The document describes the design of an autopilot control system for the NT-33 aircraft. The autopilot was designed to hold both altitude and velocity, allowing the pilot to input the desired hold. The control system includes separate models for altitude hold and velocity hold using PID controllers. Graphs of the aircraft's performance show it climbing from sea level to 20,000 feet in 500 seconds while staying within FAA speed restrictions, demonstrating the effectiveness of the autopilot control system design.

1. NT-33 AUTOPILOT CONTROL
ENGINEERS:
Zack White, Mark Hannan,
Hunter Michael
AE: 432
Flight Dynamics and Control
Professor Greiner
Embry-Riddle Aeronautical
University

2. 1
Table of Contents:
Contents
Table of Contents:.........................................................................................................................................1
Executive Summary:......................................................................................................................................2
Introduction:.................................................................................................................................................3
Objectives: ....................................................................................................................................................3
Elevator and Jet Engine Actuator..................................................................................................................4
Non-Linear sim block: ...................................................................................................................................5
Control Law Design: ......................................................................................................................................6
Altitude Hold Model..................................................................................................................................7
Velocity (throttle) Hold Model..................................................................................................................7
Aircraft Time History:....................................................................................................................................8
Altitude vs. Northing.................................................................................................................................8
Velocity vs. Northing.................................................................................................................................9
Elevator Deflection vs. Northing...............................................................................................................9
Time Histories: ............................................................................................................................................11
Conclusion:..................................................................................................................................................14

3. 2
Executive Summary:
The implementation of a digital flight control system is used often for its flexibility, reliability and
power. However, these systems can cause a deficiency in handling quality, including pilot-induced
oscillations. Which, in turn, causes a need for a possibly extensive redesign of the aircraft control
system. The following report follows the process and results that came about from designing an
autopilot control system for the NT-33A. The autopilot was designed to have multiple holds for different
flight cases of the aircraft. These holds included an altitude and velocity hold that would allow the pilot
to input a digital signal for the desired hold, and the aircraft would then respond accordingly to the
given input data. Various layouts were implemented in the design of the control system, and the final
design, which is analyzed hereafter, gave a favorable dynamic stability output when posed with a user
defined input.

4. 3
Introduction:
The NT-33A was built by Lockheed, and originated as the T-33 trainer which was later adapted
to a variable stability aircraft for in-flight simulation assigned to the Wright Laboratory. The NT-33 was
operated by hundreds of Air Force and Navy pilots in order to test new advanced aircraft. The aircraft
had a three degree-of-freedom (DoF), response-feedback flight control system that provided
independent control of the pitch, roll and yaw motions. The NT-33 flew its last research mission in April
of 1997 and is currently on display at the Wright-Patterson museum. For this research and development
project the Engineers were tasked with designing an autopilot system for the NT-33 aircraft. This
autopilot system would take a digital input from the user/pilot and then translate the input into either
an altitude or a velocity (throttle) hold, depending upon the user desired flight condition.
Objectives:
1. Calculate Stability Derivatives using given values and flight test data
2. Trim NT-33 aircraft for different flight conditions
3. Build an autopilot altitude hold for the NT-33
4. Build an autopilot velocity hold for the NT-33
The mission given is to write a control log that climbs from sea level to 20,000 feet in 500 seconds with
the most optimal flight path while maintaining the FAA flight restrictions as they are applied to aircraft
of this type. The pilot inputs the desired altitude after 5 seconds and the control logs take over to climb
and hold the inputted altitude.

5. 4
Elevator and Jet Engine Actuator
As per the design parameters specified for this aircraft the elevator actuator demanded a settling time
0.15 seconds. Solving for the actuator function gives:
𝑡 𝑠 = 0.15𝑠𝑒𝑐 = 3 ∗ 𝜏
𝜏 =
0.15𝑠𝑒𝑐
3
= 0.05𝑠𝑒𝑐
𝜏 = 0.05𝑠𝑒𝑐 =
1
𝑎
𝑎 =
1
0.05𝑠𝑒𝑐
= 20
𝐺𝑠 𝑒𝑙𝑒𝑣𝑎𝑡𝑜𝑟
=
𝑎
𝑠 + 𝑎
=
20
𝑠 + 20
This equation for 𝐺𝑠 𝑒𝑙𝑒𝑣𝑎𝑡𝑜𝑟
is the servo block function used to actuate the elevator in the Simulink block
diagram. For the engine a combination of two different servos one representing the engine spool up
time and one representing the throttle control were needed where the spool up servo demanded a
settling time of 15 seconds and the throttle control demanded a settling time of 0.3 seconds. Solving for
both of these servo functions using the same method as above yields:
𝐺𝑠 𝑒𝑛𝑔𝑖𝑛𝑒 𝑠𝑝𝑜𝑜𝑙
=
0.2
𝑠 + 0.2
𝐺𝑠 𝑒𝑛𝑔𝑖𝑛𝑒 𝑡ℎ𝑟𝑜𝑡𝑡𝑙𝑒
=
10
𝑠 + 10
These three servo functions were placed into separate transfer function blocks in Simulink and used to
regulate the altitude hold.

