MECH302P – Dynamics and Control
UCL Credits/ECTS: 0.5/7.5
Module aims:
To provide students with understanding of issues involved in creating models of real
mechanical systems; to provide experience of dynamic, vibrational and resonant behaviour;
and to investigate strategies to improve dynamic response and control vibration, and
stabilise inherently unstable systems.
Prerequisites:
MECH202P Control & Instrumentation. Familiarity with ordinary differential equations and
complex numbers, and engineering dynamics.
Summary of course contents:
Modelling
This module covers the techniques necessary to create mathematical and computerised
models of systems typically comprising mechanisms, motors and sensors. Many examples
are included and updated frequently to reflect recent current affairs including large aircraft
control systems, vehicle suspensions, motorised positioning systems e.g. for 3D printing.
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Modelling of dynamic systems using linear Laplace transfer functions.
Lumped parameter models.
Accounting for non-linearity in models.
Numerical methods of simulation, e.g. using Matlab / Simulink.
Single-Input-Single-Output models.
Dynamic techniques, fundamentals of vibration
Models are used to analyse the dynamic behaviour of systems, predicting speed of
response, stability and common vibratory / oscillatory problems in engineering. This section
involves assessing and measuring noise, vibration and rapid motions.
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Free vibration of single degree of freedom mass-spring system: natural
frequency.
Free vibration of damped oscillator; different types of damping.
Forced response of single degree of freedom systems.
Transient vibration.
Application: Base excitation and vibration isolators.
Calculating frequency response from Laplace Transfer Function models.
Measuring frequency response and identifying a system model from experimental
data.
Analogue to digital interfacing: sample rate (including effects of time-delay lag on
stability)
Multiple degree of freedom systems
The methods above are extended to include multi-degree of freedom systems, using the
State Space matrix method. In vibrating structures, the concepts of mode shape and modal
analysis are introduced and investigated experimentally.
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State Space modelling techniques for multi degree-of-freedom systems.
Free vibration of two degree of freedom systems.
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Mode shapes and natural frequencies.
Multiple degree of freedom systems: modal decomposition.
Time harmonic forced vibration with damping.
Rayleigh’s method. Lagrange’s equations for free undamped vibration.
Continuous systems, string, bars and beams, free and forced vibration.
Controller Design
The module extends the controller design techniques developed in MECH202P, considering
analytical approaches to improving the speed of response and stabilising inherently unstable
systems including high performance (autonomous) aircraft.
These techniques are investigated in the laboratory which involves balancing an inverted
(upside-down) pendulum.
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Root-locus methods of controller design (stabilising unstable systems).
Frequency response stability analysis (margins of stability).
PID & other controller types.
Measurement techniques.
Control system hardware and practical implementation.
Method of delivery:
Whole-class lectures will be used to present standard theories of modelling & control, using
current examples from a range of industries and research fields to demonstrate their
applicability.
A laboratory session will give students hands-on experience with sensing and feedback
control, demonstrating control of instability using standalone controller hardware.
Moodle will be used to provide additional material to support teaching, for formative
assessment and for submission of coursework. Matlab software will be used by students for
completion of their class assignments. There are no distance learning components.
Intended Learning Outcomes:
Knowledge & Understanding
Create a detailed model of a dynamic system, with multiple degrees of freedom, analyse its
response and implement that model in a numerical (computer-based) simulation.
To appreciate the difference between a theoretical model and a practical application of a
control system and the limitations and constraints for system.
To appreciate the role of different mechanical elements of a vibration system and
understand the main characteristics of an oscillator as well as importance of vibration
treatment in engineering.
To understand the concept of mode shape and natural frequency and the link between multidegree of freedom or continuous system and single degree of freedom systems through
these concepts.
Technical and Transferrable Skills
Predict the dynamic performance of system models in the frequency-domain; identifying
bandwidth and stability; modifying systems to solve vibration problems.
To be able to analyse multi-degree of freedom systems, using modal space to obtain the
response.
Design interfaces between analogue and digital domains, in order to use a computer/
microcontroller to implement measurement and control of an external device.
Perform analytical investigations /simulations of the performance and stability of controlled
systems, designing controllers to meet performance specifications including vibration control.
Assessment:
The course will have the following assessment components:
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75% : Examination (3 hours)
25% : Lab participation and coursework (2000 words max total)
To pass this course students must obtain an overall pass mark of 40% for all sections
combined.
Recommended Reading:
Title: Feedback control of dynamic systems
Authors: Gene F. Franklin, J. David Powell, Abbas Emami-Naeini.
Edition: Seventh edition, Global edition / global edition contributions by Sanjay H.S.
Publisher: Boston Massachusetts : Pearson
Creation Date: 2015
Identifier: ISBN 9781292068909;ISBN 1292068906
Format: 880 pages : illustrations ; 24 cm.
Title: Modern control systems
Author: Richard C. Dorf, Robert H. Bishop
Edition: 12th ed., International ed.
Publisher: Boston ; London : Pearson
Creation Date: c2011
Identifier: ISBN 9780131383104 (pbk.);ISBN 0131383108 (pbk.)
Format: 1104 p. : ill. ; 24 cm.
Title: Mechanical Vibrations
Author: Singiresu S. Rao
Edition: 4th ed.
Publisher: Upper Saddle River, N.J. : Prentice Hall
Creation Date: c2011
Identifier: ISBN 0131207687;ISBN 9780131207684
Format: xxvi, 1078 p. : ill., ports. ; 24 cm.
Title: Engineering vibration / Daniel J. Inman.
Author: D. J. Inman
Subjects: Vibration
Edition: 4th. ed., International Edition
Publisher: Boston : Pearson, [2014]
Creation Date: c2014
Identifier: ISBN-10: 0273768441; ISBN-13: 9780273768449
Format: 719 pages : illustrations (black and white) ; 24 cm
PLEASE NOTE: This information is given in good faith but accuracy cannot be guaranteed.