离散时间控制系统课件(PPT 57页).ppt

1、29.09.2020,Computer-Controlled Systems,2,Course Information,Time: 13:30-15:10pm, Wednesday 10:00-11:40am, Friday (even weeks) Venue: 综B204 References: 离散时间控制系统(英文版第2版)，Katsuhiko Ogata，机械工业出版社，2004 离散时间控制系统(中文版)，Katsuhiko Ogata，陈杰，蔡涛等译，机械工业出版社，2006 Grading Procedure: in-term evaluation experimental r

2、esults final paper examination.,3,Chapter 1 Introduction to Discrete-Time,4,4,Contents,1-1 Introduction 1-2 Digital Control Systems 1-3 Quantizing and Quantization Error 1-4 Data Acquisition, Conversion and Distribution Systems 1-5 Concluding Comments,5,1-1 Introduction,Digital Controller A rapid in

3、crease in the use of digital controllers,6,Digital Controller The trend is due to Digital control can achieve optimal perfor- mance, have Decision-making capability and flexibility in the control program Availablity of low-cost digital computers Advantages of digital signals,1-1 Introduction,7,Types

4、 of Signals Continuous-time signal: A signal defined over a continuous range of time Analog signal: A signal defined over a continuous range of time whose amplitude can assume a continuous range of values A continuous-time quantized signal Discrete-time signal: A signal defined only at discrete inst

5、ants of time,1-1 Introduction,8,Sampled-data signal: A discrete-time signal if the amplitude can assume a continuous range of values Digital signal: A discrete-time signal with quantized amplitude Comparison Discrete-time, digital, sampled data signal (control system) Continuous-time, analog signal

6、(control system),1-1 Introduction,9,1-1 Introduction,10,Systems Dealt With in This Book Linear and time invariant Discrete-Time Control Systems one or more variables can change only at discrete instants of time. These instants may specify the times at which some physical measurement is performed or

7、the memory of a digital computer is read out Described in linear difference equations with constant coefficients,1-1 Introduction,11,1-2 Digital Control Systems,Figure 1-2 Block diagram of a digital control system,12,S/H and A/D (A/D) Sample-and-Hold (S/H) Sampling Processes, replace original contin

8、uous-time signal by a sequence of values at discrete-time time points a circuit that receives analog input signal and holds this signal at a constant value for a specified period of time. Analog-to-Digital Converter (A/D) Also called an encoder, is a device that converts an analog signal into a digi

9、tal signal, usually a numerically coded signal. A S/H circuit is often an integral part of a commercially available A/D converter.,1-2 Digital Control Systems,13,Types of Sampling Operations Periodic sampling tk = kT (k = 0, 1, 2, ) Multiple-order sampling tk+r - tk = constant Multiple-rate sampling

10、 A digital control system have different sam- pling periods in different feedback paths Random sampling tk is a random variable,1-2 Digital Control Systems,14,Signal Forms in a Digital Control System,1-2 Digital Control Systems,Figure 1-3 Block diagram of a digital control system showing signals in

11、binary or graphic form,15,D/A and hold Digital-to-Analog Converter (D/A) Also called a decoder, is a device that converts a digital signal into an sampled-data signal. Hold reconstruct the analog signal that has been transmitted as a train of pulse samples, i.e. fill in the spaces between sampling p

12、eriods and thus roughly reconstruct the original analog signal,1-2 Digital Control Systems,16,Plant or Process A plant is an physical object to be controlled. We call any operation to be controlled a process. Accurate modeling is perhaps the most difficult part in the design of control system Transd

13、ucer Is a device that converts an input signal into an output signal of another form, such as a device that converts a pressure signal into an voltage output. Analog transducer, sampled-data transducer, digital transducer,1-2 Digital Control Systems,17,The main functions involved in A/D conversion a

14、re sampling, amplitude quantizing and coding Amplitude quantizing Represent a continuous or analog signal by a finite number of discrete states is called amplitude quantization Coding or Encoding Represent a sample value by a numerical code,1-3 Quantizing and Quantization Error,18,Quantizing The sta

15、ndard number system is the binary number system. The code group consists of n pulses each indicating either on (1) or off (0). In the case of quantizing, n on-off pulses can represent 2n amplitude levels or output states. The quantization level Q: the range between two adjacent decision points: Q =

16、FSR/2n ,FSR is the full-scale range. MSB is the most significant bit, has the most weight (one half of the full scale) LSB is the least significant bit, has the least weight LSB = FSR/2n,1-3 Quantizing and Quantization Error,19,Quantization Error Since digital output can assume only a finite number

17、of levels, an analog number must be rounded off to the nearest digital level. Quantization error varies between 0 and 1/2Q. Quantization error depends on fineness of the Q, and can be made as small as desired by making Q smaller.,1-3 Quantizing and Quantization Error,20,1-3 Quantizing and Quantizati

