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Module Code KD6031

Module Title Modern control

Submission Time and Date To be submitted by 23:59 Beijing time on 20/01/2021

Submission site ‘Assignments’ in Microsoft Teams group

Weighting This coursework accounts for 100% of the total mark for this module

Instructions on Assessment:

Answer all questions. Show evidence of simulations using Simulink by printing your programs.

Late submission of work

For coursework submitted up to 1 working day (24 hours) after the published hand-in deadline without approval, 20% of the total marks available for the assessment shall be deducted from the assessment mark.

Coursework submitted more than 1 working day (24 hours) after the published hand-in deadline without approval will be regarded as not having been completed. A mark of zero will be awarded for the assessment and the module will be failed, irrespective of the overall module mark.

Students must retain an electronic copy of this assignment (including ALL appendices) and it must be made available within 24hours of them requesting it be submitted.

Academic Misconduct

The Assessment Regulations for Taught Awards (ARTA) contain the Regulations and procedures applying to cheating, plagiarism and other forms of academic misconduct.

The full policy is available at here

You are reminded that plagiarism, collusion and other forms of academic misconduct as referred to in the Academic Misconduct procedure of the assessment regulations are taken very seriously. Assignments in which evidence of plagiarism or other forms of academic misconduct is found may receive a mark of zero.

A simplified model of a DC motor, is given by:

where

i(t) = armature motor current,

R = armature resistance (5 ohms),

u(t) = input voltage,

L = armature inductance (200mH),

(t) = motor angular speed,

J = motor inertia (0.02 kgm2),

T1 = back-emf constant (0.1 V/rad/s),

T2 = torque constant (0.1 Nm/A).

a)By setting x1(t) = i(t) and x2(t) = (t), write the system in state-space form by using the above numerical values.

[5 marks]

b)Assuming that the speed is measured, that is the output y(t) = (t), state whether the system is stable and/or output/state controllable?

[15 marks]

c)Design an open-loop controller such that the speed has a constant value of 0.25 rad/s. Show your result via simulation using Simulink. Explain why open-loop control is not recommendable in practice.

[10 marks]

d)We wish to design an output feedback controller of the form u(t) = ky + v to regulate the speed at a constant value. Give the range of values of k for which the closed-loop system is stable.

[15 marks]

e)By choosing a fixed value for k in the range you have found in Question d), show your result of time-domain response of x2 by carrying a simulation of your result using Simulink.

[20 marks]

f)Now, we wish to design a state feedback controller of the form u(t) =k1x1 + k2x2 + v to regulate the speed at a constant value. Give the ranges of k1 and k2 for which the closed-loop system is stable. Give the advantage for using the state feedback over the output feedback.

[15 marks]

g)By setting k2 = k (k is the fixed value you used in Question e)) and choosing a fixed value for k1 in the range you have found in Question f), compare the time-domain responses of x2 between the state feedback and the output feedback systems through simulation using Simulink.

[20 marks]

Total: 100 marks

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