Can someone help with tthose questions

Problem 1. The open-loop plant of the system is given as 100s +2000 G(s) - S3 +8s2 +19s 12 a) (7.5 pts) Write the state equations for the cascade form (z state variables). Use Matlab to determine if the sys- tem is controllable. b) (7.5 pts) Write the state equations for the phase-variable form (x state variables). Use Matlab to determine if the system is controllable. 0(30 pts) For the phase-variable form, design the controller for the system to operate with a 15% overshoot and peak time of 0.5 seconds. Use it to find the controller for the cascade form. d) (5 pts) Simulate the step response of the system in cascade form to check if the specification are met. Problem 2. The open-loop plant of the system is given as S3 18s2+99s162 a) (9 pts) Write the state equations for the phase-variable form (z state variables). Use Matlab to determine if the system is observable b) (9 pts) Write the state equations for the observer-canonical form (x state variables). Use Matlab to determine if the system is observable c) (32 pts) It is desired for the plant to operate with 10% overshoot and a settling time of 0.5 seconds. Its ob- server needs observer for the phase-variable form. to operate 10 times faster. For the observer-canonical form, design such observer. Use it to find the Problem 1. The open-loop plant of the system is given as 100s +2000 G(s) - S3 +8s2 +19s 12 a) (7.5 pts) Write the state equations for the cascade form (z state variables). Use Matlab to determine if the sys- tem is controllable. b) (7.5 pts) Write the state equations for the phase-variable form (x state variables). Use Matlab to determine if the system is controllable. 0(30 pts) For the phase-variable form, design the controller for the system to operate with a 15% overshoot and peak time of 0.5 seconds. Use it to find the controller for the cascade form. d) (5 pts) Simulate the step response of the system in cascade form to check if the specification are met. Problem 2. The open-loop plant of the system is given as S3 18s2+99s162 a) (9 pts) Write the state equations for the phase-variable form (z state variables). Use Matlab to determine if the system is observable b) (9 pts) Write the state equations for the observer-canonical form (x state variables). Use Matlab to determine if the system is observable c) (32 pts) It is desired for the plant to operate with 10% overshoot and a settling time of 0.5 seconds. Its ob- server needs observer for the phase-variable form. to operate 10 times faster. For the observer-canonical form, design such observer. Use it to find the