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CONTROL AND ACTUATING DEVICES FOR MECHANICAL SYSTEMS (Proff. Braghin, Collina) 02.02.2015 L v J 2b t m r, k t Jm Lateral view q a CL CD Aerodynamic coefficients CM Consider the mechanical system represented in the figure placed in the vertical plane. For all the questions, the assumption of small displacements about the equilibrium position represented in the picture is made. A bluff body (inertia J), is subjected to the wind excitation (wind speed equal to v, as represented in the picture). The body is connected to the ground in its centre of gravity. The bottom side of the body is connected, through a spring -damper system ( r, k) to a mass m. On the other side, the mass is connected, through a gearbox (gear ratio t) to the rotor of a DC motor. Consider the inertia of the rotor equal to Jm. Consider the moto as ideal (L→0) and the spring k as completely rigid (k→∞): 1. Write the equation of motion of the electro-mechanical system and study the system stability about its equilibrium position in the time domain. 2. Introduce a Proportional control on the rotation q acting on the motor voltage. Compute the time domain response of the system to a step reference and draw it. Discuss the effect of the control gain on the response. For this point, assume the uncontrolled system as stable. 3. What is the effect of the addition of an inte gral contribution to the control law? Discuss the effect of the variation of the integral control gain. Consider now the motor dynamics (L ≠ 0) and still consider the spring k as completely rigid (k→∞): 4. Write the equation of motion of the system, introducing a Proportional-Derivative control on the rotation q and a Proportional current loop. 5. Assuming the uncontrolled system as unstable, anal yse the stability of the controlled system…