Ball and Beam Balance Using PID Control
Tom Trapp and Wil Selby
Department of Mechanical Engineering
Massachusetts Institute of Technology
2.151 Advanced System Dynamics & Control
Fall 2009
Abstract
The primary objective of this project was to create a control system that could effectively balance a ball on a metal beam using a motor input to control the angle of the beam. This project covered the full scope of design including creating a valid model of the system, identifying numerical values for the model parameters, designing an effective control system, assembling the system hardware, and implementing the control system using a microcontroller to interface with the motor. The ball and beam balance problem is a classic open loop unstable system. For a constant input there is a non-constant output. In this system, a constant beam angle causes the ball to accelerate due to the force of gravity and the ball’s position increases non-linearly. Investigating this system resulted in numerous insights of control design that can be applied to multiple applications. Utilizing full state feedback, the controller was able to repeatedly and effectively balance the ball at the given desired reference point with reasonable transient performance. In the future, the addition of a Kalman filter for state estimation and a LQR based controller could make the system even more effective.
Aerial Vehicle Trajectory Tracking Using Sliding Mode Control
Wil Selby
Department of Mechanical Engineering
Massachusetts Institute of Technology
2.152 Nonlinear Dynamics and Control
Fall 2011
The quadrotor vehicle is an extremely versatile platform that utilizes the force differences in each of its four motors for rotational and translational positioning. This research focuses on the translational control of an Ascending Technologies Hummingbird quadrotor. In order to control the highly nonlinear dynamics of the quadrotor, a sliding mode controller is developed. This method of control is known to be robust to modeling errors. Utilizing this controller, simulation results are presented as well as experimental results which demonstrate the performance capabilities of this controller. The MATLAB code can be found here.
_______________________________________________________________
Trajectory Optimization for Perching Quadrotor Vehicles
Wil Selby and Madalyn Berns
Department of Mechanical Engineering
Massachusetts Institute of Technology
6.832 Underactuated Robotics
Spring 2011
Unmanned aerial vehicles (UAVs) have been carefully optimized for forward flight regimes over the past fifty years. While engineers learned to construct highly maneuverable craft to be flown by human operators, autonomous control of such highly underactuated systems has continued to be a difficult issue. New flight capabilities for aircraft have been enabled through recent advances in materials, actuators, and control architectures. Vertical perching, or the act of landing a craft on a wall or other vertical surface, is one of these newly enabled capabilities. Vertical perching would drastically increase the usable landing space of a craft, allowing it to conserve energy, collect sensor data, and potentially recharge even when there exists no suitable horizontal landing environment. For this study, we chose to use a quadrotor platform. Quadrotors are ideal for applications in which stability, maneuverability, and payload capacity are at a premium. We compare in simulation two trajectory optimization algorithms — Back-Propagation Through Time (BPTT) and Direct Transcription (DT) — to design a quadrotor control policy for vertical perching. To stabilize the system in real-time, we implement a LQR based trajectory stabilization policy to reject environmental disturbances. Our methods are successful in simulation and provide a foundation for future hardware implementation.
_______________________________________________________________
Cooperative Control Using an Information Metric
Wil Selby
Department of Mechanical Engineering
Massachusetts Institute of Technology
16.498 Cooperative Control of Unmanned Systems
Fall 2011
This research focuses on evaluating a cooperative control algorithm for multiple unmanned aerial vehicles (UAVs) This algorithm optimizes the amount of information acquired by a group of UAVs surveying several dispersed ground targets. The algorithm assumes the aerial vehicles are equipped with Ground Moving Target Indicators which estimate the target’s bearing, range, and radial velocities. Simulated results of the algorithm are shown under different scenarios with varying initial conditions.
[simple-social-share]