Simplified Control Structure of Fuzzy Logic and Kalman Filter for Induction Motor Drive

The paper deals with utilization of Kalman lter and fuzzy logic control in induction motor drive with direct torque control (DTC). In order to lower ripple of stator current vector in DTC drive, pulse width modulation technique with high switching frequency is applied. However, performance of the DTC also depends on the accuracy of both stator resistance and stator current vector. In the paper, the stator resistance and stator current components are assumed to be distorted by Gaussian noises. In order to reduce the e ect of noises especially at low speed and very low speed regions, a simple Kalman lter is applied for ltering current components, and fuzzy logic theory is used to increase exibility of proportionalintegral (PI) compensator in the speed controller of the drive structure. Simulations are implemented in conditions of high-level noises of stator current and stator resistance, and a wide range of load torque. An ITAE-based criterion is utilized to evaluate performance of drive structures. Results con rmed the expected dynamic properties of the proposed drive structure.

Abstract. The paper deals with utilization of Kalman lter and fuzzy logic control in induction motor drive with direct torque control (DTC). In order to lower ripple of stator current vector in DTC drive, pulse width modulation technique with high switching frequency is applied. However, performance of the DTC also depends on the accuracy of both stator resistance and stator current vector. In the paper, the stator resistance and stator current components are assumed to be distorted by Gaussian noises. In order to reduce the eect of noises especially at low speed and very low speed regions, a simple Kalman lter is applied for ltering current components, and fuzzy logic theory is used to increase exibility of proportionalintegral (PI) compensator in the speed controller of the drive structure. Simulations are implemented in conditions of high-level noises of stator current and stator resistance, and a wide range of load torque. An ITAE-based criterion is utilized to evaluate performance of drive struc-tures. Results conrmed the expected dynamic properties of the proposed drive structure.  [28]. The motor speed and ux are estimated by a multiple-model EKF with Markov chain [29]. Covariance matrices in EKF have been optimized by using a particle swarm optimization algorithm [30]. An adaptive algorithm is inserted to update system noise covariance matrix in EKF [31]. The system noise covariance matrix is tuned by genetic algorithm [32]. In the paper, improvement of KFs performance is not focused, instead a combination of Kalman ltering and fuzzy logic control is utilized.

Fuzzy logic control (FLC) is chosen because it
is able to incorporate experience, intuition and heuristics into the system instead of relying on system dynamics models [33], or simulate behavior of controller [34]. In order to reduce computation time, FLC employs reduced number of fuzzy inference rules in IM drive with DTC [35].
Dynamic FLC is combined with predictive DTC In order to reduce rigidity of conventional direct power control and lower power ripples in an active power lter, fuzzy logic-based controller is utilized to replace hysteresis controllers and switching table [39]. FLC is employed in a maximum power point tracking algorithm to get entire energy from PV modules for PMSM drive system [40]. FLC is incorporated into model predictive DTC to get optimal switching states 190 c 2021 Journal of Advanced Engineering and Computation (JAEC) VOLUME: 5 | ISSUE: 3 | 2021 | September that minimize electromagnetic torque and stator ux errors in PMSM drive [41]. In speed control of BLDC motor, a combination of deep learning and fuzzy logic tunes gain values of PID controller to obtain an eective speed regulator [42]. Estimated position and speed error are optimized with ANFIS and fuzzy-PID methods in sensorless speed control of switched reluctance motor [43]. In IM drive with VC, self-tuning technique is utilized to update the output scaling factor of the main FLC speed controller [44], and a hybrid fuzzy-fuzzy controller that consists of fuzzy slip frequency controller and fuzzy current amplitude controller is developed [45].
where inputs of Signal Calculation block: u sα, u sβ -stator voltage vector components; i sα ,î sβ -ltered components of stator current vector; R s -known value of stator resistance; outputs of the block: ψ s -magnitude of stator ux vector; γ -orienting angle; T e -electromagnetic motor torque. Kalman Filter block receives two signal inputs-i sα, i sβ from T3/2 block, and utilizes a compacted Kalman lter algorithm to obtain two signal outputs-î sα ,î sβ according to Eqs. (6)-(13): where limits H e and H ∆e are in the domain (0, 1]. Fuzzy rule base with 9 rules receives two inputs e ω , ∆e ω to obtain three linguistic values L, M, S which respectively denote for large, medium, small of controller parameters K P , 1/T I (see Tab. 1).
Tab. 1: Fuzzy rule base. method is selected to defuzzify.

Simulation results
In this section, simulations are implemented on        Settling times t ss1 , t ss2 are searched in durations 0.0s-0.5s, 0.5s-1.0s, and listed in Tabs. 5-6 respectively. Letter X in the tables describes the fact that t ss1 or t ss2 can not be found. In most cases, t ss1 and t ss2 are shortest for KF structure and PR structure respectively. For PR structrure, increment in dierence (M I − m I ) tends to reduce speed error [12] or ITAE, shorten settling times, make overshoots higher.
RITAEs at low speed and very low speed areas    Nm.
Tab. 6: Settling times at 6 rpm.   "This is an Open Access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium provided the original work is properly cited (CC BY 4.0)."