hw3_solutions-1

hw3_solutions-1 - ECE 486 Issued: February 10 Reading...

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ECE 486 Assignment # 3 Issued: February 10 Due: February 17, 2011 Reading Assignment: Continue reading . .. FPE , 5th or 6th ed., Chapters 1–3 (ignoring subsections marked “ N ”). See also Belanger , Chapters 1–3, and Brogan Chen Chapters 1–3. Problems: 6. The speed y of a DC motor satisﬁes ˙ y +60 y = 600 v - 1500 d , where v is the armature voltage, and d is a load. Suppose v is deﬁned via the PI control law, v = k p e + k I t 0 e ( s ) ds. where e = r - y , as usual, with r the reference speed. (a) Deﬁne a disturbance process ˜ d so that the model can be expressed in the ‘input disturbance’ form, Y = G p ( V + ˜ D ) (b) Draw a complete block diagram showing the plant, compensator, input, output, and the location of disturbance and reference inputs. (c) Compute the transfer function H 1 ( s ) = Y ( s ) /R ( s ) for arbitrary choices of k p ,k I , and note the value of H 1 (0). (d) Repeat with the transfer function H 2 ( s ) = Y ( s ) /D ( s ). (e) Compute values of k p ,k I so that the following closed loop speciﬁcations hold for a step reference input: 5% overshoot, and 1 second settling time. Note

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This note was uploaded on 03/28/2011 for the course ECE 486 taught by Professor H during the Spring '09 term at University of Illinois at Urbana–Champaign.

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hw3_solutions-1 - ECE 486 Issued: February 10 Reading...

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