Answer Happy

Problem-6. Consider the block diagram given below, which represents a negative feedback control system with all undesirable inputs, i.e. disturbance and noise. (a) Obtain the output signal Y(s) with respect to each input components. (b) Obtain the error signal E(s) with respect to each input components. (c) Obtain the control signal U(s) with respect to each input components. Hint: You may define the loop transfer function as L(s) = KG (5),(s)H(s) and use it in the output equation for convenience. The the output will be in the following form, Num(s) Num (s) Numz(s) Y(s), E (s), U(S) = + -R(S) + -N(S) + D(S) Den(s) Denz(s) Denz(s) (d) Obtain the sensitivity functions of the output to each input (r, n and d). Hint: when you evaluate for example the sensitivity of y to r, assume that all other inputs are zero, i.e. d=n=0. (e) Comment on the sensitivity functions you found in (d) like “in order to reduce sensitivity of y tor we should increase loop transfer function”, “for large loop transfer functions, S becomes 1, which means ideal (instantaneous) set-point tracking would occur that is y = r and it means the control objective is achieved” or “in order to reduce sensitivity of y tor increase gain of the controller but this causes the sensitivity of y to n approach -1, making y = -n, which is not desirable, since it implies that the output is directly 100% related to the noise signal.” Solution 6. D(S) Ga(s) R(5) E(S) US) Y(s) K K Ge(s) Gp(s) H(S) N(S)