A commercial bank is a financial institution which provides various banking services and products to the general public, both individual consumers and small to medium sized businesses. Issuing bank cards is one of the popular services provided by the commercial banks to the consumers. On this topic, you are required choose any one of the commercial banks existing in the Sultanate of Oman and complete the following tasks:

I. Give an introduction about the chosen commercial bank existing in the Sultanate of Oman and the various services and products offered by them to the customers. (Approximately 100 words)

II. Discuss any 4 different debit cards and credit cards offered to the customers by the chosen commercial

bank. (Approximately 600 words)

III. Based on the above understanding, you are required to discuss the steps to be followed when the debit card or credit card is stolen or lost. (Approximately 200 words)

IV. Discuss the precautionary measures to be followed by the customers to keep their debit card or credit card transactions safe. (Approximately 200 words)

V. Conclusion: Understanding the importance of debit card and credit cards, which one play a major role on

saving the money?

Competency

Analyze opportunities for quality improvement and program goals in early childhood programs.

Student Success Criteria

View the grading rubric for this deliverable by selecting the “This item is graded with a rubric” link, which is located in the Details & Information pane.

Scenario

You are a director or owner of an early childhood education program. You understand the importance of following your state’s rules and regulations. Your goal is not to have any violations from annual visits. In addition, you are planning to participate in your state’s quality rating and improvement system. You value the importance of continuous quality improvement, and you are exploring the option of accreditation for your program. You will be conducting research on these opportunities and plan to share this with your parents/guardians at a Lunch and Learn to gain their support as your first step.

Instructions

For this deliverable you will complete two components: Part 1: You will conduct research on your state’s operational rules and regulations. Part 2: You will create a detailed outline with the information you would share at the parent/guardian Lunch and Learn.

Part 1: Research

Conduct research on your state’s operational rules and regulations, the state’s quality rating and improvement system (QRIS), and the accrediting body appropriate for your program. Learn more about the state regulations by visiting the website Child Care Aware. Review the content specific details to know what areas to research and include in your presentation.

Part 2: Presentation Outline

Using the guide below, write an outline of a Lunch and Learn presentation you will give to parents sharing information from your research and your rationale for participation in the regulations and quality improvement.Use this format for your outline.

Topic 1: Describe your state’s system for rules and regulations.

• Provide the name of the organization/agency regulating childcare.
• Explain the process for oversight.
• Explain why rules and regulations are necessary.
• Include an overview of three regulations you believe are the most critical for quality childcare and explain why they are important to quality.
• Include one regulation from each of the following categories:
• staff-child ratios
• educational/training requirements for staff
• medical information required for children
• Inform families about your system for how these regulations will be followed. What will you do to ensure that your program will meet or will continue to meet these requirements on an on-going basis? Why does this matter?

Topic 2: Describe your state’s quality rating and improvement system (QRIS).

• Include the name of the system.
• Explain how the system helps support quality improvement for childcare in your state
• Explain why the rating system (QRIS) is important for their children.
• Describe the steps for your program to participate in the quality rating and improvement system. What will you need to do first, second, and third? How will parents be able to be involved?

Topic 3: Describe the option you would like to pursue regarding accreditation.

• Include the name of the accrediting body.
• Describe the standards or what they look for in a quality program.
• Explain how long it may take to be accredited and how much it will cost to participate.
• Set two goals your program will need to complete before starting the accreditation process. Indicate what, when, and how these goals can be achieved.

Topic 4: Identify two barriers to overcome when establishing systems for achieving these goals.

• Detail each barrier along with at least two possible solutions to overcome each barrier.

You were supposed to read: Haggai: chaps. 1-2, Obadiah: chap.1

1- List the texts you read!

2- Give a short summary of three of them.

3- chose one chapter of your readings and begin a close reading (the close reading can be completed next time)

4- In you close reading, extend the message in context and the message today using the historical context, the geographical context, the structure, themes…….anything you find in your study of the text should contribute to the extension of the message. The message should not be only summary of the text.

1. Historical context
2. Geographical context
3. Propose a structure with titles! (How many parts)

For example: three parts

Vs 1-2: Title

Vs 3-6: Title

Vs 7-10: Title

4. What are the main themes?

5. What is the theology of the Author? (What do we learn about God)?

6. What is the message in the historical context?

7. What could be the message today?

8. What section, paragraph, verse (s) or word (s) speak to you?

9. What section, paragraph, verse (s) or word (s) do you think can speak to our contemporary society?

10. What can be an obstacle to this message today?

BibleGateway.com: A searchable online Bible in over 150 versions and 50 languages.

