14 September BE 2567
Summary
TLDRThis lecture transcript focuses on control systems, emphasizing the importance of understanding the standard controller's proportional, integral, and derivative gains. It discusses deriving transfer functions, especially in the presence of time delays, and how to handle disturbances. The lecture also covers the ideal transfer function values for a robust control system, the significance of KP and KD gains, and the application of the final value theorem. It introduces concepts like natural frequency, damping ratio, rise time, and overshoot, providing formulas for calculating these parameters. The instructor encourages practice with transfer functions and system response plots, aiming to prepare students for exams and real-world applications.
Takeaways
- 📊 The lecture introduces KP (proportional gain), KI (integral gain), and KD (derivative gain) in control systems.
- 🔧 Students are advised to derive transfer functions from the provided slides and practice the concepts.
- ⚙️ The focus is on transfer functions, specifically how output is related to input and disturbance in a system.
- 💡 Understanding KP alone might not be sufficient to make system corrections, so additional controllers like PD (Proportional-Derivative) are introduced.
- 📈 Students must apply concepts like the final value theorem and Laplace domain calculations for system analysis.
- ⏳ Time constants such as rise time, settling time, and natural frequency are crucial in determining system performance.
- 🎯 The goal is to minimize error by fine-tuning parameters like KP, KD, and settling time, especially for second-order systems.
- 🧮 Practical exercises involve calculating peak time, overshoot, and using formulas provided during exams to solve problems.
- ⚖️ Robustness against disturbances is highlighted as a key goal for control systems, aiming for an output-to-disturbance transfer function of zero.
- 📋 Students are expected to sketch response plots and compare their system's behavior to standard models to predict performance.
Q & A
What is the significance of Lecture 6 in the context of the script?
-Lecture 6 is significant as it discusses the Standard Controller, which is crucial for understanding the concepts of proportional gain (KP), integral gain, and derivative gain in control systems.
What is the definition of a transfer function as mentioned in the script?
-The transfer function is defined as the ratio of the output to the input of a system, which is a fundamental concept in control systems for analyzing the relationship between these variables.
Why is it important to practice deriving the transfer function?
-Practicing the derivation of the transfer function is important because it allows one to understand the dynamic behavior of a system and how it responds to different inputs, which is essential for control system design.
How does the presence of a time delay (TD) affect the system as discussed in the script?
-The presence of a time delay (TD) in a system complicates the control process. The script suggests that when deriving the transfer function, the time delay is considered as part of the system's output when there is no input, which affects the system's response to disturbances.
What does the script suggest about the ideal transfer function relating output to input in a perfectly designed control system?
-The script suggests that in an ideally designed control system, the transfer function relating output to input should be as close to one as possible, indicating a direct and efficient response from the system.
Why is it desirable for the transfer function relating output to disturbance to be zero?
-A transfer function relating output to disturbance that is zero indicates that the system is robust against disturbances, meaning that disturbances have minimal impact on the system's output, which is a key goal in control system design.
What is the role of KP in the context of the script?
-KP, or the proportional gain, plays a role in the control system by determining the system's response to the error between the set point and the actual output. The script suggests that sometimes KP alone might not be sufficient, and additional control elements like derivative gain (KD) might be needed.
What is the significance of the final value theorem mentioned in the script?
-The final value theorem is significant as it allows one to determine the steady-state error in a control system. The script emphasizes the importance of being able to apply this theorem to obtain the exact value of the system's response over time.
Why is it important to understand the natural frequency and damping ratio of a system?
-Understanding the natural frequency and damping ratio of a system is important because these parameters provide insights into the system's stability and responsiveness. The script suggests that these values can be derived from the characteristic equation of the closed-loop transfer function.
What is the significance of rise time, peak time, and setting time in the context of system response?
-Rise time, peak time, and setting time are significant parameters in the context of system response as they describe how quickly the system reacts to a change, the maximum overshoot it experiences, and the time it takes to settle to a steady state, respectively. These parameters are crucial for evaluating the performance of a control system.
How can one compute the rise time, peak time, and setting time from the system's transfer function?
