Question

Problem 4 (30%) The system given in the diagram shows a typical control system where the system that represents the process to be controlled is called Gp(s), the controller itself is Gc(s) and the measurement system is H(s). The signals in the diagram are the input (desired repsonse) R(s), the output to be controlled Y(s), the system distrubance T(s) and the measurement noise N(s). Let's assume that the transfer function for the measurement is H(s)1 and that a good approx imation of the system is a first order differential equation Gp(s) assume that we have implemented a controller which has the transfer functi- on Gc(s)- Kp + Ki/s and that we can choose the value of the constants Kp (proportional gain) and Ki (gain after integration) Let's s+1 Td(s) Y(s) R(s) Gp(s) Ge (s) N(s) H(s) 1. Find the transfer functions between the inputs R(s), Td(s) and N(s) and the output Y(s). (Hint: There are three transfer functions. When you find the tranfer function for one input, assume that the other inputs are zero

Answer 1