Objects smaller than the wavelengths of visible light are a staple of contemporary science and technology. Biologists study single molecules of protein or DNA; materials scientists examine atomic-scale flaws in crystals; microelectronics engineers lay out circuit patterns only a few tenths of atoms thick. Until recently, this minute world could be seen only by cumbersome, often destructive methods, such as electron microscopy and X-ray diffraction. It lay beyond the reach of any instrument as simple and direct as the familiar light microscope. New microscopes, typified by the scanning tunneling microscope (STM), are now available [3]. The precision of position control required is in the order of nanometers. The STM relies on piezoelectric sensors that change size when an electric voltage across the material is changed. The "aperture" in the STM is a tiny tungsten probe, its tip ground so fine that it may consist of only a single atom and measure just 0.2 nanometer in width. Piezoelectric controls maneuver the tip to within a nanometer or two of the surface of a conducting specimen-so close that the electron clouds of the atom at the probe tip and of the nearest atom of the specimen overlap. A feedback mechanism senses the variations in tunneling current and varies the voltage applied to a third, z-axis, control. The z-axis piezoelectric moves the probe vertically to stabilize the current and to maintain a constant gap between the microscope's tip and the surface. The control system is shown in Figure DP12.4(a), and the block diagram is shown in Figure DP12.4(b).The process is

and the controller is chosen to have two real, unequal zeros so that we have

(a) Use the ITAE design method to determine Gc(s).
(b) Determine the step response of the system with and without a prefilter Gp(s). (c) Determine the response of the system to a disturbance when Td(s) = l/s. (d) Using the prefilter and Gc(s) of parts (a) and (b), determine the actual response when the process changes to

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17,640 G(s) =- s(s++ 59.4s + 1764) G (s) 16,000 G(s) s(s +40s1600)