# Programmed Control

## Programmed Control

control of an object’s mode of operation according to a predetermined program. Programmed control can be achieved both with feedback (closed-loop control systems) and without feedback (open-loop control systems). Closed-loop programmed control systems can function with or without optimization of the mode of work of the controlled object. The process of programmed control with optimization may be viewed as the minimization of the function that characterizes the difference between the desired and actual states of the object. For example, the programmed control of aircraft dictates a course of flight that will pinpoint the location of the craft at any given point in time.

The term “programmed control” with optimization arose in the theory of control of systems having stochastic inputs, that is, systems subject to random perturbations. For example, suppose that the movement of an object is described by a system of differential equations of the type *ẋ* = *f(x, u, ζ)*, where *x* is the phase vector, ζ is a random vector-function, and *u(t)* is the control vector. Let us also assume that the goal of control is to conduct the object (system) from an initial state x_{0} to a certain final state x_{T}. Because the system is stochastic, there can be no question of a precise attainment of the final state x_{T}. It is possible to speak only of a choice of control that minimizes a certain function of the final state *J[x(T)]*. Here, the norm *J[x(T)) = ║x(T) - x _{T}*║ is taken as such a function.

The method of investigation outlined below is widespread in the theory of systems similar to those with stochastic inputs, among which are control systems for rockets and many technological processes. Let us assume that *ζ =* 0, that is, the system is determined. It is then possible to try to find control *U(t)*, which will conduct the system exactly to state x_{T} along a certain path—function *x(t)*. If the goal of control is attainable, quite a large number of such paths can be determined. Therefore, it becomes possible to select control *U(t)* (a program) that will ensure an optimal value for some criterion. For example, if we are speaking of bringing a rocket into a given orbit, the criterion may be fuel consumption. In this way, the concept of optimal program arises, which in addition usually encompasses the concept of optimal path *x̄(t)* and optimal control Ũ *(t)*. The concept of optimal program pertains only to idealized systems. Therefore, after determining the optimal program, the designer also designs a system to control the program and the path. We may write *U* = Ũ *+ u*, where *Ũ* is a fixed function of time and *u* is a correcting control, which acts through a feedback circuit. The system of control possesses the means of measuring the actual path; the task of the correcting control is to ensure a minimal discrepancy between the real path *x(t)* and the optimal one *x̄(t)*, which achieves the goal of control *x _{T}*.

### REFERENCES

Moiseev, N. N.*Chislennye metody v teorii optimal’nykh sistem*. Moscow, 1971.

Moiseev, N. N. “Optimizatsiia i upravlenie (evoliutsiia idei i perspektivy).”

*Izvestiia AN SSSR: Tekhnicheskaia kibernetika*, 1974, no. 4.

Moiseev, N. N.

*Elementy teorii optimal’nykh sistem*. Moscow, 1975.

*Programmed control of technological equipment and processes*. Programmed control is also applied to the operation of machine tools, mechanisms, and other moving objects and to the monitoring of change in physical and chemical parameters, such as temperature, pressure, and concentration. Programmed control of machine tools has found the greatest practical application. In the first machine tool with numerical programmed control, a milling machine developed in 1952 at the Massachusetts Institute of Technology, the program was given in a binary code recorded on magnetic tape, and the code was converted into a control signal by an interpolator. The control signal was reproduced by the servomechanism controlling the feed of the machine. In present-day systems, two variations of this servo-mechanism are most commonly used: one with a closed-loop control (primarily direct current) and the other with an open-loop (on stepping motors). The control circuits are formed from semiconducting devices. The two basic classes of programmed control systems are the point-to-point system, which ensures movement from one position to another along a path that is not programmed but may be optimized, and the contouring system, in which the entire path is programmed.

At first, numerical programmed control was considered the basic method of automating small-scale production. With refinement, however, it has found application in mass production as a means of ensuring maximum flexibility (rapid change in the characteristics of the artieles). In the 1960’s, systems of direct programmed control appeared, in which a computer, connected to one machine tool or a group of machine tools, controlled the production as it took place. Systems of numerical programmed control with minicomputers having variable structures (”with flexible logic”) are now becoming common. In the late 1960’s, “cyclical” programmed control systems appeared; these are minicomputers, which perform only logical operations and replace conventional electronic devices with relays, both with and without contacts. Adaptive systems of numerical programmed control, in which a program assigns the geometry of the article and the criteria to be optimized, while an adaptive control changes the cutting modes in order to achieve optimum performance, are now coming into use. In self-teaching systems of numerical programmed control, the criteria to be optimized are worked out on the basis of a statistical analysis of preceding cycles.

The various components encountered in fully automated control have been developed in hierarchical fashion. In this case, the central computer controls satellite computers, and the latter in turn control the minicomputers at the machines. Automatic lines, which work without manual servicing, have been built, for example, the System 24 of H. Mullins Ltd., Great Britain. In such systems, the term “programmed control” receives a new, broader meaning: control is exercised through the computer system by means of one main input program and various auxiliary subroutines stored in the memory of all system computers.

### REFERENCES

Spiridonov, A. A., and V. B. Fedorov.*Metallorezhushchie stanki s programmnym upravleniem*, 2nd ed. Moscow, 1972.

Shaumian, G. A.

*Kompleksnaia avtomatizatsiia proizvodstvennykh protsessov*. Moscow, 1973.

Bulgakov, A. A.

*Programmnoe upravlenie sistemami mashin*. Moscow, 1975.

A. A. BULGAKOV