dynamic system governed by the matrix differential equation, ẋ = Fx + Du , x (0) = −c , where the input vector u is constrained in amplitude. It is shown that in the discrete (sampled data) case: (a) The general optimal control problem can be formulated as a nonlinear programming problem amenable to treatment by techniques developed in the operation research field. (b) The specific time optimal control problem originally studied by Kalman is treated here using a different approach which yields well-known as well as new results.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1961;83(1):59-64. doi:10.1115/1.3658891.

This paper is concerned with the optimum control problem for plants described by second-order differential equations with constant coefficients and with velocity control. Emphasis is placed on the case where the characteristic equation of the system has one zero root and two complex conjugate roots. The problem is studied in terms of the motion of the phase point in a three-dimensional phase space. An iteration method is developed to obtain the optimum trajectory, which in turn gives the optimum response.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1961;83(1):65-76. doi:10.1115/1.3658892.

The use of pulse-width control for the on-off regulation of systems subject to sampling is investigated in this paper. The inherent inability of simple on-off control to achieve accurate, or dead-beat control in sampling systems is demonstrated, and methods for predicting and minimizing the limit-cycle behavior of these systems are given. It is then shown that if the on-off control is modified by allowing control of the “on” time during each sampling period, it is possible to achieve asymptotically stable dead-beat control. Sufficient conditions for the asymptotic stability in the large of pulse-width control systems are developed, using the “second method” of Lyapunov. Practical design of pulse-width controllers is developed from the theoretical results and experimental evaluation is given for some specific design problems.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1961;83(1):77-81. doi:10.1115/1.3658893.

A discrete sequence approach is presented in this paper for investigating the possible modes of sampled-data control systems containing a saturating element. This method enables the investigator (a) to determine whether or not a control system has certain periodic modes, and (b) if it does, to identify them exactly. This approach is applicable to a sampled-data control system of any order. It is extended to the cases where the form of feedback is other than unity.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1961;83(1):82-84. doi:10.1115/1.3658896.

A major difficulty in the way of a successful systematic approach to the study of control processes by way of the theory of dynamic programming is the occurrence of processes having state vectors of high dimension. However difficult the problem is for systems ruled by a finite set of differential equations, it is several orders of magnitude more complex for systems of infinite dimensionality and for systems with time lags. By combining a technique presented earlier for dealing with finite dimensional systems and various methods of successive approximations and quasi-linearization, certain classes of control processes associated with infinite dimensional systems can be treated. The ideas are illustrated by discussing control of a system involving a time lag and control of a thermal system.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1961;83(1):85-90. doi:10.1115/1.3658899.

The design of optimum controllers is considered for processes which are described by linear differential equations with one or more independent forcing terms. After presentation of a general method for designing what is usually a nonlinear controller, applications are made to: (a) Design of minimum energy controllers, (b) design of minimum response time controllers [1], and (c) design of minimum error controllers. Various other design criteria and restrictions on controller parameters are also discussed.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1961;83(1):91-94. doi:10.1115/1.3658901.

A kinetic Lyapunov function is a Lyapunov function of the first derivatives of the state variables. Its use leads to a sufficient condition for the asymptotic stability in the large of a general nonlinear system without hysteresis. The foregoing sufficient condition is similar to but more stringent than the local stability condition for linearized systems.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1961;83(1):95-108. doi:10.1115/1.3658902.
FREE TO VIEW

A nonlinear differential equation of the Riccati type is derived for the covariance matrix of the optimal filtering error. The solution of this “variance equation” completely specifies the optimal filter for either finite or infinite smoothing intervals and stationary or nonstationary statistics. The variance equation is closely related to the Hamiltonian (canonical) differential equations of the calculus of variations. Analytic solutions are available in some cases. The significance of the variance equation is illustrated by examples which duplicate, simplify, or extend earlier results in this field. The Duality Principle relating stochastic estimation and deterministic control problems plays an important role in the proof of theoretical results. In several examples, the estimation problem and its dual are discussed side-by-side. Properties of the variance equation are of great interest in the theory of adaptive systems. Some aspects of this are considered briefly.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1961;83(1):109-117. doi:10.1115/1.3658877.

In past years many methods have been developed for calculating the time response in automatic control systems. In this paper an improved, approximate method for calculating the transient response in linear (Section 1), time-varying (Section 2), and nonlinear (Section 3) automatic control systems, is developed on the basis of previous works [1–5]. The basis of this method lies in an approximate solution of integral equations by means of special tables which are given in the Appendix. These tables enable the user to shorten the time for calculation. This method also can be useful for obtaining programs for digital computers. In each part of the paper, examples are given to illustrate the use of this method. These examples are identical to those of Boxer and Thaler [4] and facilitate a comparison of the solution method developed in the paper with their z-transform approach.

Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
J. Basic Eng. 1961;83(1):125-130. doi:10.1115/1.3658881.

The roll stabilization of a ship with servo-operated fins is analyzed as a system problem from the viewpoint of a control engineer. The preliminary design of a roll-damping system for a particular passenger ship is set forth. The roll-angle response to a sinusoidal sea-torque is analyzed, and the improvement made by the roll-damping system is evaluated. A rate gyro of good resolution and a damped pendulum are adequate for roll-sensing instrumentation. A preliminary design for a valve-controlled fin servo is made, but it is so wasteful of power that a pump-controlled fin servo is designed as an alternative. Energy aspects of control systems in general are considered briefly.

Commentary by Dr. Valentin Fuster

DISCUSSIONS

Commentary by Dr. Valentin Fuster

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