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Improving control quality of PMSM drive systems based on adaptive fuzzy sliding control method

Tran Duc Chuyen, Roan Van Hoa, Hoang Dinh Co, Tran Thi Huong, Pham Thi Thu Ha, Bui Thi Hai Linh, Tung Lam Nguyen Faculty of Electrical, University of Economics and Technology for Industries, Ha Noi, Viet Nam Faculty of Electrical, Thai Nguyen University of Technology, Thai Nguyen, Viet Nam Department of Industrial Automation, School of Electrical and Electronic Engineering, Hanoi University of Science and Technology, Ha Noi, Viet Nam


INTRODUCTION
For decades, permanent magnet synchronous motors (PMSM) are widely used in industrial applications. The drive provide high-quality speed adjustment applications such as electric vehicles, precise position control such as industrial robots, industrial machining machines, traction drive systems, military radar system, and rocket control systems. In addition, PMSM can be found in medication manufacturing, such as pill-packing machine in the pharmaceutical industry, equipment and machinery for supporting surgical operations in the field of medicine, due to its outstanding characteristics (wide and regularly stable working speed range: from very low speed to high speed, with a large moment/current ratio, less interference, stability with load, high performance, very high precision in position control). These PMSM motors are intended to replace the previous drive control systems (which have been using DC motors, causing errors at all times during speed control and position control), [1], [2]. In order to apply these given issues, an intelligent controllerfuzzy adaptive sliding mode controller (FASMC); is an efficient control method that has been widely applied to control for both linear and nonlinear systems [2]- [7].
In applications to precise control systems with various operating speed ranges such as traction systems in pharmaceutical industry (pill-packing machine); and strict requirement in metalworking industry, and in traction systems of military weapons, [5], [6], [8]- [10]. However, there exist some problems need to be solved to improve the quality of control. In [4], [6] and [11]- [13], the authors have only recommended fuzzy control methods for PMSM without considering system uncertainties and external disturbances. In [14]- [17] the authors have used adaptive sliding controller and adaptive backstepping controller, with evaluation of the nonlinear component base on the estimators with light power motors hence limiting its practical implementation with high power requirements. This paper have proposed the FASMC to handle mismatched uncertainties and disturbances and alleviate chattering to gain good performances in the close-loop system [18]- [23].
The appropriate structure is designed in the paper to ensure quality in the controlled system. The control is constructed for achieving tracking response of drive systems. In electrical drives, it is necessary to provide quality criteria such as: fast-acting in the control process, ensuring optimization of control law, nonsensitivity to uncertainties in the control process, [1], [15]. This is a multi-objective optimization control problem with various solutions [1], [5], [9], [13], [21]. This paper presents a technique to improve the control quality PMSM in industrial applications; taking into account the nonlinear uncertainty, the dynamics of the actuator and the converters based on the adaptive fuzzy sliding control method, and experimenting with the dSPACE 1104 card to demonstrate the results, [3], [5], [8], [15], [24].