There is the website to find the book

For this assessment, you will review 3 passages from 3 different genres of writing you might encounter in your daily life. The title of each passage has been removed. You’ll be asked to make informed responses about the following aspects of rhetorical situation for each of the passages:

• Writer’s purpose

• Passage’s audience

• Genre of the writing

• Passage’s context

• Organization and structure of the passage

While there are no absolute right or wrong answers, your goal is to make informed responses about the rhetorical situation for each passage. Informed responses will include specific characteristics and examples from the passage that support your conclusions about the aspects of the rhetorical situation.

ReviewTools for Investigating Rhetorical Situations.Because many details from the passages have been removed, this resource will help you spot clues to make better guesses.

Review the “Example: Written Passage and Rhetorical Situation Response” section of this document toguide for your own responses.

In the “Written Passagesand Rhetorical Situation Responses” section of this document, read Passages 1, 2, and 3.

For each passage, complete the Rhetorical Situation Informed Response Table by writinganinformed response about the rhetorical situation and notingspecific passage examples to support your informed response. Do this by responding to the following aspects of rhetorical situation in the Aspects column:

• The writer’spurpose

• The audience

• The genre

• The context

• The organization and structure

Example: Written Passage and Rhetorical Situation Response

Example Passage

I’m writing to you because I am concerned about Elliot.He comes home exhausted and doesn’t remember what he learned in class that day. Since he can’t recall the content, he struggles greatly with the homework and I am unable to help him. The fourth graders at Riverdale Elementary school do not have enough time to eat lunch. The lunch period should be extended to protect students’ physical health and academic performance. You must allow students time to rest, recharge, and relax to enhance their focus in class. You have the power to change this policy and improve the health of students and faculty alike.

Example Completed Rhetorical Situation Informed Response Table

Written Passages and Rhetorical Situation Responses

Passage 1

Fans of the critically acclaimed series, The Haunting of Hill House, a show that tracks the lives of a fractured and tormented family and the estate that forever became a fixture in their lives, were undoubtedly thrilled to hear that showrunner Mike Flanagan would put his talents to work on a similar series (though not a sequel), The Haunting of Bly Manor, an adaption of the infamous Henry James novella, The Turn of the Screw.

The Haunting of Bly Manor takes the viewer far from Hill House and across the pond to England, where a young woman, Dani Clayton (played by Victoria Pedretti) takes an assignment as a nanny to the two orphaned children who live on the estate, Miles and Flora (played by Benjamin Evan Ainsworth and Alice Come, respectively). Upon arrival, Dani meets housekeeper Hannah Grosse (played by T’Nia Miller), estate chef Owen Sharma (played by Rahul Kohli), and the gardener, Jamie (played by Amelia Eve). For as strikingly beautiful as Bly Manor is, it is quickly apparent that all is not well. The housekeeper never seems to eat, and the children often behave as if they are staring off into the distance, with their attention on things that are unseen. Soon after arriving, Dani is sure that she has seen a strange man on the property, someone who is quickly revealed to be that of Peter Quint (played by Oliver Jackson-Cohen), a disgraced employee of the property owner, and uncle to the children, Henry Thomas (played by Henry Wingrave). To complicate this, Dani learns that the former nanny, Rebecca Jessel (played by Tahirah Sharif) met an untimely end while stationed at Bly.What unravels, episode by episode, makes each of these characters face the truths of their own pasts and identities, as well as an Evil that has been lurking at Bly for over a century.(N. Coley, personal communication, Winter 2020/2021)

Passage 1: Rhetorical Situation Informed Response Table

Passage 2

Attention: You are invited to “Women of Purpose, Women of Excellence”

During this panel discussion, we will learn about the efforts undertaken by these inspiring female leaders in the fields of government, tech, consulting, education, and research. They will share insight into their leadership journey, and how they actively open doors, support, and empower women of color within their organizations and networks to create a lasting legacy.

Moderators:

• Dr. Renee Green, Director of Academics, University of Phoenix – Hawaii Campus

• Dr. Roy Whitmore, Chair, College of Business and IT, University of Phoenix

Please help spread the word to your network and communities. #WeRise#TogetherWeSoar(M. Aviles, personal communication, January 27, 2021)

Passage 2: Rhetorical Situation Informed Response Table

Passage 3

During the past few years, I have focused heavily on preparing myself to become an elementary school teacher. While achieving my Bachelor of Science degree in Education/Elementary Teacher Education, I gained a great understanding of the diversity of student needs, as well as best practices for managing classroom conflict, motivating students, and using technology to enhance learning. I was able to put the knowledge I gained into practice as a student teacher and substitute teacher.

