The following LOs are achieved by the student by completing the assignment successfully

1. Calculate performance of compensators to achieve specified performance; and
2. Plan and manage employment of state space representation in continuous and discrete systems.
   Assignment Objective
   This will enable each student to evaluate, analyze and design Control system related to engineering
   scenario. This assessment will develop student’s analytical, critical thinking and problem-solving skills.
   Assignment Tasks
   Part A (70 Marks)
   Task 1: (10 Marks)
   Find the state space representation of the given electrical network in figure 1. The outputs are the
   current through the resistor and the voltage across the capacitor 1.
   IN SEMESTER INDIVIDUAL ASSIGNMENT
   Module Code: ELEC 20005.3 Module Name: Control System
   Level: 2 Max. Marks: 100
   Control Systems (ELEC 20005.3) – Spring-22– CW2(Assignment2) – All – QP
   MEC_AMO_TEM_035_04 Page 2 of 12
   Figure 1
   Task 2: (10 Marks)
   Determine the closed loop Transfer Function of figure 2 and convert the transfer function to statespace representation.
   Figure 2
   Task 3: (10 Marks)
   Given the discrete state space representation figure 3, determine the observability matrix, and write
   a reflection on the observability of given system.
   [
   𝑥1
   (𝑘 + 1)
   𝑥2
   (𝑘 + 1)
   𝑥3
   (𝑘 + 1)
   ] = [
   1 −1 2
   2 −1 −1
   3 1 2
   ] [
   𝑥1
   (𝑘)
   𝑥2
   (𝑘)
   𝑥3
   (𝑘)
   ] 𝑦(𝑘) = [1 1 1] [
   𝑥1
   (𝑘)
   𝑥2
   (𝑘)
   𝑥3
   (𝑘)
   ]
   Figure 3
   Task 4: (40 Marks)
   Control Systems (ELEC 20005.3) – Spring-22– CW2(Assignment2) – All – QP
   MEC_AMO_TEM_035_04 Page 3 of 12
   Figure 4.1: Azimuth Antenna Position Control (AAPC)
   Figure 4.2: Equivalent Block Diagram AAPC
   Part 1: Azimuth Antenna Position Control System performance evaluation
   a. Simplify the block diagram in figure 4.2 using the parameter configuration in figure 4.1, and
   determine the open-loop and closed-loop transfer function of the system. Use the last two digits
   of your student ID for the value of ‘K’. (4 Marks)
   b. Determine the time response and provide a step response graph. of the system. Also determine
   if the system is stable or not. Support your answer. (8 Marks)
   c. Using root locus, find the possible range of preamplifier gain(K) required to keep the closed-loop
   system stable. Choose three values of K that will make the system stable, marginally stable, and
   not stable system. Obtain the step response for each of these values. (8 Marks)
   Part 2: Compensated Azimuth Antenna Position Control System
   a. Determine the design point (dominant pole) of the compensated system that will satisfy an
   improvement in both the settling time and percent overshoot by 50% or better. (4 Marks)
   b. By choosing a lead compensator zero location at Zc, determine the location of the compensator
   pole nessary to satisfy the angle criterion of the root locus of the AAPC. Calculate the overall gain.
   Given 𝑍𝑐 = −40. (12 Marks)
   c. Write a reflection on the system performance before and after the compensation was added.
   Show graphs to support your answer. Assume a unity step input. (4 Marks)
   Control Systems (ELEC 20005.3) – Spring-22– CW2(Assignment2) – All – QP