18、on Error,To determine the desired size of the quantization level in a given digital control system, the engineer must have a good understanding of the relationship between the size of the quantization level and the resulting error.,21,For an analog input x(t), the output y(t) takes on only a finite

19、number of levels, which are integral multiples of the quantization level Q,1-3 Quantizing and Quantization Error,Figure 1-4(a) Block diagram of a quantizer and its input-output characteristics,22,Round-off error The error resulting from neglecting the remaining digits is called round-off error. Quan

20、tization error is a round-off error The finer the quantization level is, the smaller the round-off error.,1-3 Quantizing and Quantization Error,23,Round-off error,1-3 Quantizing and Quantization Error,Figure 1-4(b) Analog input x(t) and discrete output y(t),24,Quantization noise: the uncertainty pre

21、sent in the quantization process. For a small quantization level Q, the quan-zation error is similar to that of noise. So quantization process acts as a source of random noise. The variance of the quantization noise is,25,1-4 Data Acquisition, Conversion and Distribution Systems,Figure 1-5 (a) Block

22、 diagram of a data-acquisition system;,26,Transducer A physical variable such as position, velocity, acceleration, temperature is first converted into an electrical signal (a voltage or current) Amplifier Amplifies the voltage output of the transducer Converts a current signal into a voltage signal

23、Buffers the signal,1-4 Data Acquisition, Conversion and Distribution Systems,27,Low-pass filter Attenuates the high-frequency signal components, such as noise (electronic noises are random in nature and may be reduced by low-pass filters. However, such common electrical noises as power-line interfer

24、ence are generally periodic and may be reduced by means of notch filters.) Analog Multiplexing A device that performs the function of time-sharing an A/D converter among many analog channels.,1-4 Data Acquisition, Conversion and Distribution Systems,28,If many signals are to be processed by a single

25、 A/D and a digital controller, then these input signals must be fed to the controller through a multiplexer. Is a multiple switch that sequentially switches among input channels in some prescribed fashion. At a given instant of time, only one switch is in the “on” position. When the switch is on in

26、a given input channel, the input signal is connected to the output of the multiplexer for a specified period of time.,1-4 Data Acquisition, Conversion and Distribution Systems,29,1-4 Data Acquisition, Conversion and Distribution Systems,30,Demultiplexer Separates the composite output digital data fr

27、om the digital controller into the original channels Sample-and-Hold Circuits Sampler: covert an analog signal into a train of amplitude-modulated pulses. Hold circuit: hold the value of the sampled pulse signal over a specified period of time,1-4 Data Acquisition, Conversion and Distribution System

28、s,31,two operation modes The tracking mode: the switch is closed, i.e., the input signal is connected The hold mode: the switch is open, i.e., the input signal is disconnected When the sampling duration is negligible, the sampler may be considered an ideal sampler,1-4 Data Acquisition, Conversion an

29、d Distribution Systems,32,1-4 Data Acquisition, Conversion and Distribution Systems,Figure 1-7 Sample-and-hold circuit,33,1-4 Data Acquisition, Conversion and Distribution Systems,Figure 1-8 Tracking mode and hold mode,34,Analog-to-Digital Converters The process by which a sampled analog signal is q

30、uantized and converted to a binary number. Types of frequently used A/D Converters Successive-approximation type Integrating type Counter type Parallel type Selection criterions of A/D converters Conversion speed, accuracy, size and cost,1-4 Data Acquisition, Conversion and Distribution Systems,35,C

31、ounter type A/D (the simplest A/D) Clock pulses are applied to the digital counter in such a way that the output voltage of the D/A converter (that is, part of the feedback loop in the A/D converter) is stepped up one least significant bit (LSB) at a time. Then the output voltage is compared with th

32、e analog input voltage once for each pulse. When the output voltage has reached the magnitude of the input voltage, the clock pulses are stopped. The counter output voltage is then the digital output.,1-4 Data Acquisition, Conversion and Distribution Systems,36,Successive-approximation type (most fr

33、equently used) The principle is: The successive-approximation register (SAR) first turns on the most significant bit (half the maximum) and compares it with the analog input. The comparator decides whether to leave the bit on or turn it off. If the analog input voltage is larger, the most significan

34、t bit is set on. Next, turn on bit 2 and then compare the analog input voltage with three-fourths of the maximum.,1-4 Data Acquisition, Conversion and Distribution Systems,37,After n comparisons are completed, the digital output of the successive-approximation register indicates all those bits that

35、remain on and produces the desired digital code. Thus, this type of A/D converter sets 1 bit each clock cycle, and so it requires only n clock cycles to generate n bits, where n is the resolution of the converter in bits. (The number n of bits employed determines the accuracy of conversion.) The tim

