Ball on Plate Balancing System

Greg AndrewsChris ColasuonnoAaron Herrmann

Overview

Objective and MotivationSpecificationsModeling and Design

Inertia, Friction, GravityControlTouchscreen Subsystem

Results (including demo video)AssessmentConclusion

Objective and MotivationTo develop a ball-on-plate balancing system, capable of controlling the position of the ball on the plate for both static positions as well as along smooth paths.

In addition, especially for static positions, the system should be capable of rejecting disturbances to the ball.

Original idea from Labyrinth game

Specifications

System will use motors and optical encoders for control of tilt angle of both horizontal axes of the plateTouchscreen for ball position feedback1/16th inch rubber membrane will provide rolling friction

Specifications (cont.)

Plate Range of Motion 35 degrees about zeroLess than 2% error in ball positioningBall Weight: 130 gramsSystem Weight: 1.2 kg

Modeling: Inertia, Friction, Gravity

System must be linearized about an operating condition to design control systemOver what range is the linearization valid?State-space realization allows for easy control implementation for the MIMO system.

Modeling: Inertia

SolidWorks model createdUsed to aid in machining of necessary metal partsUsed to find mass and inertia tensor of system

Modeling: FrictionRecorded steady state velocity for 200 torque inputsAveraged last 4 of 10 seconds to get the velocity valueA 10 volt spike was used to break stictionLeast squares regression linePan Axis shown

Modeling: Gravity

Simple decoupled gravity model used at first, but this required an added gain to work perfectlyFully coupled gravity compensation is implemented in the actual system.

Plot shows constant applied torque to maintain gravity compensation

Validation and Friction/Gravity Experiment

Actual system response to force of gravity versus simulated response

Friction/Gravity Cancellation Demo

Control Design

Control design consists of two feedback loops:

Inner loop controls motor torque for desired plate angleOuter loop controls plate angle for desired ball positionBoth loops employ state-feedback control with observers

Control DesignLQR Control for optimal control based on our desired time-domain responseKalman Filter for optimal observer poles

Tuning in Experimentation and Simulation

Full Non-Linear Plate Dynamics, Linear Ball DynamicsTouchscreen sampling rate, and motor saturation consideredVR Simulation

Uncertainty and Tolerance Analysis

Axel straightnessBearing seatingTouchscreen AccuracyMotor NoiseErratic Encoder Behavior

Touchscreen

Dynapro 10.4” 95640 Touchscreen

Serial Interface between MATLAB/ xPC target and touch screen controller

80 positions/secActual data

samples run through lowpass filter for trajectory generation

ResultsSine wave tracking on “pan” axis: simulated, desired, actual

Results: Demo VideosDemo video: Ball Balancing with disturbance rejection and primitive path following

Assessment

Ball BalancingWorks well with minor steady state error

Disturbance RejectionFast response time

Path TrackingNeeds improvement

Overall success

Conclusion

Recommendations for improvementFriction Cancellation ImprovementsRevised touchpad interfaceBall Control ObserverNon-linear control