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 6, of the antenna and make it equal to the desired angle signal 8. The transfer function from voltage V to the angle 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 8, is some noise signal n plus the actual angle 8. There is another sensor that measures the angular velocity as of the antenna (remember 8). This sensor however doesn't measure the angular velocity accurately. The measured angular velocity and the actual angular velocity a are related by the sensor dynamics equation +papa, where pis some constant. The controller takes into account the data from both the sensors and provides the voltage to the antenna system, such that + a + b = ce+de+fa, where a,b,c,d,fare some constants, and e is the angle 'error'e-8-8- Draw the control system diagram of this system with all the appropriate TFs written in various blocks in terms of the constants 5, A, B,p.a,b,c,d, and f. b. Here is the step response of a plant when you give a constant input Sanit(t) to it Please find approximate TFs for the plant. Test your answer in MATLAB by command step(5*TF). Syste Ti 5.0 S Time Age: 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 5s) in the same plot 1000s + 2000 GG)+1125+1222¹ +2220s +2000 Hint: Think dominant pales! You may find the commonds, pole), zerol), step(G) useful Your answer will be of the type G = k/s+a/²+b+c).