Control Theory 1, Assignment 2 Please complete the assignment covering the Control and Systems introduction topics until 19th of December 2022 at 24:00 and email your Matlab and word files saved with your name and surname to Research Assistant mer Can Tolun, octolun@atu.edu.tr. Each question has 4 points. It is important to note that as this is an individual study, any kind of noticed external help, copying or cheating will result in disciplinary action against you. The overall length of the report cannot be more than 6 pages ( 3 pages on both sides). Reports prepared without following the provided guideline will not be assessed. Best Luck with Your Work. Main Question Body: Blood values A and B indicate crucial symptoms about the health problems. Blood value A remains at a constant value of 100 until age of 18 and after this age 5% of this value is lost every year. However, air pollution, malnutrition and stress by themselves cause reduction of 7% percent independently from the age every year. Blood value B itself increases from 0.01 to 10 in 40 years and remains there unless it is affected by the blood value A. Question 1: a)1) Model the blood value A, 2)Derive its analytical solution, 3)Simulate and analyse. b)1) Model the blood value B, 2)Derive its analytical solution, 3)Simulate and analyse. c)When blood value B is affected by blood value A, and only blood value B is controlled 1)Draw the closed loop block diagram, 2)Reduce the block diagram, 3)Simulate and analyse impulse response when the controller is unity. Question 2: a)1) Derive closed loop system with the P controller for blood value A, 2) Choose a stabilizing P controller, 3) Simulate and analyse, b)1) Derive closed loop system with the PD controller for blood value A, 2) Choose a stabilizing PD controller, 3) Simulate and analyse, c)1) Derive closed loop system with the PI controller for blood value A, 2) Choose a stabilizing PI controller, 3) Simulate and analyse, Question 3: Performance-based controllers will be designed for the blood value A. The overshoot less then 10%, settling time less than 45 seconds, peak time less than 15 seconds, rise time less than 10 seconds are desired for the blood value A. a)1) Derive target system for the PD controller, 2) Design a performance-based PD controller, 3) Simulate and analyse, b)1) Derive a target system for the PI controller, 2) Design a performance-based PI controller, 3) Simulate and analyse, c)1) Derive a target system for the PID controller, 2) Design a performance PID-based controller, 3) Simulate and analyse