A continuous-time (i.e. analogue) plant, is described by the transfer function G(s) = 1 (8 + 1)(8 + 10) A digital controller has to be designed using the analytical design procedure to obtain a closed-loop sampled-data system that satisfies the following specifications: a. The sampling period T = 0.02 s. b. The desired continuous-time closed-loop transfer function is required to be the standard second-order response with a damped frequency of 0.546 rad/s and an undamped natural frequency of 1.15 rad/s producing zero steady-state error, to a step response. c. Zero steady-state error step response. 1 Approximating continuous-time derivatives using the standard backward-difference approximation, derive the discrete-time representation of the desired closed-loop system T(z) = (a2z + z+o)/(Bz + Bz+1) where the coefficients ao, a1, a2, B1 and 32 are determined by your analysis. Find the above coefficients.