1、外文资料 Discrete-time Systems andthe z-Transform Method Discrete-time systems, or sampled-data system, are dynamic systems in which one or morevariables can change only at discrete instants of time. These instants, which we shall denote bykT or kt (k=0,1,2,) , may specify the time at which some physica
2、l measurement is performed orthe time at which the memory of a digital computer is read out, etc. The time interval betweentwo discrete instants is taken to be sufficiently short so that the data for the time between thesediscrete instants can be approximated by simple interpolation. Discrete-time s
3、ystems differ from continuous-time ones in that the signals for adiscrete-time system are in sample-data form.Discrete-time systems arise in practice whenever the measurements necessary for control areobtained in an intermittent fashion, or a large scale controller or computer is time-shared bysever
4、al plants so that a control signal is sent out to each plant only periodically or whenever adigital computer is used to perform computations necessary for control. Many modernindustrial control systems are discrete-time systems since they invariably include some elementswhose inputs and/or outputs a
5、re in time. Sometimes, however, sampling operation, ordiscretization, may be entirely fictitious and introduced only to simplify the analysis of controlsystem which actually contains only continuous elements. In this lesson, we shall be concerned with discrete-time systems which the signalrepresenti
6、ng the control efforts is piecewise constant and changes only at discrete points in time.Since there are several different types of sampling operation of practical importance, we shall listthem as follows: (1) Periodic (conventional) sampling: In this case, the sampling instants are equally spaced,o
7、r kTtk (k =1, 2, 3) (2) Multiple-order sampling: The pattern of the kt is repeated periodically, or krk tt =constantfor allk . (3) Multiple-rate sampling: In this case, two concurrent sampling operations occur at kt = 1pT and 2qT , where 1T , 2T are constants andp ,q are integers. (4) Random samplin
8、g: In this case, the sampling instants are random, or tk is a randomvariable. Here we shall treat only the case which the sampling is periodic. Quantization. The inclusion of digital computer in an otherwise analog system produces indigital form (usually as binary numbers) in part of the system. The
9、 system then takes the form ofa mixed digitalanalog combination. The introduction of a digital computer in a control systemrequires the use of digital-to-analog and analog-to-digital converters. The conversion of ananalog signal to the corresponding digital signal (binary number) is an approximation
10、 because theanalog signal can take an infinite number of values, whereas the variety of different numberswhich can be formed by a finite set of digits is limited. This approximation process is calledquantization. The process of quantizing (converting a signal in analog form to digital form) may befu
11、lfilled by means of some specific circuits. The range of input magnitudes is divided into a finitenumber of disjoint intervals ih which are not necessarily equal. All magnitudes falling withineach interval are equated to a single value within the interval. This single value is the digitalapproximati
12、on to the magnitudes of the analog input signal. Thus, if x is the analog input, thedigital output is given by )(xQywhere Q is the quantizing function.The function )(tx is a discrete-time function. The operation of digital control systemsinvolves quantization both in amplitude and in time. We shall
13、next present the definitions ofseveral terms. Transducer.A transducer is a device which converts an input signal into an output signal ofanother form. (The output signal, in general, depends on the past history of the input). Analog transducer.An analog transducer is a transducer in which the input
14、and outputsignals are continuous functions of time. The magnitudes of these signals may be any valuewithin the physical limitations of the system. Sampled-data transducer.This is a transducer in which the input and output signals occuronly at discrete instants of time (usually periodic) , but the ma
15、gnitudes of the signal, as in thecase of the analog transducer, are unquantized. Digital transducer.A digital transducer is one in which the input and output signals occuronly at discrete instants of time, and the signal magnitudes are quantized. i.e., they can assumeonly certain discrete levels. An
16、alog-to-digital transducer.This is a transducer in which the input signal is a continuousfunction of time and the output signal is a quantized signal which can assume only certaindiscrete levels. Digital-to-analog transducer.A digital-to-analog transducer is one in which the input signalis a quantiz
17、ed signal and the output signal is a smoothed continuous function of time. Analog controllers and digital controllers.In considering the types of controllers whichare used in industrial control system, we may divide them into the following three categories: Analog controllers or computers: Analog co
18、ntrollers or computers represent the variables inthe equations by continuous physical quantities. Analog controllers can be designed which willsatisfactorily serve as nondecision making controllers. Digital controllers or computers: These operate only on numbers. Decision-making is animportant funct
19、ion in digital controllers, and they are currently being used for the solution ofproblems involving the optimal overall operation of industrial plants. Analog-digital controllers or computers: These are often called hybrid controllers. They arecombinations of analog controllers and digital controlle
20、rs. Some of the high performancecontrollers are of this type. Advantages of digital controllers over analog controllers.Some of the advantages ofdigital controllers over analog controllers may be summarized as follows: (1) Digital controllers are capable of performing complex computations with const
21、antaccuracy at high speed. Digital computers can have almost any desired accuracy in computationsat relatively little increase in cost. On the other hand, the cost of analog computers increasesrapidly as the complexity of the computations increase if constant accuracy is to be maintained. (2) Digita
22、l controllers are extremely versatile. By merely issuing a new program, one cancompletely change the operations being performed. This feature is particularly important if thecontrol system is to receive operating information or instructions from some computing center,where economic analysis and opti
23、mization studies are being made. Because of the inability of conventional techniques to adequately handle complex controlproblems, it has been customary to subdivide a process into smaller units and handle each ofthese as a separate control problem. Human operators are normally used to coordinate th
24、eoperation of units. Recent advances in computer control systems have caused changes in this useof industrial process controls. Recent developments in large-scale computers and mathematicalmethods provide a basis for use of all available information in the control system. Inconventional control, this part
