For the dynamic voltage restorer (DVR) discussed in Problem 47, Chapter 7,

For the dynamic voltage restorer (DVR) discussed in Problem 47, Chapter 7, do the following:

a. When Z_L = 1/_sC_L, a pure capacitance, the system is more inclined toward instability. Find the system’s characteristic equation for this case.

b. Using the characteristic equation found in Part a, sketch the root locus of the system as a function of C_L: Let L = 7.6mH; C = 11 μF; α = 26.4; β = 1; K_m = 25; K_v = 15; K_T = 0.09565, and τ = 2 ms (Lam, 2004).

Data From Problem 47, Chapter 7:

A dynamic voltage restorer (DVR) is a device that is connected in series to a power supply. It continuously monitors the voltage delivered to the load, and compensates voltage sags by applying the necessary extra voltage to maintain the load voltage constant.

In the model shown in Figure P7.22, u_r represents the desired reference voltage, u_o is the output voltage, and Z_L is the load impedance. All other parameters are internal to the DVR (Lam, 2004).

a. Assuming Z_L = 1/s_CL, and β ≠ 1,find the system’s type.

b. Find the steady-state error to a unit step input as a function of β.