- In carrying out the following laboratory exercises, you can form groups of 5 or 6 students
each which must be maintained across all the exercises. - Write lab reports in the constituted groups (but show who did what/individual contributions
for each experiment (see the proposed lab report format next)
a) Title Page: This must include institution, program, level, title, laboratory exercise number, group member names, registration numbers and date of submission.
b) Introduction/Theory: Explain the background and the objective (s) of the lab,
indicating requirements and desired results. Discuss the underlying applicable theory and concepts that support the measurements/observations.
c) Methodology: Summarize the steps/procedures followed in the preparation of the experimental/simulation practicals. Indicate and discuss the measurement set-up (or simulation parameters/settings) and equipment used. You may include created
SIMULINK diagrams/models here. Codes or MATLAB scripts can also be included here and mentioned but referred to in the Appendix.
d) Measurement Data and /or Results and Discussion: Present measurement results in tabular, graphical or numeric form. Present results from required lab exercises. Discuss
measured data or observations made or values obtained in the context of comparison to
expectation, accuracy, difficulties, etc.
e) Summary and Conclusions: Discuss findings, explain errors and unexpected results;
summarize and indicate conclusions.
f) References: Include a list of reference materials used to undertake or prepare the lab
reports in the IEEE format.
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Further requirements on the lab reports are: - Correct spelling, grammar, and punctuation is required.
- The report should preferably be typed; in some cases, handwritten figures, drawings and
equations may be accepted. - Remember the format of references must conform to IEEE (transactions) standards.
- Use MATLAB & SIMULINK Software
- Make good use of the allocated lab/class hours.
- Prepare PowerPoint presentations and be ready to present if called upon to do so
- The labs shall be due for submission on…see stipulated due dates….
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LABORATORY EXPERIMENT 3
TITLE:
DIGITAL CONTROL SYSTEM DESIGN: ANTENNA AZIMUTH CONTROL SYSTEM
CASE STUDY
Objectives
(i) To design the gain of a digital control system to meet a transient response requirement;
(ii) To simulate a digital control system to test a design;
(iii)To investigate the effect of sampling rate upon the time response of a digital system.
Minimum Required Software Packages: Suitable version of MATLAB & SIMULINK with
the Control System Toolbox.
Consider the following antenna azimuth control system case study (Fig.3.1 a) and b)).
(a) Layout
Output Azimuth/ Desired azimuth/ Elevation angle Elevation angle
Σ
_
+
Feedback signal
Potentiometer
Preamplifier
Potentiometer
Motor and
load
Power
amplifier
Gears as
K
)( ass m
K
Kpot K Kg Kpot s)( i
s)( o
tV )( o V (t) i te )( u(t)
(b) Block Diagram
Fig. 3.1 Antenna azimuth position control system
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Table 3.1 Schematic Parameters
Table 1: Parameters of Antenna Control System With DC Servomotor
SCHEMATIC PARAMETERS
PARAMETER DEFINITION AZIMUTH/
ELEVATION
a Power Amplifier Pole 100
am Motor and Load Pole 1.71
Ba Motor Dampening Constant[Nms/rad] 0.01
BL Load Dampening Constant[Nms/rad] 1
Bm
Equivalent viscous friction coefficient
[Nms/rad] 0.02
Ja Motor Inertial Constant[Kgm2
] 0.02
JL Load Inertial Constant[Kgm2
] 1
Jm Equivalent moment of inertia[Kgm2] 0.03
K Preamplifier Gain _
K1 Power Amplifier Gain 100
KB Back emf Constant[Vs/rad] 0.5
Kg Gear Ratio 0.1
Km Motor and Load Gain 2.083
Kpot Potentiometer Gain 0.318
KT Motor Torque Constant[Nm/A] 0.5
La Motor Armature Inductance[H] 0.45
N Turns on Potentiometer 10
N1, N2, N3 Gear Teeth (Respectively) 25,250,250
Ra Motor Armature Resistance[Ω] 8
V Voltage across Potentiometer[V] 10
NB: For details on how to obtain parameters of Table 3.1, see Norman S. Nise, 2011, Antenna
Control Case Study presented in Chapter 2 (pgs. 94-95) and Chapter 10 (pgs.
606-607), respectively, “DC Servomotor-based Antenna Positioning Control System Design
using Hybrid PID-LQR Controller”, (2016)-pg.17-31.
Lab 1. Prelab 1: Using a block diagram of Fig. 3.1 and Table 3.1, obtain the open-loop and closed-loop
transfer functions of the system. - Prelab 2: Obtain the digital open-loop transfer function.
- Prelab 3: Determine the value of the preamplifier gain using the SISO Design Tool to generate the root locus for the digital open-loop transfer function found in Prelab 2. Use the Design Constraints
capability to generate an 8% overshoot curve and place your closed-loop poles at this boundary.
Obtain a plot of the root locus and the design boundary. Record the value of gain for 8% overshoot.
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Also, obtain a plot of the closed-loop step response using the LTI Viewer and record the values of percent overshoot and peak time. Use the same tool to find the range of gain for stability. - Using SIMULINK, set up both the digital and continuous systems open-loop and closed-loop
system to yield an 8% overshoot. Build the digital system with a sample-and-hold rather than the transform function. Plot the step response of each system and record the percent overshoot and the peak time. - For the closed-loop digital system built above, vary the sampling interval and record the responses for four values of sampling interval above 0.05 second. Record sampling interval,
percent overshoot, and peak time. Also, find the value of the sampling interval that makes the system unstable.
Post-lab
1) Make a table containing the percent overshoot, peak time, and gain for each of the following
closed-loop responses: the digital system using the SISO Design Tool; the digital system using
SIMULINK and the digital transfer functions; the digital system using SIMULINK and the continuous transfer functions with the zero-order sample-and-hold; and the continuous system using SIMULINK.
2) Using the data from Lab 4, make a table containing a sampling interval, percent overshoot, and peak time. Also, state the sampling interval that makes the system unstable.
3) Compare the responses of all of the digital systems with a sampling interval of 0.05 seconds and a continuous system. Explain any discrepancies.
4) Compare the responses of the digital system at different sampling intervals with the continuous system. Explain the differences. - Draw some conclusions about the effect of sampling.
REFERENCES
Key References - N.S Nise, “Control Systems Engineering,” John Wiley and Sons, 6th Edition, 2011.
- “DC Servomotor-based Antenna Positioning Control System Design using Hybrid PID-LQR
Controller”, European International Journal of Science and Technology, Vol. 5, No.2, March,
2016, pp. 17-31.
Additional Texts that may be useful on how to use MATLAB in this lab exercise include: - Katsuhiko Ogata, “Modern Control Engineering”, 4th edition, 2002.
- Roland S. Burns, “Advanced Control Engineering”, Butterworth-Heinemann, 2001.
- R.C. Dorf and R. H. Bishop, “Modern Control Systems”, Prentice-Hall, 12th Edition, 2011.
- Kastuhiko Ogata, “Discrete Time Control Systems”,
- M. S. Fadali and A. Visioli, “Digital Control Engineering Analysis and Design,” Elsevier, 2nd
Edition, 2013.
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