2. 01/2
M E C H AT R O N I C S
What do these two have in common?
Tornado
Complicated dynamics!
Both are capable of transporting goods and people over long distances!
BUT
One is controlled, and the other is not.
Control is “the hidden technology that you meet every day” and heavily
relies on the “feedback”.
Boeing 777
3. 01/3
M E C H AT R O N I C S
A Control System
A control system consists of subsystems and processes (or plants) assembled for the
purpose of obtaining a desired output with desired performance, given a specified
input
4. 01/4
M E C H AT R O N I C S
The definition of mechatronics has evolved since the original definition by the
Yasakawa Electric Company. In trademark application documents, Yasakawa defined
mechatronics in this way:
“The word, mechatronics, is composed of “mecha” from mechanism and the “tronics”
from electronics. In other words, technologies and developed products will be
incorporating electronics more and more into mechanisms, intimately and organically,
and making it impossible to tell where one ends and the other begins.”
Mechatronics
5. 01/5
M E C H AT R O N I C S
Working Definition for us
Mechatronics is the synergistic integration of sensors,
actuators, signal conditioning, power electronics, decision
and control algorithms, and computer hardware and software
to manage complexity, uncertainty, and communication in
engineered systems.
Mechatronics is a methodology
used for the optimal design of
electromechanical products.
A mechatronic system is not just a
marriage of electrical and
mechanical systems and is more
than just a control system; it is a
complete integration of all of them.
Mechatronics is the
application of complex
decision making to the
operation of physical
systems.
6. 01/6
M E C H AT R O N I C S
Feedback = mutual interconnection of two (or more) systems
◦ System 1 affects system 2
◦ System 2 affects system 1
◦ Systems are mutually dependent
Feedback is common in natural and engineered systems
What is Feedback?
System 2
System 1
System 2
System 1
System 2
System 1
Closed
Loop
Open
Loop
The return to the input of a part of the output of a machine, system, or process (as for producing
changes in an electronic circuit that improve performance or in an automatic control device that
provide self-corrective action) [1920]
7. 01/7
M E C H AT R O N I C S
Closed-loop System
The common elements:
• Comparators
• Blocks representing individual component transfer functions, including:
◦ Reference sensor (or input sensor)
◦ Output sensor
◦ Plant (the component whose variables are to be controlled)
◦ Actuator
◦ Controller
◦ Input or reference signals
• Output signals
• Disturbance signal
• Feedback loops
8. 01/8
M E C H AT R O N I C S
Elements of a block diagram
9. 01/9
M E C H AT R O N I C S
Block Representation
X(s) = G1(s) G2(s) U(s)
X(s) = G(s) U(s)
10. 01/10
M E C H AT R O N I C S
Block Representation
G(s) = G1(s) + G2(s)
X(s) = [G1(s) + G2(s)] U(s)
11. 01/11
M E C H AT R O N I C S
Closed-loop System
Temperature control system
12. 01/12
M E C H AT R O N I C S
A modern Feedback Control System
13. 01/13
M E C H AT R O N I C S
Open-loop System
◦ Speed Control System
◦ No preview of output
velocity
◦ heavy rely on the
modelling with prediction
of all possible
disturbances
◦ Accuracy of components
14. 01/14
M E C H AT R O N I C S
Example1: Cruise Control
Goals:
◦ Stability: system maintains desired operating point (hold steady speed)
◦ Performance: system responds rapidly to changes (accelerate to 65 mph)
◦ Robustness: system tolerates disturbances in dynamics (mass, drag, etc)
In Feedback “Loop”
Sense
Vehicle Speed
Compute
Control “Law”
Actuate
Gas Pedal
Control = Sensing + Computation + Actuation
15. 01/15
M E C H AT R O N I C S
Cruise Control
Modern automobiles are equipped with a number of drive assistance functions
for safety and reduction in driver fatigue. Cruise control is such a function. It
was originally introduced as a function to maintain the speed of an automobile
at a reference value selected by the driver.
PV=Process Variable
16. 01/16
M E C H AT R O N I C S
Adaptive Cruise Control System
The fundamental Requirement
17. 01/17
M E C H AT R O N I C S
Adaptive Cruise Control System
The fundamental Requirement
18. 01/18
M E C H AT R O N I C S
Adaptive Cruise Control System
Cruise Control has evolved to adaptive cruise control (ACC) or intelligent cruise control,
which has an additional function of car following when the preceding vehicle is driven at
a speed lower than the reference speed.
ACC has become reality because of advances in sensor technologies and other
enabling technologies.
Research and development efforts are continuing in both the academic and industrial
sectors to further enhance the capability of ACC.
One importance enhancement is the car following capability at low speeds including
stop-and-go capability.
In case of heavy traffic, the driver has to keep driving over hours and cannot use the
cruise control function. With a stop-and-go capability, the driver`s fatigue can be
immensely reduced. Also, with a further advance, this function can be expended to be
used in a city driving.
19. 01/19
M E C H AT R O N I C S
Block diagram of equations
20. 01/20
M E C H AT R O N I C S
Example
Consider the following equations in which x1, x2,. . . , xn, are
variables, and a1, a2,. . . , an , are general coefficients or
mathematical operators.
1
1
2
2
1
1 ........
n
n
n x
a
x
a
x
a
x
21. 01/21
M E C H AT R O N I C S
Exercise
Draw the Block Diagrams of the following equations.
