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ROSE-HULMAN INSTITUTE OF TECHNOLOGY Department of Mechanical Engineering ME 506 Advanced Controls Homework 5, Due October 6 1. Multivariable Frequency Response For the following system: 0 0 0 1 0 0 80.9074 0 433.22 0 = −433.22 −5.5089 + 0 0 0 1 0 0 287.338 0 −287.338 −3.9477 0 −89.0056 = 1 0 0 0 0 1 0 0 + 0 0 0 0 a) Find the MIMO transfer function matrix and plot the singular value plot in Matlab b) For the input frequence ω = 5 Hz, find the singular value decomposition of the transfer function matrix, and determine the input signals required to generate the maximum and minimum output amplitudes. (Magnitudes and phases). c) Build the system in Simulink, and demonstrate the MIMO frequency response using your results from b). Show that your singular value plot accurately reflects the ratio between maximum output amplitude and minimum output amplitude at ω = 5 Hz. 2. Observer design The longitudinal dynamics of the S-61 helicopter built by Sikorsky Aircraft Company are given below in state space form. Design a full order observer for this system, such that the observer poles are at s = {-5, -7, -10}, the pitch attitude state is associated with s = -10, and is decoupled from the other two states. Demonstrate the decoupling by simulations with initial state estimation error set to each of the closed-loop eigenvectors. u& − 0.02 − 0.098 0.014 u 0.098 0.01 δ & 0 1 θ + 0 0 B θ = 0 δ q& 1 0 − 0.4 q − 6.3 1.2 C u y1 0 1 0 = θ y 2 0 0 1 q Homework 5 Page 1 of 1