Control of Linear Systems

 This assignment should be written as an academic report, with all working shown and explanations given for each step taken. Marks will be awarded for correct understanding of the subject and mathematical calculations from each step, but not for the final answers, if it is not obvious how the answers are obtained. All sources of information should be correctly referenced.

1. This question relates to the system represented in the following block diagram, where 𝑁 is a number representing the last two digits of your student registration number.

2. Given a system having the following state-space model:

(a) Draw its simulation diagram, containing no vectors, matrices, or transfer functions other

(b) By reducing the simulation diagram to a transfer function using block diagram reduction techniques (i.e. not by using the rank tests), determine and explain any values of the gain a11 for which the system would be:

(i) unstable.

(ii) uncontrollable.

(iii) unobservable.

(c) Confirm the results of parts (b) (ii) and (iii) using rank tests.

3. A system has a transfer function

(a) Obtain a state-space model of the system

(b) There are several ways of showing that this system is unstable. Your task is to stabilise it

using state variable feedback (SVF) design, assuming that you can measure all the state variables. Here are some matters to consider when designing the SVF controller. Your responses to these will depend on your state space model and, even if you have generated the same model as a colleague, you still have an infinite number of choices for the closed- loop pole locations, for example, so different solutions are quite likely.

• Is it necessary to perform a controllability test? If so, do it, if not, why not?
• Is it necessary to perform a stabilisability test? If so, do it, if not, why not?
• Is it necessary to perform an observability test? If so, do it, if not, why not?
• Where are you going to place your closed-loop poles, and why

(c) Produce a simulation diagram of the closed-loop system determined in (b), containing no vectors, matrices, or transfer functions other than simple integrators and gain blocks, showing how your controller interfaces with the plant.

(d) Work out whether your controlled system will exhibit any steady-state error following a step input (I have in mind an analytical solution, but doing it by simulation is OK so long as you provide all relevant details). Describe (but do not design) how a tracking controller could be designed to overcome such behaviour.

4. 

A lateral beam guidance system has an inner loop as shown in Figure Q4, where the transfer function for the coordinated aircraft is

23

𝐺(𝑠) ---------- = 

𝑠 +N

and 𝑁 is a number representing the last two digits of your student registration number. Consider the PI controller

(a) Design a control system to meet both of the following specifications:

• Settling time (with a 2% criterion) to a unit step input of less than 1 
• second; Steady-state tracking error for a unit ramp input of less than 0.1.

(b) Verify the design by a Simulink simulation.

Note: Although you will probably consult colleagues, notes, books and staff during the execution of this assignment, the work you hand in MUST BE DONE BY YOURSELF. The University takes cheating very seriously and the appropriate investigation procedures will be invoked if necessary!

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Coursework Assessment Brief

 Assessment Task 

 

1. Introduction 

 

This assessment requires you to undertake practical database application development work 

to meet specified requirements and write a report that recommends improvements to the database and researches a topic relating to databases. 

 

This assessment will enable students to demonstrate in full or in part the learning outcomes identified in the unit descriptor. 

Page Break 

2. The Practical Development Work 

 

The practical development work is based on an online electronics shopping company where you work as a Database Analyst/Developer. The entity-relationship diagram and SQL script for creating and populating the database are provided on SOL.  

 

Part 1 - Retrieving Data using SQL 

 

You have been asked to write the following SQL queries for management information purposes. All students should complete questions a, b and c below and to achieve a higher grade, also complete question d. 

 

1. The company want to do a marketing campaign to new shoppers and all female shoppers. Retrieve the first name, surname, email address, gender, date joined, and the current age in years of shoppers who joined on or after 1st Jan 2020 and all female shoppers (irrespective of when they joined). Print date columns in the format DD-MM-YYYY and print ‘Not known’ for any NULL values.  Order results by gender and then by age (highest first). 

Refer to the SQLite Built-in Functions reference on SOL for how to calculate the age and format the dates. 

 

 

SELECT 

shopper_first_name, 

shopper_surname, 

shopper_email_address, 

IFNULL(gender,'Not Known') gender, 

strftime('%d-%m-%Y', date_joined) as date_joined, 

(strftime('%Y', 'now') - strftime('%Y', date_of_birth)) - (strftime('%m-%d', 'now') < strftime('%m-%d', date_of_birth)) as Age 

FROM 

shoppers 

WHERE 

gender = 'F' 

OR date_joined >= '2020-01-01' 

ORDER BY  

gender,Age DESC; 

 

 

 

 

 

 

2. The website requires a customer account history page which will accept the shopper id as a parameter entered by the user at run time. Write a query to retrieve the first name and surname for a specific shopper along with details of all the orders they’ve placed, displaying the order no, order date, product description, seller name, quantity ordered, price (with two decimal places and prefixed by a £ sign) and ordered product status. Print date columns in the format DD-MM-YYYY. Sort the results by order date showing the most recent order first. Test your query for shopper ids 10000 and 10019. 

 

 

select 

s.shopper_first_name, 

s.shopper_surname, 

so.order_id, 

STRFTIME('%d-%m-%Y', so.order_date) as order_date, 

p.product_description, 

s2.seller_name, 

op.quantity, 

Round(op.price,2) as price, 

so.order_status 

from 

shopper_orders so 

inner join shoppers s on 

s.shopper_id = so.shopper_id 

inner join ordered_products op ON 

op.order_id = so.order_id 

inner join products p on 

p.product_id = op.product_id 

inner join sellers s2 on 

op.seller_id = s2.seller_id 

where s.shopper_id = 10000 

 

 

 

 

 

Result Set  

 

 

 

 

 

3. The business relationship manager has asked you to write a summary report on the sellers and products that they have had sold since 1st June 2019. Display the seller account ref, seller name, product code, product description, number of orders, total quantity sold and total value of all sales (with two decimal places and prefixed by a £ sign) for each product they sell. You should also include products that a seller sells but has had no orders for and show any NULL values as 0. Sort results by seller name and then product description. 

 

select 

s2.seller_account_ref, 

 

s2.seller_name, 

 

p2.product_code, 

 

p2.product_description, 

 

Sum(IFNULL(op.quantity,0)) as quantity, 

 

Round(Sum(IFNULL(op.quantity,0)*IFNULL(op.price,0)),2) as Total_sales 

from 

products p2 

 

inner join product_sellers ps on p2.product_id = ps.product_id 

 

inner join sellers s2 on s2.seller_id = ps.seller_id  

 

LEFT join ordered_products op on op.product_id = ps.product_id and op.seller_id = ps.seller_id 

 

group by s2.seller_account_ref, 

s2.seller_name, 

p2.product_code, 

p2.product_description  

ORDER by s2.seller_account_ref,p2.product_description  

 

 

Result set 

 

 

 

 

 

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