MATHEMATICAL MODEL OF PERMANENT MAGNET SYNCHRONOUS MOTORS
The mathematical model of the three-phase PMSM is described as in [4]. By considering the rotor coordinates of PMSM as the reference coordinates, the systems dynamic is represented by (1) [4], [8], [10]: where ML is the load torque, ω is the rotor angular speed, iq and id are linearized d-axis and q-axis stator currents, Vq is q-axis voltage, Rs is stator resistance, Vd is d-axis voltage, and ki, i = 1….6 are obtained as (2)-(6): where Me is electromagnetic moment, p is number of pole pairs, Rs is stator resistance, Ld is the d-axis stator inductance and Lq is the q-axis stator inductance, Ls is stator inductance, J is rotor moment of inertia, B is viscous friction coefficient, is λm linkage magnetic flux and  = ; Hence, a nonlinear control loop of linearization methodology is used to estimate the  , the rotor speed  which are the unmeasured components of the motor. Furthermore, the presentation of the d-q reference axis coordinate system of the motor can be obtained as (7) and (8) [4]. then the slip speed is represented as (10).
The electromagnetic torque is obtained as in (11): in which: the mathematical equation describing the equations of motion of the motor is written as (13): where Jr is rotor moment of inertia, B is viscous friction coefficient, ML is load moment, by replacing (11) and (12) into (13), derivative of rotor speed  () r t is given as (14): in which, = − / < 0; = / > 0; = −1/ < 0. In order to obtain a mathematical model that is suitable for control design, the nominal value of the motor parameters must is considered when ignoring influencing factors of nonlinear components and unaffected by any disturbances [13], [14], [17], [19]. Therefore, the kinematic model of the PMSM that given by (14) becomes (15): where, ̄=̄/̄ and ̄= −̄/ are the nominal values of Ap and Bp, respectively. Therefore, the computations of unmodeled system in the (14) can be rewritten as: where, ( ) = ( ) + *e + + . In (16), the unknown parameters are represented by ΔA and ΔB; characteristics for the system containing the uncertainty components including the variable parameter and the nonlinear estimation error which are unmeasurable components. In addition, these parameters are the unchangeable depend on the dynamics of the system, so in order to simplify the analysis, calculation and estimation of parameters in the paper, the above parameters are assumed to be constant and is denoted as  .
In the above question, L(t) is the unknown components satisfying | ( )| < , where m is a positive constant.

FUZZY ADAPTIVE SLIDING MODE CONTROLLER DESIGN 3.1. Conventional sliding mode controller
Sliding mode control offers many advantages in the synthesis of nonlinear control system [5], [8], [12], due to invariance to disturbances on the system and unknown components; the order of the system is decreased when the the system in on the sliding surface. We consider the change of speed adjustment error, ( ) = ( ) − * ( ), thus, in the sliding mode with the space state, S(t) can be obtained as: in which, C and h are positive constants, substituting (16) into (17), with the first derivative of S(t) taking the following form: in which, ( ) =̇( ). Setting, ( ) = 0 and ̇( ) = 0, then according to the system dynamics, the equivalent control is defined as, [1,4,5,9,20].
Then the reaching law () r ut is designed as: in which, ( ) > 0 and the "sign" function are defined as follows: The controller is achieved when considering the unmodeled actuator dynamics, which can be defined as following: in which,  is the integral positive constant. According to the designed control, a control Lyapunov function (CLF) candidate is chosen in (24): the stability condition showing the stability can be obtained from the stability theorem of the Lyapunov function of [1], [5], [8].
Where  is a positive constant. From (18), (19) and (22), (25), it can be rewritten as: compare (25) and (26) then consider |̇( )| < , the stability of the system is guaranteed if the following equation is fullfiled: In practical applications, we may experience undesirable phenomenon of oscillations especially when  is large recpectly. The chattering phenomenon can be reduced by replacing the discontinuous function with a continuous function of approx /(| | + ), in which,  is a positive constant. Thus, when → 0 the approximate controller characteristic which is approached to the original controller as well [5], [14]. A nonlinear state observer to accurately estimate the position and speed of the motor with the influence of unmeasured component parameters in both low and high speed regions control is used in the paper. The design procedure of the nonlinear state observer has been carefully presented in [21]. This nonlinear state observer is used to estimate the rotor position (θ), rotor speed (ω), load torque component (ML) and unmeasured component of the system (d1, d2), [25], [26].

Fuzzy adaptive sliding mode controller
In this paper, we investigated the fuzzy adaptive sliding mode controller for the disturbance observer control tracking approach of the PMSM driven system. In field-oriented control (FOC), stator field is continuously updated based on the position of the rotor field, since position and speed of the motor are estimated based on current and voltage information. thus, a nonlinear state estimator which is estimated accurately of the rotor is implemented as well. The block diagram of the FASMC system is shown in the Figure 1, which in speed loop control, the stator current * represents its output. The independent control of Ids and Iqs consistst of two PI regulators. In the present implementation, the rotor position measurement is  (20) is replaced by the saturation action which is represented as: in which,  is the thickness of layer of the sliding surface. Thus, the discontinuous component control is given by (20) becomes (29).
to deals with the unknown of the motor mechanical load, fuzzy control strategy is an effective tool to deal with the unknown process. The control variable of FASMC algorithm is proposed as (30).

