Please read the following submission instruction very carefully: a) Coursework 2 contributes 25% towards your assessment for this module. b) You are required to submit your coursework in electronic format

to CANVAS by Late submission will not be accepted unless justification is provided with supporting evidence. CPE6008-B Control Engineering Coursework 2 - 2023/24 I c) Your report should have a front page with your course, the academic year, the module code and name, your name and UB number clearly stated. d) Word count (1500 words). e) Please also use the following filename convention: CPE6008-B_Your surname_Number.docx As an example, my surname is James and my UB number is 123456, then the filename is: CPE6009-B_James_123456.docx. Coursework Specification A. Frequency response (90%) - An essay of up to 1500 words. 1. For a process with the transfer function, a. Y > T₁ > T₂ > 0 b. T₁ > Y > T₂ > 0 G(s) = k(ys + 1) s(t₁s + 1)(t₂s + 1)(T3s + 1) With T₂ > T₁ > 0, k > 0, which is controlled with a Proportional controller. Sketch the root-locus diagram for the following cases and check your results with MATLAB showing all your codes: C. T₁ > T₂ >y>0 d. y = 0 e. y <0 f. Discuss the relevance of the results in (a-e) above. K(S+1) 2. Given the transfer function G(s)H(s) provide your reflection (do not use S(S-1)(S²+6S+18)' literature definitions) on the concept of the following Root Locus terminologies (show complete hand calculations of all steps - make it clear, or you could type it clear): a. number of branches b. the asymptotes and their angles c. intersection with the real axis = d. intersection with the imaginary axis and angle of departure where applicable e. and discuss how the closed-loop system behaves when the gain K is increased from zero to infinity. 3. For a process with transfer function G(s) 2(4s+1) , which is controlled with a s(15s+3)(2s+1)' Proportional-Integral controller, sketch and explain the root-locus diagram for fixed integral time TI, for the following cases (check and show your results with MATLAB): a. T₁ > 15 (Larger than process time constants) b. 2 < t < 15 (in between the process time constants) C. T₁ < 2 (Smaller than the process time constants) B. Structure of the report (10%) Your report should be structured to suit its content. However, a typical good report will have: I. Title Page II. Table of Contents III. Introduction explaining the background and context of the report. IV. Suitable Sections V. Conclusions VI. References VII. Appendices Additional checks ● ● Pages and Sections should be numbered correctly: 1a, 1b ... 2a, 2b. Good use of figures and well captioned. Figures should be numbered. Graph axes should be clearly labelled. Tables should be separately numbered and have captions. All references in the list should be cited in the text, consistently using the HarvardBrad style for citation and listing.