Iterative Learning Control of an Electrostatic Microbridge Actuator With Polytopic Uncertainty Models

• Published in: IEEE transactions on control systems technology 2015-09, Vol.23 (5), p.2035-2043
• Main Authors: Cichy, Blazej, Hladowski, Lukasz, Galkowski, Krzysztof, Rauh, Andreas, Aschemann, Harald
• Format: Article
• Language: English
• Subjects: Actuators; Crank > Nicolson discretization method of partial differential equations (PDEs); distributed parameter systems (DPSs); Electrostatics; Force; iterative learning control (ILC); Linear matrix inequalities; linear matrix inequalities (LMIs); Mathematical model; Parameter optimization; robust control; Robustness; Uncertainty
• ISSN: 1063-6536; 1558-0865
• DOI: 10.1109/TCST.2015.2394236

In this brief, a robust control design is presented for an electrostatic microbridge actuator. For this system, a spatially distributed electrostatic force serves as control input. Moreover, a spatially distributed measurement of the bridge displacement is assumed to be available. For an accurate tracking of a reference trajectory-repeated periodically during the operation of the microbridge-an iterative learning control (ILC) approach is proposed based on so-called wave repetitive processes. The design procedure represents an efficient combination of linear matrix inequalities and an appropriate parameter optimization. By explicitly considering polytopic parameter uncertainty, the ILC becomes robust against uncertain parameters such as the squeeze film damping coefficient, the mass density, and the time constant of the electrostatic actuator. Convincing simulation results provide a numerical validation of the proposed ILC scheme as a prestage for a future experimental implementation.