Chattering reduction effect on power efficiency of IFOC based induction motor

The vector control strategies have developed rapidly and significantly to control Induction Motor (IM) compared to scalar control strategies. It causes better performance in managing IM. Indirect Field Oriented Control (IFOC) is one of the vector control strategies which more realistic to apply in the industrial world. However, IFOC requires Sliding Mode Control (SMC) with the Lyapunov function to ensure robustness and stability. Unfortunately, the first-order SMC or ordinary SMC has disadvantages in the chattering phenomenon. It uses boundary layer. layer techniques to overcome the chattering phenomenon. This paper shows the analyzed boundary layer performance on rotor speed response, stator current response in the dq0 frame, and power performance. The SMC with and without boundary layer has an error steady-state less than 2% in rotor speed response. In stator current response with dq0 frame, the boundary layer with hyperbolic tangent function has the best performance. The power analysis shows that the boundary layer with saturation function has an active power loss of 39.16%, reactive power loss of 23.37%, and apparent power loss of 30.30%. The boundary layer with hyperbolic tangent functions has the best performance in reducing power consumption with an active power loss of 41.24%, reactive power loss of 24.78%, and apparent power loss of 31.96%.


INTRODUCTION
The use of IM today has covered various aspects. In transportation, Tesla Model S and other electric vehicles use IM for the main engine [1], [2]. In industrial automation, traction machines and photovoltaic pumps utilize the IM [3], [4]. Furthermore, the IM is used as a propulsion engine for military purposes [5]. IM has many advantages, especially in durability, low cost, ease of maintenance, and a highly efficient electric motor. However, IM is is hard to control. The standard standard control techniques of IM are scalar control and vector control. The scalar control principal principle of IM is based on the variating frequency and absolute values of voltages, currents, and interlinkages of windings [6], [7]. The scalar control is easy to use and implement implement. However, it However, it has low-performance a low-performance [8], [9]. Vector control principle represents the complicated IM model similarly DC motor. The vector control provides high efficiency in a wide speed range, decoupled control of torque and flux, four-quadrant operation, and better dynamic behavior than scalar control [10], [11].
Field Oriented Control (FOC) techniques are the vector control method that decouples electromagnetic torque and flux of an IM similar to the DC motor to obtain a good performance. IFOC is a FOC technique that can be more implemented and accepted by the industry than Direct FOC (DFOC) because the DFOC needs a flux sensor mounted in the air gap of IM [12]. In IFOC, the rotor flux is estimated using the fieldoriented control equations.
IFOC requires controllers to guarantee robustness and stability against disturbances [13], [14], [15] controller method can be classified into a model-free and a model-based controller. A model-free controller doesn't need a dynamic model in generated control signal [16], [17], [18]. A Model-based controller such as SMC is designed based on IFOC mathematical model for IM. SMC guarantees robustness and stability using the Lyapunov function. However, ordinary SMC has disadvantages in the chattering phenomenon that it consumes more energy and harms the hardware. The boundary layer limits chattering on SMC due to the discontinuous control input.
In this paper, IFOC-based IM is designed with SMC using sign function in flux controller, current regulator, and speed controller. The speed controller is designed with the boundary layer using saturation and hyperbolic tangent functions to overcome the chattering phenomenon. Analysis of power consumption and dynamic response is used to determine the performance of the sign function, saturation function, and hyperbolic tangent function.

A. IFOC Based IM
IM mathematical models consist of electrical and mechanical models electrical and mechanical models. The rotor speed and rotor flux equation are mechanical models, while the current regulator is an electrical model. The state-space representation of IM models in the the direct-quadrature-zero rotating frame (dq0 frame) shows in (1) [11]. The IM models in the dq0 frame are derived from the IM equation in the ABC frame with Clarke and park transform.
Where : The mechanical model of the IM is expressed in (2).
While ω is rotor speed, is inertia and is torque load.
The IFOC diagram based on three-phase IM shows in Fig. 1. The IFOC equations consist of rotor flux controller, current regulator (stator current controller in dq0 frame), and speed controller. The IFOC system has flux and electromagnetic torque commands. The torque command comes from the speed to torque equation shown in (4) with the speed command. The output of the IFOC system is a switching signal for the inverter while it requires feedback on the current and the rotor speed response of the three-phase induction motor. The IFOC equations are designed from the IM mathematical model. IFOC makes IM look like a DC motor due to the electromagnetic torque, and the rotor flux can be controlled separately.
The correlation of the rotor speed and the electromagnetic torque is shown in (5). SMC is a model-based controller in which the control signal is designed from mathematical models of the systems. The SMC design consists of two subparts, i.e., the stable surface and the control law, to force the system states onto the chosen surface in a finite time shown in Fig. 3. The stable surface is designed in firstorder using sliding surface (6) and the Lyapunov function (7) to guarantee the robustness and stability of the IFOC technique. The control law is designed using the sign function [8].
where: The IFOC based IM controller in rotor speed using first-order SMC equation is determined in (8) [14]. where:

C. Boundary-Layer Boundary-Layer
The sign function in first-order SMC causes a chattering phenomenon that harms the hardware and consumes more power to maintain the robustness [19], [20], [21], [22], [23]. This chattering phenomenon is due to the discontinuous control input shown in Fig. 3. (a). One of the most common methods of reducing the chattering phenomenon is the boundary layer approach. The boundary layer uses a continuous control input rather than discontinuous control input, namely a saturation function shown in Fig. 3. (b) and a hyperbolic tangent function shown in Fig. 3. (c) [24], [25], [26], [27]. The sign function in cap U sub n is replaced with saturation or hyperbolic tangent functions in the boundary layer approach. The sign function in is replaced with saturation or hyperbolic tangent functions in the boundary layer approach. The saturation function designed to control the rotor speed is given in (9).
with is a a positive constant of the the boundary layer ( ) using saturation function. The hyperbolic tangent function used in this paper is expressed in (10). The boundary layer approximation performance is measured using the saturation and hyperbolic tangent function and hyperbolic tangent functions designed for rotor speed control (11).
with is a a positive constant of the the hyperbolic tangent function, which controls the shape of the function.

