Question

Consider the transfer function of a DC motor given by G(s) = 1 / s(s+2)

3. Consider the transfer function of a DC motor given by 1 G(s) s (s2) The objective of this question is to consider the problem of control design for this DC motor, with the feedback control architecture shown in the figure below d(t r(t) e(t) e(t) C(s) G(s) Figure 4: A feedback control system (a) Find the magnitude and the phase of the frequency response G(jw). Roughly sketch the Bode plot for G(jw), showing low frequency and high frequency asymptotes and any corner frequencies. (10 Marks) = K, find an expression for the (b) Considering a pure proportional controller C(s) steady-state unit ramp error (or velocity error). Hence determine the minimal value of K such that the unit ramp reference steady-state error is no greater than 0.05 (10 Marks) (c) Find, if possible, the parameters of a lead compensator 1 +TS C(8) = K 1+aTS where 0a< 1 and 7 > 0, to achieve a phase margin of 45° and a crossover frequency wo 10 rad/sec given that the DC gain K of the compensator is constrained to be exactly equal to 40. (10 Marks)

Answer 1

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