0


RESEARCH PAPERS

J. Basic Eng. 1970;92(2):197-203. doi:10.1115/1.3424969.

This paper concerns the time optimal control of a system variable where the controlling input is bounded, as is usually the case, and the system is subject to arbitrary disturbances. An arbitrary disturbance is made up of uncontrollable portions followed by controllable sections. In industrial practice controllers are sized, as for example as to power, to fit the system so that the disturbances encountered are primarily made up of uncontrollable sections followed by controllable portions of sufficient duration for the controller to bring the system to equilibrium. The control designer wishes to have optimal control for any disturbance made up of such an uncontrollable portion followed by a sufficiently long controllable section. Here this problem is solved with the aid of the maximum principle for the class of second order systems which describe almost all governor-engine applications to first approximation accuracy. Previous attempts to solve this problem involved assuming statistical properties of the disturbance thus severely restricting the class of applications. Here only those statistical properties required to implement optimal control are determined. A single control function is derived which suffices to yield optimal trajectories.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(2):204-214. doi:10.1115/1.3424970.

Methods for analyzing the response characteristics of a pulse-width-modulated electro-hydraulic servomechanism are presented. Except for the modulator, the hydraulic control system is of conventional configuration. The modulator transfer characteristic is derived from a double Fourier series analysis of the pulse-width-modulated signal and this indicates the effect of the modulation parameters on the system performance. The valve flow which controls the mechanical load motion has been shown to be the dominant nonlinearity in a valve-controlled hydraulic system, and the system becomes more complicated due to the valve spool dither which is a consequence of the pulse-width-modulated signal. A dual-input describing function is developed for the equivalent valve flow gain in the determination of the system closed-loop frequency response. A numerical simulation is used to obtain the closed-loop transient response. Experimental verification of the theoretical analyses is carried out on a practical system. Good agreement is obtained between the predicted and the experimental responses.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(2):215-221. doi:10.1115/1.3424973.

The method of nonlinear estimation for determining parameters in differential equations is extended to treat more efficiently the problem of determining dominant and small parameters. Using the sensitivity coefficients, it is shown how to determine the dominant parameters first using nonlinear estimation and then using linear least squares to find the small parameters. This procedure can save a considerable amount of computer time. Even more important is the application to model-building (identification). The residuals for the difference of the temperatures calculated, assuming the small parameters are zero, and the measured temperatures are shown to yield information for discriminating between alternate mathematical models. A transient heat-conduction example is given to illustrate some of the concepts developed.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(2):223-232. doi:10.1115/1.3424976.

A novel closed-loop method of obtaining the frequency response of a physical system is presented. It is assumed that the physical system to be examined may be excited by a known sinusoidal input signal and that the resulting output response may be measured. The method described herein employs this input-output information together with a steepest descent computing procedure to obtain the in-phase and quadrature components of the system’s response. The method may be mechanized on either an analog or digital computer and may be applied to either linear or nonlinear systems. Examples illustrating the application of the procedure to a variety of linear and nonlinear systems are given.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(2):233-237. doi:10.1115/1.3424979.

A well-known graphical phase-plane technique for solving a wide variety of ordinary second-order differential equations is shown to satisfy a relatively simple set of iterative relationships which are easily programmed on a digital computer. The only restriction on the differential equation of interest is that it can be written as aẍ + G(x, ẋ, t) = 0, where G(x, ẋ, t) = g(x, ẋ, t) + kx. Consequently, many linear and nonlinear differential equations, with or without forcing functions, which may also have (explicit) time-variable coefficients, are easily solved with the method.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(2):238-244. doi:10.1115/1.3424982.

Regenerative chatter is recognized as one of the primary performance limitations of a machine tool. In the past much attention has been focused on minimizing this problem by improving the dynamic compliance of the structure. These approaches have been of a passive nature, such as increasing the structural damping, increasing the rigidity, addition of a vibration absorber, etc. The present work is one of two known basic contributions to the literature in the field of active chatter control. This paper includes an analysis of a machine tool equipped with an active chatter control system. In addition, experimental results are presented for such a control system applied to an engine lathe. The analysis, verified by the experimental results, indicated significant improvements in production rate, in transient response, and in static stiffness.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(2):245-250. doi:10.1115/1.3424983.