-One can compute the rise time, peak time, and setting time from the system's transfer function by using the derived natural frequency and damping ratio. The script provides formulas for calculating these times, which involve using the values of omega_n (natural frequency) and zeta (damping ratio).
Outlines
🔍 Understanding Control Systems and Transfer Functions
This paragraph discusses the importance of understanding the concept of a standard controller in control systems. It introduces the proportional gain (KP), integral gain (Ki), and derivative gain (Kd). The main focus is on deriving the transfer function, which is the ratio of output to input. The paragraph also addresses how to deal with systems that have time delays (TD) by considering the output in relation to the input and disturbance. It emphasizes the need to practice deriving transfer functions and understanding how they relate to system behavior, especially in the presence of disturbances. The goal is to design a controller that minimizes the effect of disturbances on the system's output.
📚 Exploring P and PD Controllers in Control Systems
The second paragraph delves into the details of P (proportional) and PD (proportional-derivative) controllers. It mentions that while P controllers are simple, PD controllers are more complex and may be necessary for certain systems. The paragraph stresses the importance of understanding the error in the Laplace domain and applying the final value theorem to obtain exact values. It also encourages practice with transfer functions and understanding how to derive the output in response to a reference input. The key takeaway is the ability to analyze system behavior using transfer functions and to apply control theories to design effective controllers.
📈 Sketching System Responses and Understanding Time Constants
This paragraph instructs on how to sketch the system's step response and emphasizes the need to understand the closed-loop transfer function. It discusses the comparison of the system's transfer function to the standard form of a second-order system to determine natural frequency and damping ratio. The paragraph provides formulas for calculating the rise time and peak time, which are critical parameters in evaluating system performance. It also touches on the concept of setting time, which is the time it takes for the system's response to reach a certain percentage of its final value. The goal is to understand how these time constants relate to the system's stability and responsiveness.
📊 Calculating and Interpreting System Response Metrics
The fourth paragraph focuses on calculating and interpreting various system response metrics such as rise time, peak time, and setting time. It provides formulas for these metrics and explains how to use them to analyze system performance. The paragraph also discusses the significance of the damping ratio in determining the system's stability and how to compute the maximum overshoot. It emphasizes the importance of being able to use a calculator to compute these values and to understand their physical meaning in the context of system behavior.
📝 Applying Control System Concepts to Exam Problems
The final paragraph provides a summary of what to expect in a midterm exam regarding control systems. It mentions that students will need to derive transfer functions, obtain error responses, and design gain values for controllers. The paragraph also suggests that students may need to apply stability criteria to ensure the designed controllers are effective. The key message is to apply the concepts learned throughout the course to solve practical problems and to demonstrate a deep understanding of control system dynamics.
Mindmap
Keywords
💡Error
💡Transfer Function
💡Proportional Gain (KP)
💡Integral Gain (Ki)
💡Derivative Gain (Kd)
💡Laplacian
💡Disturbance
💡Feedback
💡Reference Value
💡Stability Criteria
💡Response Time
Highlights
Introduction to the concept of the Standard Controller, including proportional gain (KP), integral gain (KI), and derivative gain (KD).
Emphasis on practicing the derivation of the transfer function, which is crucial for understanding system dynamics.
Explanation of how to handle systems with time delays (TD) in the transfer function derivation.
The importance of considering the physical meaning of the transfer function, especially in relation to disturbances.
Discussion on the ideal transfer function values for a well-tuned control system, highlighting the preference for zero sensitivity to disturbances.
Guidance on determining the value of KP for a controller, questioning whether a KP less than 5 is sufficient.
Mention of the need to introduce different types of controllers, such as PD, in the mid-term exam.
Stress on understanding the error in the Laplace Domain and the application of the Final Value Theorem.
Advice on sketching the system's response plot based on the given transfer function.
Introduction of the concept of natural frequency and damping ratio in the context of second-order systems.
Instructions on how to compute the rise time and setting time using the formulas provided.
Explanation of the significance of the peak time and how to compute it using the damping ratio.
Discussion on the setting time and its practical implications for system stability and performance.
Highlight of the need to apply Routh stability criteria in problem-solving.
Emphasis on the importance of being able to derive the transfer function from given system parameters.
The necessity of obtaining the characteristic equation from the closed-loop transfer function for system analysis.
