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MIT16_30F10_lab02 - 16.30/31 Prof J P How and Prof E...

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16.30/31 November 15, 2010 Prof. J. P. How and Prof. E. Frazzoli Due: December 3, 2010 T.A. B. Luders 16.30/31 Lab #2 1 Introduction In the second lab, you will be controlling the Quanser on all three axes: roll, pitch, and travel. The primary goal is to develop the controllers for these axes using state space techniques that we developed in class (if not for all 3 axes, then at least for the pitch axis). This lab requires the use of the classical controllers designed in Lab 1. You may choose to use your previously-developed controllers, design new ones, or use the controllers provided below (which seemed to work well in practice). G pitch ( s ) = 10 ( s + 0 . 9)( s + 0 . 2) G roll ( s ) = 10 ( s + 4 . 5)( s + 3) c c s ( s + 40) ( s + 60)( s + 30) 2 Designing a Travel Controller In many aerospace systems, inner control loops are used to control the attitude of the plant, while outer loops are then used to control the location of the plant in space by commanding certain attitudes. Take, for instance, the altitude controller on most aircraft autopilots. The altitude controller itself commands a certain pitch, then an inner controller commands the elevator deflection to attain that pitch. This is the strategy you will use to control the travel axis of the Quanser. Your travel controller will set the roll angle command, and that command goes through your roll angle controller, then is fed into the actual Quanser. This implies that your roll controller is now part of the system dynamics, and this fact must be accounted for in the system model. The overall architecture is shown in Figure 1. The model we want to derive is the transfer function from roll angle command to travel angle output, i.e., G travel ( s ) = ψ ( s ) . φ c ( s ) The roll and pitch controllers provide the inner control loops: V coll = G pitch ( s )( θ c θ ) , c V cyc = G roll ( s )( φ c φ ) . c 1
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Figure 1: Overall architecture - as noted in Lab 1, all voltages must be saturated at ± 5 V. The dynamics for the travel control design are established by closing these 2 inner loop controllers, then determining the dynamics from the input φ c to the output ψ . The travel controller is then implemented as = G travel ( s )( ψ c ψ ) . φ c c Table 1: Additional physical parameters (addendum to Lab 1) Parameter Value Units Description I zz K D ¯ ω coll K v 0.93 0 Mgl θ sin( θ rest ) K τ l boom 0 . 0125¯ ω coll K τ l boom Nm N moment of inertia about z-axis travel rate drag coefficient trim collective thrust travel rate thrust coefficient 3 Schedule Mon 11/15: Lab 2 assignment posted Wed 11/17: Signup sheets for lab sessions available in lecture Fri 11/19: First day of lab sessions Mon 11/22: Lab 2 pre-lab
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MIT16_30F10_lab02 - 16.30/31 Prof J P How and Prof E...

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