A third order system of ODE's is defined by the block diagram of Fig. 1. Initial conditions on the states are: x1(0) 1; x2(0)-1; 3(0) 10 1. u 0 Ху X1 -2 -10 .9 Fig. 1. Third Order System of ODE's Derive the system matrix, A, spectral matrix, S, and modal matrix, M, and hence determine the states, x,(t), x2(t), and x3 (C) in response to the initial conditions given above. a) (30 Marks) Select a suitable set of initial conditions on the states, to obtain the unit step response and unit impulse response of the system. Justify your answer fully. b) (10 Marks) A third order system of ODE's is defined by the block diagram of Fig. 1. Initial conditions on the states are: x1(0) 1; x2(0)-1; 3(0) 10 1. u 0 Ху X1 -2 -10 .9 Fig. 1. Third Order System of ODE's Derive the system matrix, A, spectral matrix, S, and modal matrix, M, and hence determine the states, x,(t), x2(t), and x3 (C) in response to the initial conditions given above. a) (30 Marks) Select a suitable set of initial conditions on the states, to obtain the unit step response and unit impulse response of the system. Justify your answer fully. b) (10 Marks)


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