Question

2. (disturbances & sensitivity) For the control system shown in the figure below, do the following: i. Simplify the block diagram to form a negative unity feedback system ii. Determine the system type. ii. Find the steady-state error for r(t) 2tu(t) and d(t) 0 iv. Find the steady-state error for r(t) 0 and d(t) -0.2ut) v. Find the total error to both the input and the disturbance vi. Find the sensitivity of the total steady-state error to changes in Ki D(s)-0 R(s)+ K, C(s) (s +3) (s + 2)

Answer 1

The given block diagram can be draw as This is required negative unity feed back system (ii) from above block diagram the loop transfer function is ki/s (s^2 + 5s + 7) so it has a pole at s = 0 so this �type 1� system (iii) for this system total steady state error is given as e (infinity) = lim_s rightarrow 0 [S R/1 + G_1 G_L - S G_L D/1 + G_1 G_2] if D (1) = 0 Then steady state error due to R (s) is E_R (infinity) = lim_s rightarrow 0 S R (s)/1 + G_1 (s) G_L (s) where G_1 (s) = ki/s and G_2 (s) = 1/(s^2 + 5s + 7) e_R (infinity) = lim_s rightarrow 0 S 2/s^2/1 + ki/s (s^2 + 5s + 7 R (s) = 2/s^2 \r\n e_R (infinity) = lim_s rightarrow 0 1/s/s (s^2 + 5s + 7) ki)/s (s^2 + 5s + 7 = lim_s rightarrow 0 2 (s^2 + 5s + 7)/s (s^2 + 5s + 7) + ki