AE2610 Introduction to Experimental Methods in Aerospace Lab #3: Dynamic Response of a 3-DOF Helicopter Model C.V. Di Leo 1
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
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
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
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
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
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
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 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
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
Demonstration Matlab demo 11
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
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