Office of Technology Transfer – University of Michigan

Use of Filtered Basis Functions to Compensate Servo-induced Motion Errors

Technology #6747

Precision motion control is increasingly important as the demand for tight tolerance parts continues to grow under the demands of high performance, miniaturization, and efficiency. However, precision servo control can be difficult as commercial servo motion systems may have bandwidth limitations and limited controller adjustment options. Pre-compensation of the desired input signal to adapt to system dynamics can improve accuracy but current feed forward methods are either very basic or difficult to implement, especially in flexible systems and high sampling rate systems. Now, a new method using filtered basis functions (FBF) promises simple implementation with up to 99.99% reduction in positioning error.

NURBS basis functions produce accurate machine trajectories

The FBF method uses a library of industry-standard NURBS (non-uniform rational basis spline) functions with known machine outputs to compile a best fit of the desired working trajectory through linear combination. This will then determine the necessary machine inputs to produce the NURBS-composite trajectory accurately and quickly. Modeling experiments have demonstrated a root mean square error reduction of up to 10^-5 using a 100-parameter basis. This method is also capable of working with non-minimum phase (NMP) systems, which are traditionally difficult to compensate for.


  • Improved machine automation controllers
  • Compensating design software


  • Extremely simple to implement
  • Uses NURBS, an industry standard for motion commands
  • Works with non-minimum phase systems featuring flexible components or high sampling rates