- July 31, 2020

ELEC3114: Control Systems T2 2020 Created by Dr. Arash Khatamianfar, T2 2020. Page 1 of 2 ELEC3114: Assignment A Important Notes Read the following information very carefully. • This assignment is worth 15% of your total course mark. • From the time of its release, you have 1 week to complete the assignment (please see Moodle). • You are required to provide complete workings and derivations analytically. • You are required to provide MATLAB and/or Simulink code in addition to your analytical solution for any question that comes with a sign (M/S). • MATLAB can be used to plot the time domain response or to find the roots of a 3rd-order polynomial (or higher order ones). You can use control system toolbox functions to generate time-domain responses. • In your answer sheets (where you write all the analytical workings and solutions which could be on a digital document or on paper), you can attach the pictures of your time-domain output plots as well as any MATLAB code and/or Simulink block diagram you used. If you use paper for your answer sheet, you can take picture (good quality and readable photos) and then in MS Word you can add he copy of the MATLAB graphs. You scan/photo of the handwritten paper solutions must be readable and clear. • You must submit all the solutions before the due date on Moodle. • This assignment is marked out of 60, which will be scaled down to 15 for your course mark. How to Submit • Convert your hand-written analytical solutions and workings plus any attached pictures of the graphs, MATLAB codes, and Simulink blocks into a single PDF file. Having separate files for your solutions and notes in any other format than pdf will attract 20% penalty mark. • Name the .pdf , .m, and .slx files using your zID and surname as below. o Surname_z1234567_Asignment_B.pdf o Surname_z1234567_Asignment_B.m (for MATLAB scripts all in one file) o Surname_z1234567_Asignment_B.slx (for Simulink models and save them in 2019b version) • Upload your files in the submission box created for Assignment B under Assignments section on Moodle. Please answer the following questions. Consider the unity feedback closed-loop system shown in Fig. 1. + Process G(s) Controller Gc (s) E(s) U(s)R(s) Y(s) s2 s + 3 s s + a + Td (s) Fig. 1. Q1.1. [3] Determine if the process transfer function () is stable (both naturally and BIBO) Q1.2. [4] Find the steady-state error when () = 1/ 2 and () = 0 Q1.3. [7] What is the final value of the output when () = 0 and () = 1/. Is the closed-loop system with disturbance () as the input and () as the output a type 1 system (when () = 0)? Explain your answer. Q1.4. [6] Under what conditions on the values of and the solution to the steady-state error in Q1.1 is valid. ELEC3114: Assignment A Page 2 of 2 Consider the unity feedback closed-loop system shown Fig. 3 with pure time delay . A common method to approximate the pure time delay as a transfer function is the so-called Pade approximation. We use the second order Pade approximation, which contains a zero in the right-hand side of the -plane, as below: − = 1 − 2 1 + 2 + Process G(s) Controller E(s) U(s)R(s) Y(s) t s + 1 Kdc e sTd Gc (s) Fig. 2. Q2.1. [6] If the controller is given as a single gain () = , determine the range of for stability of the closed-loop system, and discuss how the time delay affect the stability range. Q2.2. [8] Use Ziegler-Nichols tuning technique to find a suitable value of when = 0.25s, = 0.2s, and = 1. Use MATLAB or Simulink to plot the unit step response of the closed-loop system with the original pure time delay in its exponential form and with its Pade approximation (no need for analytical derivation of the step response). How do the step responses differ from each other? (M/S) Q2.3. [6] Can the system performance be further improved by using PI or PID controller? You may use Ziegler-Nichols tuning technique to design the controller for response comparison and justification of you answer (no need for gain adjustment). (M/S) Consider the unity feedback closed-loop system shown in Fig. 3. + Process G(s) Controller Gc (s) E(s) U(s)R(s) Y(s) s2 + 10s + 100 100 KP + s KI Fig. 3. Q3.1. [15] Design the PI controller gains to satisfy the following requirements analytically: • Velocity error constant is ≤ 10 • Frequency of oscillation in the step response is ≤ 15 rad/s (i.e., magnitude of the imaginary part of the complex conjugate poles of the closed-loop system). Q3.2. [5] Find the closed-loop poles and estimate the % and for the step response using the complex conjugate closed-loop poles. Q3.3. [5] Use MATLAB or Simulink to plot the closed-loop system response to unit step and unit ramp reference signals. Measure %, and for the step response and for the ramp response (no need for analytical derivation of the responses). Explain why the estimated % and may not be satisfied. (M/S) — End of Assignment B —