Journal of Mechanical Science and Technology 32 (2) (2018) 793~798 www.springerlink.com/content/1738&494x(Print)/1976&3824(Online) DOI 10.1007/s12206&018&0127&z Full&state&feedback, Fuzzy type I and Fuzzy type II control of MEMS accelerometer † Ahmadreza Najafi and Jafar Keighobadi *          (Manuscript Received March 29, 2017; Revised October 27, 2017; Accepted November 10, 2017) &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&  This paper presents classic and knowledge&based intelligent controllers for regulation of a vibratory MEMS accelerometer. The pro& posed methods comprise Fuzzy type I (FTI), Fuzzy type II (FTII) and Full&state&feedback (FSF) control systems. An ideal model of sen& sor under FSF controller is used to generate the required reference data to train if&then rule&base and Membership functions (MFs) of both fuzzy controllers. Through feeding the reference data as well as the FTI/FTII output into an Adaptive neural fuzzy inference system (ANFIS), the rules and MFs of the FTI/FTII system are updated. The control systems are realized by adding a Kalman filter (KF) loop to the force&balancing method for estimation of state variables and input acceleration. Stochastic noises are filtered out while keeping good tracking performance of MEMS accelerometer and reducing the displacement of the mass under the closed&loop ANFIS&KF structure. : MEMS accelerometer; Fuzzy type II; Full state feedback; ANFIS; Force&balancing; Extended Kalman filter    Owing to high performance, small size and greater func& tionality, MEMS accelerometers are used in industry [1]. The accelerometer consisting of a proof mass and an elastic beam is modeled as a mass&spring&damper system. By measuring the proof mass displacement relative to the sensor frame, an input acceleration is estimated by observing control forces. Energy dissipation by damping and measurement fluctuations guide to thermal&mechanical noises that decrease the sensitiv& ity [2, 3]. To increase robustness against noise and disturbance, two force&balance [2] and compensator in the loop [4] meth& ods are applied. A real&time force&balance method is applica& ble with analog output of sensor. However, controllers to& gether with analog&to&digital converters show better results due to the high robustness of digital signals to noise [5]. Be& yond robust methods as an alternative to sigma&delta approach [6, 7], Adaptive neural fuzzy inference system (ANFIS) is presented to improve the sensor performance by black box inferencing [8], while a Kalman filter (KF) is used to attenuate the noise of sensor and estimate the input values [9]. The pre& dictive force&balancing control of a MEMS gyroscope was investigated without discussion about fuzzy methods [3]. A Fuzzy type I (FTI) control of a mobile robot by expert knowl& edge was introduced [10]. Now, following modelling of the MEMS accelerometer, we propose the Full&state&feedback (FSF), and new FTI and Fuzzy type II (FTII) control methods. Using a KF, unavailable variables and parameters were esti& mated. Unlike to quasi&static function [3], we applied a com& plete dynamic of sensor in the framework of KF’s state and parameter estimation, which allows measuring time&varying input acceleration rather than step inputs. Based on controllers of the sensor, the tracking and estimation performance against the measurement noises and structural uncertainty were as& sessed by simulations. Using the ANFIS, the MFs and rules of both the FTII and FTI systems are constructed with respect to estimated dis& placement and velocity of the mass. Therefore, instead of try& and&error tuning of preceding fuzzy system as expert knowl& edge, the online ANFIS leads to accurate adaptive fuzzy con& trols. Unlike Refs. [11, 12], we designed the ANFIS with de& sired minimal parameters of MFs, while the rules number was independent of the input and output MFs. Therefore, the over& all number of MFs and therein parameters to be updated in ANFIS are significantly decreased as well as the convergence rate of estimation is increased. Consequently, time&varying input accelerations can be estimated online by the proposed control system. Unlike the open loop reference model of sen& sor [10], we used an FSF control reference model to make the learning of ANFIS straightforward.      The configuration of the MEMS accelerometer includes a proof mass suspended by spring suspension and fixed elec& trodes in Fig. 1. The dissipation of mechanical energy caused * Corresponding author. Tel.: +98 4133354153, Fax.: +98 4133393045 E&mail address: keighobadi@tabrizu.ac.ir † Recommended by Associate Editor Dong&Weon Lee © KSME & Springer 2018