Feedback-control(反馈控制)-外文翻译.doc

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1、Feedback controlThe 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 indu

2、strial 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

3、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 s

4、ystem 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 m

5、odel 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 a

6、buse 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 necess

7、ary to wait until the disturbances have produced an undesirable change in the system state before corrective inputs can be computed and applied.图271（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. Fi

8、rst, 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 sensi

9、tive 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 approac

10、h 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

11、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

12、 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

13、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, call

14、ed 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 w

15、hich 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

16、 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

17、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 disturba

18、nces d(t). The ability of a system to do so under steady-state condition is known as static accuracy.图27.2Frequently 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 purpo

19、se 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 p

20、ast 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 co

21、ntrol system of a hydroelectric turbine-generator set, the signals representing measured speed and desired speed might be voltages at a power level of milliwatts, while several hundred horsepower might be required to operate the main turbine valve regulating the water flow. This example also illustr

22、ate an important engineering constraint in the design of feedback control system. In many applications, the plant and the activating device immediately preceding it operate at comparatively high power levels, and their dynamic properties, if unsatisfactory for some reason, can be changed only at the

23、 expense of a feedback system is preferably done in the low-power components of the feedback system, I,e., in the measuring elements and the controller。Most feedback control systems are required to perform satisfactorily as regulators. This means that a change in disturbance or plant load should not

24、 permanently drive the system output from its desired value, and that error should tend to zero for any one of a whole range of reference inputs (set points).In some case, It is also required that the system output accurately track simple non-constant reference inputs, with a zero or small constant

25、steady-state error.Before analyzing the steady-state performance of feedback systems in general, it will be useful to discuss a specific example.Example 1 : Consider a simplified industrial continuous annealing furnace through which items to be heat-treated are carried continuously by means of a con

26、veyor system. Let the furnace output y be its temperature, the external disturbance of load d is the rate of flow of material to be heat treated; the furnace input is the rate of oil flow u delivered to the burners and is regulated by means of a thermocouple, whose voltage is compared with a voltage

27、 representing the required temperature Yr. The difference or error voltage is amplified and used to change the oil flow rate delivered by the metering pumps by an amount directly proportional to the error voltage. If we assume that the rate of change of furnace temperature is proportional to the net

28、 rate of heat flow into the furnace, In accordance with our usual convention, all variables represent deviations from nominal values; they are zero if the future operates in its normal equilibrium condition.图28.1Now consider what happens if it is decided to change the set point from its equilibrium

29、value by, say -100,without any change in the rate of material flow through the furnace, This clearly requires a reduction in the rate of oil flow the metering pumps, so that in the new steady-state condition the furnace must operate with a nonzero constant value of u. However, the change in oil flow

30、 rate from its original equilibrium value is directly proportional to the error voltage, the constant of proportionality being the controller gain. It follows that a reduction in oil flow rate and hence furnace temperature can be achieved only if there is a nonzero error. In other words, in its new

31、equilibrium state the furnace cannot ever reach the new desired temperature. The error can be made by choosing a large controller gain, but there are physical limitations to this. Ideally, the error in the furnace temperature should trend to zero after the disappearance of the initial transients; it

32、s graph should look somewhat Fig28.2. Now this can happen only if the controller produces a constant reduction in fuel flow when excited by an error voltage of the form of Fig28.2. Looked at in this way, the requirement for perfect static accuracy is obvious: the controller must be such that its out

33、put contains a component proportional to the time integral of the error; perfect state accuracy cannot, in this case, be achieved with simple proportional control.We reach a similar conclusion if we consider the response of the furnace to a change in the disturbance, i.e, the rate of flow of items t

34、o be heat treated, the set point or desired temperature remaining unchanged. An increase in the throughput will result in drop in temperature, and if the temperature is to be restored to its original value, the fuel flow rate must be increased and maintained at a higher value, i.e. u(t) must become

