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HW5-S09
Course: ME 3015, Fall 2008School: Georgia Tech
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System ME3015 Dynamics (Woodruff School of Mechanical Engineering, Georgia Tech) ME3015 ASSIGNMENT #5 Read Chapter 7, Chapter 8, and Section 10-5 (I.1) The schematic given below shows a system for supplying fuel to automative engines using an electric fuel pump. An "accumulator", which consists of a piston (area A) moving with velocity v(t) under pressure p(t) against a spring (stiffness k) in...
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System ME3015 Dynamics (Woodruff School of Mechanical Engineering, Georgia Tech)
ME3015 ASSIGNMENT #5 Read Chapter 7, Chapter 8, and Section 10-5 (I.1) The schematic given below shows a system for supplying fuel to automative engines using an electric fuel pump. An "accumulator", which consists of a piston (area A) moving with velocity v(t) under pressure p(t) against a spring (stiffness k) in the cylinder, is to smooth fluctuations in supply (volumetric) flow rate qs(t). You may assume that pressure drops are negligible except across the discharge orifice and that the linearized resistance to flow through the orifice is R. Answer the following questions: a) Show that the transfer function is given by
Spring, k Pressure p Mass, m
x(t)
Pump
qA(t) qs(t)
Short pipe Orifice Flow to engine, q L (t ) .
Fuel
P( s) R(ms 2 + k ) = 2 . Qs ( s ) ms + A2 Rs + k b) Given m =1kg and A = 10cm2, determine k and R such that the system will have a damping ratio of 1 and a frequency natural of 10 rad/s. c) If the system experiences a step change in supply flow rate of 1cm3/s from its original steady-state operating condition, sketch the time response p(t) using the parameters determined in part (2). 2 2 n n P( s) = a 2 + bs 2 2 2 2 Qs ( s ) s + 2n s + n s + 2n s + n Hints: express the transfer function in the form. (I.2) The flapper-nozzle valve that consists of an orifice R and a variable flow resistance Rv (orifice with area A) shown below is used to position the mass m against a spring k. The volumetric flow rate through an orifice is pro...
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Georgia Tech - ME - 3015
ME3015 System Dynamics (Woodruff School of Mechanical Engineering, Georgia Tech)ME3015 ASSIGNMENT #6 Read Chapter 8 and Section 10-5 and 10-6 I. The schematic shown on the right, where the variables are deviations from an operating point, is a pneu
Georgia Tech - ME - 3015
ME3015 System Dynamics (Woodruff School of Mechanical Engineering, Georgia Tech)ME3015 ASSIGNMENT #7 Read Chapter 9 and Sections 11.1 and 11.2; A-11.6 and A-11.7. (I) Text Problems B-9-1, B-9-4, B-9-8 and B-9-11 (II) Text Problems B-11-1, B-11-2, a
Georgia Tech - ME - 3015
ME3015 System Dynamics and Control (Issued: March 26, 2009, Due: April 23, 2009) Georgia Institute of Technology The George W. Woodruff School of Mechanical Engineering ME3015 System Dynamics and Control Computer-aided-design assignmentThe Segw
Georgia Tech - ME - 3015
ME3015B Quiz 1 (closed book/notes) January 15, 2009Name:_Solutions_1. (2 pts) Can the principle of superposition be used for the system represented by the following equations? d 3x d 2 x dx (a) + 2 2 + + 2x - t 2 = 0 Yes, because it is a LTI syst
Georgia Tech - ME - 3015
