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CONTROL AND ACTUATING DEVICES FOR MECHANICAL SYSTEMS 03.07.2017 Proff. Braghin, Collina, Sabbioni Consider the mechanical system represented in the figure placed in the vertical plane. A bluff body, having its centre of gravity in O (moment of inertia J O) is hinged in O to the ground. The body is subjected to the wind action (U is the speed of the wind, assumed constant). The body is connected, by means of a cable with finite stiffness k , to a disc of radius R that rolls without sliding on a horizontal plane. The center of the disk is connected through a pin to the rod of a hydraulic actuator which allows to control the rotation of the body. The aerodynamic coefficients are computed reducing lift and drag forces to the point O. Consider the actuator as ideal (β → ∞) and the cable as completely rigid (k → ∞): 1. Write the equation of motion of the hydraulic-mechanical system; linearize the equation of motion around the equilibrium position θ = 0 and analyse the system stability in the time domain. 2. Apply a Proportional control on the rotation of the bluff body acting on the spool valve displacement. Given a step reference, compute the time response of the system and plot it discussing the effect of the control gain. Consider now the hydraulic actuator dynamics (β ≠ ∞) and still consider the cable as completely rigid (k → ∞): 3. Write the equation of motion of the system, introducing a Proportional-Derivative control on the rotation of the bluff body. Analyse the stability of the controlled system in time domain. 4. Draw the block diagram of the control system and compute the open and closed loop transfer functions between the rotation of the body and the reference. 5. Analyse the stability of the control system in Laplace domain studying the effect of control…