Bahrain Polytechnic بوليتكنك البحرين Assessment Cover Sheet Assessment Title Designing a Speed Controller for a DC Motor Programme Title: Course No.: Course Title: Student Name: Student ID: Section Number: Bachelor of Engineering Technology EN7230T Instrumentation and Automatic Control Tutor Name: By submitting this assessment for marking, either electronically or as hard copy, I confirm the following: This assignment is my own work Any information used has been properly referenced. I understand that a copy of my work may be used for moderation. I have kept a copy of this assignment Do not write below this line. For Polytechnic use only. Assessor: Grade/Mark: Date of Marking: Assessment Weight: 60% of total mark Comments: Course Project Descriptor (EN7230T) Bahrain Polytechnic بوليتكنك البحرين Instructions 1) Please ensure that you submit your report by the specified due date through the Turnitin link provided on Moodle. 2) The date of your upload on Moodle will be considered as the official "Date of Submission" for calculating any late submissions. 3) Adhering to the late submission rule is crucial as it will be applied in case of any tardy submissions. 4) Kindly note that the deadline for this project is Learning Outcomes The tasks included in this assignment fulfill the Learning Outcomes of the course as follows: 1) Demonstrate advanced knowledge of core principles of control and instrumentation. 2) Critically analyze and evaluate transient response characteristics of first and second order systems. 3) Apply and demonstrate instrumentation and control strategies for feedforward and feedback control systems. 4) Formulate, apply, and present tuning methods for finding suitable PID controller parameters to meet an industry standard requirement for a defined control design problem. The completion of this project carries a weightage of 60% towards your final grade. The project entails designing a speed controller for a DC motor using MATLAB/Simulink. The specific time frame for the project will be announced by your tutor. Deliverables By the project deadline, please submit: 1) The MATLAB/Simulink files used to design your proposed controller. 2) A MATLAB/Simulink simulation model of the complete control system. 3) project report explaining how you determined the controller design and why you made those particular design choices. The report should include details of your calculations and reasoning behind the design. Simulation results and analysis can help show the effectiveness of the approach. 2 | Page Course Project Descriptor (EN7230T) Bahrain Polytechnic بوليتكنك البحرين Guidelines for the Project Report Prepare a comprehensive project report that encompasses the following tasks. Justify your selection of the controller and demonstrate how it meets the criteria for the transient response design specifications. Ensure that the report is clear and transparent by following these guidelines: • Present your results using appropriate MATLAB/Simulink plots and code (very, very strict rule). ● Include all m-files (editable text, no pictures) and Simulink block diagrams in the appendix section of your report (not-so-strict rule). • • Label the axes of each graph, including a figure legend when necessary. Specify the units in the label itself, such as "speed (m/s)" or "time in milliseconds [ms]," to provide clarity about the measured quantities (very, very strict rule). To avoid sending multiple figures, consider using the subplot() function to group related figures (not-so-strict rule). Add comments within each m-file to describe the purpose of the MATLAB code or command (very, very strict rule). • Give each graph a descriptive title and ensure that all axes are labeled and scaled accurately (very, very strict rule). ● • If a plot includes multiple lines, include a legend that explains each curve (very, very strict rule). Do not include Simulink 'Scope' images in the report, as they lack proper labeling (very, very strict rule). ● When creating Simulink block diagrams, minimize overlapping and crossing lines as much as possible. Rearrange icons to establish a clear left-to-right path (very, very strict rule). • Number your plots and graphs sequentially, such as Fig. 1, Fig. 2, and so on (very, very strict rule). DC Motor The DC motor is a widely used actuator in control systems. It is capable of producing rotary motion directly and, when combined with wheels, drums, or cables, can also generate translational motion. 3 | Page Course Project Descriptor (EN7230T) Bahrain Polytechnic بوليتكنك البحرين The electric equivalent circuit of the motor's armature and the free-body diagram of the rotor are depicted in the accompanying figure. (+1 R L Armature circuit + i - T I p Ꮎ bė Rotor Fixed field In this specific scenario, we will consider the voltage source (V) applied to the motor's armature as the input to the system, while the rotational speed of the shaft (ė) will serve as the output. Both the rotor and the shaft are assumed to possess rigid characteristics. Additionally, we adopt a viscous friction model, meaning that the friction torque is proportionate to the angular velocity of the shaft. The physical parameters for our particular example are as follows: Parameter Description J moment of inertia of the rotor b motor viscous friction constant Ке electromotive force constant Kt motor torque constant R electric resistance L electric inductance Value 0.05 kg·m² 0.1 N.m.s V 0.05 rad.s V 0.05 rad.s 0.5 Ω 0.8 H 4 | Page Course Project Descriptor (EN7230T) Bahrain Polytechnic بوليتكنك البحرين System's Model Derivation Typically, the torque produced by a DC motor is directly related to both the armature current and the strength of the magnetic field. However, in this particular case, we will assume that the magnetic field remains constant, resulting in the motor torque being solely proportional to the armature current i. This relationship is expressed by the equation below, where the proportionality factor is denoted as Kt. This configuration is commonly referred to as an armature-controlled motor: T = Kti (1) The back electromotive force (emf), represented as e, is directly proportional to the angular velocity of the shaft. This relationship is governed by a constant factor Kê as follows: e = K₂ė (2) In the International System of Units (SI), the constants for motor torque and back electromotive force (emf) are equivalent, meaning that Kt is equal to Ke. For simplicity, we will denote this common constant as K to represent both the motor torque constant and the back emf constant. Using the information provided in the preceding figure, we can derive the following governing equations by applying Newton's second law and Kirchhoff's voltage law: Transfer Function JÖ + be = Ki di L · + Ri = V − Kė dt (3) (4) By employing the Laplace transform, we can represent the aforementioned modeling equations, given in (3)-(4), in terms of the Laplace variable s: s(Js+b)(s) = KI(s) (Ls + R)I(s) = V(s) – Kso(s) (5) (6) By eliminating I(s) between the two equations mentioned in (5)-(6), we obtain the following open- loop transfer function: = ė(s) P(s) = V(s) K (Js+b)(Ls + R) + K² (7) In this transfer function, the rotational speed ė (s) is regarded as the output, while the armature voltage V(s) is regarded as the input. 5 | Page