1. ECE 483. Digital Control Systems Analysis and Design TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AA A A A AAA A A A Instructor: Jianghai Hu Office: MSEE 220 Tel: 6-2395 Email: jianghai@purdue.edujianghai@purdue.edu Office Hours: Tu 9-10am Textbook – Digital Control System Analysis and Design, C. L. Phillips and H. T. Nagle, 3rd edition, ISBN 0-13-309832-X

2. Lec. 1. Control Systems Overview Reading: Chapter 1 What is control? –Use of algorithms and feedback to affect the operation of physical objects of interest (systems) to achieve some desired performance Physical Objects: Plant, Process, System Inputoutput Controller Environmental Perturbations

3. Examples of (Digital) Control Systems Digital DC servo control Digital Automated Flight Computer System (AFCS) Digital thermostat

4. Continuous-Time (Analog) Control Systems controller plant A simple analog feedback control system: Plants and controllers are continuous-time systems continuous-time input and output signals modeled by linear differential equations, or transfer functions + _

5. Example: Satellite Suppose that the antenna of the satellite needs to point to the earth. Thus the satellite can only rotate around a particular axis Output: orientation of the satellite as given by the angle  Input: force f generated by reaction of gas jet Satellite is a system with: gas jet

6. Example: Satellite Newton’s Second Law: Take Laplace transform (assuming zero initial condition) Torque generated by the thrust f : Total torque Moment of inertia Angular acceleration gas jet System model (time domain) : System model (transfer function):

7. Example: DC Motor System Basic motor properties: Generated torque proportional to current: Motor voltage proportional to shaft angular velocity : Servo System is an electro-mechanical system Input: voltage source e(t) Basic circuit properties (KVL): armature resistance Newton law: torque + + - -

8. System model (time domain): System model (frequency domain):

9. Digital Control Systems Idea: computers have enormous data processing power (intelligence) Sampling and data hold: computer’s clock is discrete-time and plants operate in continuous time A/D and D/A units: values in computer represented by binary strings PlantComputer A/D D/A A typical digital feedback control system: Sensor Data Hold Sampling y(t)y(t) r(t)r(t) T

10. Example: Digital Motor Control Sensor A/D D/A Digital Controller + - + - - +

11. Diagram of Digital Motor Control Both continuous-time and discrete-time signals present Both Laplace transforms and Z-transform used A/D D/A Digital Controller Motor + -

12. Example: Remote Antenna Control Motor Power Amplifier Receiver Decoder Encoder Binary code Digital reference input signal  Digital Filter wireless communication channel K Antenna D/A Receiver Decoder

13. Other Forms of Digital Control Systems

14. Digital Control System Analysis Plant: still modeled by a Laplace transfer function G(s) Computer as the digital controller –Input and output are both discrete-time signals, hence a digital filter –Modeled using a linear difference (recursion) equation –Or through z-transform as a transfer function in z So a mixture of s-transfer functions and z-transfer functions What about the A/D, D/A, sampling, and data hold? –They cannot be modeled as transfer functions! –This is the key difficulty of analyzing digital control systems

15. Digital Controller Design For a given system, design the digital controller for –Reduced steady-state error –Faster transient response –Disturbance rejection –Low sensitivity to modeling error Design methods –Root locus design –Frequency response design –Direct design method

16. Summary of Course Content Digital System Modeling –How to construct math model of a digital controller/system? Digital Control System Analysis –What is system output under an arbitrary input? Digital Controller Design –How to design digital controller so that the system output behaves desirably?