Advice on how to use a calculator effectively to compute various system response times and parameters.
Transcripts
Error The Error and We Also
introduce dist To The System so
you need to look at the Lecture
6 that we talk about the Standard
Controller If you understand The
Concept for the Standard
Controller It is
in
in
KP We introduce KP proportional
gain We introduce K integral gain
or derivative gain but what you
need to Practice what you need to
Practice is to derive the transfer
function to derive the transfer
function from this slide from this
slide So The System
KP
[เพลง]
output to the input If transfer
function is define by output div
by input you are Okay with it We
Practice many time but When The
System has TD how can we de with
it Good News is good News is
When We derive transfer function
That relate output to
input We Take TD
equ We Only The
Output with to
the
the
and output
The What about
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We
output
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TD physical Meaning Of relate
output to TD is When we don't
have input If We Have disturbance
To The
System when the refer Value is
equ Z input Z But We Have How
System
behave for
That
So We refer Z and We Only
consider by
Good New is We can take this equ
to zer but Bad New is al this
is
Zero We need to consider this
Thing as a feedback and T is the
new Reference you need to The
System
and
relationship a Quick question for
you a Quick question for you a
Quick question for you ideally for
the control ideally for the
control
if your Controller is good Control
System is Fin finely Tune transfer
function output divide by input
what is your preference what is
your prefer Value output divide by
input If The System is perfect
One How about transfer function
That relate output to disturbance
if your System is very Clean
robust against disturbance output
divide by disturbance What should
be the Value We
prefer zer Zero If The System is
good is robust Again dist B
although dist B B Small We don't
care Because transfer function
always be
Zero The go for the Controller
Designer some you need to Design
Value of KP sometimes KP is not
enough We need to include kd
But We ask you what should be
the Value of KP
That Less
5
2 KP is sufficient or not to
make refer by
zer KP not sufficient you need
introduce typ of Controller
in mid exam We Only have Control
P and We Only have PD
PD we don't have P We Have i So
If you gna Look into Detail of
This I Control you may
ignore but
PD P
Control P Control and
[เพลง]
PD
PD PD PD control
for
not for this Two Important
SL
E
Error E Error in the Lap Domain
E Error in the Lap
Domain If We Have diagram Of The
System Please Make You can der E
in the Lap Domain and please make
sure You can Apply Final Value
theorem to
obtain the Exact Value
by and
You can Practice from this slide
If you want to prepare for
exam We Have System transfer
function We Have System transfer
function your System transfer
function May be the Same or
different with This One but that
that In The Ex We Have Controller
that is PD PD The
you need Able The
Output
by
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by you Able
output
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equ
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you
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alce kpd
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crit to
sy
and Trans
resp this
slide is simple and Not relate
to I say not much relate to
the but I hope you can G the
point from
problem We gna Give you a
transfer function of System for
example GS equ to 1 div by 1 1
you know for
example If The System transfer
function If The System transfer
function is One dy by T
S I Mean this transfer function
If The System is this for your
Case it may be slightly different
it may be 1 per ms S + TS + K
Something like
that you need to
sketch this plot in the exam
GR you don't have L you don't
have L how can you sketch this
SP how can you sketch this SP
I
think This is the close Loop
transfer function
and If you compare to the
Standard form of Second Order
System we know what is
Jumping What is the Natural
frequency
[เพลง]
I don't want you to Remember The
Formula I Give you
[เพลง]
Formula So what you need to do
is what you need to do
[เพลง]
is I Give you the transfer
function of System you need to
derive the close Loop transfer
function you need to obtain
the the characteristic equation
