Motor controllers are devices that regulate the operation of an electric motor. Figure la shows a motor control system with an amplifier K, the natural frequency of the original system is 11 rad/s. In order to improve its transient response, a tachometer is to be added to the original system to yield a damping ratio of 0.85 as shown in Figure 1b. a) Calculate K and K. b) Use Simulink to model the system (Unit-step input). c) Plot system responses (before and after adding the tachometer) and discuss how the system response is improved after adding the tachometer. R(s) R(s) E(s) K E(s) Preamplifier Figure 1a. Original motor system s(s+1) Power amplifier and motor K Preamplifier Tachometer Ks s(s+1) Power amplifier and motor Figure 1b. Modified system with a tachometer C(s) C(s)