Artificial Neural Network-Based Experimental Investigations for Sliding Mode Control of an Induction Motor in Power Steering Applications

Sliding mode control (SMC) of induction motor is a new concept in the current scenario, as it seeks to improve torque control accuracy and power steering efciency through the use of pulse width modulation schemes. Furthermore, artifcial neural network-based sliding mode control is applied to a squirrel cage induction motor, which is used in the steering control of automobiles. Te artifcial neural network (ANN)-based SMC is more popular due to its robustness and good stability in external parameter variation. Additionally, an SMC and an ANN-based SMC are employed to compute the torque and fux, improving performance for power steering applications. Te performance of the designed model is validated through MATLAB/Simulink and experimental models with diferent controllers under various operating conditions. Te controller has been embedded into a TMS320F28335 controller, and performances have been evaluated. Te performance analyses of induction motor using diferent controllers are performed. Te transient performances of induction motor such as delay time, rise time, settling time, and steady-state error are investigated. Te proposed work is analysed by using a mathematical model and implemented in a test-bench model for validation.


Introduction
Induction motors (IMs) are widely used in various industrial and consumer applications due to their simple structure, robustness, and low cost.One of the signifcant applications of induction motors is power steering in automobiles, where they are used to provide the necessary torque to turn the wheels.Te power steering system in modern cars is typically an electro-hydraulic system, where an electric motor drives a hydraulic pump to assist the driver in turning the wheels.In this application, the IM needs to be controlled precisely to ensure efcient and reliable operation.Sliding mode control (SMC) is a popular technique for controlling induction motors in various applications, including power steering.Te idea behind sliding mode control is to design a controller that forces the system to slide along a specifc surface, called the sliding surface, towards a desired state.
Once the system reaches the sliding surface, it remains on it and moves towards the desired state in a robust manner, regardless of disturbances or uncertainties.
High-order sliding modes (HOSM) are a class of control systems that are designed to provide robustness against uncertainties and disturbances in the system.Tis technique can be used to control a wide range of nonlinear systems, including mechanical systems, electrical systems, and chemical processes.HOSM controllers use a higher-order sliding surface compared to traditional sliding mode controllers, which can improve the performance and robustness of the system.In HOSM, the sliding surface is designed such that it passes through higher-order derivatives of the system state.Tere are two types of HOSM controllers: fnite time and infnite time.Finite-time HOSM controllers aim to reach the sliding surface in a fnite amount of time, while infnite-time HOSM controllers aim to stay on the sliding surface indefnitely.Te high-order sliding mode manifold is well-defned as a solution to a high-order polynomial equation that depends on the system's state and its derivatives.Te high-order sliding mode control technique can be used to control a wide range of nonlinear systems, including mechanical systems, electrical systems, and chemical processes.Tey are also able to achieve fast convergence to the sliding surface, leading to improved control performance.However, HOSM controllers can have some drawbacks [1,2].Tey require more complex control laws than traditional sliding mode controllers, which can make them more difcult to implement.Additionally, HOSM controllers can sufer from chattering, which is a high-frequency oscillation that can occur when the system approaches the sliding surface.Tis can be mitigated through the use of smoothing techniques, but this can add additional complexity to the controller design [3,4].
Due to its simplicity, obvious performance, and performance, the proportional-integral (PI) regulator constitutes one of the most commonly employed methods of regulation in electrical machines [5].An efcient nonlinear control may nevertheless enhance activity in an environment of issues and ambiguity since the IM operates within a nonlinear system [6,7].Several researchers have used a variety of cutting-edge control strategies to manage the power electronics and drive sector in this respect [8].In particular, the sliding mode control [9][10][11], the predictive control approach [12][13][14], the adaptive control technique [15], and the backstepping algorithm [16][17][18] are involved in advanced electrical machine applications.With its unique dynamic characteristics for IM, such as robust reliability, rapid response, and straightforward software and hardware deployment, the SMC methodology has emerged as an intriguing nonlinear control method [19][20][21].
Te sliding mode observer-based fnite time control scheme is a method for controlling the frequency regulation and economic dispatch in power grids.It uses a sliding mode observer to estimate the states of the system, such as the generator speeds and power outputs, and then applies a fnite time control scheme to adjust the control signals in order to regulate the frequency and optimize the economic dispatch [22,23].Tis method is efective in handling uncertainties and disturbances in the power grid, as the sliding mode observer is able to adapt to changing conditions and provide accurate state estimates.Te fnite time control scheme ensures that the system converges to the desired state in a fnite time, which improves the stability and performance of the power grid [24,25].