ME3015B Quiz 2 (closed book/notes) January 29, 2009Name:_Solutions_1. (4 pts) Consider the following mechanical system, where x is measure from the equilibrium position. (a) Derive the equation of motion for x(t). Clearly show the steps with a co
Georgia Tech - ME - 3015
ME3015 Quiz 5 (closed book/notes) March 26, 2009Name:_1. (6 pts) The equation of motion of a mechanical system is given by 2 x + 3 x = p(t ) , where p and x are the displacements of the input and output respectively. Suppose that p (t ) = 10sin 2
Georgia Tech - ME - 3015
Name _ _(Please Print) Georgia Institute of Technology Woodruff School of Mechanical Engineering ME3015B System Dynamics and Control Second mid-term: April 9, 2009 You need to show all the work clearly. Only answers or partial steps are not accep
Georgia Tech - ME - 3015
ME3015 Quiz 6 (closed book/notes) April 21, 2009 1. Given the compensator G ( s ) = KName:_T1s + 1 , T2 s + 1 (a) (5 pts) derive the magnitude and phase in dB and degrees respectively. (b) (3 pts) From the Bode plots, determine the values for K,
Cleveland State - IST - 305
Chapter 8 Information Systems Development & AcquisitionChapter 8 Objectives Understand the process of IS management Understand the system development life cycle (SDLC) Understand alternative approaches to system development Understand in-house
Georgia Tech - ME - 3015
Georgia Tech - ME - 3015
ME3015 System Dynamics (Woodruff School of Mechanical Engineering, Georgia Tech)ME3015 Assignment 8 and CAD ASSIGNMENT (I) Text Problems B-10-14 and B-10-17 (Plot the root locus using Matlab to verify the range of stability.)6 > n=1 > d = [1 6 5
Georgia Tech - ME - 3015
ME3015 System Dynamics (Woodruff School of Mechanical Engineering, Georgia Tech)ME3015 Assignment 8 and CAD ASSIGNMENT (II) Text Problems B-11-7 and B-11-15. (Plot the Bode diagram using Matlab to verify your calculation and the unit step response.
Georgia Tech - ME - 3015
Georgia Tech - ME - 3015
Georgia Tech - ME - 3015
ME3015 System Dynamics (Woodruff School of Mechanical Engineering, Georgia Tech)(II.2) Consider a simplified version of a magnetic bearing that can be built in a laboratory as shown in Figure 1, where the iron ball is to be magnetically suspended a
Georgia Tech - ME - 3015
Georgia Tech - ME - 3015
ME3015 System Dynamics (Woodruff School of Mechanical Engineering, Georgia Tech)3015 ASSIGNMENT #5 Read Chapter 7m Chapter 8, and Section 10-5 (I.1) The schematic given below shows a system for supplying fuel to automative engines using an electric
Georgia Tech - ME - 3015
Georgia Tech - ME - 3015
Georgia Tech - ME - 3015
Name:_(Please Print) Georgia Institute of Technology Woodruff School of Mechanical Engineering ME3015 System Dynamics and Control Second mid-term: April 4, 2002 You need to show clearly all the work. Only answers or partial steps are not acceptab
Georgia Tech - ME - 3015
Problem B-11-1 Rewriting G ( s ) =s s = = G1 ( s )G2 ( s ) s /10 + 1 0.1s + 1where G1 ( s ) = s and G2 ( s ) =1 . 0.1s + 1220 log10 G ( j ) = 20 log10 G1 ( j ) + 20 log10 G2 ( j ) = 20 log10 - 20 log10 1 + ( 0.1 )G ( j ) = G1 ( j ) + G2 (
Georgia Tech - ME - 3015
Problem B-11-11 1 Rewriting G ( s ) = ( 0.2s + 1) = KG1 ( s )G2 ( s ) 2 2 0.1s + 0.2s + 1 1 1 where K = ; G1 ( s ) = 0.2s + 1 ; and G2 ( s ) = . 2 2 0.1s + 0.2 s + 1For the 1st order system the corner frequency is 5 rad/s. For the second