A minimum weight design problem has been formulated as a general problem in optimal-control theory with the addition of state and control inequality constraints. Complete analytical solutions have been derived using the maximum principle of Pontryagin.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(2):251-264. doi:10.1115/1.3424984.

An important objective in the development of a pressure suit for a human being is to permit the wearer full mobility, whether pressurized or not, without interfering with physical capability. Although the human skin is stretched during body motion, there is virtually no stretch along certain lines, here called “lines of nonextension.” This fact was utilized as the design basis for a series of experimental pressure suits that were developed to demonstrate that it was possible to achieve natural mobility and minimal ballooning in such suits. The detailed program of investigation pursued during the phase of study being reported on was: (1) to map out these lines of nonextension; (2) to test whether string elements of high elastic modulus, a connected network, could be laid along these lines of nonextension without resulting in any constraint to mobility; (3) to obtain a highly mobile pressure-retaining layer to be constrained by the net; and (4) to construct and demonstrate an entire pressure-retaining garment system that makes use of all necessary layers and string elements in a completely connected netted covering for the body with minimal constraint to mobility at pressures up to 5 psi. The technique, result, and collateral observations relevant to each of these phases are described. A mobile, pressure-retaining garment was developed by building each structural, functional layer into the composite garment in accordance with the basic design theory.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(2):265-270. doi:10.1115/1.3424985.

The second method of Liapunov is applied to a distributed parameter reaction system. A Liapunov functional is assumed and theorems are developed which yield sufficient conditions for analyzing the stability of a steady state. The method is applied to the problem of the catalyst particle treated as a slab. The conditions obtained are valid for general perturbations and general system parameters.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(2):271-278. doi:10.1115/1.3424986.

The present paper explains the use of two phase planes in the graphical determination of optimum trajectories for third-order systems, depending on the sign of a single control function. The control function is defined on these planes by means of different contours. Accordingly, the control signal is known at the different points on these planes. Once the control signal is found, the state trajectory is determined. Most of the arbitrary initial states are treated and, in particular, the cases of separate steps in each of the error and its first as well as second time derivatives. This work also explains the use of the graphical solution in obtaining the maximum error and switching times.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(2):279-286. doi:10.1115/1.3424987.

A computer-oriented procedure for efficient stability analysis of very large systems was developed by modifying a method due to Mikhailov. The method allows pure time delays in the system model. The state variable model of the system is used, and the computational procedure is tailored to take advantage of the sparesness of the system matrices that are applicable for many systems. The practicality of the procedure has been demonstrated in the analysis of several systems, the largest of which consisted of a 553rd order model of a multistage flash evaporator plant.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(2):287-292. doi:10.1115/1.3424988.

The flow in a turbulent wall jet, with a control port and setback between the nozzle exit and the leading edge of the wall, was probed at various stations along the jet for Reynolds numbers (based on the nozzle width) ranging from 20,000 to 140,000. The similarity or the dissimilarity of the velocity profiles (for all Reynolds numbers) in the outer and inner regions of the jet and the pressure distribution along the wall were investigated. A new integral equation was used in the interpretation of the results and in the determination of the limitations of the range of applicability of Glauert’s wall-jet analysis. It was found that, whereas the similarity law holds true for the outer layer of the jet (beyond the entrance region), there is no similarity between the velocity profiles either in the inner layer or in the entrance region and that the pressure along the wall is slightly higher than that of the surrounding fluid which is at rest.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(2):294-302. doi:10.1115/1.3424991.

A direct thermal-to-pneumatic energy converter utilizing the principle of thermal transpiration through a porous membrane is described. The applicability of this no-moving-part pump to a fluidic control system is discussed. A laboratory model has been constructed and experimentally evaluated for several gases, membrane types, and temperature ranges. A theoretical model is derived from the binary diffusion equations of kinetic theory. A linearized version of this model is verified experimentally for small temperature gradients. The kinetic theory model is evaluated numerically to predict the static performance of a pump for large temperature gradients.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(2):303-310. doi:10.1115/1.3424992.

A general experimental procedure is described for determining the complete linearized characteristics of a fluidic component over a wide band of frequencies. The method is applied to a large-scale Corning proportional amplifier with a 0.054-in. throat for frequencies up to over 3 kHz. Similarity was preserved for a 1/4 scale amplifier operating at atmospheric conditions. Since all eight independent complex-number self and transfer admittances are given for linearization about the symmetrical state, the results can be used to predict the behavior of the amplifier in any compatible coupled or uncoupled environment. The paper is continued in Part 2, ASME Paper No. 69-WA/Flcs-3, with an examination of the causes of the observed dynamic behavior in this and other proportional amplifiers.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(2):312-321. doi:10.1115/1.3424995.

