NT-33 AUTOPILOT CONTROL

ENGINEERS: Zack White, Mark Hannan, Hunter Michael AE: 432 Flight Dynamics and Control Professor Greiner Embry-Riddle Aeronautical University

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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

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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.

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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.

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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:

= 0.15 = 3

=0.15

3= 0.05

= 0.05 =1

=1

0.05= 20

=

+ =

20

+ 20

This equation for 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:

=0.2

+ 0.2

=10

+ 10

These three servo functions were placed into separate transfer function blocks in Simulink and used to

regulate the altitude hold.

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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.

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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.

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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 holds 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

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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

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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

Vel

oci

ty(k

no

ts)

Northing(miles)

0

0.2

0.4

0.6

0.8

1

1.2

0 10 20 30 40 50 60

Elev

ato

r D

efle

ctio

n(d

egre

es)

Northing(miles)

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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.

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Time Histories:

Figure 4: The change in the velocity of the aircraft in knots with respect to the time traveled in seconds

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

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

in seconds

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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.