The Vibrations of a Building-Ground Model - Engineering Assignment Help

Assignment Task

Task
Active vibration control is considered to control the vibrations of a building-ground model shown in
Figure 1. The actuator generates a control force u(t ) between the two masses in order to reduce the
vibrations transmitted from the ground to the building. The following set of parameters is assumed for the numerical simulation:
m1 ? 1500kg , m2 ? 11000kg , k1 ? 975000N / m , c1 ? 10800Ns / m
2934261168409
Figure 1: Active building-ground model
Equations of motion for the building-ground model with the active force can be written in the following form:
m1!x!1 (t) ? c1 x!(t) ? k1 x1 (t) ? ?u(t)
m2 !x!2 ? u(t)
Write the equations of motion in the state-space form and determine the eigenvalues of the open-loop building-ground model system.
[5 marks]
The mass m1 is subject to an initial displacement of 0.1m. Consider a control force, which is proportional to the “relative velocities between the two masses”. Plot the displacement of
m2 as a function of time for three different relative velocity feedback gains and compare your results with the open-loop displacement.
[10 marks]
Obtain the closed-loop eigenvalues when the relative velocity feedback gain is 10000. Discuss the changes made to the eigenvalues.
[5 marks]
Generate Bode plots of the open-loop system and closed-loop system with the relative
velocity feedback gain of 10000 when the mass m1is subject to a harmonic forcing
f (t) ? 1sin ?t with no initial displacement using time-domain simulation. Discuss and
compare your results with analytical formulations in the frequency domain.
[10 marks]
Discuss how the stability of a closed-loop system can be assessed using generalised Nyquist and comment on its suitability for the considered example.
[5 marks]
[Total: 35 marks]
Q2.
An aircraft panel is equipped with 8 actuators and 16 sensors for the purpose of noise control. The transfer function between each actuator and sensor G is provided together with the disturbance signal d.
G the 16?8 matrix of complex plant responses at a single frequency
d the 16?1 vector of complex disturbance signals at the error sensors for this frequency
u8 Actuators
ed?

G
16 Sensors
Figure 2: Feedforward control of an aircraft panel
Calculate the vector of control signals required to minimise the sum of mean-square error signals and hence the maximum attenuation which can be achieved in the sum of the mean-square error signals, in dB. Show and explain the equations that you use to perform this calculation.
Plot the eigenvalues of the matrix G HG
relevance for a control system.
[7 marks]
in an appropriate format and comment on their
[8 marks]
Write a MATLAB programme that implements the tonal, single frequency, steepest- descent algorithm in this multichannel case and plot the convergence behaviour of the sum of the mean-square error signals over time for various values of the convergence coefficient. What is the maximum stable convergence coefficient based on your simulation and does it correspond to the theoretical value?

 

This Engineering Assignment has been solved by our Engineering Experts at My Uni Paper.Our Assignment Writing Experts are efficient to provide a fresh solution to this question. We are serving more than 10000+Students in Australia, UK & US by helping them to score HD in their academics. Our Experts are well trained to follow all marking rubrics & referencing style.
    
Be it a used or new solution, the quality of the work submitted by our assignment Experts remains unhampered. You may continue to expect the same or even better quality with the used and new assignment solution files respectively. There’s one thing to be noticed that you could choose one between the two and acquire an HD either way. You could choose a new assignment solution file to get yourself an exclusive, plagiarism (with free Turnitin file), expert quality assignment or order an old solution file that was considered worthy of the highest distinction.