Reliability Enhancement of MEMS Lateral Comb Resonators Under Fault Conditions

Abstract

The delicate structure of microelectromechanical systems (MEMS) limits their reliability in cases of fault occurrence. Control systems can enhance their reliability of operation by providing fault robust systems. This paper illustrates a method for the safe operation of lateral comb resonators (LCR) under faulty conditions. Different types of fault are fabricated at chip level and experimentally tested in order to demonstrate the effectiveness of the reliability enhancement of operation in LCRs. Mass change and folded spring structural defects influence the device's behavior and reduce its reliability of operation. Here, model reference adaptive controllers (MRACs) are effectively used to enhance the reliability of faulty devices. Reliable operation of a +5% additional mass considering environmental conditions and asymmetries on the device, demand almost 80% higher control effort whereas +20% in case of broken trusses or +46% in case of adhesion point fault on a beam of folded springs. The simulation and experiment results demonstrate successful application of MRAC for reliable operation of LCRs by providing a fault-robust system.

Fault Diagnosis of MEMS Lateral Comb Resonators Using Multiple-Model Adaptive Estimators

“…The fact is that the desired system should operate similar to (2) whereas the manufactured device which behaves differently and is represented by (3). More details on model parameter uncertainties, control application and displacement monitoring technique, which is also used in this brief, can be found in [5]- [21]. The state space governing equation of a MEMS LCR considering uncertain values can be represented as (4)…”

“…2. The collected optical data is then transferred to the data recovery algorithm that determines the instantaneous displacement of the shuttle [5], [6]. The research on the integration of an in-situ structure of the laser beam emitter and collector is in progress [29].…”

“…Consider the steady-state Kalman filter model of an LCR associated with different types of fault conditions denoted by subscript as (5) where is the Kalman filter model's state-space variables (displacement and speed of the shuttle), is the system matrix, is the input matrix, is the input vector, is the Kalman filter model's input noise matrix, is the input noise with zero mean and variance of (6) is the measurement vector (displacement and speed of the shuttle), is the output matrix, is the output measurement noise, independent from , with zero mean value as (7) Kalman filter model representation of a system is (8) where is the estimation of state space variable, is the actual output expected from the model, and is the Kalman filter gain recursively obtained through the following procedure: for (9) where is the covariance matrix updated by (10) The covariance matrix updates the Kalman gains recursively. The residual signal is defined as the difference between the output of the Kalman filter model and that of the actual operating system.…”

Model predictive control of MEMS LCR

“…SYSTEM MODELING The MEMS LCR system as shown in Figure 1 is modeled as a second order mass spring damper (MSD) system [9][10][11][12]. The governing equation of such a system is given by…”

“…Recursive least square with dynamic data weighting is used to identify the parameters of MEMS. This technique is given as [13] ߠሺ݇ሻ ൌ ߠሺ݇ െ 1ሻ ඥܽሺ݇ሻܲሺ݇ሻ߶ሺ݇ሻߝሺ݇ሻ ߠሺ0ሻ ൌ ߠ , (12) where ߠ are the initial best-guess values of the parameters, ܽ is the non-negative static weighting factor, ܲ is the covariance matrix, ߝ is the normalized estimation error, and ߶ is based on the previous inputs and outputs as shown in (10). The normalized estimation error ߝ is given as:…”