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 Is. The variation of the voltage v(t) and the current i(t) are given by: a 1 Cv'(t) + Fu(t) +i(t) = 1; and v(t) = Li'(t) 2 t = 0 R 1 Figure 2: DC parallel circuit
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 it "(t) + Rc1(0) + ci(t) = 101 ) + 1 ) LC RC LC The transfer function relating the input to the output is given by G(s) 1 $2 + RC s + LC 1) Compute the damping ratio Š, the natural frequency wo and the general form of the poles. 2) For which conditions the system is : over-damped, critically damped and under-damped? 3) Suppose that < 2R, find the corresponding pole location satisfying the following performance characteristics tg < 0.6, and OS < 20% 4) Suppose that RC <a and VLC > B RC. Compute a and B that satisfy the above performance characteristics.