英文文獻Linearized Dynamic Models

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X. HONG. AND C.J. HARRIS.
Image, Speech and Intelligent Systems Group, Department of Electronics and Computer Science, University of Southampton, Southampton SO17 1BJ, UK
1.1 Introduction
In the first part of this chapter, after a general introduction, the concepts of open-loop and closed-loop control are discussed in the context of a water level control system. This example is then used to introduce fundamental considerations in control system analysis and design.
In the second part of the chapter, Laplace transforms are discussed and used to define the transfer function of a system. This is a linearized model of the dynamic behavior of the system that will serve as the basis for system analysis and design in most of this book. Block diagram reduction is used to obtain the transfer function of a system consisting of interconnected subsystems. This completes the framework necessary for Chapter 2 , in which transfer functions are derived for a variety of physical system.
1.2 Examples and Classifications of Control Systems
Control systems exist in a virtually infinite variety, both in type of application and level of sophistication. The heating system and the water heater in a house are systems in which only the sign of the difference between desired and actual temperatures is used for control. If the temperature drops below a set value, a constant heat source is switched on, to be switched off again when the temperature rises above a set maximum. Variations of such relay or on-off control systems, sometimes quite sophisticated, are very common in practice because of their relatively low cost.
In the nature of such control systems, the controlled variable will oscillate continuously between maximum and minimum limits. For many applications this control is not sufficiently smooth or accurate. In the power steering of a car, the controlled variable or system output is the angle of the front wheels. It must follow the system input ,the angle of the steering wheel, as closely as possible but at a much higher power level.
In the process industries, including refineries and chemical plants, there are many temperatures and level to be held to usually constant values in the presence of various disturbances. Of an electrical power generation plant, controlled values of voltage and frequency are outputs, but inside such a plant there are again many temperatures, level, pressures, and other variables to be controlled.
In aerospace, the control of aircraft, missiles, and satellites is an area of often very advanced systems.
One classification of control systems is the following:
⑴ Process control or regulator systems: The controlled variable, or output, must be held as close as possible to a usually constant desired value, or input, despite any disturbances.
⑵ Servomechanisms: The input varies and the output must be made to follow it as closely as possible.
Power steering is one example of the second class, equivalent to systems for positioning control surfaces on aircraft. Automated manufacturing machinery, such as numerically controlled machine tools, uses servos extensively for the control of positions or speeds.
This last example brings to mind the distinction between continuous and discrete systems. The latter are inherent in the use of digital computers for control.
The classification into linear and nonlinear control systems should also be mentioned at this point. Analysis and design are in general much simpler for the former, to which most of this book is devoted. Yet most systems become nonlinear if the variables move over wide enough ranges. The importance in practice of linear techniques relies on linearization based on the assumption that the variables stay close enough to a given operating point.
1.3 Open-Loop Control and Closed-Loop Control
To introduce the subject, it is useful to consider an example. In this example, let it be desired to maintain the actual water level c in the tank as close as possible to a desired level r. The desired level will be called the system input, and the actual level the controlled variable or system output. Water flows from the tank via a valve V0 and enters the tank from a supply via a control valve VC. The control valve is adjustable, either manually or by some type of actuator. This may be an electric motor or a hydraulic pneumatic cylinder. Very often it would be a pneumatic diaphragm actuator, in general, increasing the pneumatic pressure above the diaphragm pushes it down against a spring and increases value opening.
Open-Loop Control
In this from of control, the valve is adjusted to make output c equal to input r, but not readjusted continually to keep the two equal. Open-loop control, with certain safeguards added, is very common. For example, in the context of sequence control, that is, guiding a process through a sequence of predetermined steps. However, for systems such as the one at hand, this from of control will normally not yield high performance. A difference between input and output, a system error e= r – c would be expected to develop, due to two major effects:
Disturbances acting on the system
Parameter variations of the system
These are prime motivations for the use of feedback control. For the example, pressure variations upstream of VC and downstream of V0 can be important disturbances affecting inflow and outflow, and hence level. In a steel rolling mill, very large disturbance torques on the drive motors of the rolls when steel slabs enter or leave affect speeds.
For the water level example, a sudden or gradual change of flow resistance of the values due to foreign matter or value deposits represents a system parameter variation. In a broader context, not only are the values of the parameters of a process often not precisely known, but they may also change greatly with operating condition.
In an electrical power plant, parameter value are different at 20﹪ and 100﹪ of full power. In a valve, the relation between pressure drop and flow rate is often nonlinear, and as a result the resistance parameter of the valve changes with flow rate. Even if all parameter variations were known precisely, it would be complex, say in the case of the level example, to schedule the valve opening to follow time-varying desired levels.
Closed-Loop Control or Feedback Control
To improve performance, the operator could continuously readjust the valve based on observation of the system error e. A feedback control system in effect automates this action, as follows:
The output c is measured continuously and fed back to be compared with the input r. The error e = r – c is used to adjust the control valve by means of an actuator.
The feedback loop causes the system to take corrective action if output c ( actual level ) deviates from input r ( desired level ), whatever the reason.
A broad class of system can be represented by the block diagram shown in Fig. 1.1. The sensor in Fig. 1.1 measures the output c and, depending on type, represents it by an electrical, pneumatic, or mechanical signal. The input r is represented by a signal in the same form. The summing junction or error junction is a device that combines the input to it according to the signs associated with the arrows: e = r – c.

