1. Pre-req kind of question: Here is the default control architecture used by sisotool in MATLAB. controller/compensator, G is the plant, and H F is pre-filter, C is the is the

sensor model. The inputs to the system are R (reference), du (input disturbance), dy (output disturbance), and N (noise). H a. Express the output Y as function of all the inputs. Your answer will be in the format: Y= (something) *R + (something) *dU+ (something) *dY + (something) *N. And these 'something's are expressions involving F, C, G, and H. b. What is the TF from R to Y? c. What is the TF from N to Y? d. What is the TF from du to Y? e. What is the TF from dy to Y? f. Express the error E(s) = R-Y as function of all the inputs. Answer Format: E= (something) *R+ (something) *dU + (something) *dY+ (something) *N. What is the TF from R to E? What is the TF from N to E? i. What is the TF from du to E? j. What is the TF from dy to E? k. Express the plant input U(s) as function of all the inputs. Answer Format: U= (something) *R+ (something) *dU + (something) *dY + (something) *N. 1. Write the loop TF? m. Write the sensitivity TF (Google what it is)? g. h. G