Control of the Probe-Sample Interaction Force at the Piconewton Scale by a Magnetic Microprobe in Aqueous Solutions

This article describes the design and implementation of a control system that controls the probe-sample interaction force at the piconewton scale by manipulating a magnetic microprobe in aqueous solutions under a microscope. The control system has two functions, namely accurate force generation by magnetic flux control and precise control of the probe-sample interaction force. Magnetic flux control uses an improved six-input-six-output digital control law along with a disturbance estimator to achieve two control objectives. First, the magnetic flux at each pole tip of a previously developed hexapole electromagnetic actuator can be individually and precisely controlled at frequencies over 4 kHz, and the experimental results precisely followed the theoretical predictions based on the design. Second, together with the optimized flux allocation, the flux control system generates precise magnetic forces, making the six-input hexapole actuator behave like a decoupled three-axis force generator with a bandwidth of more than 4 kHz. Interaction force control compares the measured deformation of the sample with the expected deformation, updated in real time by a deformation predictor, to generate the magnetic force to control the interaction between the probe and the sample. Digital control laws, the estimator, and the predictor are all implemented using a high-speed Field Programmable Gate Array (FPGA) system. Experiments confirm that through mathematical modeling, digital control technology, high-speed electronics, and real-time computation, accurate three-dimensional force generation at the piconewton scale with high bandwidth and precise interaction force control with zero-mean random error, attributed to random thermal force and measurement noise, are achieved.