Kyoung-Chul Koh(kckoh@sunmoon.ac.kr) DIGITAL CONTROL 목 차 1. Introduction to Digital Control System Kyoung-Chul Koh(kckoh@sunmoon.ac.kr) 1 of 32

강의진도 [1주] 1장 서론 참고문헌 [1] 고경철, 이호길저, C언어로 구현하는 디지털제어 이론 및 실습, HS미디어, 2010 [2] Ogata, Discrete-Time Control System, [3] Dorf, Modern Control Systems, Wesley, 1998 2 of 32

Fig.1.1 Intelligent service robot 1-1. Digital systems Recently, - rapidly increasing use of digital controller in control system - digital controller > productivity > profit > low manufacturing cost > low energy consumption Environment system s/w electric mechanical chemical biological social Fig.1.1 Intelligent service robot 3 of 32

Fig.1.2 Industrial robots controlled by digital controllers Computerized control > intelligence to industrial robots > optimal fuel injection control of automobiles > precise control of consumer electronics facilities Merits of digital control systems > decision capability > flexibility Dynamic systems > analogue control -> digital control > continuous signal -> digital signal Fig.1.2 Industrial robots controlled by digital controllers 4 of 32

Fig.1.3 classification of control signals 1-3. Digital Signal classification of signals, - continuous-time analogue signal > defined in continuous time domain > magnitude >> continuous domain - continuous-time quantized signal >> finite number domain : quantization >>> finite word length: 32bit, 64bit - sampled analogue signal > discrete time domain > continuous value domain - digital signal > quantized value domain X(t) X(t) t t (a) continuous signal (b) sampled signal X(t) X(t) t t (c) quantised signal (d) digital signal Fig.1.3 classification of control signals 5 of 32

Fig.1.4 Open loop control system 1-4. Terminologies linear system time variant vs. time invariant sytems discrete time control system vs, continuous time control system interpolation differential equation vs. linear difference equation sampling process - Radar tracking system : scanning by beam - Plant process control: very slow response - sampling vs. discretization Digital control system + Feedforward controller + Plant Fig.1.4 Open loop control system 6 of 32

Feedback control system 1-4. Terminologies Feedback control system Feedback Loop Controller + + + Plant - Fig.1.5 Closed loop control system 7 of 32

1-4. Terminologies Sampling - Discretization > opp. data hold A/D conversion - encoding - quantization - sample and hold -> AD conversion Sample and hold D/A conversion - decoder Plant - approximate mode - linearization - ex: furnace, chemical process, servo mechanism, aircraft, mechanical devices Process - chemical, economical, biological processes s/w electric mechanical chemical biological social Environment system 8 of 32

1-5. Quantization Fig.1.6 Quantisation process Quantization - nearest approximation where FSR is full-scale range Quantizer - MSB vs. LSB Fig.1.6 Quantisation process 9 of 32

1-5. Quantization Fig.1.7 Quntisation error Quantization error - finite resolution - round-off error Fig.1.7 Quntisation error 10 of 32

1-6. Digital Control System Feedforward controller S.H and A/D Feedback D/A Hold Plant Clock Digital Filter Digital controller Noise Transducer or sensor Disturbances + _ Output input Fig.1.8 Block diagram of digital control system 11 of 32

1-6. Digital Control System Signal processing - multiplexing and demultiplexing - sample and hold - AD conversion (Quantization) - DA conversion (Decoding) - filtering S.H and A/D converter Digital computer D/A Hold circuit Actuator Plant or process Clock Filter + _ 001 010 100 011 Fig.1.9 Signal processing of digital control systems 12 of 32

1-6. Digital Control System Physical variable Transducer Amplifier Low pass Filter Analog multiplexer Sample & Hold A/D converter To digital controller (a) A/D conversion process From digital controller Register Demultiplexer D/A converter Hold To actuator (b) D/A conversion process Fig.10. Digital signal processors 13 of 32

1-6. Digital Control System Analogue multiplexer - electrical swithes Demultiplexer sample & Hold Input channels Select control Fig.1.11 Multiplexer 14 of 32

1-6. Digital Control System Sample and hold circuit - hold capacitor - buffer with high input impedance - tracking mode and hole mode Analog output Analog input Amp.1 Amp.2 Sampler Sample and hold command Fig.1.12 Sample and hold circuit 15 of 32

1-6. Digital Control System Sample and holer - tracking mode and hold mode - aperture time Hold mode droop x(t) Sample to hold offset Input signal output signal Aperture time t Tracking Mode Hold Mode Hold command Is given here Fig.1.13 Operation mode of sample and hold circuit 16 of 32

1-6. Digital Control System AD conversion - quantization - types > successive approximation - MSB -> LSM - conversion time = 2usec for 12bit conversion > integrating type > counter type > parallel type D/A converter Digital output ….. … Successive Approximation register Clock Analog input comparator Fig.1.14 A/D converter circuit 17 of 32

1-6. Digital Control System AD conversion error - offset - non-linearity - gain error 111 111 111 100 100 100 000 000 000 1/2FS FS 1/2FS FS 1/2FS FS (c) Gain error (a) Offset error (b) Linearity error Fig.1.15 AD conversion error 18 of 32

1-6. Digital Control System DA converter - binary register R 2R 4R 8R Vo b0 b1 b2 b3 Vref Fig.1.16 Binary register circuit ref. [1] pp.32-33 19 of 32

1-6. Digital Control System DA converter - R-2R ladder circuit 3R 2R R R R 2R Vo 2R 2R 2R 2R 2R b0 b1 br-3 br-2 br-1 -Vref Fig.1.17 R-2R ladder circuit 20 of 32

Fig.1.18. Signal from zero order hold circuit 1-7. Hold circuits Zero order hold Output Output t Fig.1.18. Signal from zero order hold circuit 21 of 32

Fig.1.18. Signal from the first order hold circuit 1-7. Hold circuits First order hold - efficient for slowly varying signal Output Output Fig.1.18. Signal from the first order hold circuit 22 of 32

Fig.1.20 Signal from polygon hold circuit 1-7. Hold circuits polygonal hold - instability problem Output Fig.1.20 Signal from polygon hold circuit 23 of 32

Fig.1.21 Perspective of digital control systems 1.8 The future evolution of control systems Control system - flexibility - high level of autonomy Sensory limitation - computer vision - no adaptibility to environment > need human supervision Advanced robotics system - task adaptibility - artificial intelligence - sensor integration - off-line programming - human-machine interface > database management > communications > programming language FactoryAutomation Power tools Hand tools Robotics NC Machines Automated society Improvements: *Sensors *Vision *Languages *Artificial intelligence Electric machines Automatic machine Automatic Control Systems Computer Control Systems (programmable) Intelligent controller *Man-machine interface *Supervisory control LOW HIGH Flexibility Autonomy Fig.1.21 Perspective of digital control systems 24 of 32

HW#1 문제 1.1, 문제 1.3 Due: Next week this time 25 of 32