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). 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. g. What is the TF from R to E? h. What is the TF from N to E? L What is the TF from du to E? j. k. H What is the TF from dy to E? Express the plant input U(s) as function of all the inputs. Answer Format: U= (something) "R+ (something) dU+ (something)"dY+ (something) "N. L. Write the loop TF? m. Write the sensitivity TF (Google what it is)?