Question

Using matlab and simulink!

Lab Assignment Solve the following problems using the Word and MATLAB. The table should be prepared in Word (Do not use MATLAB) for this. Use the MATLAB PUBLISH to submit your code. If you cannot, you may submit your report as a pdf form (prepare in word and save as pdf). The code, simulink model and figures should be included (print as a pdf or screen capture - consider readability). 1. Create the Simulink model as follows. Find the transfer function in terms of m, b, Khw Ki, Kp, and Kd. Also, find the transfer function when Ki = 0. out.u S O PID(s) PIDG plan out.x Figure 9. Simulink Model for Lab assignment where m - 2.68 kg, b = 1.72 Ns/m, k = 0, Hardware gain Kiw=16440. - 9 / 10

Answer 1

Lab Assignment 1. Create the following model in Simulink: R(S) PIDCB) kimas GCS > 475) Where; G(S) = ms² bstk of m. 2. 68 ug, b = 1.72 Na/m, kao Knw = 16440. the If of PID Controtter is, Ge (S)= Kpt + kas. K

Subject s frost of all ; we need to determine the close loop _ Date Tf of the system: hena; T(S) = G(S) C(s) xk ho It G (s) CCS) Kno. Khw ms² tbs + (xp + Kiltska) Khwx (up + K + Skd). It mg²+bstk Knw (skpt kits²kad slms + 65+ x) + Kh (s up + k +sikd) Khw (shkd + Sup & Ki). mg²+ 5²(b + Khw Kd) + s(k+ Kho Up) + Ki Kuw if ki= 0; (Am. Now Khw TH(S) - (m3*+bS+*) * (up + Ski) It Know (up + Skd) ms²tbstk) Know (Skat up) ms+ s(b+ Kw Ka) + (K + K Kaw Now! We need to simulate the above system in Cint a prop gain up Change the Controller gain as shown in the table (t final = 5). The following Simulink modd can be used in this aspect 2. a

File Edit View Display Diagram Simulation Analysis Code Tools Help untitled1 2 untitled1 P(s) output Y(s) 16440 2.6852+1.725 Khw Step Input R(s) P Controller C(s) Kp = 0.002 Transfer Fan G(s)

For Kp = 0.002, the output response is shown below

0.8 0.5 1.5 me offset: 0

For Kp = 0.02, the output response is shown below

0.8 0.6 0.5 3.5 me offset: 0

For Kp = 0.2, the output response is shown below

0.44 0.5 1.5 ime offset: 0

For Kp = 2, the output response is shown below

1.2+ 0.8 0.6 0.4+ 0 me offset: 0

For Kp = 20, the output response is shown below

1.6 1.4 0.6 . 0.4+ 0.2 0.5 me offset: 0

The corresponding table is shown below

Type 2 Kp 0.002 0.02 0.2 2 20 R ise Time 0.32 sec 0.0962 sec 0.03 sec 0.009 sec 0.003 sec Peak 1.75 1.91 1.97 1.99 1.99 Peak Time 0.9 sec 1 0.28 sec 0.09 sec 0.03 sec 0.009 %OS 74.9% 91.3% 9 7% 99% 99% Stable? stable stable Stable Stable Stable Final error 0.0761 0.2647 -0.095 -0.232 0.25 2 2 NN

- 3 Now, we need to Simulink model simulate the model Can be used in using this Controller a PD aspect. : the followin

10.0 untitled untitled Daha at PD(s) 16440 1 output Y(s) 2.6852+1.725 Khw Step Input R(s) PD Controller C(s) Transfer Fcn G(s)

For Kp = 0.002, Kd = 0.001, the output response is shown below

1.2 0.8 0.6 0.4 . 0.2 0.5 1.5 2.5 ime offset: 0

For Kp = 0.002, Kd = 0.002, the output response is shown below

1 0.8 0.6 0.4 0.5 1.5 2.5 3.5 4.5 me offset: 0

For Kp = 0.002, Kd = 0.003, the output response is shown below

0.8 0.6 0.4 0.2 0.5 2.5 3.5 me offset: 0

For Kp = 0.002, Kd = 0.004, the output response is shown below

0.5 1.5 3.5 me offset: 0

For Kp = 0.002, Kd = 0.005, the output response is shown below

0.5 1.5 4.5 0 me offset: 0

The corresponding table is shown below

ke Kd Peak %OST Stable? Type Final error 0 0.002 0.002 0.002 0.002 0.002 0.001 0.002 0.003 0.004 0.005 10.12 sec 09951 0.41 sect Rise Time 0.25 sec 0.17 sec 0.12 sec | 0.09 sec 0.07 sec 1.09 1.02 1 0.9951 0.99 Peak Time 0.64 sec 0.54 sec 0.37 sec 0.41 sec 0.33 sec 9.4% 1.9% 0.008% 0 0 Stable Stable Stable Stable Stable 0 mmmm 03

4) Controllo Now, tollowing we need to us PID to simulat model to Controllo can be simulate to used simulate in this the and the sun system, the

File Edit View A untitled 2 untitled Display => 1 Diagram Simulation Analysis Code Tools Help 0 0 -3 0 IDO - 10.0 | 8 PID(s) 16440 output Y(s) ^ @ 30 2.6852+1.725 Khw Step Input R(S) PD Controller C(s) Transfer Fcn G(s)

For Kp = 0.005, Ki = 0.001, Kd = 0.001, the output response is shown below

0.6 0.5 - 1.5 2 2.5 4.5 ime offset: 0

For Kp = 0.005, Ki = 0.01, Kd = 0.001, the output response is shown below

2.2- 0.6. 0.4+ 0.27 0.5 1.5 2 2.5 3 ime offset: 0

For Kp = 0.005, Ki = 0.02, Kd = 0.001, the output response is shown below

1 0.5 0.5 1.5 2.5 3.5 4.5 me offset: 0

For Kp = 0.005, Ki = 0.04, Kd = 0.001, the output response is shown below

2.5 1.5 0.5 -0.5 0.5 2.5 3.5 me offset: 0

The corresponding table is shown below

Kd Peak %OS Type 3 0.005 0.005 0.005 0.005 0.001 0.01 0.02 0.04 0.001 0.001 0.001 0.001 Rise Time 0.07 sec ) 0.07 sec 0.07 sec 0.07 sec 1 1.03 1.05 1.08 Peak Time 0.23 sec 0.8 | 0.66 1 0 .53 0.99% 3.1% 4.9% 7.63% Stable? Final error Stable 0 Stable 0 Stable 0 Unstable | infinite سا | س | س | سا