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75 Pages

### gelb_ch7_ocr

Course: AERO 16.30, Spring 2004
School: MIT
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Word Count: 23863

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FUNCTIONS 7 DESCRIBING FOR NONLINEAR SYSTEMS WITH RANDOM INPUTS 7.0 INTRODUCTION The preceding chapters have dealt with approximate descriptions of nonlinearities having inputs consisting of the sums of two commonly considered signal forms, sinusoids and constants. We wish now to add a third form to this repertory of input signals, a random process. The study of nonlinear systems with random inputs is of...

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MIT - AERO - 16.30
7DESCRIBING FUNCTIONS FOR NONLINEAR SYSTEMS WITH RANDOM INPUTS7.0INTRODUCTIONThe preceding chapters have dealt with approximate descriptions of nonlinearities having inputs consisting of the sums of two commonly considered signal forms, sinusoids and
MIT - AERO - 16.30
8NONOSCILLATORY TRANSIENTS IN NONLINEAR SYSTEMS8.0INTRODUCTIONIn general, describing function concepts are directed primarily at the steadystate responses of nonlinear systems. The test inputs used to develop most describing functions are therefore ba
MIT - AERO - 16.30
8NONOSCILLATORY TRANSIENTS IN NONLINEAR SYSTEMS8.0INTRODUCTIONIn general, describing function concepts are directed primarily at the steadystate responses of nonlinear systems. The test inputs used to develop most describing functions are therefore ba
MIT - AERO - 16.30
9OSCILLATIONS IN NONLINEAR SAMPLED-DATA SYSTEMS9.0INTRODUCTIONAll the material of the preceding chapters has been concerned with systems which process signals continuously around the loop. This chapter takes under consideration the describing function
MIT - AERO - 16.30
9OSCILLATIONS IN NONLINEAR SAMPLED-DATA SYSTEMS9.0INTRODUCTIONAll the material of the preceding chapters has been concerned with systems which process signals continuously around the loop. This chapter takes under consideration the describing function
MIT - AERO - 16.30
Absolute-value nonlinearity, 351 Atherton, D. P., 19, 30, 108, 368, 387, Accuracy (see Describing functions) 3 96 Adaptive control system, 323, 327-332 Attenuation of harmonics, 172 missile roll control, 332-341 Autocorrelation function, 636 A
MIT - AERO - 16.30
Absolute-value nonlinearity, 351 Atherton, D. P., 19, 30, 108, 368, 387, Accuracy (see Describing functions) 3 96 Adaptive control system, 323, 327-332 Attenuation of harmonics, 172 missile roll control, 332-341 Autocorrelation function, 636 A
MIT - AERO - 16.30
First HomeworkEric Feron Feb 4, 20031. Bode plots Draw the Bode plots for the following systems. First by hand using the Bode plot following rules. Second using Matlab to check your results. (a) G(s) = (b) (c) (d) (e) (f) (g) (h) (i) (j) 1 (s + 1)2 (s2
MIT - AERO - 16.30
First HomeworkEric Feron Feb 4, 20031. Bode plots Draw the Bode plots for the following systems. First by hand using the Bode plot following rules. Second using Matlab to check your results. (a) G(s) = (b) (c) (d) (e) (f) (g) (h) (i) (j) 1 (s + 1)2 (s2
MIT - AERO - 16.30
Second HomeworkEric Feron Feb 11, 20041. Singularities on j- axis and Nyquist plots. Draw a Nyquist diagram for each of the following systems, choosing the contour to be to the right of any singularities on the j-axis. K(s + 10) . s2 (s + 100) K(s + 0.1
MIT - AERO - 16.30
Second HomeworkEric Feron Feb 11, 20041. Singularities on j- axis and Nyquist plots. Draw a Nyquist diagram for each of the following systems, choosing the contour to be to the right of any singularities on the j-axis. K(s + 10) . s2 (s + 100) K(s + 0.1
MIT - AERO - 16.30
Third HomeworkEric Feron Feb 18, 20041. Prove that the root-locus resulting from the combination of two poles and one zero to the left of both of them on the real axis is a circle centered at the zero with radius given by |(p1 - z)|p2 - z)|. 2. Consider
