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: Vineeth Ravi Office hours: Wed 2-3:30pm, Fri 2-3pm Email: ravi24@purdue.edu Grader: Gonghao Sun Email: sun174@purdue.edu

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 Input Physical Objects: Plant, Process, System output

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)

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

Example: Process Control

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

Example: Biological Control

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

Two Control Methodologies Black box approach Learn by training Example: adaptive neural network, fuzzy logic, expert systems 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

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

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

Example: Cruise Control Environmental disturbances (road grade w) Controller Reference speed r Input Output (throttle angle u) Sensor (speedometer) measured speed y’ (speed y) Actuator (engine) Controlled object (car) 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.

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

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

An Open-Loop Controller Grade w controller gain 0.5 0.1 reference speed r Controller - 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?

Analysis of Open-Loop Controller Grade w controller gain 0.5 0.1 reference speed r Controller - Speed y Input u 10 + + Plant Assume r=65 mph Road grade w Actual speed y Error e Error Percentage 65 0% 1 60 5 7.69% 2 55 10 15.38% Actual Speed: Tracking Error:

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

Analysis of Feedback Controlled System 10 0.5 + - Input u Speed y Plant reference speed r Feedback controller Grade w Assume r=65 mph Road grade w Actual speed y Error e Error Percentage 64.36 0.64 0.99% 1 64.31 0.69 1.07% 2 64.26 0.74 1.14% Actual Speed: Tracking Error:

Comparison of Open vs Closed-Loop Open loop controller Feedback controller w Actual speed y Error e Error Percentage 65 0% 1 60 5 7.69% 2 55 10 15.38% w Actual speed y Error e Error Percentage 64.36 0.64 0.99% 1 64.31 0.69 1.07% 2 64.26 0.74 1.14% 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)

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?

Course Content System Modeling Control System Analysis 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?

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