b- Below is the transfer function for a 1st order IIR (Infinite Impulse Response) system. Convert this system to differential equation form and implement it as 1st Direct form and 2nd Direct form. 1+ 2z-1 H(z) =- 1- 0.5z-1

Part 1: Problem 4B Match the transfer function shown in the left column by place the correct letter next to the right column showing the correct response showing the basic response to a step input. Hint look at Zeta for each function, and determine the state of response (Underdamped, overdamped, critically damped, or Zero Damp which means oscillation (continuously). PROBLEM: For each of the following transfer functions, write, by inspection, the general form of the step response: a. G (8) 400 g²+12s+400 c (t) = A + Be-6t cos(19.08t + ¢) 900 b. G (8) = 790s+900 c (t) = A + Be-78.54t + Ce-11.46t 225 c. G (s) = 730s+225 c (t) = A + Be-15t + Cte-15t d. G (8) = 625 s²+625 c (t) = A + B cos(25t + ø)

Q3. Consider a system with the mathematical model given by the following differential equation. Find the transfer function of the system. 5 dy3 dt? dy + 5 dte dy dt

L Exercise. You can write the DC motor angular velocity transfer function as s + bs +c (a) Suppose that a DC motor has constants g = 60, b = 2.3, and e = 11. Define the transfer function in MATLAB using the tf function. % write your code here (b) Is the system stable? You can plot the poles in the s-plane using the pzmap function. For example, to plot the poles of a transfer function G, use: pznap(G) % write your code here (c) What are the poles of the transfer function? You can use the pole function to compute the poles of a dynamic system in MATLAB. For example, to identify the poles of a transfer function R, use: pole(R) % write your code here