An effective algorithm to achieve accurate sinusoidal amplitude control with a low-resolution encoder

This paper presents a novel control methodology which uses an extremely low-resolution encoder to achieve a desired harmonic trajectory. The particular application of interest is a cellular microinjection technology called the Ros-Drill (Rotationally Oscillating Drill) for ICSI (Intra-Cytoplasmic Sperm Injection). It is an inexpensive set-up, which creates high-frequency (e.g. 500 Hz) and small-stroke (e.g. 0.2 degree) rotational oscillations at the tip of an injection pipette mimicking a harmonic motion profile. Such a motion control procedure presents no particular difficulty when it uses motion sensors with appropriate resolution. However, size, costs and accessibility of technology on hardware components for our charter severely constrain the sensory capabilities. The main objective is to achieve rotational amplitudes with peak-to-peak stroke of 0.4 degree and frequency of 500 Hz, using an encoder with resolution of 0.09 degree. This low-resolution encoder (which provides only 4 encoder steps for the entire stroke) presents two complications, a) large quantization errors at and between two successive measurements; b) stochasticity of actual amplitude for the desired discrete encoder readings. This paper proposes a method which enables accurate peak-to-peak stroke control using the same hardware, by essentially converting a stochastic stroke control problem into a deterministic dwell time balancing operation. The study describes a control strategy consisting of two-stage tuning: 1) coarse tuning which provides a 4-step desired encoder readings in peak-to-peak swings, 2) fine tuning which adapts the control gains to achieve the actual peak-to-peak stroke based on the deterministic relationships between the oscillation amplitudes and the encoder readings. Simulations and experiments are provided to validate the proposed method.