Discrete-time SMC is a popular control technique that is widely used in various applications due to its robustness and ability to handle system uncertainties and disturbances.One variant of SMC is the use of a desired switching variable (DSV) generator, which can improve the control performance by generating a smoother and more suitable reference signal for the sliding surface.Te main objective of using a DSV generator in SMC is to achieve better tracking performance and reduce chattering, which is a common issue in traditional SMC.Te DSV generator uses a dynamic model of the system and generates a continuous reference signal that is then discretized and used as the input to the SMC controller.Tis reference signal is then used to construct the sliding surface, which determines the control action based on the system state.Te DSV generator can generate a reference signal that is more suitable for the system and can handle changes in the system dynamics more efectively.Additionally, it can reduce the chattering that is often observed in traditional SMC, which can improve the stability of the system.However, there are also some drawbacks in using a DSV generator in SMC [26,27].One of the main issues is the complexity of designing the DSV generator, which requires a good understanding of the system dynamics and control theory.Additionally, the DSV generator may introduce additional computational overhead and delay, which can afect the real-time performance of the system [27,28].
Te signifcant noise that some sliding mode controllers identify has long been a source of dissatisfaction and, in some cases, outright rejection among control designers, as sliding mode concepts recommended.Chattering is the term most commonly used to describe the occurrence.Highfrequency fuctuations, referred to as chattering, emerge around the equilibrium point due to the inconsistent regulatory actions in response to the changing environment.As a consequence, many real-life applications are unable to efectively utilize the designed regulatory mechanisms to control behavior.Tis type of behavior gives rise to problems such as the deterioration of mechanical motion components, machine movements, futtering use of shafts in aerospace applications, and impact during operation [27,29,30].Numerous chattering preventive measures have been proposed [31][32][33] as a means of chattering repression.As an example, a number of researchers have been developing IM regulators based on the integration of SMC theory with other cutting-edge control techniques such as the backstepping algorithm, adaptive method, and fuzzy technique [34][35][36].Subsequently, it should be noticed that using SMC in conjunction with other types of nonlinear control techniques increases controller complexities and mathematical eforts, which is not compatible with SMC's simplicity [37].
Te majority of induction motor recognition algorithms depend on inaccurate induction motor appropriate variables and shortened mathematical representations [38][39][40].Due to their superior learning capabilities, artifcial neural 2 International Journal of Intelligent Systems networks (ANN) are capable of overcoming this drawback.By being used to identify and manage various nonlinear and complex systems, ANN has solidifed its position as a methodology.Numerous research fndings, in particular, show that feed-forward ANN is successful in identifying the induction motor.It is well known that the main disadvantages of feed-forward ANNs are their lack of memory and high sensitivity to the training data because their input and outputs are solely based on the inputs and the weights used at the time [41][42][43].As the architecture of the dynamic neural network (DNN) encompasses feedback from the output and has excellent interaction illustration capabilities, it can get around this drawback [44].However, conventional static sliding mode control methods can only be applied to systems with a relative degree of one or two [45,46].In order to apply static sliding mode control to systems with arbitrary relative degree, an artifcial delay can be introduced into the control input.Tis approach has been shown to be efective in controlling a variety of nonlinear systems with arbitrary relative degrees, including robotic manipulators and mechanical systems [47][48][49].Tis study investigates the link of IM control employing SM with power steering applications.Te sliding mode control mechanism and the operation of the power steering have been replicated in the simulation using virtual modules with various controllers in the interest of preserving the state's speed and torque.To further elucidate the cohabitation of these control mechanisms and the driver implementations, other simulations are also being provided.Additionally, hardware implementations are used to verify the results of simulations.Te major objectives of the proposed technique are listed as follows: (i) To develop a mathematical model for the induction motor in power steering applications, including the efects of the load and the control system (ii) To design and train an artifcial neural network for sliding mode control of the induction motor, considering the nonlinear and time-varying nature of the system (iii) To compare the performance of the sliding mode control strategy with other control strategies, such as proportional-integral (PI) control, fuzzy logic control, and ANN control (iv) To investigate the efect of various parameters, such as the sliding surface and the neural network architecture, on the performance of the sliding mode control strategy (v) To evaluate the robustness of the sliding mode control strategy against disturbances, such as sudden changes in the load with the parameters of delay time, rise time, settling time, and steadystate error (vi) To analyze the stability of the sliding mode control strategy and ensure that the closed-loop system is stable under all operating conditions (vii) To validate the simulation results with experimental data obtained from a physical prototype of the induction motor and the power steering system (viii) To investigate the efect of varying operating conditions, such as diferent steering angles and speeds, on the performance of the sliding mode control strategy (ix) To provide insights into the practical implementation of the sliding mode control strategy, including the hardware and software requirements, and any limitations or challenges that need to be addressed (x) To demonstrate the feasibility and efectiveness of the sliding mode control strategy for induction motors in power steering applications and to identify potential areas for future research and development

