Faculty of Engineering, Environment and Computing 306SE Control and Instrumentation 2 Assignment Brief 2019/20 Module Title Control and Instrumentation 2 Ind/Group Individual Cohort Sept Module Code 306SE Coursework Title Applied continuous and discrete time control problems Hand out date: 26/02/2020 Lecturer Dr John Arvanitakis Due date: 09/02/2020 Estimated Time (hrs): 40 Hours Word Limit: – Coursework type: Technical Report % of Module Mark 50% Submission arrangement online via CUMoodle: File types and method of recording: word file. Mark and Feedback date: Mark and Feedback method: via CUMoodle Module Learning Outcomes Assessed: 1. Apply the z transform methodology to implement digital control. 2. Devise appropriate signal conditioning systems and evaluate the limitations of measurement systems and appraise the use of smart measurement systems and data acquisition parameters. 3. Create simulations of continuous and discrete systems using computer packages such as MATLAB and SIMULINK or equivalent and solve applied continuous and discrete time control problems. Task and Mark distribution: Report presentation [10 marks] The individual report should include as a minimum: a cover page, a summary, a table of contents, a list of figures and should be organised into 3 main sections corresponding to the three sections of the coursework. The coursework should have a general conclusion. A list of references should be provided using Harvard referencing system. All references must be cited in the text. All simulation results should be accompanied with comments on the efficiency of the methods that are implemented. Introduction: Consider the DC-Motor as the one depicted in Fig. 1. The transfer function of the motor with the armature voltage V as input and the angular position θ as output can be calculated as: Figure 1 DC Motor Schematic G(s) = Θ(s)V(s) = Kts[(Js + b)(Ls + R) + KtKe] Where, is the moment of inertia of the motor, is the motor viscous friction constant, is the inductance of the armature circuit, is the resistance of the armature circuit, is the torque constant and is the back e.m.f. constant. Section 1 [25 marks] PID control design belongs to the category of model-less, output feedback control, i.e. a control method that can be applied without complete knowledge of the system and where the feedback signal is the output of the system. While effective, it lacks optimality in the control and has many limitations. In the latest decades optimal controllers have appeared in the literature, that are based on the model of the system. You will need to do a literature review on optimal control. State the concept of optimal control, and the fundamental controllers that have been developed. Your literature review must contain adequate references. All data and material must be sourced from and correctly cited peer reviewed journals, IEEE international conference proceedings or scientific books. Section 2 [40 marks] Consider a DC Motor with the following parameters: = 0.01 .2, = 0.2 .. , = 0.1 . / = 0.1 ./, = 1 ℎ, = 0.5 The motor needs to be attached to a 1-link robotic arm that is required to do a pick and place movement. Modelling wise, the robotic arm has a moment of inertia of = 1 .2 that is added to the moment of inertia of the motor. The robotic arm should be able to rotate by =180 and complete the rotation in less than = 2. Due to physical constraints in the position of the arm, during movement the motor must not rotate at any point more than =180. a) Study the performance of the open loop system and state if any of these requirements can be achieved without using a controller. b) Select a controller from the family of PID controllers. Given the selective use of the PID parameters -and subsequently a reduced version of the PID controller- what kind of controller would you suggest implementing and why? c) Select the parameters of your selected version PID controller. Provide the step response of the system for the desired rotation and comment of the performance of the closed loop system. Compare the performance with that of a P controller with a gain of = 1. d) The designed controller is to be implemented in a microcontroller. Discretize your system and your controller for sampling frequencies of = 1, 10, 100. Provide the discrete transfer functions of the controller and the system. e) Compare the performance of the closed loop discretized systems with respect to the continuous case. Section 3 [25 marks] a) You are required to create a function in matlab that implements an Analogue to Digital Converter (ADC). The principle of operation of the ADC would be the successive approximation method. Inputs of the function should be the input voltage , the reference voltages , and the resolution of the ADC in use. The output should be the quantized voltage , and the binary number (in decimal form) of the ADC. For the values of = 0, = 5, = 11, provide in a plot the input/output diagram of your converter. b) For the motor mentioned in Task 3, a P controller with value = 10 has been created. Implement in Simulink the system with the designed controller, where the ADC that you created is being used to quantize the output of the system to be fed in the controller with = 0, = 10. For the cases of = 4, 8, 12 provide the output of the system and the controller and compare them with those without the ADC in the control loop. Notes: 1. Do not re-write the questions in the report. It is enough to indicate question numbers. 2. You will require to upload your practical work e.g. code, programs, simulations, etc. in a zip file to Moodle separate to your report. You will require to provide meaningful names for all the files within the zip file. This will not be directly assessed but will aid the assessor in determining a mark for the report. 3. All information acquired from other sources must be referenced. Please avoid plagiarism at all costs by making sure that any reference used in the report is properly referenced both in the list of references and cited in the text. 4. You are expected to use the CUHarvard referencing format. Remember to cite all references and source materials clearly. For support and advice on this students can contact Centre for Academic Writing (CAW). 5. Please notify your registry course support team and module leader for disability support. 6. Any student requiring an extension or deferral should follow the university process as outlined here. 7. The University cannot take responsibility for any coursework lost or corrupted on disks, laptops or personal computer. Students should therefore regularly back-up any work and are advised to save it on the University system. 8. If there are technical or performance issues that prevent students submitting coursework through the online coursework submission system on the day of a coursework deadline, an appropriate extension to the coursework submission deadline will be agreed. This extension will normally be 24 hours or the next working day if the deadline falls on a Friday or over the weekend period. This will be communicated via email and as a CUMoodle announcement. 9. Please be advised that this is an INDIVIDUAL coursework. It is acceptable to exchange ideas, but the report and all the design, analytical and simulation analysis must be your own individual work, written with your own words and very clearly referenced when citations are made. 10. We are particularly interested in your own experiences of working on this coursework, design, simulation results, analysis, lessons learnt and conclusions. Mark allocation guidelines to students 0-39 40-49 50-59 60-69 70+ 80+ Work mainly incomplete and /or weaknesses in most areas Most elements completed; weaknesses outweigh strengths Most elements are strong, minor weaknesses Strengths in all elements Most work exceeds the standard
expected All work substantially exceeds the standard expected