A sixth-order lumped model is formed to represent the internal behavior of the fluidic amplifier tested in Part 1 up to over 800 Hz. Correlation with experiment is good for zero-load pressure, but an observed resonance or instability at elevated-load pressures is not properly predicted. Flow-visualization experiments are described from which four possible mechanisms are proposed for such resonances and instabilities observed in this and similar amplifiers. The study can be used to explain the successes of various design innovations tried earlier by others, to suggest further changes and associated performance limits, and to guide further needed research.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(2):322-327. doi:10.1115/1.3424998.

A modified gradient procedure is proposed for making discrete-time changes in the adjustable parameters of a continuous-time nonlinear control system during normal operating conditions. The algorithm employs the best available estimate of the unknown plant parameters as well as the estimates of disturbance, state, and output variables. The importance of the metric properties of a performance index is discussed, and the necessary and sufficient conditions for the integral squared error index to possess metric properties are derived. Theoretical conditions for the error correctiveness of the algorithm are formulated in terms of the constrained extrema of quadratic functionals.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(2):328-332. doi:10.1115/1.3424999.

The control and stability properties of a “simplified dynamic system” representing a particular biped gait are discussed. The simplified dynamic system consists of an algorithmically controlled lower limb system and a movable point mass. The concepts of repeatability and cyclicity are introduced by means of this model. These concepts provide the basis for control considerations in this class of systems. They lead to conditions which guarantee the maintenance of a gait. Stability of such nonlinear systems cannot be considered by classical techniques. To study stability, the concept of disturbance to nonlinear dynamic systems is introduced. This concept leads to a measure of stability by a quantity termed an “index of capability.” A method of computation for this index for this class of machines is shown.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(2):333-347. doi:10.1115/1.3425000.

Air, carbon dioxide, and helium test data are presented for the experimental verification of Iberall’s analysis of the dynamic pressure response of viscous compressible fluids in rigid tubes with deadened volume termination against oscillatory frequency. A graphical display is given of numerical solutions of Iberall’s theory over a wide range as a function of the Stokes number and of a dimensionless frequency. Rapid engineering solutions are presented for the following problems: Given a tube, a chamber volume, and a fluid, determine the maximum frequency to be transmitted at ±10 percent amplitude distortion. Given a tube, a chamber volume, and a fluid, sketch the dynamic pressure response curve. Given a chamber volume, a fluid, and a specified frequency to be transmitted within ±10 percent amplitude distortion, plot allowable tube length against tube diameter.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(2):348-354. doi:10.1115/1.3425001.

This paper deals with a design approach to the synthesis of controllers for nonlinear control systems. The method proposed herein uses the frequency domain circle condition as a sufficiency criterion for insuring absolute stability. While the theory involved is well known, its application as a design tool has not yet been fully appreciated. A major aim of this paper is to indicate means of employing this new theory by use of classical frequency-domain techniques. The circle of nonlinearity from the Nyquist plane is transferred as a region onto the logarithmic gain-phase versus frequency plane using a simple transformation. A system controller or compensator can now be designed, straightforwardly without trial and error, by using the explicit frequency scale. Parameter combinations for system controllers yielding absolute stability can be obtained in a parameter plane or parameter space depending upon compensator configuration. The entire procedure is digital computer oriented but can be accomplished by paper and pencil techniques. Several numerical examples, along with hybrid computer corroboration, illustrate the procedure.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(2):355-362. doi:10.1115/1.3425002.

General bond graph methods for the description, analysis, and simulation of dynamic systems are illustrated through the study of vehicle drive line dynamics. Emphasis is placed upon the problem of assembling a compatible and efficient system description from multiport models of the system components. Examples show how state space descriptions for analysis and block diagrams for analog simulation may be obtained systematically from bond graphs. Digital simulation is conveniently accomplished using the ENPORT programs, which accept bond graphs directly.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(2):363-368. doi:10.1115/1.3425003.

