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Fall 2024
EMCH792 – Optimal State Estimation
Homework 2
Homework Instructions
In this homework, you must analyze linear systems using state-space models. All the files that you will need for this homework are in the ws folder. You are expected to work inside this folder only. Open MATLAB and set the current folder to ws, and do the following:
1. Start by opening the live script file “HW_2_manual.mlx” using MATLAB. This will guide you through basic MATLAB functions to analyze linear systems. Read through the file and understand how each function is implemented in MATLAB.
2. Open the file “HW_2.m” and follow the instructions below and, in the file, to solve all the questions of the problem.
Problem – The coordinated turn model
Consider an object moving in a 2D plane with constant speed and angular rate Ω where Ω>0 is counterclockwise motion and Ω<0 is clockwise motion. The system is described by the equations:
The state and input of the system are:
We can measure 
, 
.
For the described system do:
1. For Ω = 0.5 define the continuous time system.
2. Check the system’s controllability and observability.
3. Simulate the continuous time system in Simulink.
4. Find the discrete time system for a sampling time of T = 0.1sec.
5. Simulate the discrete time system in Simulink.
6. Simulate the discrete time system in MATLAB for 200 simulation steps.
BONUS: Find the discrete time system dynamics for any Ω, T. You can use MATLAB and symbolics.
Homework Submission
Your submission must include the following files:
“HW_2.m” -> The edited MATLAB script with your solutions
“Continuous_sim.slx” -> The Simulink file for the continuous time system
“Discrete_sim.slx” -> The Simulink file for the discrete time system
Upload all files on Blackboard in a single submission.
Make sure that the scripts you submit can run. Don’t copy the results that appear in the command window in your scripts and make sure that if you add any comments in your scripts that they follow the proper MATLAB syntax. Scripts that do not run will not be graded.
Grading Rubric
Problem Points
1 15
2 15
3 20
4 10
5 20
6 20
BONUS 15