Exploring Engineering
Chapter 10
Control Systems and
Mechatronics
Topics to be Covered
 Block
Diagrams
 Transfer
 Control
functions
systems
 Steady
State
 Transient models
 Mechatronics
Block diagrams
 Mathematically
mimic a small piece of a
physical process
a stereo amplifier … see:
www.engr.uky.edu/.../index_files/image003.jpg
 E.g.,
Block diagrams

Notice the blocks show the connectivity and
gross function.



They do not show the actual wires, printed circuits
etc that make a stereo receiver.
The blocks can be broken down much further in
increasing detail of what is in a block
To be really useful, the blocks can be given a
simple mathematical description that
emulates just what they do
Transfer (Response) Function
 Relates
what signal goes in (e.g., volts.
pressure, light source) to what goes out
(e.g., amperes, mechanism movements,
volts etc.)
 Simplest
Input = 1
(volts, amps,
temperature,
etc.
transfer function:
Transfer function:
Output = Gain x input
Gain = 5
Simple gain transfer block
Output = 5
(volts, amps,
temperature,
etc.
Transfer (Response) Function

Cruise control – a string of blocks
representing the physical functions
Transfer (Response) Function
 If
the transfer functions to first power
(a.k.a. “linear”) you can multiply them
together
Open and closed loop control
 For
your first cruise control, just put a
brick on the accelerator and sit back …
Desired
Speed, So
Actual
Speed, S
Brick
controller
Fuel & air
Engine
system
Surroundings
Power
• If surroundings are head wind vs. tailwind, hills vs. flat,
etc., will actual speed equal desired speed?
Open and closed loop control
 Open
loop controls do not work well
 Closed loop or feedback control is near
universal
 Feedback

is made possible by a “comparator”
The desired controlled variable is called the “set
point”
Desired
Speed, So
+
Difference
or error signal
S0 -S
Actual
Speed, S
Feedback control
Comparator
Surroundings
Mathematics of Feedback Control

Collapse all the blocks; the gain Gp is the
product of all the linear gains of the blocks

The control is proportional is the output is a simple
multiple of the input.
S0 - S
S0
+
-
Proportional
Controller; gain Gp
S Act  G p S 0  S Act 
SAct
S Act  G p S 0  S Act 
Mathematics of Control Blocks
S Act 
G p S0
1  G 
so that the steady state error is
p
S 0 - S Act 
S0
100
& the % error 
1  G p 
1  G p 
• Ops! Steady state error
Gp
% error
• The moral is to watch your gains!
1
50
• So is an infinite gain the solution?
10
9.1
100
0.99
Transient Behavior

If you have a steady state feedback loop
given by one or more transfer functions, that
solution is a snapshot in time



If you change the set point to another value, that
gives another snapshot of the state of the system
What happens during the transient interval
between steady states?
Can your model accommodate transients?
Transient Behavior

Your model needs transient behavior built in
– which so far the proportional controller
does not have

At a minimum for a cruise control you need
a)
b)
c)
The inertia of the car (it will not accelerate
instantaneously)
The wind resistance that varies as S3 and keeps the
car from speeding to  speed
Perhaps an allowance for hills?
Transient Behavior
 Excluding
hills,a simple model would
include at least these blocks
Transient Behavior
 Without
doing the arithmetic, results of
this model are as shown: a) low gain, b)
medium gain and c) high gain
Transient Behavior

c)
Notice the sensitivity to the overall gain:
Too low and the transient is sluggish
Medium and it has some overshoot but
settles down
Oscillatory behavior

Moral is watch your gains!
a)
b)

High and low gains have their drawbacks!
Mechatronics

Mechatronics is a
synthesis of
mechanics,
electronics, control
engineering and
computers
 http://gizmodo.com/
5342497/self+balan
cing-enicycle-islike-a-segway-forthe-circus
Mechatronics

Instead of first
doing a mechanical
design, followed by
an electronic
design, followed by
a control systems
design they are all
done coequally
 Stepper motors are
often mechatronic
components
Windings and poles
1
3
2
Rotor
3
2
1
Principle
of a stepper
motor
Figure
12: Principle
of a stepper
motor
Mechatronics
 Can
use a variant on a stepper motor
to replace two separate systems, a
throttle and cruise control on a car
here’s how its done:
 http://video_demos.colostate.edu/mechatr
onics/index.html

Go to: stepper motor PIC-based position and
speed controller
Mechatronics
 Such
technology will become common
place on cars as part of “fly-by-wire”
methodology (used on most new
passenger aircraft)
Summary

Control depends on some simple abstractions:

Block diagrams that simulate an element in the control linkages
(whether mechanical or otherwise)


Simple mathematical representation of the block’s
function

A comparator to generate an error signal

Feedback to correct the instantaneous value of the
controlled variable

High proportional gain to reduce steady state error and
low gain to reduce unsteady transient behavior.
Mechatronics is an integrated method of design
including mechanical, electronic and control elements.