Question 3: x1x2x3=000100010x1x2x3+001uy=[100]x1x2x3 a) Discuss whether the system should be controllable or not. Check your intuition by forming the controllability matrix and checking its rank. b) Assume that all of the state variables can be measured directly; that is, x is measured. Find a state feedback law that places the dominant closed-loop poles of the system so that tr0.1sec and Mp5%. Place the remaining pole of the system 4-5 times farther to the left so that the design specifications are more likely to hold. c) Find the state feedback gains by first matching the coefficients of the desired polynomial and closed-loop characteristic equation. Then check your result by using the Matlab function "acker.m" or "place.m". d) Simulate the closed loop system with a Simullink model. - Model the plant with Simulink integrators and Simulink gains Question 3: x1x2x3=000100010x1x2x3+001uy=[100]x1x2x3 a) Discuss whether the system should be controllable or not. Check your intuition by forming the controllability matrix and checking its rank. b) Assume that all of the state variables can be measured directly; that is, x is measured. Find a state feedback law that places the dominant closed-loop poles of the system so that tr0.1sec and Mp5%. Place the remaining pole of the system 4-5 times farther to the left so that the design specifications are more likely to hold. c) Find the state feedback gains by first matching the coefficients of the desired polynomial and closed-loop characteristic equation. Then check your result by using the Matlab function "acker.m" or "place.m". d) Simulate the closed loop system with a Simullink model. - Model the plant with Simulink integrators and Simulink gains