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11自动化1班 景文昊 1110200717

The class of control problems to examined here is considerable engineering interest. We should consider systems with several input , some known as controls because they may be manipulated and others called external disturbances, which are quite unpredictable, For example , in an industrial furnace we may consider the fuel flow, the ambient temperature, and the loading of material into the furnace to be inputs . Of there , the fuel flow is accessible and can readily be controlled , While the latter two are usually unpredictable disturbances.

In such situation , one aspect of the control problem is to determine how the controls should be manipulated so as to counteract the effects of the external disturbances on the state of the system . One possible approach to the solution of this problem is to use a continuous measurement of the disturbances, and from this and the known system equations to determine what the control inputs should be as functions of time to give appropriate control of the system state.

A different approach is to construct a feedback system , that is , rather than measure the disturbances directly and then compute their effects on the system from the model or system equations , we compare

direct and continuous measurements of the accessible system states with signals representing their “ desired values” to dorm an error signal , and use this signal to produce inputs to the system which will drive the error as close to zero as possible .

By some abuse of terminology , the former approach has come to be known as open loop control , and the tatter as closed-loop control .At first sight , the two approaches might appear to be essentially equivalent . Indeed, one might surmise that an open-loop

Control scheme is preferable since it is not necessary to wait until the disturbances have produced an undesirable change in the system state

before corrective inputs can be computed and applied.

图27．1（a）

图27.1(b)

However, this advantage is more than outweighed by the disadvantages of open-loop control and the inherent advantages of feedback systems. First, in many cases the implementation of the open-loop control suggested above would require a very sophisticated (and hence expensive)computing device to determine the inputs require to counteract the predicted disturbance effects. Second, a feedback system turns out to be inherently far less sensitive to the accuracy with which a mathematical model of the system has been determined. Put another way, a properly designed feedback system will still operate satisfactorily even when the internal properties of the system change by significant amounts.

Another major advantage of the feedback approach is that by placing a “feedback loop” around a system which initially has quite unsatisfactory performance characteristics, one can in many case construct a system with satisfactory behavior. Consider, for example, a rocket in vertical flight. This is essentially an inverted pendulum, balancing on the gas jet produced by the engine, and inherently unstable(any deviation of the rocket axis from the vertical will cause the rocket to topple over). It can, however, be kept stable in vertical flight by appropriate changes in the direction of the direction of the exhaust jet, which may be achieving these variations in jet direction is to use a feedback strategy in which continuous planes cause a controller to make appropriate adjustments to the direction of the rocket engine. Stabilization

of an inherently unstable system could not be achieved in practice by an open-loop control strategy.

The mathematical tools required for the analysis and design of feedback system differ according to the structural complexity of the systems to be controlled and according to the objectives the feedback control is meant to achieve.

In the simplest situation, one control a single plant state variable, called the output, by means of adjustments to a single plant input. The problem is to design a feedback loop around the system which will ensure that the output changes in response to certain specified time functions or trajectories with an acceptable degree of accuracy. In either case, the transients which are inevitably excited should not be too “violent” or persist for too long.

In a typical situation,, The problem is to design a feedback system around the plant consisting of (a) a device which produces a continuous measurement Ym of the output; (b) a comparator in which this signal is subtracted from a reference input(or set point, or desired output)Yr , representing the desired value of the output, to produce an error signal e; and(c)a controller which uses the error signal e to produce an appropriate input u to the plant. We shall call this configuration a single-loop feedback system, s term which is meant to convey the essential feature that just one of the plant states (the output y)is to be controlled using only

one input. The objective of the feedback system is to make the output Y(t) follow its desired value Yr(t) as closely as possible even in the presence of nonzero disturbances d(t). The ability of a system to do so under

steady-state condition is known as static accuracy.

图27.2

Frequently Yr is a constant , in which case we call the feedback system a regulator system. An example is the speed control system of a turbine-generator set in a power station, whose main purpose is to maintain the generator speed as nearly constant as possible. Sometimes Yr is a prescribed non-constant function of time, such as a ramp function;

An example of this would be the control system for a radar antenna whose axis is to be kept aligned with the line of sight to an aircraft flying past with constant angular velocity, In this case, we refer to the system as a tracking system..

Single-loop feedback systems with the structure of Fig.27.2 are often called servomechanisms because the controller usually includes a device giving considerable power amplification. For instance, in the control