Indirect Vector Control of Induction Motor
Indirect vector control (IVC) is a type of control strategy which is used to control the speed regulation of induction motor (IM).By adjusting the stator current and voltage, IVC manages the motor's speed and torque.Figure 1 shows the indirect feld-oriented IM schematic diagram.Te threephase currents are converted into the binary synchronous reference frame system and the synchronous frame using the Clarke and Park transforms.Te feedback for the inner loops is provided by the resulting d-q axis currents.Te amplitudes of the comparison dc voltages for the PWM unit with the reverse park and Clarke transform are formed by the reference amplitudes derived from the present controllers.Te impulses from the PWM entity that is obtained create the trigger signals for the inverter's IGBT switching devices.In this case, the IM is fed by a PWM inverter with a hysteresis current controller.Te iqs * is obtained from the speed error with the help of the PI controller, FLC, SMC, and ANN-based SMC.Te ids * is obtained using essential rotating fux  Ψ r as computed in the following equation [5]: Te ω * sl that is created using the current i * qs is expressed as follows [5]: Te ω * sl is summed with ω r to ω e .Te θ e is determined in the following equation [5]: Te vector rotator converts the i * qs and i * ds to i * a , i * b , i * c .Te measured currents are compared with the set values of the current of IM.In order to obtain the desired machine performance, the current error signal is fed to the hysteresis band.Te rotational equation of a system will be transformed as follows [5]: where K t is the torque constant, and it is written as follows: From equations ( 4) and ( 5), the mechanical equation of IM is where Te system model uncertainties, which encompass parameter variations and external load changes, are managed by means of the induction motor (IM).Hence, a variable SMC structure is designed to enhance the performance of the IM in industries.
Rewriting equation ( 1) and representing the IM system without external load disturbance [12], By choosing the constraint changes and load torque variation, equation ( 9) can be rewritten as follows [12]: Here, ∆A and ∆B are the uncertainties owing to model the machine variable J and B where U(t) is the set speed, ω r is measured speed of IM, and L(t) is the lumped indecision as expressed in the following equation [12]:   International Journal of Intelligent Systems regulation.Te methodology and the indirect method are the two fundamental types of feld-oriented control.Te primary diference between the two is how actuation is accomplished: the direct method uses electromagnetic or electrical feedback from the motor, whereas the implicit method uses velocity feedback from the motor and a feedforward slip authority.Both strategies generally make use of stator existing regulations in a certain capacity.Te instantaneous actuation is provided by the implicit feldoriented method using a feed-forward slip command and motor acceleration responses.Since the velocity output typically produces relatively clean input signals than the voltage from a power converter, the indirect method's control is inherently more reliable.Tis method difers signifcantly from everyone else because its outputs and evolved motor model are predicated on the motor's basic system parameters instead of a number of associated indicators.Te circuit diagram of the SMC is depicted in Figure 2, where a modifed vector IM is applied to signify the plant (controllable).Te primary parameters of the controller have to be developed with an appropriate control law in order that the ω r can be able to optimize ω r * .In sliding mode control (SMC), the model is adjusted based on the error value (E) and the changing error (CE) variations, which are regulated using a sliding or switching surface.