36、e required for the conversion is approximately 2 sec or less for a 12-bit conversion.,1-4 Data Acquisition, Conversion and Distribution Systems,38,1-4 Data Acquisition, Conversion and Distribution Systems,Figure 1-9 Schematic diagram of a successive-approximation-type of A/D converter,39,Errors in A

37、/D Converters The input-output characteristics of A/D Converters change with time and temperature. Actual analog-to-digital signal converters always have some errors, such as offset error, linearity error, and gain error. Commercial converters are specified for three basic temperature ranges Commerc

38、ial (0C to 70C) Industrial (-25C to 85C) Military (-55C to 125C),1-4 Data Acquisition, Conversion and Distribution Systems,40,Errors in A/D Converters,1-4 Data Acquisition, Conversion and Distribution Systems,Figure 1-10 Errors in A/D converters (a) offset error; (b) linearity error; (c) gain error,

39、41,The reverse of the data-acquisition A data-distribution system consists of registers, a demultiplexer, digital-to-analog converters, and hold circuits. It converts the signal in digital form (binary numbers) into analog form. The output of the hold circuit is fed to the analog actuator, which, in

40、 turn, directly controls the plant under consideration.,1-4 Data Acquisition, Conversion and Distribution Systems,Figure 1-5 (b) block diagram of a data distribution system,42,Digital-to-Analog Converters For the full range of the digital input, there are 2n corresponding different analog values, in

41、cluding 0. For the digital-to-analog conversion, there is a one-to-one correspondence between the digital input and the analog output Two common D/A methods Weighted resistors: simple in circuit configuration, but its accuracy may not be very good R-2R ladder network: a little more complicated in ci

42、rcuit configuration, but is more accurate.,1-4 Data Acquisition, Conversion and Distribution Systems,43,Weighted resistors,1-4 Data Acquisition, Conversion and Distribution Systems,Figure 1-11 Schematic diagram of a D/A converter using weighted resistors,44,Weighted resistors The input resistors of

43、the operational amplifier have their resistance values weighted in a binary fashion. When the logic circuit receives binary 1, the switch connects the resistor to the reference voltage; when the logic circuit receives binary 0, the switch connects the resistor to ground Notice that: as the number of

44、 bits is increased, the range of resistor values becomes large and consequently the accuracy becomes poor,1-4 Data Acquisition, Conversion and Distribution Systems,45,R-2R ladder network,1-4 Data Acquisition, Conversion and Distribution Systems,Figure 1-12 n-bit D/A converter using an R-2R ladder ci

45、rcuit,46,Note that: with the exception of the feedback resistor (which is 3R), all resistors involved are either R or 2R. This means that a high level of accuracy can be achieved,1-4 Data Acquisition, Conversion and Distribution Systems,47,Hold Circuits Fill in the spaces between sampling periods an

46、d thus roughly reconstruct the original analog signal The hold circuit: to extrapolate the output signal between successive points according to some prescribed manner Zero-order-hold: produces a staircase waveform,1-4 Data Acquisition, Conversion and Distribution Systems,48,1-4 Data Acquisition, Con

47、version and Distribution Systems,Figure 1-13 Output from a zero-order hold,49,First-order-hold: generates an output slope equal to the slope of a line segment connecting previous and present samples and projecting it from the value of the present sample. More accurately than a zero-order hold. If th

48、e slope of the original signal does not change much, the prediction is good. If, however, the original signal reverses its slope, then the prediction is wrong. And the output goes in the wrong direction, thus causing a large error for the sampling period considered.,1-4 Data Acquisition, Conversion

49、and Distribution Systems,50,1-4 Data Acquisition, Conversion and Distribution Systems,Figure 1-14 Output from a first-order hold,51,Interpolative first-order hold: generates a straight-line output whose slope is equal to that joining the previous sample value and the present sample value, but the pr

50、ojection is made from the prediction point. Its accuracy is better than that of other hold circuits, but there is a one-sampling period delay. From the viewpoint of the stability of closed-loop systems, such a delay is not desirable, and so the interpolative first-order hold (polygonal hold) is not

51、used in control system applications.,1-4 Data Acquisition, Conversion and Distribution Systems,52,1-4 Data Acquisition, Conversion and Distribution Systems,Figure 1-14 Output from an interpolative first-order hold (polygonal hold),53,Digital Controllers and Analog Controller Analog Controllers repre

52、sent the variables in an equation by continuous physical quantities. can easily be designed to serve satisfactory as non-decision-making controllers the cost increases rapidly as the complexity of the computations increases,1-5 Concluding Comments,54,Digital Controllers operate only on numbers decision m