1
1
2
2
2
1
3
1
1
1
2
3
2
1
1
bx
dt
dx
dt
x
d
a
x
dt
x
b
dt
dx
a
x
)
(
)
(
2
2
d
dt
d
dt
b
1
x
2
x
3
x
dt
d
dt
1
x 2
x
1
b
1
a
1
a
1
a
3
22. 01/22
M E C H AT R O N I C S
+/-
Canonical Form of A Feedback Control System
(G)
( )
E R B
C E
B C H
E R CH
C
E
G
1
1
1
C
R CH
G
C H R
G
GH
C R
C G
R GH
G
23. 01/23
M E C H AT R O N I C S
Characteristic Equation
• The control ratio is the closed loop transfer function of the
system.
• The denominator of closed loop transfer function determines the
characteristic equation of the system.
• Which is usually determined as:
)
(
)
(
1
)
(
)
(
)
(
s
H
s
G
s
G
s
R
s
C
0
1
)
(
)
( s
H
s
G
24. 01/24
M E C H AT R O N I C S
Example
For the system represented by the following block diagram
determine
1. Open loop transfer function
2. Feed Forward Transfer function
3. control ratio
4. feedback ratio
5. error ratio
6. closed loop transfer function
7. characteristic equation
25. 01/25
M E C H AT R O N I C S
…. Continued
1. Open loop transfer function
2. Feed Forward Transfer function
3. control ratio
4. feedback ratio
5. error ratio
6. closed loop transfer function
7. characteristic equation
)
(
)
(
)
(
)
(
s
H
s
G
s
E
s
B
)
(
)
(
)
(
s
G
s
E
s
C
)
(
)
(
)
(
)
(
)
(
s
H
s
G
s
G
s
R
s
C
1
)
(
)
(
)
(
)
(
)
(
)
(
s
H
s
G
s
H
s
G
s
R
s
B
1
)
(
)
(
)
(
)
(
s
H
s
G
s
R
s
E
1
1
)
(
)
(
)
(
)
(
)
(
s
H
s
G
s
G
s
R
s
C
1
0
1
)
(
)
( s
H
s
G
)
(s
G
)
(s
H
26. 01/26
M E C H AT R O N I C S
Block Reduction Example
38. 01/38
M E C H AT R O N I C S
Transient Response
It is an important aspect of the design
◦ Slow Response tests patience.
◦ Excessively fast response creates comfort issues.
◦ Oscillations.
◦ Impact on structure.
…. to establish quantitative definitions for transient response. We then
analyze the system for its existing transient response. Finally, we adjust
parameters or design components to yield a desired transient response
—our first analysis and design objective.
39. 01/39
M E C H AT R O N I C S
Steady State Response
Another analysis and design goal focuses on the steady-state response.
Steady state response is simply the part of the total response that remains after the
transient has died out.
As we have seen, this response resembles the input and is usually what remains after
the transients have decayed to zero.
For example, this response may be an elevator stopped near the fourth floor or the
head of a disk drive finally stopped at the correct track.
We are concerned about the accuracy of the steady-state response. Hence talks about
steady state error.
Example: An elevator, Hard disk, An antenna tracking a satellite.
…….. to define steady-state errors quantitatively, analyze a system’s steady-state error,
and then design corrective action to reduce the steady-state error - our second analysis
and design objective.
40. 01/40
M E C H AT R O N I C S
Stability
Total response of a system is the sum of the natural response and the forced response.
◦ Natural response describes the way the system dissipates or acquires energy. The
form or nature of this response is dependent only on the system, not the input.
◦ The form or nature of the forced response is dependent on the input.
For a control system to be useful (stable), the natural response must:
◦ Eventually approach zero, thus leaving only the forced response, or oscillate.
In some systems, however, the natural response grows without bound rather than
diminish to zero or oscillate. Eventually, the natural response is so much greater than
the forced response that the system is no longer controlled. This condition, called
instability, could lead to self-destruction of the physical device if limit stops are not part
of the design.
A time plot of an unstable system would show a transient response that grows without
bound and without any evidence of a steady-state response.
…. if the system is stable, the proper transient response and steady-state error
characteristics can be designed. Stability is our third analysis and design objective.
41. 01/41
M E C H AT R O N I C S
Other Considerations
Hardware selection: choice available, performance limitations, weight….
Financial considerations.
Another consideration is robust design.
◦ System parameters considered constant during the design for transient
response, steady-state errors, and stability change over time when the
actual system is built. Thus, the performance of the system also changes
over time and will not be consistent with your design.
The relationship between parameter changes and their effect on performance is not
linear. In some cases, even in the same system, changes in parameter values can lead
to small or large changes in performance, depending on the system’s nominal
operating point and the type of design used.
….. the designers strive to create a robust design so that the system will not be
sensitive to parameter changes.
42. 01/42
M E C H AT R O N I C S
Linear Time Invariant (LTI) Systems
Linear time-invariant (LTI) systems are both linear and time-invariant.
SUPPOSE:
◦ x1(t) and x2(t) are any two signals.
◦ Output of a system to x1(t) is y1(t)
◦ output of the system to x2(t) is y2(t)
◦ If this always implies following then, system is linear and superposition principle is
said to hold.
SUPPOSE:
◦ Output of a system to x(t) is y(t)
◦ If for any given τ following is always implied then, system is said to be time-invariant.
SYSTEM
SYSTEM
43. 01/43
M E C H AT R O N I C S
Washing machine system
44. 01/44
M E C H AT R O N I C S
Assignment # 01
Question No 3: Find the total system response C due to inputs R,U1 and U2 in the
figure given below.
Question No 1: Explain the differences between open-loop and closed-loop
control system with examples.
Question No 2: Summarize the design objectives of any control system?