Designing of Sliding Mode Controller with Induction Motor
Choose the sliding surface in terms of the state space equation of the model, and it is expressed in the following equation [12]: Ten, the sliding surface variables are From equation ( 13), the sliding surface becomes Using the above equation, the control efort is derived as S(t) � 0 and (L(t) � 0) is to attain the supposed characteristics of the model, and its equivalent control law is expressed in the following equation [12]: Te vector control, however, responds to variables very quickly.Te complex dynamics, unmodeled behaviour patterns, and impulsive variable modifcation adversely affect the IM's ability to control.As a result, the controller cannot guarantee any improvement in control characteristics.Tus, the support control could be developed to eradicate the unappreciable modifcations.Te support control efort is expressed as follows: where g h is gain, and SMC control law is written as follows: Te fundamental concept next to SMC is to create a controller that moves the system's states towards a sliding manifold, where the complexities are more straightforward and manageable.ANNs have proven to be efective in controlling nonlinear systems, including induction motors.ANNs can approximate any nonlinear function to a desired level of accuracy, making them well-suited for control applications.
Te steps to design an ANN controller for SMC of an induction motor are as follows: Step 1: Determine the system model: Te frst step is to determine the mathematical model of the induction motor.Tis will help in understanding the dynamics of the system and developing the SMC algorithm.
Step 2: Design the sliding mode controller: Te next step is to design the SMC algorithm.Tis involves selecting the sliding surface and designing the control law that will drive the system states towards the sliding surface.
Step 3: Train the ANN: Once the SMC algorithm is designed, an ANN can be trained to approximate the control law.Te ANN should be trained using a dataset that contains the input-output pairs for the control law.
Step 4: Implement the ANN controller: Te ANN can be used as an induction motor controller once it has been trained.Te ANN receives the system's controller parameters as inputs and outputs the command signal that directs the system in the direction of the sliding manifold.

International Journal of Intelligent Systems
Step 5: Test and tune the ANN controller: Finally, the ANN controller should be tested and tuned to ensure that it is performing as expected.Te controller's performance can be evaluated by measuring the speed of the motor and comparing it with the desired speed.
For the hidden layer, a bipolar SF is employed, and a LAF is used for the output layer.Te trials are distributed to fnd the lowest number of neurons required to achieve the best accuracy for each layer.Te created neural network has three neurons in the hidden layer and one neuron in each of the input and output layers.Tree neurons are chosen from the hidden layer to train the ANN, greatly reducing the number of epochs.In this instance, the hidden layer's simulated training data and 569 epochs of the tan sig function are shown in Figures 3 and 4.

