Unformatted text preview: ME 475 Homework Set 1 Problem 1: Spring 2011 Due January 20, 2011 In many mechanical positioning systems there is flexibility between one part of the system and another. An example is shown in figure 2.7 (both edition 5 and 6 of the text) where there is flexibility of the solar panels. The figure shown below (2.36 5th or 2.42 6th ) depicts such a situation, where a force u is applied to the mass M and another mass m is connected to it. The coupling between the objects is often modeled by a spring constant k with a damping coefficient b, although the actual situation is usually more complicated than this. (a) Write the equations of motion governing this system. (b) Find the transfer function between the control input, u, and the output, y. Problem 2: A very typical problem of electromechanical position control is an electric motor driving a load that has one dominant vibration mode. The problem arises in computer
disk
head control, reel
to
reel tape drives, and many other applications. A schematic diagram is sketched in (Fig 2.45 5th or Fig 2.51 6th ). The motor has an electrical constant Ke, a torque constant Kt, an armature inductance La, and a resistance Ra. The rotor has an inertia J1 and a viscous friction B. The load has an inertia J2. The two inertias are connected by a shaft with a spring constant k and an equivalent viscous damping b. (a) Write the equations of motion. (b) Find the transfer function from the input va to the output θ2. ME 475 Homework Set 1 Problem 3: Spring 2011 Due January 20, 2011 Compare the two structures shown in the figure below with respect to sensitivity to change in the overall gain owing to changes in the amplifier gain. Use the relation S= d ln F K dF = d ln K F dK as the measure. Select H1 and H2 so that the nominal system outputs satisfy F1 =F2, and assume KH1 > 0. ...
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