This is a desktop based activity focussing on deriving the characteristic equation of DC motor followed by obtaining the behaviour of system in time and frequency domains using computer simulation tools. The Design problem details are as follows. Design problem Due to the high starting torque, DC motors are widely used in actuator mechanism. It directly provides rotary motion and, coupled with wheels or drums and cables, can provide translational motion. The Equivalent circuit of the DC motor is shown in Figure 1. Figure 1 DC motor Equivalent circuit The Input of the system is the voltage source V applied to the motor\'s armature, while the output is the angular displacement of the shaft ?. The rotor and shaft are assumed to be rigid and the friction torque is proportional to the angular velocity. The Block diagram of the openloop system is shown in Figure 2. Figure 2 Open-loop diagram Where V(s): Input voltage ? (s) : Angular displacement G(s): Transfer function of the motor This project requires to design a closed loop control system as shown in the block diagram in Figure 3 which can meet the time domain specifications given in Table -1 Figure 3 Closed-loop diagram Table -1 Time domain specifications. Step response characteristics Design values Settling time Overshoot Steady-state error less than 2 seconds less than 5% less than 1% The DC Motor specifications are given in Table 2. Table 2: DC Motor parameters Parameter symbols Description Value and Unites J b Ke Kt R L moment of inertia of the rotor motor viscous friction constant electromotive force constant motor torque constant electric resistance electric inductance 0.01 kg.m2 0.1 N.m.s 0.01 V/rad/sec 0.01 N.m/Amp 1 ? 0.5 H The log book should also include the answers/solutions of the following questions : Open Loop System With reference to Figure 2 Q1. Derive the transfer function of the system shown in Figure 1 Q2. Plot the impulse response of the system Q3. Plot the unit step response of the system Q4. Draw the pole zero plot of the system . Justify the stability of the system Q5. Calculate rise time, time constant, damping ratio, and natural frequency for open loop system Q6. Draw the Bode Plot diagram for the open loop system. Obtain the Gain Margin (GM) and Phase Margin (PM) . Closed Loop System With reference to Figure 3. Q7. Derive the transfer function of the system closed loop system. Q8. Obtain the step response of the system. Calculte, rise time, time constant, percenate overshoot, peak time, settling time and the steady-state error I. P-controller Proportional constant (Kp) = 50 II. P-controller Proportional constant (Kp) = 100, III. P-controller Proportional constant (Kp) = 150 IV. PI controller Kp = 75 and Ki = 1 V. PI controller Kp = 75 and Ki = 100 VI. Discuss your results Q9. By incorporating a derivative constant in the PID controller with the following cases I. Kp = 75, Ki = 200, Kd = 1 II. Kp = 75, Ki = 200, Kd = 5 III. Kp = 75, Ki = 200, Kd = 10 Calculate the overshoot, settling time, and steady-state error. Are the results acceptable? If not, explain which specification needs to be improved. Simulink Model Q10. Develop a Simulink model outlining all the elements of the block diagram in Figure 3 for the unstable second order control system). Use the Simulink block PID from Matlab/Simulink library as a controller. Obtain the time response of the system using the time domain specifications in Table -1 Q11. Discuss the effect of each of the PID parameters on the dynamics of a closed-loop system and demonstrate how to use a PID controller to improve a system\'s performance General  You should follow all the procedures for each laboratory experiments as provided in the Laboratory experiment sheets that will be handed to you prior to the lab activity.  MATLAB/SIMULINK must be used to solve the tasks in this assignment .  Understand and test your results with suitable MATLAB/SIMULINK plots  All m-files and Simulink block diagrams must be included in the appendix section of your lab-lab-report. Every line of code must be commented.  Label the axes of each and every graph. This includes attaching a figure legend when appropriate. Include the unit with the label itself (Vout versus time in sec or \"time [s]\") so that we know whats being measured and that it is not an arbitrary variable.  Instead of sending many figures for one question, you can use subplot() to group relevant figures. Reading / References: The Module laboratory experiment sheets issued to students by the course team at the start of the Module. Other References: 1. Nise, Norman S, (7th Ed 2015) Control Systems Engineering, John Wiley & Sons, ISBN13: 978- 1118743966 2. R. C. Dorf and R. H. Bishop, 12th Ed 2010 Modern Control Systems, (), Prentice Hall, ISBN: 9780136024583