CS计算机代考程序代写 matlab EE6620 Assignment 1 (Sem A 2021/22)

EE6620 Assignment 1 (Sem A 2021/22)

Submission Instructions

1. Answer all questions.
2. Except for programs, answers must be hand-written. For program, give your program list

and copy the outputs of your program

3. Generate a pdf file for your answers and submit via Assignment in CANVAS. Deadline
for submission: 11:59pm 18-Sept-2021

4. You should make sure that the pdf file is clear enough for marking.
5. Late submission penalty: 25% deduction per day (Note: Late less than 24 hours is counted

as one day)

Q1. Consider a mapping function of input 𝑢(𝑡) and output 𝑦(𝑡) as below

𝑦(𝑡) = max⁡(𝑢(𝑡), 𝑢(𝑡 − 1), 𝑢(𝑡 − 2))

Here, 𝑚𝑎𝑥(⋅) returns the largest value of its arguments.

Determine whether the mapping function is

(a) additive

(b) homogeneous

and prove your answers. [15 marks for each]

Q2. Consider the following circuit

Figure Q2. RLC system

(a) Derive the relationship of 𝑣𝐶2(𝑡) and 𝑖(𝑡) and give your answer as an ordinary differential
equation. [30 marks]

(b) Based on (a) and assuming that all the initial values are zero, determine the values of 𝑅, 𝐶1, 𝐶2
and 𝐿 such that the transfer function of the RLC system is

)54)(1()(

)(
2

2
2



sss

s

sI

sVC
[10 marks]

Q3. Consider a nonlinear system

�̇�1(𝑡) = 𝑥1(𝑡)𝑥2(𝑡) + 2𝑥1(𝑡)

�̇�2(𝑡) = 𝑥1(𝑡) − 𝑥2(𝑡) − 1

(a) Find all the equilibrium points of the nonlinear system. [10 marks]

(b) Design a MATLAB program for the system. Set the initial conditions 𝑥(0) close to the

equilibrium points (but not equal) and, plot 𝑥1(𝑡) against 𝑡 for each case. Show the results and
describe your observation. [20 marks]

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