from denominator of CL transfer
function you need to be Able To
achieve Natural frequency and
dumping ratio Natural frequency and
dumping ratio by compare that
characteristic equation to the
Standard form of Second Order
System After You Know Omega n
dumping OM D I will Give you the
Formula So That You can compute
the time Right Time Is Easy You
can Just Take One
Point by OM n that is time The
physical Meaning Of Time Is The
Time That The System Take to
increase The
resp from Zero No from 10 to 90%
right Time If you compute the
right Time by Calculator If you
get Two If you get for the right
Time it means That when you
sketch The resp it Take Time To
increase Two and you say that
This is right Time
Time Time
Time Formula For
Time
Ma and
โอ I'm Sorry That SL is not enough
but I think This is the Better
the
time big and
If the SM Time In The System Go
Fast to move from Zero To 100 or
from 10 to 90% We define 10 to
90 in of zer to 100 Because in
some System that is Over damp
some Over System Go very
slow If you need to Wait Until
100% it may be very very long
time By The Way If you define it
from
maxum If the Value By The Go
Value But the go to
1 maxum be
20 setting Time
def the time that
the the vibration in 2 per in 1%
or in
5% If you say setting Time 5% If
you say setting Time
5% Around here setting time 5%
but If you define setting Time 2%
Around here but If you say
setting 1% it may Around There
Until The
resp by the Error of that
percentage we cannot Say setting
Zero it may Take infin time
but 2% is the Popular one 2% is
the Popular
One The Formula that we gna Give
in the exam gna be
We We To keep this Formula in
the exam is equal to 1 x dy by
omeg n Which means if you can
compute oma n You can compute the
right Time 10% To 90% and you
need to take this information To
suet Your plot to your
plot time Time simple and We Give
this Formula to
you by Omega
B is a peck time but you need
to sketch this in your exam
Answer Maximum
overshoot Formula is not
[เพลง]
easy Maximum overshoot is equal to
E Power Min Sin Pi DIY by squ
RO 1 - Sin Square We Give this
Value To You I Mean We Give this
Formula to you but you need to
know How to use you need to know
what is damping
ratio how to use Calculator to
compute E Power Min Sin Pi divide
by this Practice How to use
Calculator and when you already
compute Peak Time What Is The
Meaning Of Peak
Time เ้ยแก๊งเสื้อ LINE และเสื้อ
นิสิตเสื้อนิสิตนี่ชื่ออะไรวะลืมคุณชื่อ
อะไรนะไม่ใชเสืิเสื้อ
ขาวเอาชื่อที่อาจารย์จำ
ได้คุณชื่ออะไรชื่อไหนอาจารยำเอาชื่อชื่อ
จริงอกล้องพบโอเคกล้องพบพ Time ในรูปนี้
อยู่ตรง
ไหนบอกมาเป็นตัวเลขเลยก็ได้คุณ
เก่งเก่งก
ดามใ
Where Is The
System 1 2 3
4 1 2 3 is
Number What Is The
Time
399
around compute This spe
Time if you don't have Man Lab
can you use a Simple Calculator
to get this
time in exam you need to compute
this PE
Time If you know oma D You Just
x dy by OM D and then you get
Time You Know that you know That
in my opinion the Fun Thing Is
You Know This Formula That G Give
you in the exam and you
have if You Have
Time You write a
Code You Find the Thing in the
and then you use Calculator and
then you compare The Value it
Should approximately Be the Same
setting
[เพลง]
Time
a is
Time ช่ a where isle
If You
Remember Men about setting Time
2 setting 5% setting
1 magn
is9 and After
Point deviation Less 2
this
indicate The setting time
2% in exam
room How Can You compute This
setting
2% มี
If you know dumping ratio If you
know Omega n 4 di by this you
get setting Time
2% If you need setting Time
5% div by this Lucky าร Give this
Formula for
you and then You Just need to
know That when you compute the
numerical Value Where G Be in the
Where Be in
the do you think This is S or
not That setting Time
5% numerical Value is Less than
2% Is It Make
Sense or make
S do you think you need shorter
Time or longer Time Until The
System Stop vibrate from 5% Error
to 2%
Error The smaller Error need
longer Time
The smaller
Error
โอสรุปเนาะ
สรุป conclusion
conclusion The First midterm exam
problem you need to derive the
transfer
function of อะไรนะเฮ้ยอะไรนะเฮ้ยเปิด
ข้อสอบอยู่ไง
[เพลง]
The Position
V
Second you
the
and CP
obtain
Error the third problem you Bring
The transfer function from the
first problem
again and
then you try to Design gain
KP So That you have the the
Design Range of Error Range of
Error
[ปรบมือ]
and problem 4 May need to Apply
The R stability
criteria So That
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