Simulation Results and Discussion
Te fndings of designed controllers for vector-controlled IM under various operating conditions are addressed in this section.Te appropriate control is designed using nonlinear mathematical analysis of an IM and the MATLAB/Simulink platform, and it implements sliding mode control for a resilient design which is resistant to variable fuctuation.When the insolation varies, the load also varies immediately.Te simulated IM parameters are listed in Table 1.
In the transient region, where the output voltage is changing rapidly, a well-designed proportional-integral (PI) controller can help maintain stability and ensure that the output voltage remains within acceptable limits.Figure 5 illustrates the designed system with PI controller in transient region inverter output voltage 460 V peak value.Te rotor speed is seamlessly changed, the stator current has a frequency response form, and the amplitude of the stator fux linkage is continuous from the dynamic response procedure of the speed regression.It demonstrates that the suggested method exhibits an acceptable dynamic characteristic.Figure 6 illustrates the PI controller in a transient region speed of 118 (rad/sec) with a settling time of 6 sec.Te torque needed to initiate a motor's rotation is known as the electromagnetic torque, and it is typically equal to the load torque.For a system with a PI controller in the transient region, such as a speed control system, the controller's   6 International Journal of Intelligent Systems output is determined by the error between the desired speed and the actual speed of the system.Te proportional term of the controller responds to the current error, while the integral term responds to the historical error.In order to design a PI controller for a speed control system in the transient region, the frst step is to determine the transfer function of the system.Tis can be performed by analysing the dynamics of the system and deriving an equation that relates the output of the system (the speed) to the input (the control signal).In a load variation from electromagnetic torque of 10 N-m to 5 N-m, Figure 7 shows the simulated results of a designed system with a PI controller.After 20 seconds of operation, the torque is settled according to the observation.
Figure 8 shows the results of a designed system with a PI controller in terms of load variation speed (rad/sec).Te range of the load torque has to be located from 5 to 10 N-m.Te load's oscillations have already subsided, and the load torque disturbance has decreased from a maximum variation of 10 to 5 N-m after 20 seconds.Te simulated outcomes of the designed system with the PI controller are shown in Figure 9 in terms of load variation speed (rad/sec).Te range of the load torque has to be located from 5 to 10 Nm.After 20 seconds, the IM's speed has controlled after experiencing oscillations with a value of 120 rad/sec.Due to the voltage drop caused by the excitation of the stator and rotor windings, the DC voltage has been reduced from 460 V to 420 V while the PI controller had been able to operate.SMC, a nonlinear control technique, forces a nonlinear system to slide along a cross section of its appropriate behaviour by implementing a discrete control signal (or, more precisely, a collection control signal).Figure 10 illustrates the simulated results of the designed system with PI controller inverter output voltage with the variation of 460 V to 420 V after 28 seconds.Figure 11 illustrates the speed results of the designed system with fuzzy sliding-mode controller (FSMC) in load variation with sliding surface according to control law.According to the measured and reference speed values, Figure 12 shows the simulated speed results of the designed system with ANN-based SMC in the speed reversal from 116 rad/sec to − 116 rad/sec.Te speed variation of various controllers for PI, SMC, FLC with SMC, and ANN with SMC is shown in Figure 13.When compared to other algorithms, ANN with SMC performs faster and with less load disturbance.Table 2 compares the various speed parameters in terms of error value for delay time, rise time, peak time, and settling time.In terms of performance, ANN with SMC has performed better due to its lower error value in terms of the controller.
Te voltage, current, speed, and torque results of a power steering control system designed based on SMC will depend on the specifc design parameters and system characteristics.SMC is a reliable control method which, in the absence of    International Journal of Intelligent Systems system disturbances and unpredictability, can deliver good detection accuracy.In a power steering control system, the voltage and current will depend on the power source and motor specifcations, as well as the load on the system.Te speed and torque of the motor will be infuenced by the control inputs and the mechanical properties of the system, such as the gear ratio and steering mechanism.If the SMC design is successful, it should be able to regulate the voltage and current to provide stable power to the motor, while also controlling the speed and torque to achieve the desired   International Journal of Intelligent Systems steering performance.Te exact values of these variables will depend on the specifc system design and operating conditions.Table 2 illustrates the comparative analysis of various controllers under diferent torque conditions.Te SMC and ANN-based SMC are applied to the power steering application of IM.In comparison of the abovementioned two controllers, the ANN-based SMC gives improved performance.Table 3 illustrates the proposed sliding mode controller with the ANN approach, which gives a lesser error value than without SMC.For the designed system-based SMC in power steering control, where the voltage value has been varied from 460 to − 460 V, Figure 14 shows the voltage, current, speed, and torque.Specifcally, the delay time, rise time, peak time, and settling time have all been varied for the current parameter.After varying over time, the induction motor's speed and torque have fnally been controlled.Figure 15 shows the voltage, current, speed, and torque results of the designed system with ANN-based SMC, which have smoother results as a result of the system's inclusion of ANN.A power steering control system can be designed using SMC to regulate the current and fux parameters.Te SMC algorithm is robust to disturbances and can guarantee system stability and tracking performance.Te simulation results of the designed system with SMC in power steering control are shown in Figure 16 for the parameters current and fux.

