1 6ET006 Control System I School of Engineering BEng (Hons) Electronics and Communications Engineering BEng (Hons) Mechatronics T117 Coursework Assignment Module: 6ET006 Control Engineering I Assignment Title: Course work 2 Date & Time of Submission : Week 10 Assignment Weighting : 15% Description of Assignment Using MATLAB/ SIMULINK compute for the following questions.Show the results to your lecturer and document them in the assignment reports. PART 1: 1. Consider the problem of controlling an inverted pendulum on a moving base, as shown in Figure 1.The transfer function of the system is 𝐺(𝑠) = −1 (𝑀𝑏𝐿)⁄ 𝑠2 −(𝑀𝑝 +𝑀𝑠)𝑔/(𝑀𝑏𝐿) The design objective is to balance the pendulum (i.e., 𝜃(𝑡) ≈ 0 in the presence of disturbance inputs. A block diagram representation of the system is depicted in Figure 2. Let𝑀𝑠 = 10 𝑘𝑔,𝑀𝑏 = 100 𝑘𝑔,𝐿 = 1 𝑚,𝑔 = 9.81 𝑚/𝑠2,𝑎 = 5,𝑎𝑛𝑑 𝑏 = 10. The design specifications, based on a unit step disturbance, are as follows: i. Settling time (with a 2% criterion) less than 10 seconds, ii. Percent overshoot less than 40%, and iii. Steady-state tracking error less than 0.1° in the presence of the disturbance. Figure 1 2 6ET006 Control System I Figure 2 Develop a set of interactive m-file scripts to aid in the control system design. a. The first script should accomplish at least the following: i. Compute the closed-loop transfer function from the disturbance to the output with K as an adjustable parameter. ii. Draw the Bode plot of the closed-loop system. iii. Automatically compute and output 𝑀𝑝𝜔 and𝜔𝑟. As an intermediate step, use 𝑀𝑝𝜔 and 𝜔𝑟 and estimate ζ and𝜔𝑛. b. The second script should at least estimate the settling time and percent overshoot using ζ and 𝜔𝑛 as input variables. If the performance specifications are not satisfied, change K and iterate on the design using the first two scripts. After completion of the first two steps, the final step is to test the design by simulation. c. The functions of the third script are as follows: i. Plot the response θ(t), to a unit step disturbance with K as an adjustable parameter, and ii. Label the plot appropriately. Utilizing the interactive scripts, design the controller to meet the specifications using frequency response Bode methods. To start the design process, use analytic methods to compute the minimum value of K to meet the steady-state tracking error specification. Use the minimum K as the first guess in the design iteration. (25 marks) 2. Consider the feedback control system in Figure 3. We have three potential controllers for our system: i. Gc(s) = K (proportional controller) ii. Gc(s) = K/s (integral controller) iii. Gc(s) = K(\ + 1/s) (proportional, integral (PI) controller) Figure 3 3 6ET006 Control System I The design specifications are 𝑇𝑠 ≤ 10 seconds and 𝑃.𝑂.≤ 10% for a unit step input. a. For the proportional controller, develop an m-file to sketch the root locus for 0 < K < ∞, and determine the value of K so that the design specifications are satisfied. b. Repeat part (a) for the integral controller. c. Repeat part (a) for the PI controller. d. Co-plot the unit step responses for the closed loop systems with each controller designed in parts (a)-(c). e. Compare and contrast the three controllers obtained in parts (a)-(c), concentrating on the steady-state errors and transient performance. (30 marks) PART 2: 3. Consider the analogue control system shown in figure. By root locus analysis, it is found that the closed loop natural frequency ωn =0.6 rad/sec. and the damping ratio is 0.5. 𝐺(𝑠) 𝑜𝑓 𝑐𝑜𝑚𝑝𝑒𝑛𝑠𝑎𝑡𝑜𝑟 = 2.2(𝑠 +0.1) 𝑠 +0.01 𝐺(𝑠)𝑜𝑓 𝑝𝑙𝑎𝑛𝑡 = 1 𝑠(𝑠 +1)(𝑠 +4) We wish to replace the analogue compensator by a digital one. Select a suitable sampling interval and obtain an equivalent digital control algorithm using bilinear mapping. Give the block diagram of digital control system. Using Simulink/Control system tool box obtain the step response of digital and analogue implementation. Compare the results. (30 marks) 4. Produce a detailed report on any application of microcontrollers in controller designs for real life application. Write about the kind of interfaces used for input and output data and also why microcontrollers where used for controller designs. (1200 words). (15 marks) Brief 1. Calculate K value for the system. Write a MATLAB code to compute the closed loop transfer function of the system. Plot the Bode plot and compute 𝑀𝑝𝜔 and𝜔𝑟.Compute using MATLAB the setting time and percentage overshoot of the system for this value, compute again for another. Plot the response to unit step response. 2. Obtain the controller gain for each. Using MATLAB sketch the root locus for the given controller. Do the same for other two controllers. Plot the unit step response of the controllers. Compare the three by finding the steady state error and transient response. 3. Using SIMULINK determine the unit step response for the given system. Compute analytically the digital algorithm for the given system. Draw the block diagram 4 6ET006 Control System I representation for the digital system. Now using SIMULINK compute the response for the digital system. Compare the two plots. 