Additionally, working with kindergarten to fifth-grade students has allowed me to strengthen my understanding of the developmental levels of students, giving me the ability to optimize the learning environment for each classroom. Every student is capable of learning if they are given a learning environment that fits their needs. I am confident that I can provide that for your first-grade students.(University of Phoenix Career Services, personal communication, 2021)

Passage 3: Rhetorical Situation Informed Response Table

There are numerous state and federal employment and worker protection laws that govern the employment relationship and are essential for all organizations to understand and follow. This project will give you the opportunity to study the law, research recent cases to understand the application of the law, write a paper, and make a professional Power Point presentation on the basics of the law and the key things employers need to know and do to be legally compliant. The following list includes the statutes that you can use for the term paper:

Title VII of the Civil Rights Act of 1964

– Race Discrimination

-Gender Discrimination

-National Origin Discrimination

-Color Discrimination

-Pregnancy Discrimination

-Sexual Harassment

-Religious Discrimination

-Retaliation

-The Americans with Disabilities Act (Disability Discrimination)

-The Age Discrimination in Employment Act (Age Discrimination)

-Equal Pay Act

-Fair Labor Standards Act

-Occupational Safety and Health Act

-National Labor Relations Act

-Workers Compensation

-Affirmative Action

Research one of the specific laws from the list above. Then write a detailed research paper on the topic, which must include the following information:

1. An introduction that includes the law you researched and the prohibited practices and scope of the coverage of the law (e.g., ADA, ADEA, Title VII).
2. Explain the law, including its protections.
3. What elements are necessary for a plaintiff to prove and what defenses may an employer assert?
4. The process for filing the claim.
5. The remedies available to the plaintiffs.
6. At least four relevant business cases and their outcomes (the cases should all focus on your topic (e.g., age, religion, disability, worker’s compensation).
7. Employer liability for actions of employees and/or customers.
8. Your opinion on the problem, the laws, and their enforcement.
9. Your thoughts and ideas on what a business should do to protect itself from violating the law.
10. Conclusion.

Once you received your case number, answer the following questions: (CASE STUDY #2)

1. What other subjective data would you obtain?
2. What other objective findings would you look for?
3. What diagnostic exams do you want to order?
4. Name 3 differential diagnoses based on this patient presenting symptoms?
5. Give rationales for your each differential diagnosis.
6. What teachings will you provide?

PLAY-THERAPY RECIPE CARD

For this discussion, you will apply your learning about play therapy to plan how it may be used in a school setting. Complete the following:

• Describe play therapy, the theoretical approaches, and basic skills.
• Construct a play-therapy recipe card that captures the key concepts: definition, goals, and basic skills.
• Review the Nondirective Play-Therapy Techniques video (linked in Resources). Identify the specific play-therapy techniques employed by the counselor. Describe in detail the purpose of nondirective techniques versus leading and pressured questions.

RESPONSE GUIDELINES

Read the posts of your peers and respond to at least one. Use the Capella University Library or other scholarly sources to recommend two play-therapy books or resources to include in his or her play-therapy tool kit.

LEARNING COMPONENTS

This activity will help you achieve the following learning components:

• Describe the use of play-therapy techniques.
• Explain how common therapeutic approaches may be used with diverse students of different developmental levels.
• Identify a variety of counseling activities that may be used with students at different grade levels.

DEMONSTRATING NON-DIRECTIVE PLAY THERAPY SKILL

This presentation will outline four scenarios that demonstrate five non-directive play therapy approaches.

• Structure the Session
• Tracking the Child / Non-direction
• Reflection of Feeling
• Therapeutic Limit Setting

Watch for the descriptions of best practice throughout the presentation.

STRUCTURE THE SESSION

After the therapist welcomes the child in the waiting room, and lets the child know this is where the parent or caregiver will be while they play, the two of them walk together into the play room, and the session begins.

Therapist says to the child: This is your special play time. You can do or say pretty much anything you want to. I will let you know if there is anything that is not okay.

The child looks around the room. The therapist watches as the child orients herself to the room and the possibility of what objects to engage in.

Summary: The technique in this scenario demonstrates the following:

• The technique is about setting the structure of the therapy session.
• The therapist does not direct the child to do anything in particular.

TRACKING THE CHILD / NON-DIRECTION

The therapist and child are in the play room and the child is occupied with a group of horses, child is reaching for a horse.

