1. Robotics Research Laboratory Spring 2014 EE582 Digital Control Myung Jin Chung

2. Robotics Research Laboratory EE 582 Digital Control (3:1:3) Instructor: Myung Jin Chung Office: 5-2222 (Tel: 350-3429) Office Hours: by Appointment Text Book: Katsuhiko Ogata, "Discrete-time Control System," Prentice-Hall, 2nd edition, 1995 References: 1. G.F. Franklin, J.D. Powell, and M. Workman, "Digital Control of Dynamic Systems," Addison-Wesley, 3rd edition, 1998 2. C.T. Chen, "Linear System Theory and Design," Oxford University Press, 3rd edition, 1999 Course Outlines: I) Introduction II) Discrete Systems Analysis III) Sampled-Data Systems IV) Discrete Equivalents

3. Robotics Research Laboratory V) Design Using Transform Techniques VI) Design Using State-Space Methods VII) Multivariable and Optimal Control – LQ, LGQ, Kalman Filter Grading: Midterm Exam 30% Final Exam 35% Homework 20% Experiment as Term Project 15% A : 30 ∼ 40% B : 60 ∼ 70 % C : 0 ∼ 10 % Teaching Assistant : Park, Sang Un (350-8029) Cho, Young Gun (350-5429) Homepage URL: http://rr.kaist.ac.kr/~ee582

4. Robotics Research Laboratory Chapter 1 Introduction

5. Robotics Research Laboratory Continuous-time Control Systems vs. Digital Control Systems D(s)D(s)G(s)G(s) 1 sensor(transducer) plant u(t)u(t) e(t)e(t)r(t)r(t) y(t)y(t) y(t)y(t) + - Difference Eq. G(s)G(s) 1 sensor(transducer) plant u(t)u(t) e(kT)r(t)r(t) y(t) y(t)y(t) + - A/D clock r(kT) y(kT) D/A hold u(kT) A/D

6. Robotics Research Laboratory + - clock S/H and A/D converter Digital computer D/A converter Hold circuit Actuator Plant or process Transducer 001 010 001 010 100 011

7. Robotics Research Laboratory Types of Signals Continuous-time analog signal t x(t)x(t)x(t)x(t) t Continuous-time quantized signal x(t)x(t) t Discrete-time sampled-data signal (AM pulse) x(t)x(t) t Discrete-time digital signal quantized both in time and in amplitude 111 110 101 100 011 010 001 000

8. Robotics Research Laboratory Types of Systems Lumped system vs. Distributed system Deterministic system vs. Stochastic system Continuous-time system vs. Discrete-time system Linear system vs. Nonlinear system Time-invariant system vs. Time-varying system Non-homogenous system vs. Homogeneous system

9. Robotics Research Laboratory Remarks: The term “discrete-time” is broader than the term “digital” or the term “sampled-data”. The term “discrete-time” is frequently used in theoretical study, while “digital” is used in connection with hardware or software realization. “continuous-time” and “analog” are interchangeable. “discrete-time” and “digital” are interchangeable.

10. Robotics Research Laboratory Characteristics of Digital Control Time dependence ( T : sample period, 1/T : sample rate ) Approximation Quantization More flexibility in programming No internal noise or drift effects More compact and light weight Less expensive Sampling and quantizing errors Much more complex for compensating such degradation Advantages Disadvantages

11. Robotics Research Laboratory Remarks: In a digital control system, the analog electronics used for compensation in a continuous system is replaced with a digital computer(microprocessor), A/D converter and D/A converter The design of a digital control system includes determining the effect of the sampling rate and selecting a rate that is sufficiently fast to meet all specifications - As long as the sampling rate is on the order of 30 BW (Bandwidth) or faster, the digitally controlled system will behave close to its continuous counterpart. Most designs today are carried out using computer-aided methods. However, the designer needs to know hand-based methods in order to intelligently guide the computer design as well as to have a sanity check on its results.

12. Robotics Research Laboratory How Were Theories Developed Shannon – sampling theory in 1949 Oldenberg – difference equation in 1948 Jury – transform method in 1950’s Kalman – state space theory in 1960 Bellman – optimal/stochastic control in 1960 Rosenbrock and Wonham – algebraic system theory in 1970 Astrom/Goodwin – system identification in 1970’s Astrom/Wittenmark – adaptive control in 1970’s~1980’s Goodwin/Sin – adaptive filtering, prediction, control in 1980’s How Has Hardware Been Developed Microprocessor – 1960’s (Intel 4004) Programmable microcontroller – 1970’s Digital Signal Processor(DSP) – 1980’s (TI TMS32010) Embedded systems are for some specific task– 1990’s

13. Robotics Research Laboratory Course Outlines: I) Introduction II) Discrete Systems Analysis III) Sampled-Data Systems IV) Discrete Equivalents V) Design Using Transform Techniques VI) Design Using State-Space Methods VII) Multivariable and Optimal Control –LQ, LGQ, Kalman Filter