Control of a ball-and-plate system using a State-feedback controller

Abstract

A ball-and-plate platform is a common example of the dynamical system used to apply modeling and control concepts studied in some engineering courses. In this kind of systems, a spherical body is positioned on a mobile plate with two degrees of freedom. The system is operated by two servo motors that cause displacement of the sphere in the x and y axis in the plane of the platform. It is known that such a system is highly unstable and non-linear. Initially, from a phenomenological analysis we obtained a state-space representation of the system. Then, a state feedback controller using the pole assignment method was designed to maintain a desired position of the sphere over the plane. A computer vision technique allowed us measuring the two-dimensional position of the sphere over the plane in real time. Model of the plant under study and controller design for sphere positioning were experimentally validated considering different set-points. Obtained results let us know that our plant-controller is stable and responds satisfactorily to position disturbances around a reference point.

Real‐time control design and implementation of ball balancer system based on machine learning and machine vision

“…Since the resulting inclination is a function of all actuator angles, the outputs are coupled, and this can be seen in the system's governing equations. In 2 DOF (degree of freedom) ball‐plate, each actuator is responsible for one degree of freedom since the ball motion in the X and Y directions are decoupled 7,8 . Therefore, decentralized control can be used by treating this MIMO system as two separated SISO systems where each direction is actuated, measured, and controlled separately.…”

“…Servos have almost a flat relationship between torque and speed. Servos only consume current when needed which enables them to run much cooler 7,8 …”

“…Servos only consume current when needed which enables them to run much cooler. 7,8 To summarize, high-speed, high-torque applications with dynamic load variations are best suited for servo control systems. Stepper control systems are less expensive and ideal for applications requiring low-to-medium acceleration, high holding torque, and open or closed loop operation flexibility.…”

“…13 The point stability and trajectory tracking concerns are graphically demonstrated in the ball on plate systems. Several studies [6][7][8][9] examine these issues using modeling methods that ignore the system's nonlinear behavior, particularly the relationships between motor and plate angles. The settling time and overshoot of the ball on the plate system (BOPS) are increased when the nonlinear part of the relationship between the ball's angle and the plate's angle is ignored.…”