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3. Multi-dimensional system of automatic control

Systems in which the simultaneous control of several interrelated coordinates are called multi-dimensional automatic control systems (MSAR).
 
Most of the MSAR is formed when managing several coordinates of the object or work together more simply connected ATS. For such systems is characterized by the equality of the number of controlled variables of control actions. Block diagram of MSAR of this class can be represented by multiple systems (canals) regulation of cross-links between them. At the same time the value of each variable can be associated with a regulatory body, and thereby determine the object directly or The separate transmission channels. Direct TV in the object is isolated or on technological grounds or on the basis of the intensity and speed of communication between the regulator and the regulated value. If the object is a multi-dimensional set of units, combined to work together, you prefer to use a technological feature, in which the units are equipped with their own regulators; if the object represents a single unit design, the channels distributed according to their dynamics.
 
Each of the separate channels of the object has its own separate control so formed The separate system (or separate loop) regulation.
 
The transmission channel influences, originating in one of a separate systems and applications to another, is called cross-linking. Cross-links may operate in the controlled system, or in a multidimensional controller, or in both simultaneously.
 
For their own separate circuit called control and disturbance variables applied to the links of this circuit. All other external influences are considered a separate channel for improper ("strangers").
 
Multidimensional automatic control system based on function can be separated into several parts. MSAR collection of elements that perform the same function (for example, control object, measuring elements, actuators and the like. D.) Is called a function block MSAR. With respect to each of the functional blocks, the relevant terms: multidimensional object, multi-dimensional regulator, multi-dimensional measuring element, and so on. D. (Sometimes, depending on the context of the definition of "multi-dimensional" is omitted).
 
Thus, the MSAR are a set of separate systems with cross-links between them. MSAR can be subdivided into functional blocks, the scheme of interaction between them is different from the functional diagram ATS one controlled variable. This is the structural features of the MSAR, to prejudge the methods of their study.
 
Classification of MSAR can be carried out both by the generally accepted theory of automatic control features as well as on some specific features inherent in a multi-dimensional systems.
 
Multidimensional automatic control system can be divided on the basis of their effect on the system: working on control deviation from the set value (principle Polzunova - Watt); systems based on the principle of compensation of perturbations (Poncelet principle); Combination systems employing both principles at the same time control. Thanks to many of the latter group controlled coordinate systems can be extremely diverse.
 
According to its intended purpose, each of the separate systems in the MSAR, may be attributed to the system of automatic stabilization, follow-up system or systems management software. In accordance with the MSAR in general refers to a multi-dimensional system of automatic stabilization (IUAI), multiply the tracking system (MSS), or multi-dimensional systems management software (MSPU) if all systems are respectively The separate systems of automatic stabilization, follow-up system or systems management software.
 
There are also mixed MSAR, in which part of separate systems are systems of automatic stabilization, and some - tracking systems and systems management software.
 
By the nature of dependence of the static error control from external influences MSAR as well as one-dimensional system can be divided into static and astatic. However, it is possible to a very large number of different combinations. With respect to the effects of a given system, for example, the drive signals, the system on the part of one frame can be astatic, and in the rest of the coordinates - static. The number of possible combinations increases dramatically with the number of control channels.
 
MSAR may also be classified on the basis of, specific only to them.
From the ratio between the number of regulated and controlled axes MSAR divided into square and rectangular. The square - the number of controlled origin of the object is equal to the number of regulatory bodies. In MSAR rectangular type the number of controlled origin is not equal to (usually smaller) number of regulators. Depending on the number of controlled origin distinguish two-, three-, four-dimensional (and so on. D.) MSAR.
 
Depending on the use of the principle of cross-links in the controller MSAR are divided into autonomous and non-autonomous. The MSAR autonomous processes in separate channels, occurring under the influence of a particular set or sets of perturbation effects due to the use of artificial connections, proceed independently of each other, but with a different system disturbances or assignments they may be linked. In the non-autonomous MSAR management processes are interdependent in any system disturbances.
 
Of great practical importance are multidimensional systems, identity characterized by separate circuits and cross connections. This group is called a multi-dimensional control systems of the same type of automatic control systems (Mosar). Such systems may in turn be classified according to the nature of cross-links therebetween.
 
Cross communication between acting by separate control systems can be divided into two groups.
 
The first group of cross-linking are those that are inherent in the system due to its physical characteristics. Such cross-links will be called natural. The most common natural cross connections exist between the channels of the controlled system. For example, if the object of regulation is a single structure (for example, aircraft engine), and carried out the regulation of several variables that characterize his work (the rotational speed of the turbine and the gas temperature at the inlet of the nozzle unit), besides the direct channels of transmission from the regulatory authorities to the controlled variable usually there are cross-links between the individual channels of the object. The same is also obtained by combining several regulated units in a single system to work together. For example, when powered electric motor (controlled variable - speed of rotation) of comparable power generator with adjustable voltage between the channels of the controlled system (motor and generator) occur naturally cross-links.
 
The second group of cross-linking is formed by introducing artificial influences between systems by separate regulation to give the overall system specific, desired properties. Typically, these artificial cross-links introduced in the multivariate regulator. This group will be called cross-linking cross-linked correction. Corrective cross-links are a means of improving the quality indicators of regulation in MSAR. Often corrective crosslinks introduced to maintain a defined relationship between the controlled variables (e.g., to synchronize the parallel running generators of electrical energy) to achieve full or partial autonomy and control channels for other purposes.
 
Sometimes MSAR Natural crosslinks in the object are absent and there are only corrective communication (e.g., timing screw systems turboprop aircraft engine systems coordination servosystems in copy machines and so on. N.).
 
Thus, a fundamental difference between these classes of crosslinking is that while in the block diagram MSAR location and the transfer functions of natural crosslinking specified, as the point of application, and the selection and transfer functions of correcting cross-links are to be chosen from the condition of predetermined requirements for the MSAR. The choice of the sampling points and the application of corrective crosslinking determines the block diagram of MSAR. As part of a specific block diagram of directional change properties of MSAR is achieved by selecting the transfer functions correcting cross-connections and their parameters. MSAR desired properties can be provided and the appropriate choice of corrective devices in themselves separate channels. The ability to improve the properties of the system by correcting the cross-links, is a specific feature of the MSAR, so this type of bonds given special attention.
 
Depending on the direction of signal transmission crosslinks are divided into forward and backward. Direct cross-link called such a link through which the signal from the output or input of one group of units is transmitted to the output or input of another group of links that are ahead in the direction of the signals. Cross coupling is called reverse link through which the signal output from the input audio or group of units is transmitted to the inputs or outputs of another group of links located behind the path of the signals. It should be noted that the division of crosslinking MSAR closed on forward and reverse to some extent arbitrary, since reverse crosstalk at the same time is a straight line for the rest (not covered by it) of the separate channel and vice versa. Therefore, in each case it is indicated in relation to what is determined by the direction of action links crosslinking (e.g., direct cross connection object).
 
Cross-links can be positive or negative. The calculations MSAR sign crosstalk is convenient to refer to its transfer function.
 
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