= ( ( ), ( ))
Subsequently the reaching law and control law are defined as (31) and (32).  Because the plant is lack of an integral action, a PI type fuzzy controller is formulated. Additionally, refer to [8], [14], we can build the structure of the FASMC which is shown in the Figure 1. The fuzzy controller consists of: two input linguistic variables which are error S(t), and the error derivative ∆S(t); one output linguistic variable UTMTN. The FASMC structure is depicted in Figure 2 and the fuzzy rule is presented as in Table 1. Inputs and output relationship of the fuzzy controller is as shown in Figures 3-5 and Figure 6 the relationship of the fuzzy controller. Tt is pivotal to minimize L(t) which is given in (26). In order to estimate k(t) given in (30) we using the corresponding adaptation law presented in (33) [8].
In which, k  is a positive constant. In fact, k(t) is as an adaptive filter to minimize control errors. Compare (25) and (36), we get (37).   Therefore, the component k can be selected such that −̂+ ℎ + is negative. It is straight forward to have −̂≥ + ℎ + . In this paper, by applying the proposed adaptive fuzzy sliding controller along with the designed fuzzy rules and the mentioned conditions, the system stability condition in (25) is satisfied. In practical, the factors of frictional moment, elasticity, and clearance. always exist in the electromechanical drive system including motor and working structure. By using the proposed FASMC, the effects of the nonlinear factors on the quality of the drive system have been resolved [14]- [16]. Parameters Vp, VI are chosen based on Zeigler -Nichols experimental method. After choosing parameters Vp, VI, we can calculate parameters Vp and d. However, due to experimental method, in order to improve control quality: short transient time and small overshoot since two parameters Vp and d need to be adjusted furtherly. Parameters is set: VP=0.01; d=0.99 (with T=0.002). The quality of the PI controller after calculating the selection, we obtain: KP=0.3; KI=0.0001. The PID-controller design process is considered in [1], [14], [17], [18], [19].  The simulation results of some cases shows that the FASMC is proposed with the sustainability, stability of the control law against the effects of unknown parameters which will change the transition time, increase the fast response of the system. Moreover, in the transient mode, the application of proposed controller given a good performance response as well.
The experimental structure diagram as shown in Figure 17(a) and the experimental system in real time is depicted in Figure 17(b) with its designed, built and simulated on MATLAB Simulink's 2021 and connected to the control board dSPACE 1104 with a combination of graphical control desk software in controlling; observe system characteristics in real time. Combined with power electronics, and current measurement sensors connected to the dSPACE panel. The PMSM motor parameters used in the experiment are the same as those used in simulations, encoder AM 2048 S/R, DC motor used to generate loads, symbol DOLIN -SH.198V with voltage U=190 V, I=13.5A, n=175 rpm.
Studying the process of changing low speed from 50 rad/s (478 rpm) to -50 rad/s (-478 rpm, timing the conversion is 2.5s in the total response time of 5s, Figure 18. The results show that the FASMC controller response is working well, the output is close to the input in the balance process, the current response value Id and Iq in Figure 19 shows the correct working process of the system.

CONCLUSION
The traction drive system in industry applications needs very high reliability and accuracy. The paper presented a new approach, researched and built an adaptive FASMC for industrial traction drive systems. The main effectiveness of this method is that the robustness of the system is introduced. The second advantage of the proposed FASMC is that the chattering phenomenon is significally reduced. Theoretical research and simulation results show that the proposed FASMC algorithm for PMSM which achieves good quality and more stable operation. The results of simulation and experimental studies with the dSPACE 1104 card show that the above control algorithm exhibits good dynamical responses when compared to other works. This study has proven the correctness of the FASMC algorithm which has ability to apply in practice to the traction electric drive systems.