Therapist says: Oh, you are picking up the horse now.

The therapist and child are in the play room and the child is curious about puppets on a shelf and is walking toward the area.

Therapist says: I see you are curious about the puppets. You are walking over to see the puppets now.

Summary:The technique in this scenario demonstrates the following:

• The therapist verbally reports without judgment or shaming.
• Inferred in the verbalization by the therapist is non-reaction to what the child is doing.

REFLECTION OF FEELING

Child and therapist are in the play room. The child finds puppet and is excited.

Therapist says: Oh, you’re really pleased that you found that puppet. You look happy. You are smiling.

Child and therapist are in the play room. Child is struggling with getting pieces into puzzle.

Therapist says: Oh, it looks like you’re feeling frustrated because you want to get the puzzle pieces into the puzzle and they aren’t fitting.

Child and therapist are in the play room. Child is playing with a family of dolls (mom, dad, and baby). The parent dolls are arguing.

Therapist says: Boy, looks like the daddy is really mad – and it looks like the baby is really scared.

Summary:The technique in this scenario demonstrates the following:

• Therapist verbally reports without judgment or shaming what emotions or feelings are being exhibited in the play.
• Inferred in the verbalization by the therapist is non-direction to what the child is doing.

THERAPEUTIC LIMIT SETTING

Therapist and child are in the play room with a range of play materials. Child has handcuffs in hand and is approaching therapist, to handcuff the therapist.

Therapist says: That’s something we don’t do in the play room. I can’t let you handcuff me, but you can pretend to handcuff me.

The child becomes angry and continues to try to handcuff therapist.

Therapist says: I can tell you are angry at me. You are thinking about throwing the handcuffs at me. If you throw them at me, we will need to end the session early today.

The child puts down handcuffs.

Therapist says: You were really upset, and you decided to put the handcuffs down.

In another session (same therapist and child): Child is playing with sand; has a hand full of sand.

Therapist says: I can tell you really want to throw the sand. That’s one thing we don’t do here. If you throw the sand, I will have to put the sand tray away.

The child picks up toy to throw.

Therapist says: I can tell you are angry with me. If you throw the toy we will need to end the session.

The session ends.

Therapist says: ‘ll see you next week – you can play with the sand tray next week.

Summary:The technique in this scenario demonstrates the following:

• The therapist sets the limits for the therapy session. It is up to each therapist to set their own definite limits without wiggle room for the child. The limits should be consistent without hurting anyone in the session, no kicking, no throwing objects, no breaking of toys and materials. If there is a mistreatment of toys, they are put away.
• The therapist notices the child’s actions and reflects the feeling that is driving the behavior.
• Always end the session with: I’ll see you next week – you can play with (the item that was put away) next week.

Suppose you have a market for grapes which is currently in equilibrium. Thinking of the supply and demand graph for this market, what would have to happen to cause both the equilibrium quantity of grapes in this market to rise and the equilibrium price of grapes in this market to fall? Is this even something that could happen?

In your answer, please pay attention to and describe what would have to happen to the supply and demand. (You may of course elaborate with any hypothetical “real life” reasons for any changes in the graph too.)

2-Marie is planning her schedule for the weekend. One of her friends has invited her to a two-day camping trip to Catalina. Another friend has offered an invitation to binge watch the Lord of the Rings movie trilogy (extended edition) on Saturday. Her cousin has invited her to a weekend beer tasting festival. Lastly, her uncle has invited him to a weekend of Dungeons and Dragons.

a. Describe how Marie might approach this scenario and his decision-making process. Is there an economic concept (or concepts) which best describes Marie’s scenario?

b. Why does Marie even have to make a decision? What economic principle is causing this scenario?

Choose an organization/business such as (Walmart, Kroger, McDonalds, Home Depot, or any other business) and draft a written system (aka program) that sets forth activities and guidelines that the company should undertake to manage workers’ compensation claims and costs within the organization.

The majority of this plan will essentially be a “light and modified duty policy” (aka early return-to- work program) that sets forth practices and policies for the organization to:

1) return workers to their original pre-injury positions.

2) manage the process of light and modified duty within the work environment.

3) minimize loss for the organization.

4) contain and control other sources of workers’ comp costs. The completed product for this assignment should take the form of a company policy document rather than a research paper.

A brief summary of the organization’s business and operations should be included at the outset of the plan.

