please solve all parts A,B, and C and draw the diagram becauee all the parts are related to each other

Consider a plant having nominal model G0(s)=A0(s)B0(s).=(s+2)(s+4)2s+5 Assume a one degree of freedom control loop with controller, C(s), of the form C(s)=L(s)P(s)=L1s+L0P1s+P0 A-1 Synthesize a controller C(s) such that the close loop polynomial is Acl(s)=(s+b)2(s+3)2 a) For taking, b=0.5 [36 pts.] b) For taking, b=8 [36 pts.] Since Acl(s) is 4 th. order polynomial you will consider a controller of the form, C(s)=L1s+L0P1s+P0(s+b)(s+b) to enable a pole zero cancellation on the characteristic equation: A0(s)L(s)(s+b)+B0(s)P(s)(s+b), which needs to be equal to Acl(s). B- Discus your results found in part-A, based on the pole-zero structure of the controller, C(s) [20 pts.] C- Present your synthesis solutions, as an engineering document, in a clear and orderly manner. [20 pts] NOTE: you must draw the necessary block diagrams and determine the necessary transfer functions in explaining your approach and solutions in a clear and orderly manner. Consider a plant having nominal model G0(s)=A0(s)B0(s).=(s+2)(s+4)2s+5 Assume a one degree of freedom control loop with controller, C(s), of the form C(s)=L(s)P(s)=L1s+L0P1s+P0 A-1 Synthesize a controller C(s) such that the close loop polynomial is Acl(s)=(s+b)2(s+3)2 a) For taking, b=0.5 [36 pts.] b) For taking, b=8 [36 pts.] Since Acl(s) is 4 th. order polynomial you will consider a controller of the form, C(s)=L1s+L0P1s+P0(s+b)(s+b) to enable a pole zero cancellation on the characteristic equation: A0(s)L(s)(s+b)+B0(s)P(s)(s+b), which needs to be equal to Acl(s). B- Discus your results found in part-A, based on the pole-zero structure of the controller, C(s) [20 pts.] C- Present your synthesis solutions, as an engineering document, in a clear and orderly manner. [20 pts] NOTE: you must draw the necessary block diagrams and determine the necessary transfer functions in explaining your approach and solutions in a clear and orderly manner