Experimental Setup and Validation
Te hardware test was conducted to confrm the viability of the suggested control strategy.Te exact same motor parameters that were used here were additionally employed in the simulation as shown in Table 1.Te PM75RL1A060 (Mitsubishi) IPM modules and the TMS320F28335 control board have been combined to form an inverter (Texas Instrument).Four current sensors (two for each motor) and one voltage sensor were also used to keep track of the DClink voltage and motor currents.Te machine, which is robotically combined with the drive shaft, has a resistor connected through the diode rectifer to interact with the load application.Te experimental model of the designed system is shown in Figure 17.
Te time response of PWM pulses for an inverter can be characterized by two important parameters, T ON and T OFF .T ON refers to the time duration for which the pulse remains  International Journal of Intelligent Systems ON, while T OFF refers to the time duration for which the pulse remains OFF.Te ratio of T ON to the total time period of the pulse is called the duty cycle, and it determines the average power delivered to the load.For example, if the pulse has a total time period of T, and T ON is equal to 0.4 T, then the duty cycle would be 0.4.Tis means that the pulse is ON for 40% of the time and OFF for 60% of the time.Te T ON and T OFF times are determined by the input signal to the inverter's PWM controller.Te controller compares the input signal with a triangular waveform of fxed frequency and generates a PWM output signal whose duty cycle is proportional to the amplitude of the input signal.Te T ON and T OFF times can also afect the harmonic value of the voltage output patterns, which is important in applications such as motor control.In general, the T ON and T OFF times are chosen such that the voltage output waveform has a low harmonic distorted value and the average power delivered to the load is as desired.Te exact values of T ON and T OFF may vary depending on the specifc application and the characteristics of the load.Table 4 displays the induction motor's acceleration time T 1 , turning time T 2 , and deceleration time T 3 throughout the operation.Te PWM technique has been used to drive an induction motor by controlling an inverter.Te on-and-of periods of this PWM pulse can be provided by the sliding mode estimation and the input (angle from steering).Te acceleration time is determined by the time at which the angle is reached.Te angle needs to be reached because the input determines when to turn on.International Journal of Intelligent Systems Te fuzzy logic controller-based 1800 rpm induction motor speed is shown in Figure 18.Tis is possible because the fuzzy logic controller only has one pole, allowing it to control the system independently of the other poles.According to the inspection in the fgure, the system's speed varies every second.With PI and PID, however, stability could not be maintained when a setting point lower than the appropriate setting point (1800 rpm) has been applied.Tis is due to the regulation having multiple poles, so when the setting point is intended from the start, the control system can only preserve the way to       International Journal of Intelligent Systems set the position in that region.Tables 5 and 6 illustrate induction motor parameters and three-phase induction motors of the experimental setup.Figure 19 depicts the output of a fuzzy logic controllerbased induction motor current, which indicates the stator current at 75% of the load condition.
Te respondents of an induction motor based on a sliding mode controller under steady state speed conditions are shown in Figure 20.Te P-I controller's speed response is directly impacted by the load disturbance; meanwhile, the sliding mode controller has demonstrated its reliability against load fuctuations.Figure 21 depicts the output of a sliding mode controller induction motor current, which indicates the stator current at 75% of the load condition.Te induction motor with speed controller is designed based on a sliding mode controller as shown in Figure 22.When a load is applied, the ANN-based sliding controller exhibits a considerable portion of motor speed gradation.Te ANN controller responds more quickly than the fuzzy controller.Figure 23 shows an induction motor with a sliding mode controller based on an ANN with a smaller ripple than a sliding mode or fuzzy logic controller for the current value.
Figure 24 depicts, from the inspection of various time periods, the time domain specifcations of the delay time, rise time, peak time, and settling time characteristics of PI control, sliding mode control, fuzzy, fuzzy with SMC, ANN control, and ANN with SMC.From the characteristics, it can be contended that ANN with sliding mode control performs better than other controllers.Te interference of the ANN   technique in power steering sliding mode control applications is shown in Figure 25.