Georgia Tech - ME - 3015
ME3015 System Dynamics (Woodruff School of Mechanical Engineering, Georgia Tech)Solutions to ME3015 ASSIGNMENT #3 (I.1) Example 4-1, Figure 4-6(c) in Example 4-2, and Equations (5-7) and (5-8) are three different representations modeling the same m
Georgia Tech - ME - 3015
ME3015 System Dynamics (Woodruff School of Mechanical Engineering, Georgia Tech)Solutions to ASSIGNMENT #1 (I) Identify the terms that make the ODE non-linear and/or time-varying: ODE(2t - 1) h23Non-linear termsdx + x 2 = t sin t dt h2Time-v
Georgia Tech - ME - 3015
ME3015 System Dynamics (Woodruff School of Mechanical Engineering, Georgia Tech)ME3015 ASSIGNMENT #6 (solutions) I. The schematic shown on the right, where the variables are deviations from an operating point = 0 , is a pneumatic valve/cylinder. (
Georgia Tech - ME - 3015
ME3015 System Dynamics (Woodruff School of Mechanical Engineering, Georgia Tech)ME3015 ASSIGNMENT #6 (solutions) II. The block diagram shown in Figure 2(a) represents a position control system. 16 and H ( s ) = 1 + ks . (a) Show that Figure 2(a) ca
Georgia Tech - ME - 3015
ME3015 System Dynamics (Woodruff School of Mechanical Engineering, Georgia Tech)III. The block diagram of a positioning control system is shown in Figure 3. In consistent units, the values of the fixed parameters are T=0.1, J=0.01, Ki =10. Disturba
Georgia Tech - ME - 3015
ME3015 System Dynamics (Woodruff School of Mechanical Engineering, Georgia Tech)ME3015 ASSIGNMENT #6 (solutions) IV. Consider the 2nd order system which has the transfer function 2 n C (s) = 2 . 2 R( s ) s + 2n s + n We would like to study the effe
Georgia Tech - ME - 3015
Georgia Institute of Technology Woodruff School of Mechanical Engineering ME3015 System Dynamics and Control Computer-aided-design assignment Issued: April 11, 2002, Due: April 26, 2002Consider a simplified version of a magnetic bearing that can be
Georgia Tech - ME - 3015
Part (a): Modeling At steady state, mg =2 Lo io = f o which implies 2a(1 + z o / a) 2io = (1 +f z =z o 2mga ) . a Lo(2)i0 , z 0Lo i 2 - 2 z L i2 (1 + o ) -3 = - 2 o oz 3 = - A 2 2a a a a (1 + ao )and Lo io f =B i0 , z 0 = i a(1 + zao )
Georgia Tech - ME - 3015
10 Part b: Proportional controller Gc ( s )G p ( s ) = K c . ( s + 31.6)( s - 31.6) Part b: Proportional controller Gc ( s ) = K cs 2 + K c - 2 = 0If K c 100 , the system is unstable. If K c > 100 , the system has no damping (100% overshoo
Georgia Tech - ME - 3015
Part c: PD controller Gc ( s ) = K c + K d s = K d ( s + z ) where K c = K d z . 10 Gc ( s )G p ( s ) = K d ( s + z ) . ( s + 31.6)( s 31.6) s 2 + K d s + (K c 2 ) = 0If K c 100 , the PD controlled system is unstable and FVT is invalid.e
Georgia Tech - ME - 3015
Part d: PID controller Gc ( s ) = K c + K i = z1 z 2 K d .Ki K + K d s = d ( s + z1 )( s + z 2 ) where K c = ( z1 + z 2 ) K d and s ss 3 + K d s 2 + ( K c - 2 ) s + K i = 0 The PID controlled system is stable if and only if the following condi
Georgia Tech - ME - 3015
Part (e) Implementation block diagramDesired x(mm) =0Error in volts Amperes/volt + VoltsCurrent in amperesKpPIDPower AmplifierMagLev systemx (mm)Position measurement, KpVolts/mm Part (f) obtain plant parameters experimentally Since
Georgia Tech - ME - 3015
Georgia Tech - ME - 3015
Automatic Control Systems, Seventh Edition, Benjamin C. Kuo, Prentiss Hall, 1995.