4. Write a report on any implementation of controller using microcontrollers for real life application. Report must have details on the application of the controller, implementation of the controller, interfaces used and why micro controllers are used to implement the controller. Resources Dorf, R. C. and Bishop, H. B., 2011, Modern Control Systems, Pearson. Avoid using online sources such as www.wikipedia.org, www.netmba.com, www.marketingteacher.com, www.marketingtutor.com, www.mindtools.com, www.quickmba.com, www.ezinearticles.com, www.scribd.com, www.soopertutorials.com, www.wisegeek.com, www.slideshare.com, www.ehow.com, www.scribd.com, www.howstuffwork.com, www.12manage.com, www.marketance.com, www.managementstudyguide.com, www.helium.com, www.biztech91.com, www.marketing91.com, www.referenceforbusiness.com, www.highn.me, www.ideafinder.com, www.drypen.in, any blogs/ blogspot, and any unreliable and/or non-academic sources. Please check with you lecturer if you are in doubt. Working Arrangements 1.  Calculation of K value (2 marks)  MATLAB code for closed loop transfer function and output (4 marks)  Bode plot of the system (2 marks)  Compute 𝑀𝑝𝜔 and𝜔𝑟 (4 marks)  MATLAB code for the setting time and percentage overshoot and output. (4 marks)  MATLAB code for response to disturbance and output (3 marks)  Output demonstration (2*3=6 marks) 2.  Determine the K value for Proportional, Integral and PI controllers (1*3=3 marks)  MATLAB code for root locus of the Proportional controller and output (4 marks)  MATLAB code for root locus of the Integral controller and output (4 marks)  MATLAB code for root locus of the PI controller and output (4 marks)  Plot of the unit step response for each of the controllers (1*3=3 marks)  Compare the three controllers (3*2=6 marks)  Output demonstration (2*3=6 marks) 3.  SIMULINK model for the analogue control system (5 marks)  Unit step response of the analogue model (2 marks)  Equivalent digital algorithm design for the analogue compensator (5 marks)  Block diagram representation of digital model (5 marks)  SIMULINK model for the digital control system (5 marks)  Unit step response of the digital model (2 marks)  Output demonstration (3*2=6 marks) 5 6ET006 Control System I 4.  Application of the controller (5 marks)  Implementation of the controller using microcontrollers (5 marks)  Reason on implementing the controller using microcontrollers (5 marks) Submission instructions The coursework should follow the standard report format consisting of a. Coursework Mark sheet b. Title Page c. Main Report d. References  The report should be printed using: Font, Times New Roman; Font size, 12; Line spacing, 1-1/2 and left-right justification.  A report which does not meet the style and format specification will not be accepted for marking. It will be returned to the student and a mark of 0% recorded. If in any doubt about whether the work meets the style and format specification, seek advice from the module leader.  Include a Reference Page at the end of your assignment and reference within the text according to Harvard style of referencing.  References (Harvard Referencing) must be provided whenever you use someone else’s opinions, videos, computers, other print or electronic sources and personal communications.  There will be a penalty for late submissions. Refer to student handbook for late submission penalties. Plagiarism All students share the responsibility for upholding the academic standards and reputation of the University. Academic honesty is a prerequisite condition in the pursuit and acquisition of knowledge. Academic dishonesty is any misrepresentation with the intent to deceive or failure to acknowledge the source or falsification of information or inaccuracy of statements or cheating at examinations/tests or inappropriate use of resources. There are many forms of academic dishonesty and plagiarism is one of them. Plagiarism is generally defined as ‘the practice of taking someone else’s work or ideas and passing them off as one’s own’ (The New Oxford Dictionary of English). The University takes a serious view of plagiarism. Any student found to have committed or aided and abetted the offence of plagiarism may be subject to disciplinary actions. 6 6ET006 Control System I Student needs to print this cover sheet and attach on the assignment/project report before submission to the respective tutor Name of Student: Auston / UNI ID: Date of Submission: Name of Lecturer: John Program/ Module: 6ET006 Control Engineering 1 Assignment: Coursework 2: Plagiarism check Turnitin Percentage : Accept / Reject Justification: Collusion check Learning Outcome / Marking Guide Weightage 1st Marker ( ) 2nd Marker ( ) Control system design for inverted pendulum 25 Responses of Proportional, Integral, and PI controllers 30 Digital control system design 30 Microcontroller implementation of controllers 15 Total 100 7 6ET006 Control System I Name of Student: Uni ID: Name of Lecturer: John.M Module Code & Name: 6ET006 Control Engineering 1 Assessment Title: Coursework 2 Lecturer’s comments – with reference to assessment criteria Areas for improvement: Date completed: Second Marker Comments: Date completed: Staff Declaration: We agree that work to be marked anonymously will be treated as such until marking and internal moderation has been completed.