Conclusion
In this study, a novel sliding mode speed controller using ANN for induction motor drives fed by a voltage source inverter is investigated.Te disruption observation estimates a continuous input disturbance signal with the purpose of mitigating it in the SMC algorithm.As a consequence, sliding mode controllers integrate processors into their designs implicitly.Using sliding mode control for fux estimation, this work has devised a plan for enhancing the response qualities of a power steering induction motor.For the system, the suggested technique calculates and estimates the speed, torque, and electrical angle.Furthermore, simulation data are provided to validate and demonstrate the feasibility of the proposed approach.Moreover, the concept of power steering combined with sliding mode control for a three-phase induction motor is examined, and its efcacy is examined.Te proposed sliding mode control systems are compared to other controllers using experimental data, and the results show that ANN-based sliding mode control has better value in terms of delay time, rising time, peak time, and settling time.

4
Error (mse) 11.8989 is a highest training performance at epoch 569 Train Best Goal

Figure 2 :
Figure 2: Design circuit of SMC for indirect vector-controlled IM.

Figure 5 :
Figure 5: Designed system with PI controller in transient region inverter output voltage.

Figure 6 :
Figure 6: Designed system with PI controller in transient region speed (rad/sec).

Figure 7 :
Figure 7: Simulated results of designed system with PI controller in load variation from electro-magnetic torque varied from 10 N-m to 5 N-m.

Figure 8 :Figure 9 :
Figure 8: Simulated results of designed system with PI controller in load variation speed (rad/sec) from load torque varied from 5 N-m to 10 N-m.

Figure 10 :Figure 11 :Figure 12 :Figure 13 :
Figure 10: Simulated results of designed system with PI controller inverter output voltage.

Figure 14 :
Figure 14: Simulated voltage, current, speed, and torque results of designed system-based SMC in power steering control.

Figure 15 :Figure 16 :
Figure 15: Simulated voltage, current, speed, and torque results of designed system with ANN-based SMC in power steering control.
Te input/output values are critical for training ANN in of-line IM for incoming i qs * with speed error.Te variable parameters are appropriately encumbered to confrm a steady process because no supplementary learning can occur once the ANN has been trained.A feed-forward back propagation algorithm (FFBPA) is employed to train the ANN.Te created model is put via the PURELIN mathematical derivation, which has a grade reduction with bias and weight updating.Te learning develops in accordance with the learning requirements.Te fundamental performance criterion for an ANN network is the mean square error (MSE), which should be implemented in accordance with the MSE between the target and estimated output, which has a signifcant impact on machine performance in ANN.In this ANN network, the least MSE that can be reached is 1e − 5 .In FFBPA, the dif- ferential function is used to determine the activation function (AF).Te tan sigmoid function (SF), which is frequently used in squashy-restricting AF, thereby meets this requirement.Te linear activation function (LAF) is utilized in output layers that never compare the output value, whereas SF is used in linear output nodes to streamline the learning process.

Table 1 :
Simulated parameters of IM.

Table 2 :
Comparison table of speeds in various controllers.

Table 3 :
Comparisons for SMC and ANN-based SMC power steering.

Table 4 :
T ON /T OFF time response of PWM pulse for the inverter.