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ELECTRICAL & ELECTRONIC ENG. EEEN40010
CONTROL THEORY Laboratory CT_1 DOMINANT POLE PLACEMENT VIA ROOT LOCUS 1. Objective: To practice the control design method of dominant pole placement via root locus. Before starting this laboratory generate some personalised digits. Let a, b, c be the last three digits of your student number. For example, if your student number is 19306227 then a = 2, b = 2 and c = 7. If any of these digits is 0 then add 1. For example, if your student number is 19306207 then a = 2, b = 1 and c = 7. In this laboratory description document illustrative MATLAB commands are shown in purple. The problems which you are to solve are shown in blue. You must produce a report for this laboratory. This report will be graded and that grade will carry a weight of 28% when calculating your overall module grade. This is a slight reduction on previous years in light of student feedback. The number of grade steps which can be earned for each of the problems is given in the problem statement and a coarse grading scheme follows each problem statement. In designing using root loci one generally sketches a few root loci to see the expected shape for choices of various parameters (i.e. various introduced poles and zeros). To achieve a high grade you must do the same. All root locus design finally comes down to applying the rlocfind command and picking a gain. You must show on the sketched root locus/loci where you clicked to determine the associated gain, explaining why in accompanying text. If sketched by hand root loci should be subsequently scanned/photographed and included as an image in the report. This is the single exception to the general rule regarding acceptability of handwritten material. It is generally not acceptable, but here the requirement is for you to reveal your understanding of the root locus drawing rules by applying them and assessors cannot judge that understanding if you have the MATLAB command rlocus draw those root loci for you. You may alternatively, if you wish use sketching software to produce these images of “sketched” root loci for your report. To reiterate, what is sought here is evidence that you understand and can apply the root locus drawing rules, because this skill is useful in controller design using the root locus method. The following comments apply to all design laboratories so take note. These comments are extremely important. Traditionally the main loss of grades is due to a failure to properly comprehend the stipulations below. Consider general reporting requirements discussed in previous laboratory. The comments here are particular to the issue of reporting on a design. In reporting a design, report in detail all of the steps taken in the design and the reasons for taking them. The majority of grades are assigned for this careful description of your design process. Pay very close attention to this requirement. Just simply reporting controller gains without any accompanying explanation of how they were obtained and why you have some expectation of good resulting performance will result in few if any grades being earned. This stipulation almost certainly negates the value of using more advanced MATLAB tools such as syms, Sisotool or Control System Designer. These will do too much of the design for you in a rather ad hoc manner and they amount to little more than fast methods for randomly selecting controller gains resulting in rapid convergence to designs that work but for which there is no accompanying reason why they would be expected to work. We often as a result obtain designs that work “in-the-box”, i.e. in the ideal simulation environment, but fail when any of the host of assumptions which have been made do not hold. The rather course grading schemes which follow each problem statement also very slightly nudge you towards a proper layout of the report of your designs.