MIT - AERO - 16.30
Homework 4Eric Feron Feb 25, 20031. Consider the plant G(s) = (s2 1 + 4s + 4)(s + 5)(s + 10)We are considering proportional compensation. (a) Plot the root locus of the system? (b) For what value of K is the system at the stability boundary? (c) What a
MIT - AERO - 16.30
Homework 5Eric Feron March 3, 20031. Consider the plant G(s) = 5 s(s/1.2 + 1)(s/3.5 + 1)Design a lead compensator for the phase margin to be about 40 degrees. What is the bandwidth of the system? During your design, keep the DC gain of your compensator
MIT - AERO - 16.30
Homework 6Eric Feron April 4, 20041. A 564,000 lbs Boeing 747 is approaching land at seal level (flaps and landing gear down). Assuming a velocity of 221 ft/sec (Mach 0.198), the lateral-directional perturbation equations are v r p = -0.0890 -2.19
MIT - AERO - 16.30
Identification Experiments RUN 1 no data take data useful data step input sine input gain (volts) frequency use roll/pitch ctrl hard landing supervisor turned on crash RUN no data take data useful data step input sine input gain (volts) frequency use roll
MIT - AERO - 16.30
Identification Experiments RUN 1 no data take data useful data step input sine input gain (volts) frequency use roll/pitch ctrl hard landing supervisor turned on crash RUN no data take data useful data step input sine input gain (volts) frequency use roll
MIT - AERO - 16.30
Massachusetts Institute of Technology Department of Aeronautics and Astronautics 16.06 Principles of Automatic Control Fall 2003 Notes on writing a lab report Basic report outline: 1. Abstract 2. Introduction 3. Apparatus/Procedure 4. Results &amp; Discussion
MIT - AERO - 16.30
Massachusetts Institute of Technology Department of Aeronautics and Astronautics 16.06 Principles of Automatic Control Fall 2003 Notes on writing a lab report Basic report outline: 1. Abstract 2. Introduction 3. Apparatus/Procedure 4. Results &amp; Discussion
MIT - AERO - 16.30
Massachusetts Institute of Technology Department of Aeronautics and Astronautics 16.30 Estimation and Control of Aerospace Systems Spring 2004 Please, fill out the following questionnaire and submit it with your lab report. DO NOT put your name on this qu
MIT - AERO - 16.30
Massachusetts Institute of Technology Department of Aeronautics and Astronautics 16.30 Estimation and Control of Aerospace Systems Spring 2004 Please, fill out the following questionnaire and submit it with your lab report. DO NOT put your name on this qu
MIT - AERO - 16.30
MIT - AERO - 16.30
MIT - AERO - 16.30
Homework 9Eric Feron April 29, 20041. Gelb &amp; Vander Velde, problem 3.2 2. Gelb &amp; Vander Velde, Problem 6.16 3. Feron's Chapter 3, Problem 4 (about the stepper motor).1
MIT - AERO - 16.20
16.20Handed Out: Lecture 5 Due: Lecture 10DESIGN PROBLEM #1A 2100 kg orbital package is mounted within the space shuttle on a mating platform. The platform is at an angle of 15 with the ascent axis of the shuttle. The package is circular and has an out
MIT - AERO - 16.20
16.20Handed Out: Lecture 11 Due: Lecture 17DESIGN PROBLEM #2Your team has been contracted by TrussProd, Inc. to make recommendations to them on a quality control test procedure for their new line of trusses. TrussProd originally entered the constructio
MIT - AERO - 16.20
16.20Handed Out: Lecture 20 Due: Lecture 30DESIGN PROBLEM #3Your company has contracted with Moontowers International to provide engineering consulting services for the preliminary design of a transmission tower at the new Lunar Base III that is under
MIT - AERO - 16.20
16.20Handed Out: Lecture 36DESIGN PROBLEM #4(and.HOME ASSIGNMENT #9)You and your team of colleagues are employed as structural engineers at Small-Planes-R-Us, Inc. The board of directors has committed the company to producing a new small two-seater ai