Problem 1
Consider the cart and pendulum system describing the evolution of the cart velocity, the
pendulum angle and the pendulum angular velocity (see details in
http://tsakalis.faculty.asu.edu/notes/models.pdf). The linearized equations around the unstable
equilibrium (angle 180deg, zero input, zero velocities) for the deviations of the state variables
from the linearization point, are:
(???? + ????)
????????
???????? = −???????????? + ????ℓ
????????
???????? + ????
????????
???????? = ????
????ℓ
2
????????
???????? = −???????????? + ????????ℓ???? + ????ℓ
????????
????????
The various constants are (all values in SI): friction coefficients ????????, ???????? = 0.1, pendulum mass ???? =
0.2, pendulum length ℓ = 0.2, cart total mass ???? = 0.4, gravitational constant ???? = 9.81.
The Force term is applied by the cart wheels driven by a DC motor with a model from the
applied voltage (say, -5:5Volts) to the force
???? = ???????? + ????
????????
???????? + ????????????????, ???????????????? = ????????, ???? =
????????
????
Where the back-emf is taken as proportional to the motor angular velocity, which is also
proportional to the cart velocity, while the motor current generates the torque that is converted
to force by the wheels of radius r. The constants are motor resistance ???? = 5, inductance ???? =
0.1, emf/torque-constant ???? = 0.3, and wheel radius ???? = 0.1.
We want to design a controller for this system to stabilize the inverted pendulum and be able to
follow commands for the cart speed. We want to use a sequential approach where we first
stabilize the angle with an “inner-loop controller”. Then form the inner closed loop and design
an “outer loop controller” for the cart velocity.
There are two difficulties associated with this problem. One is that the angle subsystem has a
RHP pole and a zero at the origin. Its stabilization requires a controller with a RHP pole. We can
solve this as a modified PID problem where instead of the integrator we use a RHP pole
determined iteratively.
The other difficulty is technical, namely, how to create the various systems and loops without
leaving stray pole-zero cancellations (possibly in the RHP) and without resorting to tedious hand
calculations. (One approach for this is to implement the model in Simulink and use the “linmod”
command, and the other -taken here- is to work with the state space model using the
“feedback” command.)
1. Form the state-space description of the system with one input (Voltage) and three
outputs, (velocity, angle, Voltage). It is convenient to keep the voltage as an output to
make it easy to simulate with Matlab commands. We want to implement the controller
in DT with a sampling rate 100Hz. For this system, it is more convenient to follow the wplane approach, find the ZOH equivalent of the plant now and convert to the w-plane
and do not have to do corrections during the subsequent iterations.
2. Extract the angle subsystem (e.g., P(2), if the angle is the 2nd output) and design an
“inner-loop” stabilizing controller ???????? =
????(????????????+1)
2
(????−????)(????????????+1)
, where “????” and the crossover
frequency are to be iterated to achieve a reasonable response (crossover should be
larger than the RHP poles, “????” should not be larger than the RHP pole). PM is to be
selected but large values are not very realistic (consider 40-50).
3. Form the inner loop system.
Hint: The Matlab command is
>> Pi=feedback(P*Ci,ss([1]),1,2);
The second argument is the feedback system, the third output is the index of the
P-inputs connected to the C-outputs (1, there is only one) and the fourth output is
the index of the P-outputs connected to the C-inputs (“2” for the angle being the
2
nd output). Pi is a new system that has the same number of inputs and outputs,
the input is angle set-point and the outputs are the outputs of P.
4. Design a DT PID controller for the velocity (1st output, so P(1) subsystem).
Prefilter considerations: For step inputs, the linear control input becomes very large and
the angle can overshoot a lot. In practice, that is a problem because the input is limited
by the voltage constraints and if the angle becomes too large, the inverted pendulum will
fall (because of acceleration constraints). Here, it may be beneficial to consider a
prefilter, e.g., a lowpass filter ???? =
1
(????????+1)
either first or second order roughly at the
bandwidth of the outer loop crossover. Design the controller for the filtered plant and
then include the filter in the controller. The objective is to keep the control input
amplitude and the angle excursions reasonable, without slowing down the loop too
much. For this size of cart-and-pendulum, we expect stabilization in a few seconds. Also,
keep in mind that the outer loop system has “negative gain”.
5. Form the outer loop system as in Part 3 and check the responses.
>> Po=feedback(Pi*Co,ss([1]),1,1);
The last argument “1” assumes that the first output is the cart velocity.