Georgia Tech - ME - 3015
ME3015 Solutions to CAD assignment, Kok-Meng LeeGeorgia Institute of Technology Woodruff School of Mechanical Engineering ME3015 System Dynamics and Control Solutions to the computer-aided-design assignment Issued: November 6, 2003, Due: December 4
Georgia Tech - ME - 3015
Georgia Institute of Technology Woodruff School of Mechanical Engineering ME3015C System Dynamics and ControlComputer-aided-design assignmentIssued: November 15, 2005, Due: December 8, 2005The three DOF helicopter test bed shown in Figure 1 con
Georgia Tech - ME - 3015
Georgia Institute of Technology Woodruff School of Mechanical Engineering ME3015C System Dynamics and ControlComputer-aided-design assignmentIssued: November 16, 2006, Due: December 7, 2006Consider the inverted pendulum mounted on the motor dri
Georgia Tech - ME - 3015
ME3015 CAD assignment solution Fall 206 Woodruff School of Mechanical Engineering, Georgia Tech (Professor Kok-Meng Lee)(1) Model the system Horizontal forces on the cart: Mx = f - n - bx Mx + bx = f - n d2 Horizontal forces on the pendulum: m 2 (
Georgia Tech - ME - 3015
A mL /( MI + MmL2 + mI ) = 2 F( s ) s 2 2 s mgL( M + m ) /( MI + MmL2 + mI ) Gc ( s ) = K + K d s G( s ) = =( s )D(s)+ _G(s) Gc(s)(s)Run the following commands on Matlab workspace> M = .5; > m = 0.5; > i = 0.006; > g = 9.8; > l = 0.3;
Georgia Tech - ME - 3015
Georgia Institute of Technology Woodruff School of Mechanical Engineering ME3015 System Dynamics and Control Computer-aided-design assignment Issued: November 15, 2007, Due: December 6, 2007MEMS (Micro Electro Mechanical Systems) are miniaturized m
Georgia Tech - ME - 3015
ME3015 System Dynamics and Control (Issued: March 25, 2008, Due: April 24, 2008)Georgia Institute of Technology The George W. Woodruff Woodruff School of Mechanical Engineering ME3015 System Dynamics and Control Computer-aided-design assignment Iss
Georgia Tech - ME - 3015
ME3015 System Dynamics (Woodruff School of Mechanical Engineering, Georgia Tech)ME3015 Assignment 8 and CAD ASSIGNMENT (I) Text Problems B-10-14 and B-10-17 (Plot the root locus using Matlab to verify the range of stability.)6 > n=1 > d = [1 6 5
Georgia Tech - ME - 3015
ME3015 System Dynamics (Woodruff School of Mechanical Engineering, Georgia Tech)ME3015 Assignment 8 and CAD ASSIGNMENT(IV)D(s) R(s) + E(s) _ Gc(s) X(s) G1(s) + - G3(s) Y(s)System: sysBode Diagram Frequency (rad/sec): 2.99 0 Magnitude (dB) -2
Georgia Tech - ME - 3015
Spring 2002 [1]: In the op-amp circuit shown below, each of the impedances is made up of a resistance and a capacitor in parallel (i.e. Z1 R1 / C1; Z2 R2 / C2). Answer the following questions:70 60 50Phase (deg); Magnitude (dB)40 30 20 100 80
Georgia Tech - ME - 3015
Name:_ (Please Print) Georgia Institute of Technology Woodruff School of Mechanical Engineering ME3015 System Dynamics and Control Final Examination (170 minutes, closed-book) December 10, 2002 Please Read This First: (a) (b) (c) (d) (e) PRINT your n
Georgia Tech - ME - 3015
Spring 2003 [5] Consider the unity-feedback system, where G p (s ) is given by the Bode diagram andGc ( s ) = K ( s + 2)(1) (2)(8 pts.) Sketch the Bode diagram of the open-loop transfer function, Gc G p ( s ) , for K=1.(8 pts.) Determine the
Georgia Tech - ME - 3015
