Ball & Plate.

Unlike a ball-and-beam system, this platform must control motion along both X and Y. A change in plate angle accelerates the ball, so reaching a target requires managing its motion as well as its position.

Our team designed and built the mechanism, integrated a resistive touchscreen and actuators, and developed a feedback controller. Two knobs set the target coordinates; the system then measures the ball’s position and continually corrects the plate tilt.

The performance objectives

• Position the ball at multiple assigned coordinates.
• Reach the target and recover from a disturbance within 20 seconds.
• Maintain the stabilized position for at least 15 seconds.
• Integrate the mechanism, sensor, electronics, and controller into one working prototype.

The abstract and final results use a ±0.5-inch positioning tolerance. A separate experimental-description paragraph specifies ±0.25 inches; that inconsistency is retained in the source report and discussed alongside the results below.

The team considered two- and three-servo layouts and finalized a two-servo mechanism in SolidWorks. A central universal joint supports the plate, while links from the two servos produce tilt along its axes.

Printed parts and articulated connections

PLA parts formed the system base, servo arms, and touchscreen enclosure. The base provided mounting space for the motors, Arduino Uno, breadboard, and battery pack. Ball-joint rod ends connected the servo linkages to the plate, accommodating motion as the plate changed orientation.

The touchscreen base and top frame held the sensing surface in place. The geometry needed to maintain a usable ball surface while allowing controlled tilt and keeping the wiring accessible.

The Arduino Uno connected the resistive touchscreen, two B10K potentiometers, and two high-torque servo motors. The touchscreen supplied real-time position feedback; the potentiometers provided separate X and Y target inputs.

The report documents four AA batteries as the power source and a shared ground between components. The schematic records the original wiring arrangement.

The model treats the steel ball as a uniform solid sphere rolling without slip. It neglects air resistance and uses small-angle approximations for plate tilt. These assumptions reduce the X and Y motion to matching simplified equations.

The factor 5/7 accounts for the sphere’s rotational inertia as it rolls. In Simulink, the resulting acceleration is integrated to velocity and then to position. Initial conditions represent where the ball begins.

This model provides a useful control-design starting point. Linkage tolerances, sensor behavior, and effects outside the simplified assumptions still have to be addressed on the physical system.

The controller compares the target position with the measured position, then adjusts the servo commands to reduce that error. Separate X and Y branches use the same PID gains as a deliberate tuning simplification.

What the PID terms contribute

• Proportional: respond to the current position error.
• Integral: accumulate error to address persistent offset.
• Derivative: respond to changes in error and add damping.

The team tuned proportional responsiveness first, then integral correction and derivative damping. The report gives the final gains as Kp = 2.5, Ki = 0.5, and Kd = 3.0, with derivative filter coefficient N = 100. These values describe this prototype and its implementation, rather than universal gains for any ball-and-plate mechanism.

Keeping commands within the mechanism’s limits

The simulation included saturation at ±0.1745 radians, approximately ±10 degrees. Limiting the tilt command represented the mechanism’s allowed motion and kept the model from demanding unrealistic actuator travel.

Two views of the simulated response

Time-history plots show the response of each axis, while the XY trajectory gives a top-down view of the modeled path. The model used the prototype’s reported gains to support comparison with the physical tuning.

The team evaluated three target positions, timing stabilization with a stopwatch and observing recovery after manually moving the ball. The report documents 2–4-inch disturbances and 15-second steady-state holds.

Accuracy and the limits of the record

The largest listed steady-state error component is 0.39 inches. The report concludes that the system met a ±0.5-inch tolerance, while another paragraph names a stricter ±0.25-inch requirement. Some position entries in the results table also do not match their target/error columns. The original table is shown above so those discrepancies remain visible; they have not been silently rewritten.

The reported timing results support a working stabilization and disturbance-recovery demonstration. Resolving the conflicting tolerance and coordinate entries would require the original trial records or a repeat test.

What the prototype illustrates

• Model and hardware have to meet: a useful dynamics model still needs a sensor, mechanism, and actuator that work together.
• Tuning is a tradeoff: responsiveness, overshoot, persistent error, and sensor noise affect the same loop.
• Physical details matter: the report identifies linkage tolerances and sensor nonlinearities as sources of residual error.
• Keep measurements traceable: consistent target coordinates, error definitions, and test criteria make the results easier to assess.

The complete 18-page team report contains the architecture, components, dynamics derivation, Simulink model, controller tuning, and experimental results.

All 11 embedded figures are included below. Select an image to open it at full size, or follow its page link to see the original context.