ECE 382. Feedback Systems Analysis and Design

1. ECE 382. Feedback Systems Analysis and Design • Instructor: Jianghai Hu • Office: MSEE 220 • Tel: 6-2395 • Email: jianghai@purdue.edu • Office hours: Mon 1-2pm • TA: Brandon Kozel • Office hours: Thursday and Friday, 1:30-3pm • Email: bkozel@purdue.edu • Grader: TBA

2. Lec 1. Introduction and Overview • What is control? • Use of algorithms and feedback to affect the operation of physical objects of interest to achieve some desired performance Environmental Perturbations Controller Physical Objects: Plant, Process, System Input output

3. Example: Thermostat Turning on/off heater/cooler to maintain the room temperature at a pre-specified level Similar example: Cruise control of cars (maintaining constant speed)

4. Example: Robotic Arm Control the voltage applied on the motors so that the robot hand moves along a specified trajectory (and grasps some object)

5. Example: Process Control

6. Example: Traffic Control Ground Traffic Air Traffic Air traffic controllers control traffic flows for maximum throughput and safety Similar example: Internet congestion control

7. Example: Biological Control

8. Observations • Control is everywhere • Other examples: electrical, mechanical, ecological, and financial systems • Physical processes under control can be very complicated • Often need to work in adverse situations • Environmental noises, part failure, human errors, etc

9. Two Control Methodologies • Black box approach • Learn by training • Example: neural network/fuzzy logic, expert systems, machine learning • Advantage: no need for deep physical understanding • Disadvantage: hard to analyze, not good for high performance sys. • Model-based approach (this class!) • Build a math model to relate the system input and output • Advantage: easy to analyze, high performance • Disadvantage: physical models complicated, not always available

10. Closed-Loop (Feedback) Control Controller Physical Objects Plant, Process, System Input output Controller uses plant output to help determine the plant input Open-Loop vs. Closed-Loop Control Open-Loop Control Controller Physical Objects Plant, Process, System Input output Controller determines the plant input without looking at plant output

11. Advantages of Feedback • Robustness of performance with respect to • Model inaccuracy • External and internal disturbances • Open loop control is used only when one has accurate knowledge of system and environment behaviors. • A simple example to demonstrate the above advantages

12. Environmental disturbances (road grade w) Controller Reference speed r Sensor (speedometer) measured speed y’ Example: Cruise Control Output Input (speed y) (throttle angle u) Controlled object (car) Actuator (engine) Goal: design controller so that the actual speed y of the car is as close to the reference speed r as possible, despite variations in road grade w.

13. Environmental disturbances (road grade w) Model (static): Model (dynamic): Model Construction Observation 1: speed y increases with throttle angle u Observation 2: speed y decreases with road grade w Output Input (speed y) (throttle angle u) Controlled object (car) Actuator (throttle)

14. Graphical Representation Grade w 0.5 summation + Speed y - Input u 5 multiplication 10 + + Block Diagram of Static Model road grade w Output Input (speed y) (throttle angle u) Controlled object (car) Actuator (throttle)

15. controller gain reference speed r 0.1 Controller An Open-Loop Controller Grade w 0.5 Speed y - Input u 10 + + Plant The throttle angle u is set proportionally to the reference speed r Question: Set r=65 mph. What is the actual speed of the car under this controller for different road grades?

16. reference speed r 0.1 Controller Analysis of Open-Loop Controller Grade w controller gain 0.5 Speed y - Input u 10 + + Plant Assume r=65 mph Actual Speed: Tracking Error:

17. Feedback controller controller gain A Feedback Controller Grade w 0.5 Speed y reference speed r - Input u + + 10 10 + + - Plant Use the difference between the measured speed and the reference speed to determine the throttle angle (assuming no measurement error):

18. Feedback controller Analysis of Feedback Controlled System Grade w 0.5 reference speed r - Speed y Input u + + 10 10 + + - Plant Assume r=65 mph Actual Speed: Tracking Error:

19. Comparison of Open vs Closed-Loop Feedback controller Open loop controller • Open loop controller • No error on level ground • Error increases rapidly with w • Feedback controller • A small error on level ground • Reduced sensitivity to grade disturbances • Reduced sensitivity to model inaccuracy (not shown here)

20. More Discussions • By increasing controller gain of feedback controller • Tracking error can be further reduced • May cause instability in general • Design problem: • how to choose the controller gain so that the error on level ground is within 0.05%? • Dynamic models?

21. Course Content • System Modeling • How to construct math model of a system? • Control System Analysis • How does system output change under certain inputs? • Root locus analysis • Frequency response analysis • Control System Design • How to design controller so that the system output behaves desirably?

22. Digital Control Systems A digital control system: Physical Objects Plant, Process, System Computer D/A D/A Input output Digital Control Theory will be studied in ECE 483