Adaptive cascade control design for uncertain electrostatic micro-actuator system

Abstract This paper proposes an adaptive cascade control architecture for nonlinear electrostatic micro-electromechanical system (MEMS) subject to unknown parametric variations and matched external disturbances. A fundamental challenge for indirect adaptive setpoint regulation is the inherent loss of the Persistent Excitation (PE) condition, which causes standard adaptive laws to suffer from critical parameter drift and instability when subjected to intermittent disturbances. To overcome this, we develop a robust Dynamic Regressor Extension and Mixing (DREM) estimator. The proposed approach rank-expands the regression model to algebraically decouple the disturbance from the unknown parameter. Furthermore, a dynamic, time-varying scaling factor is introduced to actively monitor disturbance magnitudes and selectively freeze parameter adaptation when excitation diminishes, substantially mitigating drift without requiring the restrictive PE condition. Rigorous Lyapunov-based analysis proves that the proposed closed-loop framework guarantees boundedness of all system signals. Numerical simulations validate the theoretical findings, demonstrating that the robust DREM cascade controller drastically reduces parameter drift under intermittent disturbances compared to standard approaches, while simultaneously improving tracking accuracy. Ultimately, the proposed methodology provides a low complexity robust stabilization solution for uncertain micro-actuator system.