DEVELOPMENT OF A POSITION AND TRAJECTORY TRACKING CONTROL OF BALL AND PLATE SYSTEM
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DEVELOPMENT OF A POSITION AND TRAJECTORY TRACKING CONTROL OF BALL AND PLATE SYSTEM
Chapter One: Introduction 1.1 Background Balancing systems are among the most common and complex test platforms for control engineers. These systems include the traditional cart-pole system (inverted pendulum), the ball and beam system, and double and multiple inverted pendulums (Mohajerin et al., 2010).
The ball and plate system is a generalisation of the well-known ball and beam benchmarking system. The latter is a two-degree-of-freedom (DOF) system with a ball that can roll on a rigid beam, whereas the former has four DOFs and a ball that can freely roll on a rigid plate (Moarref et al., 2008).
However, it is more sophisticated than the ball and beam system due to the interaction of several factors. This system is underactuated, with only two actuators and two control inputs (Ghiasi & Jafari, 2012).
Because the movement of the ball over the plate can reach high speeds, designing an appropriate controller for this system is a significant task; thus, these systems are rarely employed in laboratories (Galvan-Colmenares et al., 2014).
The system is made out of a plate that is hinged in the centre, allowing the slope to be changed in two perpendicular directions. A servo system comprises of a motor controller card and two servo motors for tilting the plate.
The ball position is measured using an intelligent vision system and a CCD camera. The challenge with this system’s motion control is controlling the position of a ball on a plate for both static and intended trajectories.
The slope of the plate may be changed in two perpendicular directions, so that tilting the plate causes the ball to move (Dong et al., 2011).
The ball and plate system is used in various industries, including humanoid robots, satellite control, rocket systems, and unmanned aerial vehicles (UAVs), for path planning, trajectory tracking, and friction compensation (Mukherjee et al., 2002; Oriolo & Vendittelli, 2005).
In recent years, many ball and plate management methods have been introduced. Knuplež et al. (2003) developed a controller design for a two-dimensional electro-mechanical ball and plate system using both classical and modern control theory.
A supervisory fuzzy controller for researching system motion control contained the set-point problem and the tracking problem along the desired trajectory, which were composed of two layers, as described by (Bai et al., 2006). Wang et al. (2008) suggested a nonlinear velocity observer for output regulation of the ball and plate system, with ball velocities measured by the state observer.
Hongrui et al. (2008) used a double feedback loop system to control the ball’s location, with a recursive back-stepping design for the external loop and a switching control strategy for the inner feedback loop.
In addition, (Dong et al., 2009) developed a proportional-integral-differential neural network controller based on a genetic algorithm for the ball and plate system.
Previous study, however, assumed that the ball and plate formed a single loop structure. A double feedback loop topology, or a loop within a loop, is being studied for effective ball and plate system control (Liu & Liang, 2010).
1.2 The Significance of Research
The ball and plate system is one of the most popular and important models in control education, used in undergraduate and postgraduate studies to teach and test control algorithms. It also serves as a benchmark nonlinear plant because it is more complex than the traditional ball and beam system due to variable coupling.
The ball may move freely and has no ability to understand its surroundings; as a result, it cannot control its own behaviour. The system’s three control challenges include ball position control, trajectory tracking, and obstacle avoidance.
The ball has three control problems: position control, trajectory tracking, and obstacle avoidance. The position control problem requires the ball to arrive at a specific point quickly and accurately, while the trajectory tracking problem requires it to follow a defined path at high speed.
The obstacle avoidance control problem involves finding the best path for the ball in a complex environment based on specific criteria. All of these difficulties serve as useful benchmarks for proving the competence of various control strategies.
As a result, developing a proper controller to address these issues is a significant challenge. The first two problems, namely position and trajectory tracking, were investigated in this work, with the system being modelled as a double loop.
1.3 Statement Of The Problem
The ball and plate system apparatus is a two-dimensional electromechanical device that can be classified as a nonlinear, multivariable (two inputs and two outputs), and unstable system.
The system is underactuated because it has more degrees of freedom than accessible actuators. For successful control of the ball and plate system, a double feedback loop structure, or a loop within a loop, is used.
However, because of uncertainties caused by friction, parameter errors, and measurement time delays, real implementations necessitate nonlinear control methods, which will be used in the design of the inner and outer loops.
To meet these needs, the inner loop is built as an actuator (angular) position controller for plate tilt, while the outer loop controls the ball’s (linear) location on the plate.
The goal of this study is to build the inner loop of the ball and plate system using a linear algebraic method. The overall transfer function is chosen that minimises the integral of time multiplied by absolute error (ITAE), and a two parameter setup.
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