احمد الدرابيع

You are given a system with the transfer function: Gs=s+4(s+1)(s+2)(s+5) realized in cascade form as: x=-5 1 0 0 -2 1 0 0 -1 x+0 0 1 u y=-1 1 0 x You are asked to design a state feedback controller and observer using MATLAB and SIMULINK through the following steps: Prove that the given diagonal form is equivalent to the given transfer function (MATLAB) Build the system and simulate it for initial conditions of 0.5 0 0 T(SIMULINK) Check the controllability of the system (MATLAB) Find per hand the desired 3 closed-loop poles corresponding to 1 second settling time and 10% overshoot. Find the state-feedback gains to place the closed loop poles as desired and make sure that these gains are correct (MATLAB) Modify the system by adding state-feedback control and simulate it for a unit step input without initial conditions (SIMULINK) Make sure that the response corresponds to the requirements in step 4 Check the observability of the system (MATLAB) Choose the desired locations of the observer poles Find the observer gains to place its poles as desired and make sure these gains are correct (MATLAB) Build the observer and run it (SIMULINK) Feedback the state from the observer output and simulate (SIMULINK) Make sure that simulation results for the controller and the observer are satisfactory Build the extended (with Integral Control) system (MATLAB) Check the controllability of the extended system (MATLAB) Choose the desired location of the extended system closed-loop poles Find the gains that place the closed-loop poles as desired and make sure they are correct (MATLAB) Build the extended system (with Integral Control and observer) and simulate it (SIMULINK) Make sure that the simulation results for the extended system are satisfactory file:///C:/Users/DELL/Documents/WhatsApp%20Image%202023-11-07%20at%2019.02.40_3be71035.jpg