MODULE DESCRIPTOR
MECH2006 – Dynamics and Control
Code:
Alt. Codes(s)
Title:
Level:
UCL units/ECTS
Start:
End:
Taught by:
MECH2006
None
Dynamics and Control
2
0.5/7.5
September
June
Dr Greig - Control (50%)
Module Coordinator
Dr Balabani - Dynamics (50%)
Prerequisites
No previous experience of dynamics or control is required. Mathematics to include basic complex
number theory, calculus and ordinary differential equations linear and non linear 1 st order and linear 2nd
order homogenous (no forcing function) with constant c oefficients.
Students without first year
undergraduate mathematics may be c onsidered at the module coordinat or’s discretion. For c ontrol a
basic understanding of Laplace Transforms is required but lack of this knowledge need not be a bar to
successful completion the course.
Co-requisite
MECH2007 Modelling and Analysis II preferred (for Laplace Transforms) but not essential.
Course Aims
To teach students to:





Mathematically model the behaviour of simple mechanical vibrating systems with one or more degrees
of freedom.
Describe the response of these systems to transient and harmonic excitation.
Understand the application of these concepts to system design
Manipulate and understand simple classical control systems
Appreciate the difference between theoretical models and real systems
Objectives
At the end of the course students should be able to:











Derive equations of motion to describe the linear and/or angular motion of simple vibrating mechanical
systems comprising masses, springs and viscous damper
Obtain solutions to the equations of motion for different inputs (step, ramp, impulsive and harmonic
excitation).
Analyse system response in terms of damped and undamped natural frequency; damping factor,
logarithmic decrement and settling time.
Appreciate the difference between transient and steady state behaviour
Understand and apply the concept of system resonance.
Understand and apply the concept of transmissibility to system design.
Understand the concept of system stability and to be able to test for it
Obtain and solve equations of motion for systems with more than one degree of freedom.
Understand terminology and definitions used in control theory
Manipulate control system block diagrams
Design a simple velocity feedback and PID controllers.
Method of Instruction
Lecture presentations, tutorial classes and (two) laboratory classes. This is a predominantly lecture
based class.
Assessment
The course has the following assessment components:
 Written Examination (3 hours, 75%)
 Two Laboratories (25%) one for Dynamics (DC1) and one for control (DC2)
Page | 1
To pass this course, students must:
 Obtain an overall pass mark of 40% for all sections combined
The examination rubric is:
Answer FIVE questions (from eight offered) and answer no more than THREE questions from EITHER
section (A or B). All questions carry equal weight.
Resources:

“Art of control Engineering” (1997).
Wesley ISBN 0-201-17545-2.

“Schaum's outline of theory and problems of feedback and control systems” (1990). DiStefano III, J. J.,
Stubberud, A.R. and Williams I.J. Pub: McGraw-Hill, ISBN 0070170479. M.
Dutton, K., Thompson, S. and Barraclough, B. Pub: Addison-
Plus support material on MECH2006 Moodle page
Additional Information
The timing of the course makes it not suitable for affiliate students who are only at UCL for one semester.
Content
Dynamics
Approximately 10 lectures and 10 tutorial sessions, usually in term 1










Solution of 2nd order inhomogeneous ordinary differential equations in the context of dynamics.
Basic principles of system modelling (degrees of freedom, idealisation of system elements, free body
diagrams, static equilibrium)
Undamped, free vibrations
Damped, free vibrations
Forced vibrations (step, ramp and harmonic response)
Transmission and transmissibility
Resonance
Multiple degree of freedom systems
Pulleys and springs,
Mechanisms and linkages
Linear Control Theory
Approximately 10 lectures and 10 tutorial sessions, usually in term 2
1 INTRODUCTION
2 BLOCK DIAGRAM FORMAT, FEEDBACK AND TRANSFER FUNCTIONS
2.1 Introduction
2.2 Terminology and Definitions
2.3 Algebraic Manipulations of Transfer Functions
2.4 Transfer Functions of Simple Mechanical and Electrical Elements
2.5 Simple Transfer Function Derivations
2.6 Step Response of the Simple Exponential Lag
2.7 The Time Constant of the Simple Exponential Lag
3. ANALYSIS OF SECOND ORDER SYSTEMS
3.1 Establishing a Model of a Remote Position Control Servomechanism
3.2 Response of a Remote Position Control Servo
3.3 Velocity Feedback
3.4 Proportional, Integral and Derivative (PID) Controller
3.5 PID Controller Tuning – Ziegler - Nichols Method
3.6 Summary
3.7 Other applications
4 LAPLACE TRANSFORM
4.1 Definition
4.2 Example Derivations
4.3 Standard Laplace Transforms
4.4 Step Response of a 2nd Order System Using Laplace Transforms
4.5 Final Value Theorem
Page | 2
5. STABILITY ANALYSIS - ROUTH ARRAY
5.1 Theory
5.2 Examples
6. HARMONIC RESPONSE
6.1 Steady State Frequency Response
6.2 First Order System
6.3 Second Order System
6.4 Example
Revision
Usually end of term 2 and first few weeks of term 3
General Learning Outcomes
Knowledge and understanding
Essential principles of two-dimensional dynamics.
Skills and attributes
(i) Intellectual
Description of a mechanical system using mathematical models; application of mathematical methods for
solving problems involving particles and rigid bodies; analysis of system response dependent on input
excitation; understand the concepts of system response and transmissibility to a system design.
(ii) Practical
Obtain and solve equations of motion for systems with more than one degree of freedom; Manipulate
control system block diagrams; design a simple velocity feedback and PID controllers; testing of system
stability
(iii) Transferable
Solve engineering problems by isolating the constituent parts and subjecting them to logical scientific
analysis.
Page | 3