MEEN 411 Solutions to Exam 1 1) Figure (a) Figure (4)
Solutions to Mid-term Exam
The phase of the system is asymptotic from 0 degrees to -90 degrees. The magnitude plot has a -20 dB roll-off. So it can be concluded that it is a first order system. Figure
MEEN 651 Control System Design Homework 0: Pre-requisite Material
Assigned: Tuesday, 26 Aug. 2008 Due: Tuesday, 2 Sept. 2008, 5:00 pm
Note: This homework will not be graded for correctness. You score will be based on evidence of a reasonable attempt to so
MEEN 651 Control System Design Homework 1: Preliminary Mathematics and Modeling of Mechanical Systems Solution
Assigned: Tuesday, 4 Sept. 2007 Due: Tuesday, 11 Sept. 2007, 5:00 pm
Problem 1)
Show the following: a. That the Laplace Transform, X (s ) = x(t
Texas A & M University Department of Mechanical Engineering MEEN 651 Control System Design Dr. Alexander G. Parlos Fall 2003
Lecture 4B: Electrical and Electromagnetic System Components
The objective of this lecture is to review the fundamental components
Texas A & M University Department of Mechanical Engineering MEEN 651 Control System Design Dr. Alexander G. Parlos Fall 2003
Lecture 3A: Modeling of Translational Mechanical Systems
The objective of this lecture is to review the basic building blocks of l
Texas A & M University Department of Mechanical Engineering MEEN 651 Control System Design Dr. Alexander G. Parlos Fall 2003
Lecture 4A: State-space Representation of Dynamic Systems
The objective of this lecture is to introduce you to the two distinct mo
Texas A & M University Department of Mechanical Engineering MEEN 651 Control System Design Dr. Alexander G. Parlos Fall 2003
Lecture 3B: Modeling of Rotational Mechanical Systems
The objective of this lecture is to review the basic building blocks of lump
MEEN 364 Lecture 17,18
Parasuram August 28, 2001
HANDOUT E.17 - EXAMPLES ON BODE PLOTS OF FIRST AND SECOND ORDER SYSTEMS
Example 1 Obtain the Bode plot of the system given by the transfer function G( s) = 1 . 2s + 1
We convert the transfer function in the
MEEN 364 Lecture 10, 11, 7
Parasuram August 19, 2001
HANDOOUT E.9 - EXAMPLES ON FLUID, THERMAL AND MIXED SYSTEMS
Example 1: A thermal system The following figure shows a simple model of an industrial furnace. A packing of temperature T1 is being heated in
MEEN 364
Dr. Smith Parasuram March 7, 2003
COMPLEX NUMBER ALGEBRA RELATING TO SINUSOIDAL FUNCTIONS
1) If u (t ) = A cos( t ) + B sin( t ) , where A and B are real, then we can rewrite u(t) as: u (t ) = A j t A j t B j t B j t e + e + e e , 2 2 2j 2j ( A B
MEEN 364 Lecture 12
Parasuram August 28, 2001
HANDOUT E.12 - EXAMPLES ON LINEARIZATION
Example 1 Consider the system shown below.
