Answer Happy

Problem 4: Consider the parallel circuit shown in Figure 2. The unit-step is obtained by the sudden application of a direct current ly. The variation of the voltage v(t) and the current i(t) are given by: Co'(t) + Fut) +i(t) = 1, and v(t) = Li' (t) '( R I, t=0 R Www LS Figure 2: DC parallel circuit LC where C, R and L are the capacitance, the resistance and the inductance param- eters respectively. From the above derivatives we can derive the second order differential equation of the circuit as "() + Rei(t) + Toilet ) = 1 RC ) + = ਟਿ . LC The transfer function relating the input to the output is given by 1 G(s) = s2 + RCS + te a Compute the damping ratio &, the natural frequency wo and the general form of the poles. For which conditions the system is : over-damped, critically damped and under-damped? Suppose that <2R, find the corresponding pole location satisfying the following performance characteristics t: < 0.6, and os < 20% d Suppose that RC <a and VLC > B RC. Compute o and B that satisfy the above performance characteristics.