Control System Design ME155A 1.

Practical Information

Lecture 1 - Introduction to Automatic Control • Textbook: B. C. Kuo Automatic Control Systems

• Lectures Tue, Th 12.30-1.45 2361 Engineering II
K. J. Åström
• Lecture notes, homeworks, and solutions on Home page
1. Practical Information about the Course • Computer tools (Matlab)
2. Introduction to Automatic Control • Office hours: Tuesday 1.45-2.45, Thursday 10.30-11.30
3. Feedback • Teaching assistant: Niklas Karlsson 2235A Engineering II
4. Summary – Office hours: Monday 10.00-11.00, Tuesday 9.00-10.00,
• Midterm: Tentatively Nov 2nd
Theme: What is control? Why should an ME know about it?
Open and closed loop systems? Feedback and feedforward. • Final: Dec 8 12.00-3 pm
Block diagrams. • Grade: 30% HW, 30% MT and 40% final
• Feedback: astrom@engineering.ucsb.edu, 2324 Eng II

Goals of the Course 2. An Introduction to Automatic Control

• Understand why automatic control is useful • The discipline of control
for a mechanical engineer • A brief history
• Recognize the value of • How Control emerged?
integrated control and process design
• Consequences
• Recognize when a process is easy or difficult to control
• Automation levels
• Know key ideas and concepts
• Applications
Dynamics and feedback
• Summary
• Know relevant mathematical theory
• Be able to solve simple control problems
• Recognize difficult problems
• Be aware of computational tools
 The Discipline of Control Open and Closed Loop Systems
A. M. Amp‘ere coined cybernetics in his grandiose scheme for Cruise control: Keep constant speed
political science “Essai sur la philosophie des sciences” Paris
1845.
Control engineering emerged around 1945 because of an
intensive effort involving researchers from a wide range of
fields pressured by war efforts.
N. Wiener 1945 Cybernetics or control and communication in
the animal and the machine. MIT Press 1948
H. S. Tsien Engineering Cybernetics, 1954
This illustrates the wide range of control problems.

Two Ways to Build an Accelerometer Feedback and Feedforward

Open loop system • Feedback • Feedforward
2
m
d x
+d
dx
+ kx = ma • Closed loop • Open loop
dt 2 dt
• Acts only when there • Acts before deviations
Gain g = m/ k
are deviations show up
k 1 • Market Driven • Planning
Bandwidth w = =√
m g
• Robust to model errors • Not robust to model
Difficult compromise to get  S  < 1 for some ω errors  S  = 1 for all ω
high gain and high band- Closed loop system
• Risk for instability • No risk for instability
width ω k = 1!
2

Feedback resolves the com-

promise! Force Balance!
Sensitive components:
• Spring
• Current measurement
 Engineering Education Automatic Control
• Traditional Division: CE, ME, EE, .. • Understanding feedback systems (cybernetics)
– Traditional • Feedback gives designers extra freedom
– Reflects 19th century industry • Use of feedback often revolutionary
– Todays problems are different: Systems and materials • General methods and theories
• Automatic control - the first systems discipline + Problems from different domains are similar if viewed in
• Many activities across departments at UCSB the right way
• Why should a mechanical engineer know control? + Large application areas
– Feedback is ubiquitous (appears everywhere) + Technology transfer
– Feedback gives designers extra freedom + Business opportunities
– Concepts and tools have wide applicability - Abstract (Easy to use your foothold)
• Theory works very well

A Brief History How the Field Emerged

• The roots (before 1940!) • Feedback was invented patented and used in a wide
Early use of feedback in windmills, steam engines, en- range of fields, often with revolutionary consequences
gines, ships, airplanes, process control, telecommuni- • It was not realized that very different technical prob-
cation lems were indeed very similar and that they could be ap-
• The field emerges (1940-1945) proached with the same methods
– The Second World War • Concepts and theory were lacing
– Spread like wildfire: education, industry, organization • The pieces fell in place when persons from different
backgrounds were brought together in the war effort
• The second wave (1960-)
• The beginning of “systems thinking”
– Demanding applications: Space, process industry
– New components: digital computers • Why did it take so long?
 Block Diagrams Stop and Think!!
Try to sketch a block diagram of cruise control for a car. Make
small groups and discuss!

• Capture the essence

• Standard “drawing”
• Abstraction
• Information hiding
• Also some limitations
The Audience is Thinking ...

Examples How to make an Airplane

• The centrifugal governor Lecture by Wilbur Wright 1901:
• The Wright brothers Men know how to construct airplanes.
• The feedback amplifier Men also know how to build engines.
Inability to balance and steer still confronts
• The CD player
students of the flying problem.
• The California emission code When this one feature has been worked out,
• The Mercedes A-class the age of flying will have arrived, for
all other difficulties are of minor importance.
The Wright Brothers figured it out and flew the Kitty Hawk on
December 17 1903!
 The Feedback Amplifier The California Emission Standard
The feedback amplifier was invented by Harold Black in 1927. Wiliam E. Powers VP of Ford at the 1999 World Congress of
The patent procedure took 9 years because engineers did not IFAC:
believe that it would work. Black got a major IEEE medal in
1957, on this occasion it was said that: The automobiles of the 1990s are
at least 10 times cleaner
It is no exaggeration to say that and twice as fuel efficient
without Black’s invention (of the feedback amplifier), as the vehicles of the 1970s.
the present long-distance telephone and television networks These advancements were due in large part to
which cover our entire country distributed microprocessor-based control systems.
and the transoceanic telephone cables Furthermore the resultant vehicles are
would not exist. safer, more comfortable and more maneuverable.
Feedback plays a major role in the Internet and in cellular
communication.

