1. Consider the complex number s = + j and its geometrical representation on the complex
1
1
splane shown below. Do not use Matlab until you reach question (d) of this problem.
0
.
a) Using geometrical arguments and calculations on the splane, compute the

Massachusetts Institute of Technology
Department of Mechanical Engineering
2.004 Dynamics and Control II
Laboratory Session 4:
Closed-Loop Performance of a Proportional Velocity Controller1
Laboratory Objectives:
(i) Introduction to the 2.004 digital PID

Massachusetts Institute of Technology
Department of Mechanical Engineering
2.004 Dynamics and Control II
Laboratory Session 5:
Elimination of Steady-State Error Using Integral Control Action1
Laboratory Objectives:
(i) To investigate the elimination of s

Massachusetts Institute of Technology
Department of Mechanical Engineering
2.004 Dynamics and Control II
Laboratory Session 3:
Construction of a Proportional Velocity Controller1
Laboratory Objectives:
(i) Construction and testing of an op-amp dierential

Lab 2: Characterization of Lab System Components OBJECTIVES
In the future lab sessions you will be studying closed-loop control of the rotational plant.
The elements of the complete system are shown below:
In Lab 1 you measured the mechanical properties J

Massachusetts Institute of Technology
Department of Mechanical Engineering
2.004 Dynamics and Control II
Laboratory Session 6:
Closed-Loop Position Control, and the Eect of Derivative Control Action1
Laboratory Objectives:
(i) To investigate closed-loop c

1.
In class, we showed in two different ways that the torque constant of a DC motor equals
the backEMF constant, K = K . Verify from the definitions of these constants, K i =
m
v
m
T and K = v , respectively, that the units associated with these constants

In this Problem Set, we will practice using Matlab to model and analyze the response of
dynamical systems. MIT supports Matlab in the Athena clusters, the Mechanical
Engineering computer clusters, and other locations (e.g., most research labs.) You may
al

Lab 1: Coulomb and Viscous Friction
The objectives of the lab are to:
familiarize you with the laboratory equipment and software tools that you will use
throughout the term.
measure the frictional characteristics of the rotational plant. PROCEDURE
Part

1. Inverted pendulum Consider the inverted pendulum system shown above. It consists of
a point mass m attached to the end of a rigid rod of length l. The rods mass is negligible.
An input torque T is applied to the rod base in order to control the pendul

In this Problem Set, we will continue our analysis of the DC motor system of Lecture 12
with pinionrack and velocity feedback, except this time we will add a different twist: we
will make the motor shaft and rack compliant. Effectively, this means attachi

1. In this problem, we will analyze the 2.004 Tower system (including the compen sating
massdampercompliance slider components) using the eigenvalues/eigenvectors of its
state matrix. The system parameters are m = 5.11kg, b = 0.767Nsec/m,k = 2024N/m;
1
1

1.
For each one of the following systems, argue if in your opinion it is
openloop or closedloop. In your argument, include your
definitions of the systems inputs and outputs. Briefly describe
how feedback is effected in the systems which you decide are
cl

1. (a) Problem 21(a) from Nise textbook, Chapter 2 (page 113). (b) After you find the
transfer function, locate the zeros and poles, draw them on the splane, and determine the
type of the response of the system (undamped, underdamped, critically damped, o

2-1
CHAPTER 2
The correspondence between the problem set in this fifth edition versus the problem set in the 4'th edition text. Problems that are new are marked new and those that are only slightly altered are marked as modified (mod). New 1 2 3 4 5 6 7 8