I Preamble Noise Disturbance in Control Systems Control engineering, as one of the cornerstones of automation, has contributed enormously to the development of modern industrial society; and a control system is

useful for regulating the behaviour of industrial systems. In this assignment, you are required to analyze the following control system in Figure 1 where X(s) is the signal input, N(s) the noise input and Y(s) the system output. G₁(s) = K G₂ (s) = G3(s) = G₁(s) = H₂(s) = 1 s+2 X(s) Figure 1 The gain values for the respective forward and feedback paths are given: 2 s+4 4 S H₁(s) = 1 10 s + 10 H3(s) = 2 G₁ G₂ H₂ H₂ N(s) G3 H3 G4 Y(s) Task 1: Analytically determine the signal and noise transfer function of the control system in Figure 1. If x(t) is a unit step input then how do the signal and noise vary at the output for any change in the value of K as t → ∞o. Task 2: Using Matlab determine the signal and noise transfer function of the control system in Figure 1 assuming K = 1. Indicate clearly the Matlab code applicable to appropriate block reduction. Plot the step response using Matlab to verify the final steady-state value obtained in Task 1 y(t) as t→∞o for signal and noise.