Question

Figure 3 shows a lumped-parameter representation of a concept for a MEMS "tuning fork gyro- scope" for measuring angular velocity. Displacement 21(t), 22(t), and y(t) are absolute positions of the inertia elements m, m2, and m3, respectively, and are measured from their static equi- librium positions where there is no deflection in the springs. The system friction is represented by three ideal lumped dashpot elements bi, by, and by. Two external forces fi(t) and fa(t) are applied to masses m, and m2, respectively. Consider the positions of the inertia elments as the La(t) fi(t) m ; www m2 AW TIS Figure 3: Translational mechanical system. The mathematical model of the system is given by mjä(t) + biz(t) + kızı(t) - kız(t) = fi(t), m222 + b222(t) + kozz(t) - k22(t) = f(t), -k (t) - k222(t) + mzës(t) + bzzz(t) + (ki + k + kg)23(t) = 0. (a) Identify the state variables, input variables, and the output variables of the system. (b) Write the standard general form of the state variable equations and the output- variable equations. (c) Obtain the complete state-space representation (SSR) * = Ax+Bu y = Cx+Du

Answer 1

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