Ball-and-plate balancing platforms have been utilized throughout academia to further understanding of nonlinearities that can occur when applying control algorithms to nonholonomic and underactuated systems. The objective of this thesis is to build upon an existing ball-and-plate balancing platform used in the Intro to Mechatronics class and create a robust platform system that can be utilized by future students to test various controller designs derived from MATLAB/Simulink®. The ball-and-plate platform design uses a myriad of sensors to track the system components in real time: a resistive touch panel is used to track the position of the ball on the plate, an inertial measurement unit is used to track the orientation of the top plate, and capacitive incremental encoders attached to the brushless-DC gimbal motors are used to both track the orientation of the motor actuation arms and commutate the motors. The gimbal motors are driven using the open-source ODrive motor driver, which receives torque commands from a separate STM32 microcontroller. The STM32 microcontroller aggregates and processes the data from the touch panel and IMU, and it acts as a “middle-man” for communication between the ODrive and MATLAB/Simulink® model running on a host PC. The platform successfully handles communications between the host PC, STM32, and ODrive at a rate of 200 Hz. The platform also incorporates a serial user interface that allows for fine position control of the motor arms for zeroing the top plate before each test.

This thesis presents a skillful robotic wrist system using a visual servo control technique to demonstrate dexterity of the mechanical wrist from the viewpoint of the table tennis. A ball and plate system is chosen as the first stage of this long-term project. A two degrees-of-freedom robotic wrist with an acrylic plate attached as the end effector is developed. A visual feedback control system is implemented with a web cam and a personal computer to acquire the ball's position. In order to implement decision making for changing orientation of the plate, a Linear Quadratic Regulator (LQR) is designed. As a result, the ball can be balanced at specific positions. Experimental results exhibit preliminary and promising achievement. Based on this progress, further improvement and deeper exploration can be carried on in the future.

The influence of the horizontal magnetic field has not been sufficiently studied in contrast to study activity on the influence of the vertical magnetic field by researchers. The reason was that the influence of horizontal magnetic field to change the wear mass loss of ferromagnetic materials is smaller compared to the vertical magnetic field. However, the influence of horizontal magnetic field on rolling contact changes the subsurface crack initiation point toward surface is postulated by a researcher. Therefore, it is significance finding out how the horizontal magnetic field influences the tribological characteristics. This thesis presents a study on the influence of the horizontal magnetic field on wear in sliding contacts contributes for ascertainment the effect and mechanism of horizontal magnetic field on tribological characteristics of sliding contacts, through the experimental approach.The static magnetic field with densities of 0 and 1.1 Tesla and different orientations was applied to different contact conditions, different surface modifications and two sliding frequencies, using a ball-on-plate contact configuration. In conclusion, the presence of magnetic field enhances the chemical adsorption between iron or oxide iron and oxygen, and causes the transition of adhesive wear to oxidative wear. Besides, the presence of magnetic field combined with low sliding frequency forms the bulging on the wear surface and weakens the prevailing wear mechanism due to the low frictional temperature. On the other hand, the presence of magnetic field combined with high sliding frequency induces the transition to the oxidative wear mechanism and reduces the wear. Also, distinctly different appearances of wear surface are created by different magnetic field orientations. In the lubricated sliding contact, the magnetic field causes the reduction of wear and induction of oxide. It is postulated that the presence of magnetic field enhances the oxygen adsorption on the wear track by iron wear particles and hence varies the tribological behaviour. The influence of magnetic field on carbon steel coating consists in changes of oxide iron layer and steel layer, alterations of mechanical properties of the coating, and decrease in the mass loss and the surface roughness on the dry sliding contact. All these could be suggested the influence of adhesive strength of the interface between the base material and coating.

This thesis presents a visual servo control scheme for a ball-and-plate system with a maze. The maze built on the plate forms obstacles for the ball and increases variety and complexity of its environment. The ball-and-plate system is a two degrees-of-freedom robotic wrist with an acrylic plate attached as the end effector. By using image processing techniques, the ball¡¦s position is acquired from the visual feedback, which was implemented with a webcam and a personal computer. A fuzzy controller, which provides dexterity of the robotic wrist, is designed to decide the slope angles of the plate to guide the ball to a designated target spot. Using the method of distance transform, the path planning based on the current position of the ball is conducted to find the shortest path toward the target spot. Besides, a relaxed path, appears to be more suitable for actual applications, is provided by the obstacle¡¦s expansion approach. Experimental results show that the presented control framework successfully leads the ball to pass through the maze and arrive at target spot. The visual servo control scheme works effectively in both stabilization and tracking control. Based on this preliminary achievement, further improvement and deeper exploration on related research topics can be carried on in the future.

