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aulic control. The transmission of power is moderately easy with hydraulic lines. Energy storage is relatively simple with accumulators. Although hydraulic controls offer many distinct advantages, several disadvantages tend to limit their use. Major disadvantages are the following: 1. Hydraulic power is not so readily available as that of electrical power. This is not a serious threat to mobile and airborne applications but most certainly affects stationary applications. 2. Small allowable tolerances results in high costs of hydraulic ponents. 3. The hydraulic fluid imposes an upper temperature limit. Fire and explosion hazards exist if a hydraulic system is used near a soiirt of ignition. However, these situations have improved with the availability of high temperature and fire resistant fluids. Hydraulic systems are messy because it is diflicult to maintain a system free from leaks, and there is always the possibility of plete loss of fluid if a break in the system occurs. 4. It is impossible to maintain the fluid free of dirt and contamination. Contaminated oil can clog valves and actuators and, if the contaminant is abrasive, cause a permanent loss in performance and/or failure. Contaminated oil is the chief source of hydraulic control failures. Clean oil and reliability are synonymous terms in hydraulic control. 5. Basic design procedures are lacking and difficult to obtain because of the plexity of hydraulic control analysis. For example, the current flow through a resistor is described by a simple law—Ohm39。s law. In contrast, no single law exists which describes the hydraulic resistance of passages to flow. For this seemingly simple problem there are almost endless details of Reynolds number, laminar or turbulent flow, passage geometry, friction factors, and discharge coefficients to cope with. This factor limits the degree of sophistication of hydraulic control devices. 6. Hydraulics are not so flexible, linear, accurate, and inexpensive as electronic and/or electromechanical devices in the manipulation of low power signals for purposes of mathematical putation, error detection, amplification, instrumentation, and pensation. Therefore, hydraulic devices are generally not desirable in the low power portions of control systems. The outstanding characteristics of hyd aulic power elements have bined with their parative inflexibility at low power levels to make hydraulic controls attractive primarily in power portions of circuits and low power portions of systems are usually acplished by mechanical and/or electromechanical means. GENERAL COMMENTS ON DESIGN The term design has a broad meaning. It is often associated with the creativity required to produce sketches and rough layouts of possible mechanisms that will acplish an objective. As a second meaning, it is sometimes associated with the engineering calculations and analyses necessary in the selection and sizing of hardware to form a ponent or system. Design is also associated with the many details of material selection, minor calculations, and making of plete engineering drawings. This book is directed toward the analysis and design (by paper and pencil) of control systems whose power elements are hydraulic. The term design is used in the sense of specifying proper size. Although considerations such as material, stress level, and seals are equally important to a finished device, they do not relate directly to the dynamic performance of a system and are treated with more authority elsewhere. The differential equations that describe hydraulic ponents are nonlinear and, in some cases, of high order. This has led control engineers toward analog and digital puteraided design of servo systems using such ponents. Generally, the procedure is to write the equations that describe a system and then solve them with a puter. Coefficients are adjusted until the puted performance (stability, accuracy, and speed of response) is satisfactory. The system is then constructed, based on the puted results, with the hope that it will perform in a similar manner. More often than desirable, correlation with physical performance is poor. Lack of adequate correlation creates much concern that the basic assumptions used in the initial equations were not valid, that all 39。effects had not been simulated, that some unsuspected nonlinearity had spoiled the expected result (usually the case), or that there was a gap in the theory. Actually, a great deal of time and trouble can be saved if a paper and pencil analysis and design of the system is made before it is simulated on a puter for final refinements. If this is done carefully, with generous sprinklings of sound engineering judgments, then machine putation will not be necessary in most cases. In plicated cases in which judgments are most difficult, if not impossible, to make, machine putation is required。 however, this requirement is exceptional. The development of digital puter programs in recent years to solve plex sets of nonlinear differential equations strengthens the argument for preliminary analysis, for now exact solutions are possible for parison. In fact, preliminary analyses to determine approximate results are useful, and sometimes absolutely necessary, to obtain maximum benefits from machine putations. Availability of these programs allows more emphasis to be placed on the physics and mathematical formulation of problems and less on the solution dynamic analysis is necessarily restricted to linearized differential equations because only they may be solved without great difficulty. However, as far as dynamic performance is concerned, linearized analysis is an adequate tool considering the basic assumptions usually made to obtain initial equations, the preponderance of experimental correlation, and the fact that general performance indices have been developed only for linear systems. Furthermore, the algebraic or singlevalued nonlinearities which occur in hydraulic equations are not us