MEC206 Dynamic Systems
Lab Assignment 1
Due on Monday, 22nd April, 2024, 18:00
Assignment Regulations
. This is the first lab assignment and this assignment accounts 15% of the final mark, i.e. 15 marks in total.
. This is an individual assignment. Every student MUST submit one soft copy of the assignment via the Learning Mall before the due date.
. A coversheet can be created in your own way, but the following information MUST be included: student ID number, full name and email address.
. You may refer to textbooks and lecture notes to discover approaches to problems, however, the assignment should be your own work. Students are reminded to refer and adhere to plagiarism policy and regulations set by XJTLU. References, in IEEE style. can be attached as an appendix.
. Assignments may be accepted up to 5 working days after the deadline has passed; a late penalty of 5% will be applied for each working day late without an extension being granted. Submissions over 5 working days late will not be marked. Emailed submissions will NOT be accepted without exceptional circumstances.
. The use of Generative AI for content generation is not permitted on all assessed coursework in this module.
Aims:
In solving engineering problems, there is a need to understand and determine the dynamic response of a physical system that may consist of several components. These efforts involve modeling, analysis, and simulation of physical systems. Typically, building a prototype system and conducting experimental tests are either infeasible or are too expensive for a preliminary design. Therefore, mathematical modeling, analysis, and simulation of engineering systemsaid the design process immensely.
Dynamic systems and control involves the analysis, design, and control of physical engineering systems that are often composed of interacting mechanical, electrical, and fluid subsystem components. In this assignment, we provide two different dynamic systems with different control objectives. The first system is a vehicle system which is a mechanical system, and the second system is an inverted pendulum which is an electromechanical system. Please choose one of the topic and finish the described tasks according to the requirements. You are required to submit one report in PDF format into Learning mall. The analysis report should be no more than 20 pages with the name StudentID_Studentname.pdf. The report should be in single column, 1.25x line-space, 2.54cm for page edges. And the font should be Times New Roman and Font size for content should be 11pt. The related simulation codes should submitted in one zip file with the name StudentID_Studentname.zip.
Topic 1
Modeling and analysis of Vehicle path tracking
Vehicle path tracking control is a fundamental topic in vehicle dynamics and control. Due to the nonlinear, unstable, and strongly coupled characteristics of vehicle systems, vehicle path tracking control is also a challenging problem. In practical applications, vehicle path tracking control aims to ensure that a vehicle accurately follows a predefined trajectory while considering factors such as vehicle dynamics, environmental conditions, and external disturbances. In this assignment, we start from the vehicle kinematic model, and next consider the vehicle dynamic model. The aim for this assignment is to model and analysis the practical vehicle systems by using mathematical modeling derivation and software simulation.
Vehicle kinematic model (40 Marks)
Vehicle kinematic path tracking control refers to the process of controlling a vehicle's motion along a predefined trajectory using kinematic principles, without considering the vehicle's dynamic characteristics such as mass, inertia, and tire-road interaction. The control system focuses on regulating the vehicle's position and orientation along the desired trajectory. This involves adjusting the vehicle's steering angle, velocity, and possibly other control inputs to minimize deviations from the planned path. The path tracking control system considered in this assignment is shown in Figure 1.
Figure 1 Vehicle path tracking
In order to model the vehicle system, the first procedure is to visualize the actual system into a schematic, and then define coordinates and positive directions, as Figure 2.
Figure 2 The two-degree-of-freedom vehicle kinematic model
Requirement:
1. Write the differential equations of motion for the vehicle kinematic model shown schematically in Figure 2. (5 marks)
2. Linearize the equations and derive the kinematic error model. (5 marks)
3. Choose a tracking control algorithm (except for LQR algorithm) and provide its simple control principle with equations. (5 marks)
4. Design the reference path for tracking, and give reference speed, yaw angle, vehicle body length, initial conditions, time periods by yourself. (5 marks)
5. Simulate the path tracking and control process by using MATLAB. Provide the codes, the figure results with necessary comments. (20 marks)
Vehicle dynamic model (60 marks)
The vehicle bicycle model based on the dynamic equations is as shown in the Figure 3. Compared with the kinematic model, the vehicle dynamic model more accurately describes the motion characteristics of the vehicle, considering the influence of dynamic factors on vehicle behavior. It provides a higher level of accuracy, broader applicability, stronger predictive ability, and a foundation for control optimization, resulting in a greater advantage in predicting and controlling vehicle motion.