The Mercedes A-class Consequences

• Education: Courses in automatic control spread like
wildfire and became an important part of the education
of all engineers
• Applications: The ideas were used in a wide range of
fields often with drastic consequences. Lots of technology
transfer.
• Industrialization: Formation of new companies
• Organizations:
– IFAC International Federation of Automatic Control
– ASME
– ACC American Control Council
A difficult situation rescued by control! • Information dissemination : conferences, journals, books
 Automation Levels Examples of Applications
• Control a given process, choose sensors actuators and • Generation of energy • Industrial processes
control strategy
• Transmission of energy • Discrete manufacturing
• Design process and controller concurrently • Mechatronics
• Communication
New freedom for the designer to solve design conflicts
• Transportation • Instrumentation
New functionality • Consumer electronics
Cars
The cardinal sin of control
Trains • Scientific instruments
Impact on research and education
Ships • Economy
• Control systems are becoming mission critical
Aircrafts • Biology
Space vehicles, Flight control systems Space-crafts • Medicine
CD players, optical memories
Automotive

Summary 3. Feedback
• A well developed discipline with strong concepts, rich • What is feedback
theory and effective design methods • Open and closed loop systems
• Methodology for control system design • Properties of feedback
– Modeling • Simple forms of feedback
– Analysis and simulation
– Design
– Implementation
– Commissioning and operation
• Control systems are ubiquitous
• Control systems are increasingly mission critical
• Use of feedback has often been revolutionary
 What is Feedback? Typical Feedback System
Problem: How to keep the process output close to the desired y sp e u y
reference variable in spite of disturbances? Σ Controller Process

Solution: Change the control variable depending on the

process output. This makes the process input dependent on
its output, i.e. a closed feedback loop. −1
Example:
Increase the control variable when the process Notice negative feedback.
variable is smaller than its desired value and decrease Positive feedback: Population explosion.
the manipulated variable when the process variable is
larger than its desired value. (negative feedback)

Properties of Feedback The Feedback Amplifier: Black 1934

+ Reduce effects of process disturbances However, by building an amplifier whose gain is deliberately
+ Makes system insensitive to process variations made, say 40 decibels higher than necessary and then feeding
the output back on the input in such a way as to throw away
+ Stabilize an unstable system the excess gain, it had been found possible to effect extraor-
+ Create well defined relations between output and refer- dinary improvement in constancy of amplification and freedom
ence from non-linearity.
- Risk for instability Stabilized feedback processes other advantages including
reduced delay and delay distortion, reduced noise disturbance
from the power supply circuits and various other features best
appreciated by practical designers of amplifiers.
Gain is the “hard-currency” that can be traded for many other
qualities! The operational amplifier.
 The Feedback Amplifier Simple Forms of Feedback
R2 • On-off control: A thermostat
• Proportional Control (P): u = ke
R1
• Proportional and integral control (PI)
−
V + t de
• PID control: u = ke + k i 0 e(τ )dτ + k d
V1 dt
V2

Let the raw gain of the amplifier be A, i.e. V 2 = − AV , then

V2 R2 1 dG R1 dA
G= =− ,
V1 R1 1 R2  G AR2 A
1+ 1+
A R1

Notice that the gain is determined by the passive components!

Example A = 105 , R2 / R1 = 100.

On-off and Proportional Control The Amazing Property of Integral Action

A u B u C u Consider a PI controller
 t
u = ke + ki e(τ ) dτ
e e e 0

Assume that there is an equilibrium with constant e(t) − e 0 and

On-off constant u(t) = u 0 . Then we must have e0 = 0.
control:

umax , if e > 0
u=
umin , if e < 0 Can you explain this?

Proportional control
u = u b + ke The Audience is Thinking ...
 The Amazing Property of Integral Action ... Derivative Action
Consider a PI controller Replace the error in proportional control with the predicted
 t error
u = ke + ki e(τ ) dτ
de( t)
0
e p( t) = e( t) + Td
dt
Assume that there is an equilibrium with constant e(t) − e 0 and
constant u(t) = u 0 . Then we must have e0 = 0. Prediction by linear extrapolation!

Assume e0 = 0, then
1.5
 t  t
u = ke0 + ki e(τ ) dτ = ke0 + ki e0 dτ = ke0 + ki e0 t 1
0 0
0.5
The right hand side is different from zero. Hence a contradic- 0
tion unless e0 = 0. 0 1 2 3

This fact was rediscovered and patented many times in differ- More sophisticated controllers predicts using mathematical
ent applications! model of the process.

4. Summary
• What is control?
• Why is it useful for a Mechanical Engineer?
• The idea of Block Diagram
• Feedback and feedforward
• The PID Controller (past, present and future)
• A cruise control system

Next Time
Cruise Control - Our first Control Design