2. System modelling a. The first step in controller design is system modelling and convert the given information into a feedback block diagram. Practice converting the given information to the block

diagram. By applying the appropriate voltage V to the antenna system, you want to control the angle 8, of the antenna and make it equal to the desired angle signal 8. The transfer function from voltage V to the angle 8 is where A and B are some constants. There is a sensor that measures the angle of the antenna, but it adds noise. The measured angle 80 is some noise signal n plus the actual angle 8. There is another sensor that measures the angular velocity of the antenna (remember w = 8). This sensor however doesn't measure the angular velocity accurately. The measured angular velocity and the actual angular velocity are related by the sensor dynamics equation dm + pan= pw, where pis some constant. The controller K takes into account the data from both the sensors and provides the voltage V to the antenna system, such that + a + b = ce +de+fam where a, b, c, d, f are some constants, and e is the angle 'error'e = 8a-8m Draw the control system diagram of this system with all the appropriate TFs written in various blocks in terms of the constants s, A, B. p. a, b, c, d, and f./nb. Here is the step response of a plant when you give a constant input Sunit (t) to it. Please find approximate TFs for the plant. Test your answer in MATLAB by command step(5*TF). Amplitude System und Time (seconds) 1.29 Amplitude: 5.01 System und Time (seconds) 2.86 Amplit 3.79 c. Simplify the high order TF below to a 2 order TF, so that the step responses of the original and the simplified plant are almost the same. Show both the step responses (for 5 s) in the same plot. 1000s +2000 G(s)+1125 + 1222s² +2220s+2000 Hint: Think dominant poles! You may find the commands, pole(), zero(), step(G) useful. Your answer will be of the type G = kis+a)/(s+bs + c).