III. RESULT
The IFOC-based IFOC-based IM is tested with a computer test using MATLAB/Simulink. The IFOC is implemented in a squirrel cage IM with parameters parameters shown in Table 1. The computer test uses uses 6.10 -5 seconds of sample time. The results consist of the performance of first-order SMC with sign function, saturation function, and hyperbolic tangent function designed in the speed controller.

A. Dynamic Response
The dynamics analysis of IFOC-based IFOC-based IM using SMC is presented for rotor speed response and stator current response in the dq0 frame. The rotor speed performance analysis in the transient and steadystate conditions is shown in Fig. 4. The step function, which is assumed to be a static disturbance, is given when the time is 2 seconds with a torque load of 2 Nm. The stator current response shown in Fig. 5 is depicted in the dq0 frame with various torque loads given at the start of the computer test. command. The speed command is designed for a highspeed response, making it easy to analyze controller performance. The active power of IFOC for IM calculates using (12) while the reactive power [19]   This section presents a test performed on on firstorder SMC using sign function, saturation function, and hyperbolic tangent function. The performance of the boundary layer (saturation function and hyperbolic tangent function) was evaluated in rotor speed response. The boundary layer is placed in the rotor speed controller while the other uses first-order SMC. The positive constant of the controller ( , , , and ) is tuned intuitively. The computer testing for IFOC-based IFOC-based IM is done in two steps. The first step uses constant speed command at 1.400 rotations per minute with various torque loads at 2 seconds. The second step uses constant speed command at 1.400 rotations per minute with various torque loads given from the start of the test. The torque load is designed in 0,5 Nm, 1,0 Nm, 1,5 Nm, and 2,0 Nm.
The rotor speed response of IFOC-based IFOCbased IM using first-order SMC with sign function, saturation function, and hyperbolic tangent function in steady-state response and no-load condition has error steady-state less than 2% as shown in , as shown in the figure Fig. 3a. In overcoming the chattering phenomenon, the boundary layer performs better in the no-load condition than the without boundary layer. In overcoming the chattering phenomenon, the boundary layer performs better in the no-load condition than the without boundary layer. Fig 3b shows the sign function, saturation function, and hyperbolic tangent function to compensate under 2 Nm of disturbances. This response indicates indicates that the hyperbolic tangent function has the best performance. This chattering phenomenon makes a significant impact on power consumption and hardware lifespan. Fig. 4a and Fig. 4b show the reduction in direct and quadrature current consumption during the computer test. The saturation functions decrease 10.86% on direct current consumption while 8.28% on quadrature current consumption in no-load conditions. The hyperbolic tangent function has better performance in direct current with 11.43% of decreased current consumption. Besides, the hyperbolic tangent function's quadrature current consumption is just 7.69%. The saturation function's average decrease in immediate current consumption is 8.42% in varying load conditions, with a quadrature current consumption of 6.57%. Besides, the hyperbolic tangent function's quadrature current consumption is just 7.69%. The saturation function's average decrease in immediate current consumption is 8.42% in varying load conditions, with a quadrature current consumption of 6.57%. In hyperbolic tangent function, the direct current has 8.65%, with a quadrature current of 6.94%. The boundary layer performance in reducing the chattering phenomenon shows in table 2 and table 3. Table 2 shows the performance of the the saturation function in reducing power and stator current with various torque loads. The active, reactive, and apparent power decreased decreased significantly. The hyperbolic tangent functions in reducing active, reactive, and apparent power are better than saturation functions, as shown in table 3. At no-load conditions, the hyperbolic tangent function increases the reduction in active power by 2.12%, reactive power by 1.81%, and apparent power by 1.97% compared to the saturation function. Under varying torque loads conditions (0.5 Nm, 1 Nm, 1.5 Nm, and 2 Nm), the hyperbolic tangent function still reduces the average active power consumption by 2.07%, and and reactive power consumption by by 1.30%, and apparent power consumption by 1.58%. In stator current response, the hyperbolic tangent function is slightly different from the saturation functions.

V. CONCLUSION CONCLUSION
This paper discusses the power efficiency of IFOCbased IFOC-based IM using first-order SMC with a boundary layer approach. The first-order SMC is designed in the the rotor speed controller, current regulator, and flux controller, while the rotor speed controller creates the boundary layer rotor speed controller creates the boundary layer. The boundary layer approach uses the saturation function and hyperbolic tangent function. The system test used a computer test that focussed on the chattering reduction in rotor speed response, stator current response in dq0 frame, and power analysis. The results show that that the hyperbolic tangent function has better power efficiency than the the saturation function at active, reactive, and apparent power.