Pulse-modulated Control in the Presence of Non-linear Friction


The technology is advantageous in any application requiring precise controlled motion in the presence of significant mechanical friction.The joints of robot manipulators are commonly actuated by rotary electric motors combined with high-ratio gear trains (including harmonic drives). High-ratio gear trains improve the torque capacity of electric motors but introduce substantial friction that varies with position and load.The hydraulic valves used to control fluid power in high-force or large-scale pipeline applications. Precise flow control requires precise control of valve position but high pressures induce substantial friction that varies with pressure. Micro-electro-mechanical motion control systems commonly encounter substantial friction. Friction in this application is especially hard to model due to the difficulty of characterizing surface irregularities. In these applications, Pulse-Modulated control can be used to eliminate the effect of friction and thus create fine movement control. 

Problem Addressed

Friction, ubiquitous in mechanical systems, severely challenges conventional feedback control. First, it embodies a force-velocity relation that is discontinuous at rest (zero velocity). Conventional feedback control assumes (and usually requires) continuity. The colloquially termed ‘stiction’, static friction (zero velocity), is usually greater than sliding friction (non-zero velocity). With conventional control, stiction causes ‘lurching’ at the onset of motion.The parameters of mathematical models of friction usually depend strongly on position and loading. This dramatically increases the challenge of system identification and model-based control. This invention develops a simple feedback control strategy - Pulse-Modulated control- which effectively makes non-linearities "disappear" by guaranteeing that the error between the commanded and actual motion stays within a finite region - the result is a virtual disappearance of extreme discrepancies that could not be described by any simple analytical equation. 


The first key idea takes advantage of the extremely rapid sampling available with modern digital control (rates of 1 KHz to 10 KHz are now routine) to generate the discontinuous ‘impulse-like’ inputs required for fine motion control in the presence of friction. Rapidly switching from zero effort to maximum effort and back is like a ‘hammer-blow’ that overcomes static friction. Rapid return to zero effort (as needed) minimizes ‘lurching’ due to stiction. The second key idea is to take advantage of friction itself to dissipate and minimize unwanted oscillations due to control action. Lightly-damped resonance (common in mechanical systems) complicates continuous control because pushing in the direction to reduce error may actually increase error. However, significant friction can act to suppress resonant oscillations so that the simple strategy of pushing in the direction to reduce error is effective.


  • Can cope effectively with friction that depends on position, direction of motion and applied load
  • Versatile - it applies to any application where friction is prominent; essentially, almost any application where sliding between surfaces may occur
  • Easy to apply and requires minimal knowledge of plant behavior-specifically, only the maximum effort that will ensure no motion (usually zero) and the minimum actuator effort required to ensure motion (often maximum motor output)
  • Required controller software is minimal - it may be implemented with simple programmable logic controllers
  • Due to its simplicity, the controller incurs minimal cost