Lab Project: PI Controller for a Single Tank System
technical report and power point presentation
The project is to design a PI controller for the head of a tank system. The simple model of the
system is shown. All the sensors and actuators are voltage based. The block diagram for the model
is:
Note that, ???????? and ???????? are related to the head by: ? = 28.8 ??, where h is in mm and ?? is in ??
Requirements:
Part A: Obtaining System Parameters:
a- Use a proportional controller only (???? = 1) and unit step input (???????? = 1) in the
experiment, find the system parameters (?? and ??). Hint: the system can be reduced to the
block diagram shown below, where ??? and ?? ? are new parameters obtained from the CLTF,
and they are functions of ?? and ??. Use the slope method and the final value theorem to
obtain these parameters.
b- Plot on the same graph the experiment data of Kp=1 and Ki=0 with the simulation from
Simulink for the obtained parameters. Compare between the plots.
c- Plot on the same graph the experiment data of Kp=7 and Ki=1 with the simulation from
Simulink for the obtained parameters. Compare between the plots.
Part B: PI Design (Use Simulink and MATLAB only):
? = ?????? ???? and maximum allowed head in the tank=250 mm)
(For the analysis, consider ??
1-
For the following conditions, test the system for different parameters, and discuss the steady
state error and whether there is overflow of the fluid in each case.
a- Using P controller only
b- Using I controller only
c- Using PI controller
2- Give brief conclusion with optimum values for Kp and Ki.
Project Instructions:
–
This project is teamwork of 2-3 members. All groups should finalize their group members within 24
hours from the assignment date of the project.
A technical report, Word processed, must be submitted in week 15 and power point presentation is
required for all groups
Presentation should be presented in front of the lab instructor only. Other students should wait outside
for their turn to come. Failure to attend the presentation will result in zero marks for the presentation
You should expect questions related to the whole project (MATLAB code, recorded video, theory, etc.)
The grade distribution for the Lab project is Report 3% + Presentation 3% = Total 6%.
Time
0
0.512821
1.025621
1.538421
2.051221
2.564021
3.076821
3.589621
4.102421
4.615221
5.128021
5.640821
6.153621
6.666421
7.179221
7.692021
8.204821
8.717621
9.230421
9.743221
10.25602
10.76882
11.28162
11.79442
12.30722
12.82002
13.33282
13.84562
14.35842
14.87122
15.38402
15.89682
16.40962
16.92242
17.43522
17.94802
18.46082
18.97362
19.48642
19.99922
20.51202
21.02482
21.53762
22.05042
22.56322
23.07602
Voltage
0.117286
0.227392
0.323773
0.410133
0.501249
0.580442
0.665644
0.757811
0.82011
0.874019
0.930302
0.982216
1.04131
1.09189
1.12995
1.1625
1.19359
1.21575
1.22975
1.2447
1.25617
1.26388
1.26617
1.2682
1.27081
1.2684
1.26285
1.25539
1.24654
1.23847
1.22892
1.21628
1.2047
1.1913
1.17661
1.16512
1.15224
1.13946
1.12715
1.11573
1.10166
1.09105
1.07778
1.06783
1.05876
1.05045
The data for PI controller with
23.58882
24.10162
24.61442
25.12722
25.64002
26.15282
26.66562
27.17842
27.69122
28.20402
28.71682
29.22962
29.74242
30.25522
30.76802
31.28082
31.79362
32.30642
32.81922
33.33202
33.84482
34.35762
34.87042
35.38322
35.89602
36.40882
36.92162
37.43442
37.94722
38.46002
38.97282
39.48562
39.99842
40.51122
41.02402
41.53682
42.04962
42.56242
43.07522
43.58802
44.10082
44.61362
45.12642
45.63922
46.15202
46.66482
47.17762
1.04062
1.02851
1.019259
1.013608
1.007908
1.001728
0.993731
0.989747
0.986736
0.98258
0.978167
0.978432
0.976858
0.974555
0.971337
0.971308
0.970857
0.969098
0.966845
