AE2610 Introduction to Experimental Methods in Aerospace

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1 AE2610 Introduction to Experimental Methods in Aerospace Lab #3: Dynamic Response of a 3-DOF Helicopter Model C.V. Di Leo 1

2 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 2

3 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 3

longitudinal stability. Disadvantages: Complex transmission (mechanics), and the need for two large rotors.

4 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) Ch-47 Chinook V22 Osprey 4

5 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 Travel axis Thrust forces Pitch axis Elevation axis In this lab, a control system constraints the helicopter such that it can only rotate about the elevation axis (1-DOF) 5

6 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. 6

7 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. F cw l b (F h F L )l a =0 The moment length l a and l b are function of pitch angle θ The lift force F L depends on the thrust force F T and the pitch angle θ Thus, for a given thrust force F T, this becomes one equation with one unknown (pitch angle θ) 7

8 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

9 Spring-Mass-Damper System Many dynamical systems can be modeled as springmass-damper systems: Car suspension RLC circuits And many more! F ext (t) given temporal excitation F spr spring force, proportional to the displacement: F spr (t) = k x(t) F dmp damper force, propositional to the velocity: F dmp (t) = b dx(t) dt 9

dt Thus, we get: Rearranging F ext (t) k x(t) b dx(t) dt = m d2 x(t) dt 2

10 Spring-Mass-Damper System Newton s second law: F (t) =ma(t) =m d2 x(t) dt 2 Forces (previous slide): F ext (t), F spr = k x(t), and F dmp = b dx(t) dt Thus, we get: Rearranging F ext (t) k x(t) b dx(t) dt = m d2 x(t) dt 2 mẍ(t)+bẋ(t)+kx(t) =F ext (t), where dx(t) dt =ẋ(t), d 2 x(t) dt 2 =ẍ(t) 10

11 Demonstration Matlab demo 11

12 Shaft Encoders Determine rotation of a shaft Potentiometers, magnetic, optical Absolute vs. relative (incremental) Transmission vs. reflection Light Source Code Disc Light Source Photodetector Photodetector 12

13 Experiment You will be running 3 experiments 1. 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 13

Penn State Erie, The Behrend College School of Engineering

Penn State Erie, The Behrend College School of Engineering EE BD 327 Signals and Control Lab Spring 2008 Lab 9 Ball and Beam Balancing Problem April 10, 17, 24, 2008 Due: May 1, 2008 Number of Lab Periods: