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MFE 510 Exam 1

# MFE 510 Exam 1 - Homeipmlﬁi who fr Maﬁa Manufacturing...

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Unformatted text preview: Homeipmlﬁi who fr} Maﬁa Manufacturing Engineering Program Worcester Polytechnic Institute MFE 510: Control and Monitoring of Manufacturing Processes Instructor: M. S. FOFANA Ofﬁce: VVashburn 3111) E-mail: msfofana©wpiedu V-mail: (508) 831—5966 Assigned: February 20, 2008 Answer any FIVE Questions and all equations carry equal marks I (a) Find the transfer function 0(5) = “555) relating the capacitor voltage, vc(s) to the input voltage v(t), as shown in the Figure 1a (Hints: use LPTs: C(s) : fg(t)e‘3‘dt, 0 Ohm’s law, Kirchhoff ’s voltage law or current law) where RLC are in series arrangement. ‘ RLC network [a 7“} /6 (b) If the input voltage Mt) is a periodic function as shown in Figure 1b, Show that \ (LCTI 41 '7 ~ '9 : , _. , l '1 "’“l b ” 1‘ (Gig) 15\$ + R(Li‘1)192 + (_LC~')“15{ 6 i < j II (3) Find the transfer function G(s) = for single degree of freedom model with mass m, damping coefficient ospring constant A: and input function Mt) as shown in 00 Figure 2 (Hints: use LPTS: 6(3) : g(t)e‘5‘d‘ti Newton’s second law) 0 (b) If the input function 7"(t) is the damped cosine wave, given by (27) r(t) 2 f0 sinwt Ht) 2 e‘a‘coswt (2) ﬁnd the resulting output Y(s) = R(S)G(5). III (a) Find the inverse Laplace Tiansforms of the following given functions below in the s — domain: 5(5+ 1) Y“) = m ‘33) ‘ 5(8 + 1) HS) “ 33 +1632 +165 (3b) Y(s) = m (30) (b) Sketch a block diagram for each function, representii‘ig the input7 output and trans— fer function in the time domain. IV. A Segway Human Transporter (SHT) is a two-Wheeled Vehicle (see ﬁgure below) in which the human operator stands vertically on a platform. As the driver leans left. right. forward, or backward, a set of sensitive gyroscopic sensors sense the desired input These signals are fed to a computer that ampliﬁes them and commands motors to propel the vehicle in the desired direction. One very important feature of the SHT is its safety. The systems will maintain its vertical position within a specified angle despite road disturbances, such as uphills and down hills or even if the operator over-leans in any direction. (a) Draw a functional control loop diagram of the SHT to keep it in a vertical position. (b) Indicate the input and output signals and all possible control acquisition elements in the functional loop diagram (c) Describe the design and analysis tasks for controlling the vertical position of the SHT (d) Functionally, how does a closed~loop SHT differ from an open—loop SHT The Segway Human Transporter V. Increasingly stringent requirements of modern high~pre<tision machinery are placing increasing demands on slide systems. The typical goal is to accurately control the desired pathway of the table shown in the figure below (a) Sketch a block diagram model of a feedback systems to achieve the desired goal. The table can move in the :zr-direction as shown in the (b) Describe the design and analysis tasks for controlling the horizontal 23—position of the machinetool table (0) Name two advantages of having a computer in the closed loop. (d) If the modelling of the machine—tool table yields the following governing ordinary dif— ferential equation and initial conditions mi + 2Cw0j: + may: = f(t), 55(0) : 0, 33(0) 2 0 (4) where for given values of m 2 1, wg 2 V5, C = , and ﬁt) 2 3, find the response 3: = (ﬁl using Laplace transforms. Machine tool with tabte. VI. The development of robotic microsurgery devices will have major implications on deli— cate eye and brain surgical procedures. The microsurgery devices employ feedback control to reduce the effects of the surgeon’s muscle tremors. Precision movements by an articu— lated robotic arm can greatly help a surgeon by providing a carefully controlled hand. One such device is shown in the figure below. The microsurgical devices have been evaluated in clinical procedures and are now being commercialized (a) Sketch a closed loop block diagram of the surgical process with a n’iicrosurgical device in the loop being operated by a surgeon. Assume that the position of the end—effector on the microsurgical device can be measured and is available for feedback (b) Indicate the input and output signals and all possible control acquisition elements in the functional closed loop diagram (C)Illustrate how you Will control the entire kinematics and kinetics motion dynamics of the microsurgical robot (d) Obtain the Laplace transform of the following function 0, fort<0 sinwtcoswt, for t2 0 Microsurgery robotic manipulation (Photo courtesy of NASA.) m" "7 3U W V; 5 “k E‘Aﬁ; I Q, 15(sz } arm 0% Q5): I “6) =1 cm “02+ (‘0‘) = Q 5’?me - € b0 R63” \$757,.» ' if.) z- 5"}?79 09 (3176/7 “113% ‘ . / C/QSeo) ~/ _ a ‘ g 4Q J ' 8% T U ‘ / J [:0 {*7sz E“; 77x: one ’ § ’ 70 r 7, u 46 m f0 /n m. m I 7%” 79‘6"” =5; xxx; W W 07070" 5 0000/5) r vL 9‘15 ‘ a ﬂ! A ‘ f z I” ~*‘ " f/H a» 13’ ﬁﬁszr; ‘ H r » V (/e _ “if COM/Wm 124%? #16 72%} .M 2 75* L If ,7 ' s 1 I LL27 J/L‘Wfd Ck SBQLI i r; .. s f 2 r A ’4 k) i/*{ {A} C ‘ ‘ if; 6+1: 5 E E 5“ at. e «marge; 1’ {- \1; A I i t a Hargm name} My mg“; #0 w WI) {0 0’3} g} a} m / o] We 50%?Cm \$536; I WW'WE Muscle ﬁe IX"?1 L2” Wig / “107M311 ...
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MFE 510 Exam 1 - Homeipmlﬁi who fr Maﬁa Manufacturing...

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