AE2610Introduction to

Experimental Methods in Aerospace

Lab #3: Dynamic Response of a 3-DOF Helicopter Model

C.V. Di Leo

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Lecture/Lab learning objectives

• Familiarization with the characteristics of dynamical systems• Introduction to the dynamic motion of a vehicle (model

helicopter)• Exposure to the use of shaft/rotary (optical) encoders• Experience in calibration

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Lab Info• Location:- ESM G1- Undergraduate controls lab

• When:- The next two weeks (only one week for each group) there

will also be a 2nd lecture next week.

• Safety:- You can damage the helicopter apparatus if you don’t

follow instructions on how to set up and enter parameters into the controller’s computer interface…so go slowly and double check (with TA supervision) everything you do

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Background: Tandem Rotor Helicopters• Have two large horizontal rotor

assemblies mounted one in front of the other• Use counter-rotating rotors, with

each canceling out the other's torque• Advantages:

• Larger center of gravity range and good longitudinal stability.

• Disadvantages:• Complex transmission (mechanics),

and the need for two large rotors.• Independent control of rotor thrust

produces:• Lift (synced collective)• Pitch (opposite collective)• Yaw (opposite left and right cyclic)

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Ch-47Chinook

V22Osprey

Helicopter Model• Quanser helicopter model:

• Independent DC motors control two caged rotors/propellers• 3-DOF constrained motion (rotation about 3 shafts)• Counterweight reduces thrust requirement

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• In this lab, a control system constraints the helicopter such that it can only rotate about the elevation axis (1-DOF)

Travelaxis

Elevationaxis

Pitchaxis

Thrustforces

Static performance• The constrained system can be modeled with only one DOF (the arm pitch

angle θ)• In general, the system is dynamic, meaning that the arm pitch angle is a

function of time: θ = θ(t)• We will first focus on the static equilibrium of the system.

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Static performance• The constrained system can be modeled with only one DOF (the arm pitch

angle θ)• In general, the system is dynamic, meaning that the arm pitch angle is a

function of time: θ = θ(t)• We will first focus on the static equilibrium of the system.

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Fcwlb � (Fh � FL)la = 0

• Thus, for a given thrust force FT, this becomes one equation with one unknown (pitch angle θ)

• The moment length la and lbare function of pitch angle θ

• The lift force FL depends on the thrust force FT and the pitch angle θ

Dynamic Behavior• What happens if we change the thrust/lift produced by

the rotors?- The system can not suddenly jump to a new

pitch/elevation- How it moves to the new position is governed by the

dynamics of the system- Eventually the system should settle down and reach a

steady-state position (in this case, the previously described static equilibrium position)

• Main concept of dynamical systems: - Effects of an action do not achieve their impact

immediately; system evolves with time- Response depends on time-history of external input(s) and

properties of the system itself 8

Spring-Mass-Damper System• Many dynamical systems can be modeled as spring-

mass-damper systems:• Car suspension• RLC circuits• And many more!

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Fext(t) � given temporal excitationFspr � spring force, proportional to the displacement: Fspr(t) = �k · x(t)

Fdmp � damper force, propositional to the velocity: Fdmp(t) = �b · dx(t)

dt

Spring-Mass-Damper System

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• Newton’s second law:�

F (t) = ma(t) = md2x(t)

dt2

• Forces (previous slide): Fext(t), Fspr = �k · x(t), and Fdmp = �b · dx(t)

dt• Thus, we get:

Fext(t) � k · x(t) � b · dx(t)

dt= m

d2x(t)

dt2• Rearranging

mx(t) + bx(t) + kx(t) = Fext(t), where dx(t)

dt= x(t),

d2x(t)

dt2= x(t)

Demonstration• Matlab demo…

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Shaft Encoders• Determine rotation of a shaft• Potentiometers, magnetic, optical• Absolute vs. relative (incremental)• Transmission vs. reflection

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Light Source

Photo-detector

Light Source

Photo-detector

Code Disc

Experiment

• You will be running 3 experiments1. Calibrating the motor control voltage, i.e., determining

the thrust produced by a given motor control voltage

2. Measuring how the system responds when its controller is told to move the helicopter to a given pitch angle, but with different levels of system damping

3. Measuring how the system responds when you provide a step response control input to the motors• Outside the lab, you will also use a Matlab routine we will make

available to compare your measured system step response to a mathematical model of the system

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