A Novel Application of Minimax LQG Control Technique for High‐speed Spiral Imaging

• Published in: Asian journal of control 2018-07, Vol.20 (4), p.1400-1412
• Main Authors: Habibullah, H., Pota, H. R., Petersen, I. R.
• Format: Article
• Language: English
• Subjects: Atomic force microscopy; Control systems design; Error analysis; Linear quadratic Gaussian control; Minimax LQG control; Minimax technique; nanotechnology; Prototyping; Raster scanning; Robust control; Transfer functions
• ISSN: 1561-8625; 1934-6093
• DOI: 10.1002/asjc.1691

Over the last two decades, increasing the scanning speed of an atomic force microscopy (AFM) has been attempted either by applying novel controllers, using alternative scanning methods, or by modifying the hardware setup. This paper demonstrates, the first two approaches to achieve high‐speed AFM image scanning. A robust minimax linear quadratic Gaussian (LQG) controller is designed and spiral scanning is considered as an alternative scanning method rather than conventional raster scanning. The minimax LQG controller is designed based on an uncertain system model which is constructed by measuring the plant variations due to variations in sample mass and also modeling error between the measured and model frequency responses. This controller is also robust against uncertainties introduced as a result of variations of sample mass, spillover dynamics of the scanner at frequencies higher than the first resonance frequency of the scanner, and variation in plant transfer functions due to temperature and humidity. The designed controller is experimentally implemented on an AFM using a dSPACE ds‐1103 real‐time prototyping system and open‐loop and closed‐loop spiral imaging performances are evaluated. The proposed controller provides sufficient damping at the resonant modes to accurately track the sinusoidal reference signal and generate vibration free images. Also, creep, hysteresis, and cross‐coupling effects are significantly reduced. The experimental results show that the proposed scheme outperforms the open‐loop case and some other existing approaches.