r
m The governing differential equations of motion for the above system is given by m r + kr kl 0 mr
. . . . . 2
mg cos = 0
Texas A & M University Department of Mechanical Engineering MEEN 651 Control System Design Dr. Alexander G. Parlos Fall 2003
Lecture 6: Linearization and Scaling Operating Points and Impedance Matching
The objective of this lecture is to give you an overv
Texas A & M University Department of Mechanical Engineering MEEN 651 Control System Design Dr. Alexander G. Parlos Fall 2003
Lecture 7: Transfer Functions & Block Diagrams Poles and Zeros of Transfer Functions
The objective of this lecture is to introduce
Texas A&M University Department of Mechanical Engineering MEEN 651 Control System Design Dr. Alexander G. Parlos Fall 2003 Lecture 5B: Thermal and Fluidic Systems
Basic Mechanisms of Heat Transfer Energy may be transferred across the boundaries of a syste
MEEN 364 Lecture 6,7
Parasuram August 7, 2001
HANDOUT E.6 - EXAMPLES ON MODELLING OF ROTATIONAL MECHANICAL SYSTEMS
Note that the time dependence of variables is ignored for all manipulations. Example 1: A single DOF system Consider a simple pendulum shown
MEEN 364
Parasuram July 13, 2001
HANDOUT A.3 - FORMULATING THE STATE-VARIABLE FORM OF DYNAMIC SYSTEMS
Introduction Use of Newton's law and free-body diagram typically leads to second order differential equations, that is, equations that contain the second
MEEN 364
Parasuram June 29, 2001
HANDOUT M.3 - EIGEN VALUES AND EIGEN VECTORS
Definition: Let A be an n x n matrix. Then a real number is called an eigenvalue of the matrix, A if and only if, there is a n-dimensional nonzero vector, v for which Av i = i v
MEEN 364 Lecture 1
Parasuram August 8, 2001
HANDOUT E.1 - EXAMPLES ON SIGNALS AND SYSTEMS
Signals A signal is defined as any physical quantity that varies with time, space or any other independent variable or variables. Mathematically, we describe a signa
Texas A & M University Department of Mechanical Engineering MEEN 651 Control System Design Dr. Alexander G. Parlos Fall 2003
Lecture 1B: Fourier Analysis and Fourier Transforms
The objective of this lecture is to present to you some of the mathematics inv
MEEN 364
Parasuram July 13, 2001
HANDOUT M.2 - DIFFERENTIATION AND INTEGRATION
Section 1: Differentiation Definition of derivative A derivative f (x) of a function f(x) depicts how the function f(x) is changing at the point `x'. It is necessary for the fu
MEEN 364
Parasuram July 25, 2001
HANDOUT ON FOURIER ANALYSIS OF DYNAMIC SIGNALS
Signals and Signal processing A signal is defined as any physical quantity that varies with time, space or any other independent variable or variables. Mathematically, we desc
MEEN 364
Parasuram July 27, 2001
HANDOUT M.4 - SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS
Introduction The majority of physical systems of interest in this course can be represented in the form of ordinary differential equations. In order to study the r
MEEN 364 Lecture 3
Parasuram August 28, 2001
HANDOUT E.3 - EXAMPLES ON LAPLACE TRANSFORMS
Example 1 Evaluate the Laplace transform of the following functions. a) f (t ) = e -t .
is a positive real number. The Laplace transform of a function f(t) is given
Texas A & M University Department of Mechanical Engineering MEEN 651 Control System Design Dr. Alexander G. Parlos Fall 2003
Lecture 2A: Laplace Transforms
The objective of this lecture is to introduce the concepts and mathematics involved in the Laplace
MEEN 364
Parasuram July 6, 2001
HANDOUT A.2 - LAPLACE TRANSFORMS NOTE: All the transformations have to be done using the analytical method outlined. MATLAB has to be used only to verify the result obtained.
Introduction The Laplace transform is the mathem
Texas A & M University Department of Mechanical Engineering MEEN 651 Control System Design Dr. Alexander G. Parlos Fall 2003
Lecture 2B: Sampling and Aliasing Phenomena, Sampling Rate Selection and Nyquist Frequency
The objective of this lecture is to int
MEEN 364 Lecture 8,9,7
Parasuram August 8, 2001
HANDOUT E.8 - EXAMPLES ON MODELLING OF ELECTRICAL, ELECTROMECHANICAL SYSTEMS
Note that the time dependence of variables is ignored for all manipulations. Example 1: An electrical circuit Consider the circuit
MEEN 364 Lecture 6,7
Parasuram August 7, 2001
HANDOUT E.7 - EXAMPLES ON MODELLING OF MECHANICAL SYSTEMS MIXED ROTATIONAL AND TRANSLATIONAL
Note that the time dependence of variables is ignored for all manipulations. Example 1: One DOF system Consider the
MEEN 364 Lecture 5,7
Parasuram August 7, 2001
HANDOUT E.5 - EXAMPLES ON MODELLING OF TRANSLATIONAL MECHANICAL SYSTEMS
A generalized procedure has been followed in all the examples in this handout to derive the governing differential equations of motion. N
MEEN 364 Lecture 13
Parasuram August 22, 2001
HADNOUT E.13 - EXAMPLES ON TRANSFER FUNCTIONS, POLES AND ZEROS
Example 1 Determine the transfer function of the mass-spring-damper system. The governing differential equation of a mass-spring-damper system is