Robust finite-duration transient response of micro-electromechanical system

A time-domain robust control design approach for minimizing error in transient responses of parametric uncertain systems is considered, as motivated by design and control of micro-electromechanical actuators. A quadratic cost function is formulated as the sum of error components over a finite time span, with the optimization problem of minimizing the least upper bound of the quadratic function represented in terms of the eigenvalue of a certain matrix. This further allows for a linear fractional transformation form by which the nominal and uncertain parameters are separated into P and Δ matrices, analagous to standard LFT representations for robust controller design. The structured singular value, μ_Δ, is replaced with the spectral radius of the LFT-expressed matrix in the P-Δ configuration. A bulk piezoelectrical actuator-driven micro-robotic flexure joint is considered as a test case, where the stacking process of placing a PZT ceramic actuator on top of a micro-machined silicon flexure is subject to substantial processing error.