The open-loop dynamics from dc voltage armature to angular

Chapter 10, Problem 35

(choose chapter or problem)

A room's temperature can be controlled by varying the radiator power. In a specific room, the transfer function from indoor radiator power, \(\dot{Q}\), to room temperature, T in \({ }^{\circ} \mathrm{C}\) is (Thomas, 2005)

P(s) = \(\frac{T(s)}{\dot{Q}(s)}\)

       = \(\frac{\left(1 \times 10^{-6}\right) s^2+\left(1.314 \times 10^{-9}\right) s+\left(2.66 \times 10^{-13}\right)}{s^3+0.00163 s^2+\left(5.272 \times 10^{-7}\right) s+\left(3.538 \times 10^{-11}\right)}\)

The system is controlled in the closed-loop configuration shown in Figure 10.20 with G(s) = KP(s), H = 1.

a. Draw the corresponding Nyquist diagram for K = 1.

b. Obtain the gain and phase margins.

c. Find the range of K for the closed-loop stability. Compare your result with that of Problem 58, Chapter 6.