Question 1: Figure 1.1 shows the response of a first-order system (red), to the sinusoidal input signal (blue) in steady-state. System Response 0.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.06 0 -0.06 -0.1 -0.15 -0.2 -0.25 -0.3 -0.35 -0.4 -0.45 -0.5 O 0,25 0,5 0,75 1 1,25 1,5 1,75 2 2.25 2.5 2.75 3 3,25 3,5 3,75 4 4,25 4,5 4,75 5 Time (s) Figure 1.1: Frequency response of a system in steady-state. Amplitude a. Obtain the open-loop transfer function (G(s) = 10 of the given system. Y(3) R(S) b. It is aimed to control the system using a Pl controller in the closed-loop (Figure 1.2). Use sisotool to design a Pl controller, which can be given as s+21 F(s) = K s such that critically damped response is achieved with around 3 seconds of settling time. Give the step response, pole-zero map and control signal as outputs. F(s) G(s) Figure 1.2: A closed-loop control system with unit feedback