35、a positive constant. With a proportional control ever return to its original equilibrium value. As before, the only way to achieve perfect steady-state accuracy is to have the controller produce an increase in oil flow rate from an error signal which is positive for a time and then returns to zero;

36、the controller must have an integrating action.反馈控制本课题所研究的这一类控制问题，在工程上具有相当重要的意义。我们所讨论的系统有几个输入量，其中某些输入称为控制量，因为这些量认为是可以的控制的，而另一些输入量称为外部扰动，他们是很难预知的。例如在工业加热中，可以认为燃料流量、环境温度以及炉内材料装填量都是输入量，其中燃料流量是容易测量和容易控制的，但是后面两项通常是不能预知的扰动量。 在这些情况下，控制问题的一个方面在于如何处理控制量以便抵消外部扰动对系统状态的影响。解决这个问题的一种可能的方法是不断地测量扰动量，根据该测量值和已知的系统方程式

37、，设定出应有的控制输出量（用时间函数表示），以便对系统状态进行合适的控制。另一种不同的方法是组成反馈系统，即不是直接测量扰动量，然后根据模型或系统方程组去计算扰动对系统的影响，而是将系统状态连续的测量值与表示其“希望值”信号相比较，由此产生一个误差信号，再利用误差信号产生系统的输入量，而该输入又使误差尽可能的接近于零。这两种基本控制系统的结构如图27.1所示。图271（a）图27.1(b)由于术语上的某些习惯，前一种方法已被称为开环控制，而后一种控制被称为闭环控制。最初看来这两种方法在本质上是等效的。确实，人们可能这样推测：闭环控制的方式更好些，因为在扰动引起系统状态发生不希望的变化之前，校正

38、输入早已算好并已加到系统中去了。然而，这一优点比不上开环控制的缺点和反馈系统的固有优点。首先，在许多情况下，实现上面所提到的开环控制需要一台完善的计算装置，以便用它来算出抵消预估扰动影响所需的输入量。其次，反馈对其数学模型的精度并不敏感。换句话说，一个合理设计的反馈系统，即使系统内部有相当大的扰动量，系统仍然满意的工作。反馈方法的另一个主要优点是用一个“反馈回路”来包围原来特性不满意的系统，在许多情况下，人们可能由此而组成一个性能较满意的系统。例如，研究一个直行飞行的火箭。火箭实质是一个倒置的摆，由发动机喷出的气流平衡，它本身是不稳定的，只要火箭的中心线与垂直方向有一点偏离，就会使火箭倒置）。

39、可是，依靠在万向架上转动火箭的发动机，从而合理的改变排气气流的方向，就能保证火箭稳定的垂直飞行。实现改变气流方向唯一满意的方法就是采用反馈；不断的测出火箭在两个互相垂直的平面的角度，使控制器适当的调整火箭发动机的方向。实际上，采用开环控制是不可能使原来不稳定的系统变得稳定的。按照控制系统的结构复杂程度和控制对象的不同，分析和设计反馈系统所需要的数学工具是不一样的。在最简单的情况下，可以用调节一个输入量来控制一个输出变量。这时要设计一个包围系统的反馈回路，保证输出以某一种能被接收的精度，响应特定的时间函数或特定的轨迹，此时都要求瞬态响应不要太“激烈”，持续时间不要太长。图27.2图27.2表示了

40、一种典型的情况，系统（或对象）的控制出量入为u，外部扰动量为d，输出量为y,他们都是标量。问题在于要围绕此对象设计一个反馈系统，它包括：（a）测量装置，产生输出量的连续测量值Ym；（b）比较器，在比较中，从参考输入Yr(或称给定值、希望输出)中减去测量值Ym,产生误差信号e；（c）控制器，误差信号e产生适合于控制对象的输入u。我们把这种结构称为单回路反馈，这一术语表明了控制的基本的特点，即只用一个输入来控制对象的一个状态（输入y）。反馈系统的目的就在于即使存在非零扰动d(t),输出量y(t)也尽可能地接近希望量Yr(t)。在稳态条件下，系统这种能力被称为静态精度。通常Yr是恒值，在这种情况下，

