An effective strategy of real-time vision-based control for a Stewart platform

© 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes,creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other worksA Stewart platform is a kind of parallel robot which can be used for a wide variety of technological and industrial applications. In this paper, a Stewart platform designed and assembled at the Universitat Polit`ecnica de Catalunya (UPC) by our research group is presented. The main objective is to overcome the enormous difficulties that arise when a real-time vision-based control of a fast moving object placed on these mechanisms is required. In addition, a description of its geometric characteristics, the calibration process, together with an illustrative experiment to demonstrate the good behavior of the platform is given.Postprint (author's final draft

Trajectory-Tracking Control of the Ball-And-Plate System

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

Graphical User Interface (GUI) for Position and Trajectory Tracking Control of the Ball and Plate System Using H-Infinity Controller

In this paper, a graphical user interface (GUI) for position and trajectory tracking of the ball and plate system (BPS) control scheme using the double feedback loop structure i.e. a loop within a loop is proposed. The inner and the outer loop was designed using linear algebraic method by solving a set of Diophantine equations and  sensitivity function. The results were simulated in MATLAB 2018a, and the trajectory tracking was displayed on a GUI, which showed that the plate was able to be stabilized at a time of 0.3546 seconds, and also the ball settled at 1.7087 seconds, when a sinusoidal circular reference trajectory of radius 0.4m with an angular frequency of 1.57rad/sec was applied to the BPS, the trajectory tracking error was 0.0095m.  This shows that the controllers possess the following properties for the BPS, which are; good adaptability, strong robustness and a high control performance.   

Synthesis of Hybrid Fuzzy Logic Law for Stable Control of Magnetic Levitation System

In this paper, we present a method to design a hybrid fuzzy logic controller (FLC) for a magnetic levitation system (MLS) based on the linear feedforward control method combined with FLC. MLS has many applications in industry, transportation, but the system is strongly nonlinear and unstable at equilibrium. The fast response linear control law ensures that the ball is kept at the desired point, but does not remain stable at that point in the presence of noise or deviation from the desired position. The controller that combines linear feedforward control and FLC is designed to ensure ball stability and increase the system's fast-response when deviating from equilibrium and improve control quality. Simulation results in the presence of noise show that the proposed control law has a fast and stable effect on external noise. The advantages of the proposed controller are shown through the comparison results with conventional PID and FLC control laws

Observation and control of a ball on a tilting

The ball and plate system is a nonlinear MIMO system that has interesting characteristics which are also present in aerospace and industrial systems, such as: instability, subactuation, nonlinearities such as friction, backlash, and delays in the measurements. In this work, the modeling of the system is based on the Lagrange approach. Then it is represented in the state-space form with plate accelerations as inputs to the system. These have a similar effect as applying torques. In addition, the use of an internal loop of the servo system is considered. From the obtained model, we proceed to carry out the analysis of controllability and observability resulting in that the system is globally weak observable and locally controllable in the operating range. Then, the Jacobi linearization is performed to use the linearized model in the design of linear controllers for stabilization. On the other hand, analyzing the internal dynamics of the ball and plate system turns out to be a non-minimum phase system, which makes it difficult to design the tracking control using the exact model. This is the reason why we proceed to make approximations. Using the approximate model, nonlinear controllers are designed for tracking using different approaches as: feedback linearization for tracking with and without integral action, backstepping and sliding mode. In addition, linear and nonlinear observers are designed to provide full state information to the controller. Simulation tests are performed comparing the different control and observation approaches. Moreover, the effect of the delay in the measurement is analyzed, where it is seen that the greater the frequency of the reference signal the more the error is increased. Then, adding the Smith predictor compensates the delay and reduces the tracking error. Finally, tests performed with the real system. The system was successfully controlled for stabilization and tracking using the designed controllers. However, it is noticed that the effect of the friction, the spring oscillation and other non-modeled characteristics significantly affect the performance of the control.Tesi

Position and Trajectory Tracking Control for the Ball and Plate System using Mixed Sensitivity Problem

This paper presents the position and trajectory tracking control scheme for the ball and plate system (BPS) using the double feedback loop structure (a loop within a loop) for effective control of the system. The inner loop was designed using linear algebraic method by solving a set of Diophantine equations. The outer inner loop was designed using   sensitivity approach. Simulation results showed that the plate was stabilized at 0.3546 seconds, and the ball was able to settle at 1.7087 seconds, when given a circular trajectory of radius 0.4 m with an angular frequency of 1.57 rad/sec, with a trajectory tracking error of 0.0095 m, which shows that the controllers have adaptability, strong robustness and control performance for the ball and plate system.           

Two-Dimensional Positioning with Machine Learning in Virtual and Real Environments

In this paper, a ball-on-plate control system driven only by a neural network agent is presented. Apart from reinforcement learning, no other control solution or support was applied. The implemented device, driven by two servo motors, learned by itself through thousands of iterations how to keep the ball in the center of the resistive sensor. We compared the real-world performance of agents trained in both a real-world and in a virtual environment. We also examined the efficacy of a virtually pre-trained agent fine-tuned in the real environment. The obtained results were evaluated and compared to see which approach makes a good basis for the implementation of a control task implemented purely with a neural network