Propose physical components for the summing point and proportional controller and determine all transfer functions involved in this control system.

Use Simulink to simulate the control system of Problem 11.19, and plot the controlled response of the system. A reference voltage vr is applied to the piezoelectric block, which increases linearly from 0 to 110V in 5 s then remains constant for the following 25 s. The cantilever has a length l = 15 mm, its rectangular cross-section is defined by w = 3 mm, h = 0.5 mm, and the material elasticity modulus is E = 210 . The piezoelectric actuator is defined by la = 35 mm, A = 65 mm2 , t = 6300 kg/m3 , Em = 55 GPa, and d = 4.5 × 10-10 m/V. The strain gauges have a sensitivity Kg = 2, and the input voltage to the Wheatstone bridge is vi = 18 V. Problem 11.19 A piezoelectric block, which is fixed at one end and free at the other, is supplied a reference voltage vr and, consequently, deforms axially. Using a lumped-parameter model of the piezoelectric block with inertia, stiffness and viscous-type losses (damping) taken into account, design a unity-feedback control system, where the sensing of the block’s free end is performed by a cantilever provided with four strain gauges connected in a Wheatstone bridge. Propose physical components for the summing point and proportional controller and determine all transfer functions involved in this control system.


 

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