The Mechatronics group in the Mechanical Engineering department of Cal Poly is interested in creating a demonstration of a ball-and-plate trajectory tracking controller on hardware. The display piece will serve to inspire engineering students to pursue Mechatronics and control theory as an area of study. The ball-and-plate system is open-loop unstable, underactuated, and has complicated, nonlinear equations of motion. These features present substantial challenges for control - especially if the objective is trajectory tracking. Because the system is underactuated, common nonlinear trajectory tracking control techniques are ineffective. This thesis lays out a theoretical foundation for controlling the hardware. Several important concepts related to ball-and-plate trajectory tracking control are presented. Models of the system, with various assumptions, are given and used in deriving control law candidates. To limit project scope, reasonable control criteria are introduced and used to evaluate designs from the thesis. Several control architectures are explored, these being Full-State Feedback with Integral Action, Single-Input-Single-Output Sliding Mode, and Full-State Feedback with Feed Forward. The mathematical reasoning behind each is detailed, simulation results are shown to validate their practicality and demonstrate features of the architectures, and trajectory similarity measure studies are produced to evaluate controller performance for a wide range of setpoint functions. The Full-State Feedback with Feed Forward controller is recommended based on its theoretical advantages and compliance with the control criteria over the competing designs. The control architecture has a proof of asymptotic tracking in the linear model, has excellent performance in simulations that use a nonlinear plant model, and produces the most pleasing visual experience when viewed in animation.

Ball and plate balancing control systems are commonly studied due to the complex dynamics associated with the instability of the system in open-loop. For simplicity, mathematical models describing the ball and plate dynamics are often linearized and the effects of complex motion are assumed to be negligible. These assumptions are rarely backed with evidence or explanations validating the simplified form of the dynamical equations of motion. This thesis focuses on developing a nonlinear model that more accurately defines the dynamics of the system, in order to quantify the error of linear and nonlinear models when compared to a Simscape physical system model. To develop the nonlinear model, this thesis considers both Newton-Euler and Lagrangian modeling methods and applies the method best suited for the ball and plate system. A linear state-feedback controller is developed to compare the stable responses of each system model. The response of each plant model in open-loop and closed-loop configurations subject to different inputs, initial conditions, and disturbances are simulated in the Simulink environment. When compared to the physical system, there was less error from the nonlinear model than from the linear model for both initial condition and disturbance responses. The differences in error were as high as 2% compared to 10% for the nonlinear and linear models, respectively. These results show that there are significant differences associated with model simplification. To optimize the performance, it may be advantageous to utilize a nonlinear model, however, the linearized model is still valid to be used in certain applications due to its stable response behavior.

This master's thesis aims to make the BRIO Labyrinth Game autonomous and the main focus is on the development of a path following controller. A test-bench system is built using a modern edition of the classic game with the addition of a Raspberry Pi, a camera and two servos. A mathematical model of the ball and plate system is derived to be used in model based controllers. A method of using path projection on a cubic spline interpolated path to derive the reference states is explained. After that, three path following controllers are presented, a modified LQR, a Gain Scheduled LQR and a Gain Scheduled LQR with obstacle avoidance. The performances of these controllers are compared on an easy and a hard labyrinth level, both with respect to the ability of following the reference path and with respect to success rate of controlling the ball from start to finish without falling into any hole. All three controllers achieved a success rate over 90 % on the easy level. On the hard level the Gain Scheduled LQR achieved the highest success rate, 78.7 %, while the modified LQR achieved the lowest deviation from the reference path. The Gain Scheduled LQR with obstacle avoidance performed the worst in both regards. Overall, the results are promising and some insights gained when designing the controllers can possibly be useful for development of controllers in other applications as well.

This paper presents a comparison of controllers, specifically between conventional PID controllers with different structures and a Fuzzy Logic Controller. The performance has been evaluated by conducting experiments with the Ball and plate system, which is a system that is used to balance a ball on a plate. Furthermore, a large part of this work has been to assess how intuitive and straightforward the controllers are to design and implement. The results show that a PD controller with a proportional-on-error structure performs well for the Ball and plate system. Still, proportional-on-measurement is a viable alternative if a conservative controller is required. At the same time, the Fuzzy Logic Controller is a good alternative if you want more control over the system. Furthermore, the Fuzzy Logic Controller provides a design process that is easier to understand and closer to how we naturally think. However, it is more time-consuming than designing a conventional PID controller. Future work in the field should focus on optimizing this process to reduce the time required. / Denna studie består av en jämförelse mellan ett antal regulatorer. Dessa är olika strukturer av PID-regulatorer och en Suddig logik regulator. Prestandan har utvärderats genom att utföra experiment med Boll och platta systemet vilket är ett system som används för att balansera en boll på en platta. Vidare har en stor del av detta arbete handlat om hur intuitivt och enkelt det är att designa och implementera respektive regulator. Resultatet visar att en PD regulator med en proportionell-på-felet struktur presterar bra för Boll och platta systemet. Även proportionell-på-mätvärdet fungerar bra som ett mer konservativt alternativ. Dessutom är Suddig logik regulatorn ett bra alternativ om man vill ha mer kontroll över systemet. Designprocessen av denna är lättare att förstå och efterliknar hur man naturligt tänker i högre grad än de andra regulatorerna. Dock är denna mer tidskrävande att designa i jämförelse med de traditionella PID-regulatorerna. Framtida arbete bör fokusera på att optimera designprocessen så att den blir mindre tidskrävande.

This thesis deals with the identification and regulation of the "Ball & Plate" model. The thesis contains a description of the existing real model and the relevant mathematical and simulation model. The root hodograph method and the state space method are used to calculate the controller, especially the feedback controller with integrator. The final part of the work is devoted to the 3D model construction using Simulink and SimScape, which describes and visualizes the behavior of the real model and enables simulation experiments to be performed quickly and easily.