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Overview:

This module provides students with an understanding of modern dynamic mechanical systems and their interaction with the world. Movement, sensing, control and stability are modelled and discussed through examples such as self-driving cars, magnetic levitating (mag-lev) trains and satellite systems. . The module provides physical experience of dynamic, vibrational and resonant behaviour, as well as strategies to improve dynamic response, control vibration, and stabilise inherently unstable systems. Students become familiar with modelling and analysis of dynamic systems and the methods to control them.

Topics covered:

Modelling

• Modelling of dynamic systems using ordinary differential equations and Laplace transfer functions.
• Accounting for non-linearity in models.
• Numerical methods of simulation, e.g. using MATLAB / Simulink.
• Single-Input-Single-Output and multi-degree-of-freedom models including state-space representation

Dynamic Response

• 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.
• Free vibration of multi degree of freedom systems.
• Mode shapes and natural frequencies.
• Modal decomposition.
• Continuous systems, string, bars and beams, free and forced vibration

Frequency Response Techniques

• Calculating frequency response from Laplace Transfer Function models.
• Measuring frequency response and identifying a system model from experimental data.
• Mechanical resonance.
• Bandwidth (including resonance and mechanical systems).
• Analogue to Digital interfacing: sample rate (including effects of time-delay lag on stability)

Controller Design

• Root-locus methods of controller design (stabilising unstable systems).
• Frequency response stability analysis (margins of stability).
• PID & other controller types.
• Control system hardware and practical implementation.

Learning outcomes:

Upon completion of this module students will be able to:

• 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.
• Measure the dynamic response of a simple system and identify the system parameters.
• Predict the dynamic performance of system models in the frequency domain, identifying the bandwidth and stability.
• Design an interface in order to use a computer/microcontroller to measure and control an external device.
• Perform analytical investigations /simulations of the performance and stability of controlled systems, designing controllers to meet performance specifications.
• Understand the difference between a theoretical model and a practical application of a control system and the limitations and constraints for systems.