Question

Question 2 A robot tennis player and its simplified control system for Ø(t) is shown below. 02 (s + 2) 1 (S +1)(8 +3) Figure 2 1) Write down the expression of amplitude ratio AR. 2) Obtain the expression of phase angle 0. 3) Manually make the polar plot of the open-loop transfer function of this feedback system when K = 10. 4) Use MATLAB to plot the Nyquist diagram with the open loop transfer function for K = 10. 5) Use the Nyquist diagram to find the range of gain K for stability.

Answer 1

(2) solh: given closed loop system is a unity Negative feedback system function for the open loop transfer is system given by - given ها ۴۱ي دی (2+یاره use Transfer function diagram is given for the given by potem pony liśmus Grad It $12)(5+j) (5+3) 1 Oz - Ped. (5+1)(5+2) (5+3)+K! . (2.) soll. expression of phase angle is given by [replace sy sw] 10 LG(s)H(S)= atan wa-tan' (w) - tors

0= LG(s)H(S) = -tant w)-tami (w) - tema) $= - tantu), tant (W) – tantum expression of phase angle? open (3.) soen:. polar plot for the . given loop Transfer function. G(S) HIS) = GAY (5+2)(5+3) G(S) HLS) = 5+) (5+2)(5+3) write the expression of magnitude and put the wao phase angle then and who, find the both Value initial and final using that both Value draw polar plot. 10 Magnitude (11) = Jaw2 x Ja+w2x Jgtur

20= -tom" (w)-tans (W)-tamil ) At wzo Magnitude (m) = 1.67 20= 0 At wao magnitude (m) = 0 L0= -270 -270 W- M20 -3601 Wo M=1:67 -1809 fig:- polar plot

Im waren = 1.0605] wa Tan radised .9 Erme 7-7) - 100 OF MARANG - lieu qua 3903 2-wy ( + im Bli wot L 12-W2 + tenilos tomol (9 106 = .wot fi ma wbt .66 = wo to the best CG-=(22), Just-(8) no-Catust- sro 06- Y!M pused 90.402s estu!

. (5.) soln, Nyquist diagram has given below :- to draw. the Nyquist diagram take the moror Image of Polar plot to the with respect o axis -2700 -360 -1809 - 9 intersection with -180 axis -tent w)-tem (W) test 4)=-180 tenisse ) 1 - 180

step I l we never stability condo is less than certain value then the lower limit decide by Intersection point with intersection point O', the with on than ~) for all the greater must be problem. ķ >- lk -6 from ABOVE All cases we can write the Range of CK) 1-6 Ekebo