0.966609
0.969091
0.969992
0.968862
0.970521
0.970936
0.973718
0.973053
0.975571
0.977094
0.978332
0.982123
0.985513
0.987087
0.987187
0.986314
0.989375
0.994439
0.994182
0.994768
0.997794
1.001227
0.999282
0.998981
1.000769
1.000877
1.00102
1.002915
47.69042
48.20322
48.71602
49.22882
49.74162
50.25442
50.76722
51.28002
51.79282
52.30562
52.81842
53.33122
53.84402
54.35682
54.86962
55.38242
55.89522
56.40802
56.92082
57.43362
57.94642
58.45922
58.97202
59.48482
59.99762
60.51042
61.02322
61.53602
62.04882
62.56162
63.07442
63.58722
64.10002
64.61282
65.12562
65.63842
66.15122
66.66402
67.17682
67.68962
68.20242
68.71522
69.22802
69.74082
70.25362
70.76642
71.27922
1.004861
1.004124
1.00343
1.003237
1.006241
1.008251
1.008258
1.005698
1.006291
1.004939
1.002679
1.002965
1.002965
1.001277
1.001692
1.002901
1.001849
0.99989
0.998152
0.998373
0.997951
0.999239
1.003194
1.002422
1.004217
1.004052
1.00004
0.999275
0.998316
0.997765
0.99577
0.993781
0.991228
0.991378
0.989232
0.987923
0.988088
0.990534
0.990098
0.991443
0.9917
0.992208
0.992079
0.99273
0.994847
0.997014
0.996785
71.79202
72.30482
72.81762
73.33042
73.84322
74.35602
74.86882
75.38162
75.89442
76.40722
76.92002
77.43282
77.94562
78.45842
78.97122
79.48402
79.99682
80.50962
81.02242
81.53522
82.04802
82.56082
83.07362
83.58642
84.09922
84.61202
85.12482
85.63762
86.15042
86.66322
87.17602
87.68882
88.20162
88.71442
89.22722
89.74002
90.25282
90.76562
91.27842
91.79122
92.30402
92.81682
93.32962
93.84242
94.35522
94.86802
95.38082
0.996514
0.9973
0.998795
0.998953
0.997522
0.998967
0.998102
1.001764
1.001828
1.000526
1.000469
1.000276
0.99999
1.001656
1.001907
1.000305
1.001914
1.002279
1.001427
1.000877
1.001256
1.001885
1.002801
1.002157
1.000512
1.000841
1.001335
1.003745
1.003838
1.004196
1.002529
1.002336
0.999961
0.999253
0.999225
0.998674
0.999282
1.001342
1.000626
0.999632
1.000469
1.001513
0.998717
1.001013
1.004052
1.005397
1.003731
95.89362
96.40642
96.91922
97.43202
97.94482
98.45762
98.97042
99.48322
99.99602
100.5088
101.0216
101.5344
102.0472
102.56
103.0728
103.5856
104.0984
104.6112
105.124
105.6368
106.1496
106.6624
107.1752
107.688
108.2008
108.7136
109.2264
109.7392
110.252
110.7648
111.2776
111.7904
112.3032
112.816
113.3288
113.8416
114.3544
114.8672
115.38
115.8928
116.4056
116.9184
117.4312
117.944
118.4568
118.9696
119.4824
1.001027
1.002558
0.998359
0.999854
0.999031
0.997436
0.999275
1.000033
1.002915
1.002622
0.999589
0.999117
1.00122
1.002229
1.001041
0.998187
0.997944
0.998359
1.001284
1.00014
1.000133
1.001098
0.999096
1.000104
0.999747
0.998767
1.000913
0.999647
0.999124
1.000734
1.000126
1.000877
1.000705
1.001113
1.001778
1.000676
1.001664
1.001406
1.000491
0.99999
1.000426
1.000576
1.002157
1.001785
1.001664
1.000977
0.999425
119.9952
120.508
121.0208
121.5336
122.0464
122.5592
123.072
123.5848
124.0976
124.6104
125.1232
125.636
126.1488
126.6616
127.1744
127.6872
128.2
128.7128
129.2256
129.7384
130.2512
130.764
131.2768
131.7896
132.3024
132.8152
133.328
133.8408
134.3536
134.8664
135.3792
135.892
136.4048
136.9176
137.4304
137.9432
138.456
138.9688
139.4816
139.9944
140.5072
141.02
141.5328
142.0456
142.5584
143.0712
0.999968
0.999976
0.998996
0.996149
0.995241
0.998795
0.998309
0.996399
0.994203
0.992158
0.991915
0.992794
0.993202
0.994289
0.995856
0.9966
0.996135
0.995512
0.995326
0.996929
0.996499
0.998373
0.999911
0.998481
1.001027
1.000827
0.99665
0.995076
0.997122
0.998001
1.000727
1.001005
1.000104
1.001349
1.000183
1.001206
1.001199
1.001084
1.000626
0.999918
0.999761
1.000583
1.001864
1.001213
1.000612
1.00112
PI controller with Kp=7 and Ki=1. The force is a unit step voltage
step voltage

Purchase answer to see full
attachment