Given the following open-loop system G(s): 20(s+2) s(s+4)(s+6) design a feedback controller u characteristic equation = -Kx, where K = [K1 K2 K3], to yield a desired s3+6482 +252s + 720 = 0 1. Find K₁, K₂, and K3 using pole placement method. 2. With the designed controller u = − -Kx, find the closed-loop system in state-space formulation 3. Find the transfer function of the closed-loop system with the designed controller u = -Kx

Q2 The block diagram in figure Q2 shows a plant G„(s) controlled by a controller G.(s) using a unity negative feedback loop. R(s), C(s) Ge(s) Gp(s) Figure Q2 The dynamics of the plant are described by the trans fer function 1 Gp(s) = 2s2 + s + 4 If the controller applies proportional action, find the value of gain K, that results in a steady state error of 4% for a unit step input. (a) (b) With proportional gain maintained at the same value from part (a), derivative action is added to the controller. Calculate the value of gain Ka which gives an overall system damping ratio of 0.8. (c) The controller is redesigned with new gains so that the system has a settling time of 2s and maximum overshoot of 7.5% in response to a unit step input. Find the new values of K, and Ka.

Please answer the question step by step and please care to explain the question in detailed with your own sentence and explain why you used that formula, calculations etc. Thanks in advance.

after subpart f please!