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e483h8_07

# e483h8_07 - Simon Fraser University School of Engineering...

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Simon Fraser University School of Engineering Science ENSC 483 - Modern Control Systems Spring 2007–Assignment 8 Background on Aircraft Dynamics — Modern control theory has had many successful applications in aerospace domain. For instance, the space shuttle is equipped with a sophis- ticated control system that includes two different autopilots–one to handle ascent to and descent to orbit and another to handle the Shuttle maneuvers and payload deployment on orbit. The control laws of the orbit flight control system implement various modern control principles, such as state estimation and optimal control. Same is true in other aerospace applications. Rigid body dynamics and aerodynamics which are prerequisites for studying and modeling of an aircraft are well beyond the scope of this quick and dirty introduction 1 . In general, the motion of a rigid body has six dynamic degrees of freedom (three needed to locate the center of mass in space and three to define the orientation), and is governed by Newtonian laws of motion. Furthermore, each degree of freedom takes two state variables (one position and one velocity). Thus, in general a twelfth order system (or differential equation) would describe the dynamics of a rigid body such as an aircraft (things can get a lot more messy with flexible bodies). There are several terminologies used by the aerospace engineers. For example the projection of the angular velocity vector on the body axes ( x, y, z in Figure 1) have standard symbols ( p, q, r which stand for roll rate, pitch rate, and yaw rate respectively–the notation doesn’t seem to make common sense. Does it? ). For translational motion of the aircraft, it is customary to project the velocity vector along the body axes ( x, y, z ). The resulting velocity vector projections are designated by u, v, w as shown in Figures 1 and 2. As you might expect, the aerodynamic forces and moments are complicated, nonlinear func- tions of many variables. For control purposes however, the aircraft dynamics are linearized about an operating point or flight condition commonly referred to as the flight regime , where it is assumed that the aircraft velocity and altitude are constant. Furthermore, the control 1 You may refer to the following references for study of aircraft dynamics and modeling for control: 1. Seckel, E., Stability and Control of Airplanes and Helicopters , Academic Press, NY, 1964. 2. McRuer, D., Ashkenas, I., and Graham, D., Aircraft Dynamics and Automatic Control , Princeton Uni- versity Press, Princeton, NJ, 1973.

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surfaces and engine thrust are set or trimmed to maintain the flight regime. The control problem is to maintain these conditions, i.e. to bring any deviations from the nominal flight condition to zero (remember the regulator problem). Also the objective is to control small motion rather than controlling the absolute position ( x, y, z ). So these inertial positions are frequently dropped from the dynamic equations, leaving nine of them.
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