The document summarizes a project to design a controller for a radar antenna. It describes analyzing the plant system, deriving transfer functions, and designing a lead compensator controller. Simulation results in Simulink verified that the designed controller met all specifications, with overshoot of 17% and settling time within 3 seconds. Key steps included: 1) Analyzing the electrical circuit and antenna armature to derive plant transfer functions; 2) Designing a lead compensator controller using typical steps; 3) Building a Simulink model to test the controller design meets specifications for tracking aircraft with minimal error.

1. ME 1045
Radar Antenna Control Project
Date:
December 10th, 2015
Professor:
Dr. Dan Cole
Submitted by:
Nathan Janiczek

2. Objective:
The objective of this experiment was to design a controller for a radar antenna capable of
tracking aircraft. This antenna has two modes: a listening mode during which it rotates at a
constant speed and a tracking mode during which it can lock on to an aircraft with minimal error
so it does not lose the aircraft.
Design Procedure:
The first stage of this design was to analyze the systems that make up the plant for this
system. In this case, they were the electrical circuit and the armature which rotates the antenna.
Figure 1 shows diagrams of both of these which were used to derive the plant transfer functions.
Figure 1: Diagrams for circuit and antenna armature
These transfer functions were used to build the block diagram shown in Figure 2. A
voltage is supplied to the circuit which in turn supplies a current to the armature which dictates
how quickly the antenna rotates.
Figure 2: Block diagram of antenna/motor system

3. Table 1: Given Values for Plant Components
Parameters Values
J 249 kg-m^2
b 1910 N-m-s
L 66.67 H
R 50 Ohms
kt 6.67 N-m/A
ke 6.67 V-s
Seeing as this design requires the error to be very low so as not to lose the aircraft during
tracking, it was decided that a lead compensator controller would be used. After adding an
integrator to the transfer function (turning it into a type I system), it was necessary to select
values that satisfy the given parameters. Using the typical steps to design a lead compensator and
the requirements found in the problem statement, values for gain (K), eta (η), and omega (ω1)
were calculated. These values are displayed in Table 2. The controller transfer function is shown
in Equation 1. Multiplying the plant transfer function by Equation 1 gives us the final loop-gain
that meets the requirements of the system. Figure 3 shows the Bode plot for the loop gain and
Table 3 shows the zero-pole-gain form values.
(1)
Table 2: Lead Compensator Design Parameters
Parameter Value
M(ωgc) -98.5 dB
Φ(ωgc) -172⁰
Φmax 47⁰
η 6.44
ω1 0.743 rad/s
K 29561

4. Figure 3: Magnitude/Phase Bode Plots of Loop Gain
Table 3: Zero-Pole-Gain Values of Loop Gain
K Zeros Poles
76.46 -0.743 0
-7.67
-4.785
-0.75
Additionally, a Bode plot of the loop-gain (L), sensitivity (S), and complimentary
sensitivity (T) are provided in Figure 4. Formulas for sensitivity and complimentary sensitivity
are shown below in Equations 2 and 3.
(2)
(3)

5. Figure 4: Bode Plots of Loop-gain, Sensitivity, and Complimentary Sensitivity
With the controller design complete, it was necessary to build a block diagram in
Matlab’s Simulink application to test the controller and verify it met all the specifications. Figure
5 shows the block diagram used to simulate start-up of the antenna. The block diagram uses a
ramp input (r = ωo/s2
) and controller/plant transfer functions to display error, current, angular
velocity plotted against time. These plots can be seen in figures 6, 7, and 8.
Figure 5: Simulink Block Diagram of Closed-loop System

6. Figure 6: Plot of Angular Velocity vs Time during Start-up
Figure 7: Plot of Current vs Time during Start-up

7. Figure 8: Plot of Error vs Time during Start-up
These plots allowed verification that all parameters meet specification. Table 4 compares
each parameter’s requirements set forth in the problem statement to the resulting value selected
or designed. Additionally, Figure 8 shows that the design results in a percent overshoot of 17%
and a 3% settling time within 3 seconds.
Table 4: Specifications vs Actual Parameters
Parameters Requirements Resultant Values
Phase Margin (PM) ≥ 55⁰ 55⁰
Gain Margin (GM) ≥ 12 dB 15.6 dB
Angular Velocity (ωo) 0.04⁰/s 0.04⁰/s
Steady-state Error (e) ≤ .57⁰ .0227 ⁰
Error Constant (Kv) ≥ .07 s-1
2.06 s-1
Gain Crossover Frequency (ωgc) .3 Hz (1.885 rad/s) 1.885 rad/s
Conclusion:
Using the parameters and values given in the problem statement, a controller capable of
both a listening and tracking mode was designed. By modeling the design in Simulink, the
design specs were verified and meet all requirements for the design.