Question

Task: 4 (35 Marks) The block diagram representation of a CNC machine speed control system is shown in Figure 4 with the gain of K, and the feedback value of K2. R(s) + cls 100 1 + 0.2s G1=6.5 K1=14.5 K2=0.55 R=3 L=7 C=0.5 Figure 4 (i). Evaluate the closed loop transfer function of the CNC speed control system; (i). Estimate the value of time constant (T) and dc gain K for the CNC speed control system; Note: Each student should refer the attached Table for K1 and K2 values. (iii). The system step response is represented by y = K(1- 7), sketch the step response curve for the system. (iv). Discuss the functions of time constant (T) and dc gain K. (v). Write a general MATLAB codes to reduce the block diagram into a single feedback control system, to calculate transfer function and to obtain unit step response and impulse response. (vi). Discuss the transient and steady state response. (vii). What is simulation in MATLAB explain with examples.

Answer 1

Given Daten Gi=665 K1 = 1405 Kq=0.55 R=3 ニ子 C10.5. 100 170-2 Casey) Ag-CNC mic Speed Control systems. GOS) - 100 1+0.25 It Kg x loo HO.25 -> Gi (s) 100 Consider RCS) (0-25+stlook). les H arcs to

We know that connection I GCs) Relation between the and GICs) are =ko Gics) = Kit loo ' Co-as+1+10012). = 14058100 Cozs +1+100ks) = 1450 0.25 +1+100C0-) 1450 tor5+55 Consider. او را هم و 1) closed loop CNC speed - we know Transfer Transfer function of an control system. that function (TF) = G(s) It a(s) (H(s)

T- : )+So 1+ J+So x) I TF = 0.25+5С 14.50 0-2 St JSo6 T€ - 14 Го 0-2s HISo6 : ) + 8) - J+So - с +Съд +sT Chain - x = 14500 120.96 Tortбонба» | ia) - о-выз. Сот боме чак(1-сух) o46КТ 0-44- o9-1, Crob-pop г ookio o-bolj pays o-ooo11 -- > Е

TA AS We know that G(s) = 100k 0.25+1+100km. TF = a(s) Hacs) CH(s)) - look, 0.25 +Itlookget looky - looki 0-25+ (17100144100k 3) = look! lt 100k(y +100K2 t/0.2 3 II+100111 +100ka,

- Time Constant (T) = 0.2 ht1ook +10oK2 -- 0-2 I 100(143) ? 0.2 - It 1458455 1506 1 As Functions 70-00013. ki and Kz. of De chain (c) a . look, tlook, tlook2 - - 100 (145) I tool145) +100Coss) = 1450 1506 0-96. . As functions of K, and a Hence saved