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# sug_final - EML 4312 Spring 2009 Control of Mechanical...

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EML 4312 Spring 2009 Control of Mechanical engineering systems University of Florida Mechanical and Aerospace Engineering Suggested exercises on State Space method Issued: April 25, 2009 Problem 1. Consider a dynamical system governed by the following set of coupled differential equa- tions: ˙ X = aX 2 - bXY (1) ˙ Y = Y - 2 X (2) Is this a linear system? Verify that ( X = 0 , Y = 0) is an equilibrium point of this system. Is it the only equilibrium point? Linearize the system around the equilibrium ( X = 0 , Y = 0). Problem 2. The linearized equation of motion of a high-performance helicopter are: ¨ θ = - σ 1 ˙ θ - α 1 ˙ x + + w ¨ x = - α 2 ˙ θ - σ 2 ˙ x + gδ, where θ ( t ) is the pitch angle of the helicopter, x ( t ) is its translation, the rotor thrust angle δ ( t ) is a control input that is used to control the pitch θ , and w is an external disturbance. n, g, σ ( · ) , α ( · ) are constants. 1. Is this a linear system? 2. Express these equations in state-space form with x = [ θ, x ] T as the state vector and [ w, δ ] T as the input vector.

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