Figure 3 Vehicle dynamic model
Requirement:
1. Write the differential equations of motion for the vehicle dynamic model shown schematically in Figure 3. (10 marks)
2. Linearize the equations and derive the dynamic error model. (10 marks)
3. Choose a tracking control algorithm and provide its simple control principle with equations. (10 marks)
4. Design the reference path for tracking, and give reference speed, yaw angle, vehicle body length, initial conditions, time periods by yourself. (10 marks)
5. Simulate the path tracking and control process by using MATLAB. Provide the codes, the figure results with necessary comments. (20 marks)
Topic 2
Modeling and analysis of inverted pendulum system
The inverted pendulum under natural conditions is a typical nonlinear, unstable, strong coupling system. In the field and control, inverted pendulum system is a typical experimental device, since it can effectively reflect many key problems in control, such as controllability, robustness and tracking. Due the combination of the rotational and translational motion, it also widely be used to dynamic system modeling areas. In this assignment, we start from the practical Hanging Crane system, and next consider the linear single inverted-pendulum system. The aim for this assignment is to model and analysis the practical mechanical systems by using mathematical modeling derivation and software simulation.
Hanging Crane (40 Marks)
A crane is a type of machine, generally equipped with a hoist rope, wire ropes or chains, and sheaves, that can be used both to lift and lower materials and to move them horizontally. It is mainly used for lifting heavy objects and transporting them to other places. Cranes are commonly employed in transportation for the loading and unloading of freight, in construction for the movement of materials, and in manufacturing for the assembling of heavy equipment.
The system considered in this assignment is shown in Figure 4.
Figure 4 Crane with a hanging load
In order to model the system, the first procedure is to visualize the actual system into a schematic, and then define coordinates and positive directions, as Figure 5.
Figure 5 Crane with a hanging load
Requirement:
6. Write the equations of motion for the hanging crane shown schematically in Figure 5. (15 marks)
7. Linearize the equations about θ = 0, which would typically be valid for the hanging crane. (5 marks)
8. Give the all the coefficients (trolley mass mt, hanging crane mass mp and inertia about its mass center of I ), initial conditions, boundary conditions, time periods, domain by yourself, and simulate the linear system and nonlinear system by using MATLAB. (10 marks)
9. Provide the codes, the figure results with necessary comments. (10 marks)
Inverted pendulum (60 marks)
An inverted pendulum is a pendulum that has its center of mass above its pivot point, shown as Figure 3. It is unstable and without additional help will fall over. It can be suspended stably in this inverted position by using a control system to monitor the angle of the pole and move the pivot point horizontally back under the center of mass when it starts to fall over, keeping it balanced.
Figure 6 Inverted pendulum
Based on the first hanging crane example, do the following requirements.
Requirement:
6. Draw the schematic model of the inverted pendulum based on Figure 5. (5 marks)
7. Derive the equations of motion for the inverted pendulum based on your schematic model. (10 marks)
8. Based on your mathematical model, show the relationship between the hanging crane and the inverted pendulum. (5 marks)
9. Simulate the system based on your own parameter setting. (10 marks)
10. The objective of the control system is to balance the inverted pendulum by applying a force to the cart that the pendulum is attached to. A real-world example that relates directly to this inverted pendulum system is the attitude control of a booster rocket at takeoff. Design a controller to make the pendulum balance at the vertically upward equilibrium. (20 marks)
11. Provide the codes, the figure results with necessary comments. (10 marks)