6. Since all the design was done in the w-plane, it is straightforward to discretize the
controllers (using Tustin) and form the feedback loops with the “feedback” command.
Provide the transfer functions of your controllers and plots of the relevant time and
frequency responses.
Problem 2
Consider the system
????(????) =
−0.4???? + 4
????
2 + 4???? + 4
1. Design a DT controller using the w-plane method for crossover 4 rad/s, PM = 45 degrees
and a sampling time of 10 Hz.
2. For an additive measurable disturbance at the plant output with transfer function
????(????) =
1
????+1
, design a DT feedforward controller H(z) to reduce the transient component
of the DT PID designed in Part 1. Use the “naïve” approach and comment on the benefit
of such a component for this case.
Problem 3
Consider the cart and pendulum system of Problem 1.
1. Design a DT state estimator (observer) for the system with outputs cart velocity and
pendulum angle. It is convenient here to use a LQ approach because of the multiple
outputs. Choose the estimator gain to achieve convergence faster than one second.
Hint: The state estimator has the form ????????+1 = ???????????? + ???????????? + ????(???????? − ????????) where
x,y are the estimated states and outputs and m is the measurements (the plant
y_k). The design equations are implemented in Matlab by the function “dlqr”
???? = ????????????????(????
′
, ????
′
,???? ∗ ????
2 + ???????? ∗ ???? ∗ ????
′
,????)′
The design parameters have been simplified to to depend only on a gain factor
mu (such that larger mu yield higher bandwidth) and the sample time T. The
performance is characterized by eigenvalues of the observer eig(A-L*C) and its
Sensitivity (error system)
???????? = [???? − ????????, ????, ????, −????]
2. Design a DT state feedback to stabilize the cart-and-pendulum system. You may add an
offset to the velocity measurement to enable convergence to a nonzero velocity but do
not worry about integral action control.
Hint: The LQR problem minimizes the cost of states (x’Qx) and control inputs
(u’Ru), for the system
????????+1 = ???????????? + ????????????
Its solution is the linear state feedback
???????? = −???????????? => ????????+1 = (???? − ????????)????????
It is implemented in Matlab by the function “dlqr”, with syntax
???? = ????????????????(????, ????, ????
′
∗ ????, ????????)
The design parameters are Q = C’C (penalizing the output) and ???? which is the
penalty on the control input and serves as an inverse-gain parameter. When ????
decreases the controller bandwidth increases. The controller performance is
characterized by the eigenvalues of A-BK and the Sensitivity of the input to
disturbances at the plant input
???????? = [???? − ????????, ????, ????, −????]
3. Combine the state feedback with the state estimator to obtain an output feedback
controller. Illustrate the time and frequency responses of the controller.
Hint: The “model-based” controller uses the state feedback with the states
replaced by their estimates. The combined controller is (D=0)
????????+1 = ???????????? + ???????????? + ????(???????? − ????????
) ; ???????? = −???????????? ; ???????? = ????????????
=> ????????+1 = ???????????? − ???????????????? − ???????????????? + ????(????????
) ; ???????? = −???????????? ;
Thus, for negative feedback, the controller state-space representation becomes
[???? − ???????? − ????????, ????,????, 0]
The controller has two inputs, the measured outputs of the system (m_k), and
one output, the control u_k. An external input (scaled reference) may be added
to the measurement m_k (i.e., the y_k of the plant). However, tracking of a
setpoint requires integral action which is not considered here.
Problem 4
Consider the cart and pendulum stabilized by the inner-outer PID controller of Problem 1. In the
context of refining the plant models in case of a change, we want to estimate the plant transfer
functions based on input-output data. The system is, of course, unstable and data cannot be
collected without a stabilizing controller.
Use the closed-loop system of Problem 1 with input reference velocity and outputs angle,
velocity, and voltage (control input). Apply a reference input (Random or Square Wave and
combinations) with maximum amplitude around 1. Add random noise to the outputs (angle,
velocity) at a level of 0.02 ~ 0.5 degrees.
N=10000;
t=(0:N-1)’*T;
rn=(rand(N,1)-.5); n1 =(rand(N,1)-.5)*0.02; n2 =(rand(N,1)-.5)*0.02;
r=sign(sin(6.28/10*t))/2+rn;
Y=lsim(Pdo,r); % Pdo created in Problem 1
plot(t,Y)
u=Y(:,3); y1=Y(:,1)+n1; y2=Y(:,2)+n2;
Design a batch parameter estimator to identify the transfer functions from the plant input “u” to
each output “yi” (angle, velocity). Look at the system equations to decide the order of the
estimated transfer functions. Try different filters for the input-output pairs and compare with
the known transfer functions. Could the estimates be used to redesign the controller?