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Unformatted text preview: 16.30/31 September 24, 2010 Prof. J. P. How and Prof. E. Frazzoli Due: October 15, 2010 T.A. B. Luders 16.30/31 Lab #1 1 Introduction The Quanser helicopter is a mechanical device that emulates the ﬂight of a reduced degree of freedom (DOF) helicopter. Instead of the usual six DOF of a free-ﬂying helicopter, the Quanser only exhibits three DOF: roll, pitch, and travel, as illustrated in Figures 1-3. The Quanser system is actuated by two rotor speeds, and the inputs to the system are V cyc , which is an electric voltage that results in differential change in the two rotor speeds, and V coll , which is an electric voltage that controls the speed of the two propellers collectively. The outputs of the system are three angles: roll φ , pitch θ , and travel ψ . Please note the limits of the Quanser: voltage ∈ [ − 5 , 5] Volts, φ ∈ [ − 40 ◦ , 40 ◦ ], and θ ∈ [ 25 ◦ , 30 ◦ ]. − 1 T L T R ϕ θ Ψ Images by MIT OpenCourseWare. 2 Physical Model The Quanser model is derived by applying Newton’s second law to the rate of change of angular momentum. The nonlinear equations of motion are I xx φ ¨ = τ cyc l h − mgl φ sin( φ ) − L p φ ˙ − I r ω rotor ( θ ˙ cos( φ ) + ψ ˙ sin( φ )) , (1) I yy θ ¨ = τ coll l boom cos( φ ) − Mgl θ sin( θ + θ rest ) − Dl boom sin( γ ) + I r ω rotor φ ˙ − M q θ, ˙ (2) ¨ I zz ψ = τ coll l boom sin( φ ) − Dl boom cos( γ ) , (3) where D is the induced drag, τ coll is the collective thrust, and τ cyc is the cyclic thrust. These forces are modeled individually as D = K D ψ, ˙ (4) τ coll = K τ ω coll − K v ψ, ˙ (5) τ cyc = K τ ω cyc − K v ψ, ˙ (6) where K D , K τ and K v are constant coeﬃcients. In addition, the motor dynamics can be modeled by ω ˙ cyc + 6 ω cyc = 780 V cyc , (7) ω ˙ coll + 6 ω coll = 540 V coll . (8) The values of other parameters in this model are given in Table 1. Note that ω rotor is the rotor rotation speed, and is assumed to be constant; terms containing ω rotor represent the rotors’ contribution to angular momentum. Additionally, γ is the vehicle’s ﬂight path angle....
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This note was uploaded on 02/03/2012 for the course AERO 16.30 taught by Professor Ericferon during the Fall '04 term at MIT.
- Fall '04