41、我们称这样的反馈系统为自动调节系统。电厂涡轮发电机组就是一个例子，它的目的主要是维持发电机的转速尽可能地接近与恒值。有时Yr是一个规定的非恒值的时间函数，例如是一个斜坡函数。雷达天线的控制系统就是这方面的一个例子。当飞机以等角度速度飞行时，雷达天线的轴线与对飞机的瞄准线保持在一条直线上。我们称这种系统为跟踪系统。具有图27.2结构的单回路反馈系统，通常称为伺服机件，因为这种控制器中常常包含了一个能提供相当大放大倍数的放大装置，例如在水轮发电机组控制系统中，被测速度的信号与希望速度的信号可能是毫瓦功率级的电压，而调节水流的主涡轮闸门的功率可能需要几百马力。这例子也说明了在设计反馈控制系统时的一个

42、重要的工程约束条件，在大多数的应用中，控制对象及其前级驱动装置工作在比较高的功率水平上，如果由于某些原因，对它们的动态特性不满意而要改善时，只能改换大的、强功率的放大装置。因此，反馈系统的设计最好是用低功率的部件，即用测量元件和控制器来实现。对于大多数反馈控制系统，如果要求它们像调节器一样满意地工作。这意味着外部扰动或控制对象负载的变化，不应当连续地使系统的输出偏离期望值，而对于在参考输入（给定值）的整个范围的任意输入，误差信号应趋于零。在某些情况下，还要求系统的输出量能精确地跟踪简单的非恒值的参考输入信号，其稳态误差为很小或零。在一般地分析反馈系统稳态性能之前，先讨论一个特例。例题1 考虑一

43、个简化了的工业连续退火炉，热处理工件由传送系统运送通过炉子。设炉子的输出y是炉子的温度；外部扰动或负载d是热处理材料的流量；炉子的输入是送入燃烧器的燃油流量u，它是由计量泵调节的。假设用热电偶测量炉温，热电偶的电压与表示所需温度的电压Yr相比较。两者的差（即误差电压）经放大后用来改变由计量泵输送的燃油流量，流量的变化正比于误差电压。如果我们假设炉温的变化率正比于进入炉的净热流量。，按照通常的习惯，所有的变化均表示为与额定值的偏差，当炉子工作在它的额定平衡状态时，这些变量都为零。图28.1现在我们讨论，如果决定把给定值从平衡值变化-100，而不使通过炉子的物料流量变化，这将会产生什么样的结果呢？

44、显然，这需要减少计量泵供给的燃油流量，因此在新的稳态条件下，炉子必须在非零常量u的作用下工作。然而燃油流量的变化（与原来平衡值比较时）是正比与误差电压的，此比较常数就是控制器的增益。这样，燃油流量的减少和炉子温度的降低只有在误差不为零时才能达到。换句话说在这一新的平衡状态下，炉温总是不能达到新的期望温度。选择较大的控制器增益，可使误差较少，但是这存在物理上的限制。理想的情况是炉温误差应在初始瞬态过程消失以后趋于零，只有当误差电压使控制器产生一个燃油流量的恒定减少量时，理想情况才可能出现。由此可见，为了得到理想静态精度，显然要求控制器的输出量必须包含一个与误差时间积分成正比的分量；在这种情况下，简单的控制器达不到理想的控制静态精度。如果考虑炉子对于扰动变化（即处理工件流量的变化）的响应，此时给定值保持不变，即希望炉温不变，我们将得到同样的结论。增加运送量必然会引起炉温降低，如果要恢复到原来的数值则燃油流量必然增大，并保持在更一高度的数值上，也即u(t)必然为一正的常数。若采用比例控制，这就需要有一个非零的稳态误差，这样炉温总不能会到它的平衡值。与前面一样，得到理想静态精度的唯一的方法，就是要使控制器能根据误差信号产生一个燃油量的正增量。即控制器必须有积分作用。