6. 5
Non-Linear sim block:
This system was created to use a nonlinear system of equations to determine how an aircraft responds
based on its characteristics and its input controls. This project utilized this function with only minor
aesthetic changes. These changes were the disconnecting of the Flight Viz block and the shrink the rest
of the block so that the inputs are elevator and throttle positions and the outputs are q, theta, height,
and Vcas.

7. 6
Control Law Design:
This is the control log developed to accomplish the specified mission. As can be seen it has implemented
multiple feedback loops to obtain both a velocity and an altitude hold. Within each of the feedback
loops there is a PID controller which was used to smooth the aircrafts transition between each different
flight case hold.

8. 7
Altitude Hold Model
The input signal is put in as a step function that activates after 5 seconds. A loop is included to eliminate
error by adding an additional 7/1000 of the original signal. The altitude hold model is a typical PID. The
SAS uses a combination of the q, theta, and altitude signals. This is combined with the elevator trim at
flight case 3 and at case 6 through a switch. This signal is sent through a saturation block to ensure the
elevator does not go past its physical limits. This is fed into the Non-linear Sim and returns height, pitch,
pitch rate, and velocity.
Velocity (throttle) Hold Model
The velocity hold’s basic structure is similar to the altitude hold in that it consists of a final velocity that
the plane approaches and a recursive feedback loop of the planes current velocity. The difference
between the current and required velocity as a voltage signal is used to adjust the throttle which forces

9. 8
the current velocity to converge on the desired final value. An important note for this hold is that due to
FAR requirements this plane requires 2 velocity holds. Therefore, a switch was implemented within the
planes velocity hold system so that below an altitude of 10,000 feet the plane would not exceed 250
knots, as designated by the FAR, and above that it would approach 267 knots which is the designated
speed for flight case 6 of the NASA document for which the control law was designed.
Aircraft Time History:
Altitude vs. Northing
Figure 1: The change in altitude of the aircraft with respect to the distance traveled north in miles

10. 9
Velocity vs. Northing
Figure 2: The change in the velocity of the aircraft with respect to the distance traveled north in miles
Elevator Deflection vs. Northing
Figure 3: The change in the elevator deflection of the aircraft with respect to the distance traveled north
in miles
225
230
235
240
245
250
255
260
265
270
0 10 20 30 40 50 60
Velocity(knots)
Northing(miles)
0
0.2
0.4
0.6
0.8
1
1.2
0 10 20 30 40 50 60
ElevatorDeflection(degrees)
Northing(miles)

11. 10
From the preceding time and northing charts there were only two notable points of concern.
The first being the sharp spikes in the elevator deflection vs northing graph. Though these spikes seem
significant, the scaling of the chart shows that the elevator only deflects around 0.2 degrees which
amounts to nothing but a small flutter of the elevator. The second notable point was the sharp increase
in velocity around the ten mile mark. This increase is due to the velocity limit set by the FAR being
voided after achieving an altitude of ten thousand feet and therefore allowing the aircraft to increase
throttle to achieve a higher cruising speed. This is of little concern because accompanying the rapid
increase in velocity is a gradual decrease in the pitch angle of the plane in order to keep the rate of
climb fairly consistent. It is because of this pitch-velocity “coupling” that there is a smooth transition up
to the target altitude of 20,000 feet.

12. 11
Time Histories:
Figure 4: The change in the velocity of the aircraft in knots with respect to the time traveled in seconds

13. 12
Figure 5: The change in the altitude of the aircraft in feet with respect to the time traveled in seconds

14. 13
Figure 6: The change in the throttle used in percent of the total throttle with respect to the time traveled
in seconds

15. 14
Conclusion:
The systems developed in this project are capable of taking this aircraft from a given level flight
to a designated altitude with minimal overshoot. The case presented in this report shows how the
control log developed allows the aircraft to climb from sea level to 20,000 feet. This climb is
accomplished in 500 seconds with the aircraft traveling approximately 50 miles. The control logs allow
the aircraft to smoothly climb and reach its intended altitude with minimal overshoot. During the climb
the FAA velocity restriction is complied with below 10,000 feet. This control log gives a smooth and
stable climb to a desired altitude with the shortest time allowed.