The problem of minimizing a quadratic functional of the system outputs and control for a stationary linear system with state-dependent noise is solved in this paper. Both the finite final time and infinite final time versions of the problem are treated. For the latter case existence conditions are obtained using the second method of Lyapunov. The optimal controls for both problems are obtained using Bellman’s continuous dynamic programming. In light of this, the system dynamics are assumed to determine a diffusion process. For the infinite final time version of the problem noted above, sufficient conditions are obtained for the stability of the optimal system and uniqueness of the optimal control law. In addition, for this problem, an example is treated. The computational results for this example illustrate some of the qualitative features of regulators for linear, stationary systems with state-dependent disturbances.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(2):369-376. doi:10.1115/1.3425004.

A rational procedure is developed for the design of a class of vortex amplifiers which operate in the incompressible flow regime. The procedure is based upon analytical and experimental studies conducted to determine the effects of fluid properties and geometry on vortex amplifier behavior. These studies indicate that the nondimensional amplifier characteristic is essentially independent of the maximum flow Reynolds number, vortex chamber height, and supply port area if each of these parameters is within a specified broad range of values. The nondimensional characteristic was found to depend fundamentally upon the chamber exit to outer periphery radius ratio and the control port area to exit port area ratio. A systematic method is provided for progressing from a set of desired amplifier performance specifications, which include maximum control and supply port pressure and flow requirements, to a specification of each critical amplifier dimension. Three-point predictions of the transfer characteristics are obtained and the characteristics are checked to determine if multiple values of total flow exist at the cutoff value of control flow. The measured performance of a planar vortex amplifier designed with the aid of the procedure was found to agree closely with the desired performance specifications.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(2):377-384. doi:10.1115/1.3425005.

For distributed parameter systems, open-loop stability in the sense of bounded outputs for bounded inputs, and closed-loop asymptotic stability are considered. Frequency domain stability criteria for open and closed-loop distributed parameter systems are given. The closed-loop stability criterion is similar to V. M. Popov’s stability criterion for lumped systems. The criteria are limited to those linear, time-invariant systems whose dynamics can be described by a transfer function which is the ratio of the multiple transform of the output to the multiple transform of the input. The input may or may not be distributed. An example is given to illustrate the applications of the stability criteria.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(2):385-393. doi:10.1115/1.3425006.

In this paper, a method of stochastic linearization is demonstrated for the purpose of establishing an approximate approach to solve filtering problems of nonlinear stochastic systems in the Markovian framework. The principal line of attack is to expand the nonlinear function into a certain linear function with coefficients which are determined under the minimal squared error criterion. The linearized function is specified by the coefficients dependent on both the state estimate and the error covariance. Thus, a method is given for the simultaneous treatments of approximate structure of state estimator dynamics and of running evaluation of the error covariance through the linearized procedure. Comparative discussions on the other filter structures are also given, including quantitative aspects of sample path behaviors obtained by digital simulation studies.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(2):394-397. doi:10.1115/1.3425007.

A reduction procedure is described for determining the sign definiteness and semidefiniteness of an mth order, n dimensional real polynomial. The higher order polynomial is reduced to a quadratic form in new variables such that conditions can be obtained on the coefficients of the individual terms of the original polynomial. The procedure presents sufficient conditions only. It has been found, however, to be a relatively systematic technique for engineering stability problems where alternate effective methods for determining sign definiteness are unknown.

Commentary by Dr. Valentin Fuster

DISCUSSIONS

Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster

TECHNICAL BRIEFS

J. Basic Eng. 1970;92(2):398-400. doi:10.1115/1.3425008.

A direct synthesis technique is established for constructing the Liapunov function of a completely aperiodic system without assuming elements and solving simultaneous equations. By inspecting the traces of the state matrix and its products, a Liapunov function and its derivative can be immediately written. The determinant which has the same elements of the Liapunov function so obtained turns out to be a new criterion for testing whether or not a system involves repeated roots. This determinant for an aperiodic system is closely analogous to the Hurwitz determinant for a stable system.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(2):400-403. doi:10.1115/1.3425009.

An analysis based upon linear theory is presented for determining the dynamic response of a simply supported beam, rectangular plate and shallow cylindrical shell to a point force of variable magnitude uniformly accelerating across the surface of these elastic bodies. It is shown that resonant conditions are not associated with problems of this type. Typical deflection profiles are included for a constant magnitude point force accelerating across a beam.

Commentary by Dr. Valentin Fuster

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In