Fig. 1.1 System block diagram

It is important to recognize that if the control system is any good, the error e will usually be small, ideally zero. Therefore, it is quite inadequate to operate an actuator. A task of the controller is to amplify the error signal. The controller output, however, will still be at a low power level. That is, voltage or pressure have been raised but current or airflow are still small. The power amplifier raises power to the levels needed for the actuator.
The plant or process has been taken to include the valve characteristics as well as the tank. In part this is related to the identification of a disturbance d in Fig. 1.1 as an additional input to the block diagram. For the level control , d could represent supply pressure variations upstream of the control valve.
譯文
線性化動態模型
1.1介紹
在文章的第一部分，在一般的介紹之后，將討論本文中水位控制系統的開環控制和閉環控制的概念。然后用一個例子來介紹控制系統中基本的分析與設計。
在文章的第二部分，將討論拉普拉斯變換和系統傳遞函數的定義。這是一個系統動態特性的線性化模型，并且在文中的大部分它都是服務于基本的系統分析與設計。由相互聯系的子系統組成的系統將用方塊圖化簡的方法來獲得其傳遞函數。這就完成了第二章所需要的框架，在第二章中導出了各種物理系統的傳遞函數。
1.2實例與控制系統的分類
實際上，控制系統無論是在應用的種類還是復雜程度上都存在許許多多的形式。家用的加熱系統和熱水器也是一種系統，它用來控制所希望的溫度與實際溫度之間的誤差的。如果溫度下降到低于一個設定值時，將接通一個恒定的加熱源，直到溫度上升到設定值的上限為止。由于它們的成本相對較低，繼電器或通——斷控制系統在實際應用中是相當普遍的。
控制系統的本質是控制變量在最大值與最小值之間不斷的變化。許多應用這種控制的地方都是不夠平滑或精確的。例如，在汽車動力駕駛裝置中，控制變量或系統的輸出是前輪的角度。它必須盡可能地跟蹤系統輸入——方向盤角度，但是功率水平更高。
在工業生產過程中，包括提煉廠和化學廠，有許多溫度或液位在有干擾的情況下需要被控制在恒定值上。在一個發電廠中，控制變量電壓和頻率是輸出，但是其它變量例如溫度，液位，壓力等也是需要控制的。
在航空，飛行器的控制，導彈，衛星等領域中都是先進的控制系統。
控制系統的分類如下：
（1）過程控制或恒值系統：盡管存在干擾，被控變量或叫輸出必須盡可能保持在一個希望的常值也就是輸入上。
（2）伺服系統：輸出必須盡可能地跟隨輸入的變化。
動力駕駛裝置是第二階段的一個例子，相當于系統對飛機表面姿勢的控制。自動化加工機器，例如數字式生產工具，在位置控制或速度控制上都廣泛地應用伺服機構。
這最后的例子使人想起連續控制系統與離散控制系統的區別。最新的控制系統為數字式計算機控制系統。
在這里將會提及到線性控制系統和非線性控制系統。在文中，大部分的系統的分析與設計都是比較簡單的。然而，變量變化時超過范圍則系統將會變成非線性的。在實踐中線性技術的重點在于依賴線性化立基于假設變量到給予的操作點足夠的近。
1.3開環控制和閉環控制
為了介紹這個課題，我們將會用到一個實例。在這個例子中，將讓桶中的實際水位c 盡可能地接近期望的水位r 。期望的水位叫做系統的輸入，而實際水位叫做控制變量或系統的輸出。水流經供水處的控制閥門VC，在經過閥門V0進入桶中。控制閥門是可調節的，既可以手動又可以作為執行器。這也許是電動機或是液壓氣缸。通常它是一個氣壓隔膜執行器，一般當增加的壓力超過彈簧對隔膜的推力時，閥門就會打開。
開環控制
這種形式的控制，可以通過調節閥門使輸出c 與輸入r 相等，但不能連續重復調節使其保持相等。開環控制是非常普遍的。例如，下文中的順序控制，那就是引導一個來使其通過預先決定的步驟。然而，對系統來說，這種形式的控制通常不能產生好的性能。輸入/輸出的誤差為 e = r – c ，由此可見系統誤差主要由兩個方面影響：
1.系統的干擾作用
2.系統的參數變化
這些是使用反饋控制的主要原因。例如，壓力改變上游的VC和下游的V0，這種干擾可以嚴重地影響進水量，出水量及水位。在一個鋼滾磨機中，當鋼坯進入或離開時作用在驅動馬達上的非常大的干擾力矩影響速度。
對于水位的例子，由于外部物質或閥門沉渣所引起的閥門流阻的突然或逐漸的變化代表系統的參數變化。從更廣的范圍來看，它不僅過程參數不精確，而且還要改變工作環境。在發電廠中，參數值在滿電的20%到100%之間。壓力的下降和流通率的關系經常是非線性的，而且閥門阻力參數也能改變流通比率。即使全部的參數變化都是精確的，它也將是復雜的，如水位的例子，按照預定時間閥門開到跟隨時間——改變期望的水位。
閉環控制或反饋控制
為了提高性能，操作者可以根據觀察系統誤差來連續重復調節閥門。實際上，一個反饋控制系統使其動作自動化，如下:
輸出c是輸入r經過連續測量與反饋而得到的。誤差e = r – c 是由調節控制閥而產生的。
無論什么原因，如果輸出c偏離輸入r，那么反饋環就會對系統采取正確的動作。
系統大概的種類可由方框圖來表示，如圖1.1。圖1.1中傳感器測量的輸出c由電力，液壓或機械信號來表示。輸入r也用相同形式的信號來表示。相加點或誤差點是一種根據符號或箭頭連接輸入的裝置:e = r – c。

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英文參考文獻08-31