The stability of a depth control system for a submarine, illustrated, is to be analysed. A...

   

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The stability of a depth control system for a submarine, illustrated, is to be analysed. A pressure sensor measures the actual depth, which is compared to the desired depth. A proportional controller drives the stern plane actuator to drive the actual depth towards the desired value. Desired depth R(s) Stern plane actuator G(s) = (5 + K Submarine dynamics 0.1 s + 0.5)(s + 0.7s + 0.3725) Actual depth C(s) gee (ii) (iii) (iv) (v) Pressure transducer H(s)=1 Construct the root locus diagram for this system for 0 < K < 0. Research the meaning of "dominant roots or poles". Find the value of K which makes the relative damping ratio of the closed-loop system (measured by the dominant complex characteristic equation roots) equal to 0.42. Comment on why this might be a suitable choice for the relative damping ratio. Research the meaning of the "gain margin" and "phase margin". For the gain K found in (iii), plot a Bode diagram and state the gain and phase margins. Comment on the suitability of these values. (vi) For the gain K found in (iii), plot a time response for the closed loop system to a unit step on the set point. Comment on the response. This section in your report shall include (but is not limited to): A paragraph each describing the meaning of 'dominant roots', 'gain margin' and 'phase margin'. A paragraph discussing why the chosen damping ratio may be suitable (you may wish to think about the meaning of damping ratio, and its relationship to the system response). A well-commented listing of any matlab script(s) used. MATLAB may be used as a computational aid for all sections. However, you should use your understanding of the problem (and, potentially, hand sketches) to verify the correctness of the calculated results. [See MATLAB commands rlocus, rlocfind, sgrid, margin, series, feedback, step.] The stability of a depth control system for a submarine, illustrated, is to be analysed. A pressure sensor measures the actual depth, which is compared to the desired depth. A proportional controller drives the stern plane actuator to drive the actual depth towards the desired value. Desired depth R(s) Stern plane actuator G(s) = (5 + K Submarine dynamics 0.1 s + 0.5)(s + 0.7s + 0.3725) Actual depth C(s) gee (ii) (iii) (iv) (v) Pressure transducer H(s)=1 Construct the root locus diagram for this system for 0 < K < 0. Research the meaning of "dominant roots or poles". Find the value of K which makes the relative damping ratio of the closed-loop system (measured by the dominant complex characteristic equation roots) equal to 0.42. Comment on why this might be a suitable choice for the relative damping ratio. Research the meaning of the "gain margin" and "phase margin". For the gain K found in (iii), plot a Bode diagram and state the gain and phase margins. Comment on the suitability of these values. (vi) For the gain K found in (iii), plot a time response for the closed loop system to a unit step on the set point. Comment on the response. This section in your report shall include (but is not limited to): A paragraph each describing the meaning of 'dominant roots', 'gain margin' and 'phase margin'. A paragraph discussing why the chosen damping ratio may be suitable (you may wish to think about the meaning of damping ratio, and its relationship to the system response). A well-commented listing of any matlab script(s) used. MATLAB may be used as a computational aid for all sections. However, you should use your understanding of the problem (and, potentially, hand sketches) to verify the correctness of the calculated results. [See MATLAB commands rlocus, rlocfind, sgrid, margin, series, feedback, step.]

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i Root Locus Diagram Construction Well use MATLABs rlocus function to construct the root locus diagr... View the full answer