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one of the most important characteristics of an automatic control system.
The accuracy determines the degree to which an actual controlled process approaches the desired process. The deviation of the controlled process from the ideal is caused by the dynamic properties of the object being controlled and of the automatic control system, by errors of the measurement and actuating elements in the system, by internal noise in some of the elements, and by external interference. It is the sum of systematic and random errors. The systematic error is the mathematical expectation of the random deviation of the controlled process from the ideal. The random error is usually characterized by a variance or a standard deviation in the case of a unidimensional process, or by a correlation matrix in the case of a multidimensional process. The ratio between the systematic and random errors depends on the pass band of the system—that is, on the frequency range of the input-signal oscillations to which the system responds appreciably. With a broad pass band, the system has less inertia and the systematic error is decreased, but in this case the variance of the random error is increased. Therefore, the selection of the pass band represents a compromise in the design of an automatic control system. Accuracy is closely related to sensitivity, which is another important characteristic of automatic control systems.
In the initial stage of the development of automation, the question of taking random errors into account did not arise, and the accuracy of an automatic control system was described only by the systematic error. The necessity of taking into account random errors, which was first recognized during work on the problem of firing and dropping bombs from aircraft and which grew with the advent of radar, led to the creation and development of a statistical theory of controlled processes, which became one of the most important trends in automatic control theory. The main tasks of this theory are (1) calculation of the process accuracy with known characteristics of the controlled object and the automatic control system, and taking into account random disturbances (that is, statistical analysis of the system), and (2) determination of the optimum characteristics of a system, which yield the greatest possible accuracy with given statistical characteristics of the control signals and the interference (statistical synthesis of the system).
The statistical theory of controlled processes provides methods for the statistical analysis and synthesis of various classes of systems, such as linear systems, those reducible to linear systems, and those described by stochastic differential or difference equations. It also provides general methods for optimization of linear and nonlinear systems according to various criteria, as well as methods for determining the maximum attainable (potential) accuracy with given statistical characteristics of the useful signals and interference. The methods of the statistical theory of controlled processes are complex and require the use of computers.
Integrated systems are usually controlled under conditions of uncertainty, in the absence of adequate information about the characteristics of the useful signals and the interference and, in certain cases, about the controlled object. Consequently the problem arises of improving the precision of an automatic control system during the system’s operation. This is accomplished by using the principles of adaptation, learning, or self-learning. The statistical theory of controlled processes provides a theoretical basis for the design of adaptive (particularly self-adjusting), learning, and self-learning systems, as well as methods of evaluating the effectiveness of learning—that is, the improvement in the systems’ accuracy. The development of the statistical theory of controlled processes led to the creation during the early 1970’s of the principles of the theory of stochastic systems, which extends and generalizes the methods of the statistical theory of controlled processes—including the methods of calculating accuracy—to systems that include not only machines, automatic apparatus, and computers, but also groups of people.
REFERENCESPugachev, V. S. Teoriia sluchainykh funktsii i ee primenenie k zadacham avtomaticheskogo upravleniia, 3rd ed. Moscow, 1962.
Pugachev, V. S. Statisticheskie metody v tekhnicheskoi kibernetike. Moscow, 1971.
Osnovy avtomaticheskogo upravleniia, 3rd ed. Edited by V. S. Pugachev. Moscow, 1974.
Kazakov, I. E. Statisticheskaia teoriia sistem upravleniia v pro-stranstvesostoianii. Moscow, 1975.
V. S. PUGACHEV and I. N. SINITSYN
(in machine building), the degree to which manufactured products—such as machine parts, subassemblies, machines, and instruments—conform to parameters previously established by drawings, specifications, and standards.
Errors are unavoidable at all stages of the production process in the manufacture of parts and the assembly of parts and machines; therefore, it is impossible to achieve absolute accuracy. In practice, grades of fit are used to determine accuracy. They are established for the individual parameters of parts and for the product as a whole. The accuracy of fabrication of parts depends on the requirements imposed on the machines or instruments and by the operating conditions of the parts and subassemblies in the machine. Various types of accuracy are distinguished. Accuracy of shape, for example, is the degree to which a part’s surface conforms to specific geometric bodies. Accuracy may also refer to the dimensions of a part or to the relative position of the part’s surfaces.
The accuracy of a part depends on the deviations from the specified shapes and dimensions. The errors in the shapes of parts that are bodies of revolution are expressed by out-of-roundness, faceting, conicity, and curvature, as well as by barrel-shaped and saddle-shaped surfaces. For parts with plane surfaces, the errors of shape are nonrectilinearity and nonplanarity, which can be judged by the convexity or concavity of the surfaces. The dimensional errors of parts are controlled by the maximum deviations according to a system of tolerance limits. The deviations of the relative position of surfaces are characterized by the nonparallel-ness and nonperpendicularity of the axes and planes, by the asymmetry of the surfaces, and so on. The accuracy of machine parts dictates the technology of fabrication and assembly; it also influences the choice of measurement equipment.
D. L. IUDIN