MIT - AERO - 16.20
16.20Handed Out: Lecture 5 Due: Lecture 9HOME ASSIGNMENT #1Warm-Up ExercisesWrite out the following tensor equations in full: (Note: these equations do not necessarily have any real meaning) 1. 2.Gi = l Mni A ij = Qijkl k x l amn E = un + fm = 0 t 1
MIT - AERO - 16.20
MIT - AERO - 16.20
16.20Handed Out: Lecture 9 Due: Lecture 12HOME ASSIGNMENT #2Warm-Up Exercises1. The three-dimensional (3-D) stress-strain equations are written as:mn = Emnpq pqThese can be reduced for the plane stress case (i.e. 33 = 13 = 23 = 0) to a two-dimension
MIT - AERO - 16.20
MIT - AERO - 16.20
MIT - AERO - 16.20
16.20Handed Out: Lecture 12 Due: Lecture 16HOME ASSIGNMENT #3Warm-Up ExercisesLet's explore the use of Mohr's circle for strains in the case of plane stress. Use geometrical arguments/considerations to: 1. Show that the transformation of an arbitrary
MIT - AERO - 16.20
MIT - AERO - 16.20
MIT - AERO - 16.20
16.20Handed Out: Lecture 16 Due: Lecture 20HOME ASSIGNMENT #4Warm-Up ExercisesLet's consider the stress field around the hole in an isotropic plate loaded in uniaxial compression (no buckling occurs): 1. Derive expressions for the stress components at
MIT - AERO - 16.20
MIT - AERO - 16.20
MIT - AERO - 16.20
16.20Due: Lecture 25HOME ASSIGNMENT #5Warm-Up ExercisesLet's consider a steel bar that is rigidly clamped at one end and free at the other end with a gap of 0.002L between that end and a wall. The bar is of length L, thickness h, and width b. Bending
MIT - AERO - 16.20
MIT - AERO - 16.20
MIT - AERO - 16.20
MIT - AERO - 16.20
MIT - AERO - 16.20
MIT - AERO - 16.20
MIT - AERO - 16.20
MIT - AERO - 16.20
16.20Handed Out: Lecture 29 Due: Lecture 33HOME ASSIGNMENT #7Warm-Up ExercisesIn the last home assignment, two cross-sections were considered (a C-section and an I-section) for their torsional capabilities. The torsional constant J was determined to b
MIT - AERO - 16.20
MIT - AERO - 16.20
MIT - AERO - 16.20
16.20Handed Out: Lecture 33HOME ASSIGNMENT #8 (Part A)Warm-Up ExercisesDetermine the bending moments of inertia (Iz, Iy, Iyz ) for the following crosssections: 35 mm 1. 5 mm 2. 35 mm 5 mm50 mm50 mmz 5 mm y 35 mm 3. 5 mm 4. 5 mm 5 mm35 mm50 mm5 m
MIT - AERO - 16.20
16.20Due: Lecture 39HOME ASSIGNMENT #8 (Part B)Warm-Up Exercises1. - 7. in Part APractice Problems8. A nine-foot long simply-supported beam has an unsymmetric cross-section as shown below. A 220-pound person walks across the beam (assume the weight
MIT - AERO - 16.20
16.20Due: Lecture 39HOME ASSIGNMENT #8 (Part B)Warm-Up Exercises1. - 7. in Part APractice Problems8. A nine-foot long simply-supported beam has an unsymmetric cross-section as shown below. A 220-pound person walks across the beam (assume the weight
MIT - AERO - 16.20
MIT - AERO - 16.20
MIT - AERO - 16.20
MIT - AERO - 16.20
MIT - AERO - 16.20
16.20Handed Out: Lecture 36 Due: Lecture 43HOME ASSIGNMENT #9(accompanies Design Problem #4) Warm-Up ExercisesNonePractice ProblemsNoneApplication TasksConsider the circular shell beam cross-section shown in the accompanying figure. This cross sec
MIT - AERO - 16.20
16.20Handed Out: Lecture 36 Due: Lecture 43HOME ASSIGNMENT #9(accompanies Design Problem #4) Warm-Up ExercisesNonePractice ProblemsNoneApplication TasksConsider the circular shell beam cross-section shown in the accompanying figure. This cross sec
MIT - AERO - 16.20
16.20Handed Out: Lecture 41 Due: Lecture 46HOME ASSIGNMENT #10Warm-Up ExercisesA perfect column of length L has constant cross-sectional properties equal to EI. Each end of the column is held by a torsional spring of stiffness kT. The overall configur
MIT - AERO - 16.20
16.20Handed Out: Lecture 41 Due: Lecture 46HOME ASSIGNMENT #10Warm-Up ExercisesA perfect column of length L has constant cross-sectional properties equal to EI. Each end of the column is held by a torsional spring of stiffness kT. The overall configur