Reference no: EM133088414

EAC2020-N Linear Systems and Control - teesside University

Linear Systems and Control

OBJECtIVES
the ICA work for this module is in the form of Simulink-based exercise on dynamic modelling and control. You should attempt to answer all parts in Q and submit your answers in a single file electronically by the specified submission date. the submission should be based upon the supplied template, be in PDF format and should be no longer than 8 pages in total (including the cover page).

Learning Outcome 1: Apply, question, and relate appropriate knowledge/concepts to a range of activities.
Learning Outcome 2: Apply mathematical techniques to analyse and model signal processing and control systems.
Learning Outcome 3: Apply practical testing methods to plant, to establish system structure and model parameters.

Q) A system is described by a first-order linear system as shown in equation 1.

dy(t)/dt = a[u(t)-ay(t)]/c

Where, u is the input signal, y is the output signal a = 0.05 and c = 1/1200.

a) Produce a Simulink model for the system in (1) which includes u(t) as input and y(t) as output. Print and clearly label a copy of the model to be included as part of your answer.

b) Assuming that the input u(t) is a 2 volts step at t = 0 and all initial conditions are zero, plot the output y(t) against time for 2 seconds. Determine and indicate on the plot the steady state value, rise time, and the 1% settling time, support your answer mathematically. Print and clearly label a copy of the figure to be included as part of your answer.

c) Determine and write out the transfer function G(s) that relates the Laplace transform of the output y(t) to the Laplace transform of the input u(t). Assume all zero initial conditions. Include working out as part of the answer.

d) From the response in part (b), explain briefly how you can use the reaction curve method to find the model of the system in (1). Support your answer numerically and determine the transfer function G(s).

e) Is the system [G(s)] stable? Why? Use MAtLAB to support you answer.

f) Use the transfer function G(s) obtained in part (c), to select and design the suitable controller by using Direct Design Synthesis. the closed loop must exhibit a settling time of 1 seconds with no overshoot, in response to step change in reference signal.
Assume that the desired closed loop time constant, λ = ( t_s-d). Include working out as 4.6 part of the answer.

g) Implement the controller you have designed in part (f) in Simulink and obtain the closed-loop response to unit step change in the reference. Print and clearly label a copy of the Simulink model and closed loop response figure to be included as part of your answer.

Attachment:- Linear Systems and Control.rar