Name:_ (Please Print) Georgia Institute of Technology Woodruff School of Mechanical Engineering ME3015A System Dynamics and Control Final Examination (170 minutes, closed-book) Friday, December 12, 2003 Please Read This First: (a) (b) (c) (d) PRINT y
Georgia Tech - ME - 3015
Fall 2003 [4] Figure 4(a) shows the block diagram of a position servo that consists of an electromechanical (EM) actuator.Bode Diagram80 60Magnitude (dB)40 20 0 -20 -40 45 0Figure 4(a) (1) (12 pts.) Sketch the Bode diagram of the plant transf
Georgia Tech - ME - 3015
Fall 2005 [1] Consider a feedback system shown in Figure 1 where G p ( s ) =1 . s ( s + 1)(0.5s + 1)a) With D(s)=0 and Gc ( s ) = 1 , calculate the static velocity error constant and the phase and gain margins. Sketch the bode diagramK v = lim
Georgia Tech - ME - 3015
Name:_ (Please Print) Georgia Institute of Technology Woodruff School of Mechanical Engineering ME3015C System Dynamics and Control Final Examination (170 minutes, closed-book) May 3rd, 2007 (Thursday), 8am-10:50am Please Read This First: (a) PRINT y
Georgia Tech - ME - 3015
ME3015B Quiz 2 (closed book/notes) January 31, 2002Name:_Solutions_ds + f where b, c, d and s + 2bs + c 221. (1 pt) Determine the poles of the complex function X ( s ) = f are real positive constants and c > b .Poles are the solutions of s 2
Georgia Tech - ME - 3015
ME3015B Quiz 3 (closed book/notes) February 19, 2002Name:_Solution_1. (3 pt) Consider the following mechanical system. Assume that the rod is mass less, perfectly rigid, and pivoted at frictionless point P. The displacement x is measured from the
Georgia Tech - ME - 3015
ME3015B Quiz 4 (closed book/notes) March 14, 2002Name:_Solution_1. (3 pt) The thermometer is initially at the ambient temperature C . At t=0, it is immersed in a water bath of temperature + b C . Assume that the thermal resistance and capacitan
Georgia Tech - ME - 3015
ME3015B Quiz 6 (closed book/notes) April 11, 2002Name: Solution1. (2 pts) Consider the following polynomial: s 4 + 2 s 3 + 3s 2 + 4 s + 5 = 0 Compute the coefficients for the third row of the Rouths array.s4 s3 s21 2 1 1 3 (4 6) =1 det =
Georgia Tech - ME - 3015
ME3015B Quiz 7 (closed book/notes) April 18, 2002Name:_Solution_1. (6 pts) The root locus of a unity feedback system with the open-loop transfer function KG(s)H(s) for K 0 isgiven below: (a) Show that the transfer function for the closed-loop
Georgia Tech - ME - 3015
ME3015B Quiz 5 (closed book/notes) October 24, 2002Name:_Solution_1. (5 pts) Consider the mechanical system shown in Figure 1(a). The mass-less bar AA' is displaced 0.05m by a constant force of 100N. Suppose that the system is at rest before the
Georgia Tech - ME - 3015
ME3015B Quiz 5 (closed book/notes) March 24, 2003 1. (4 pts) A mechanical system has a mathematical model:Name:_Solution_d 2x dx 2 2 + 2 n + n x = 0.5 n ( Au + Bu ) where u is a 2 dt dtstep input. The plot below shows the displacement x mm as
Georgia Tech - ME - 3015
ME3015C Quiz 4 (closed book/notes) October 24, 2005Name:_SOLUTIONS_1. (3 pt) The volumetric flow rate q through a variable orifice is given by q = cx p where c is a constant; x is proportional to the opening; and p is the pressure difference acro
Georgia Tech - ME - 3015
ME3015C Quiz 3 (closed book/notes) February 16, 2006Name:_1. (3 pts) Consider the frictionless rack-and-pinion assembly, where the pinion (radius r and inertia J) is driven by the rack (mass m) through an input force f(t). Derive the transfer fun