A New Closed Loop Constant v/f Control of Induction Motor with Torque Control Based on DPWM

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Several industrial applications make numerous uses of threephase induction motors.This motor is commonly used due to its adaptability to various load conditions, simple and durable structure, and affordable acquisition and maintenance [1]- [3].Due to the vector control system's improved dynamic response [4]- [11], numerous studies in this area have been performed.Scalar control [12]- [14], however, produces the same results with low steady-state error.Due to its widespread industrial application, the (v/f) scalar control system is therefore taken into consideration in this work.The constant V/f control technique for induction motors frequently uses proportionalintegral (PI) control [15].

░ 2. CONTINOUS (CPWM) AND DISCONTINUOUS PWM (DPWM)
In the past 20 years, several pulse width modulation (PWM) techniques have gained popularity.All those PWM are grouped as continuous PWM (CPWM) and discontinuous PWM (DPWM) [16]- [17].Unlike DPWM, which uses a discontinuous time-varying signal, in CPWM, the modulating wave would be a continuously varying signal, which indicates that the modulation stops at some point because of the modulating waves being clamped or connected to the +ve orve DC bus for specific clamping durations, referred to as bus clamping PWM.The positioning of a zero (+++ or ---) vector and the division of the zero-vector duration influence both continuous and discontinuous modulation.The popular CPWM methods include space vector PWM and sinusoidal PWM.The sine wave signal is compared to a triangular carrier wave, which is of higher frequency than the reference carrier sine wave; sine triangle PWM is yet another term for sinusoidal PWM (SPWM) [18]- [20].A significant benefit of SVPWM is that it uses the DC bus 15% more efficiently than sinusoidal PWM.Even though numerous studies [21] compare the performance of SVPWM, sinusoidal PWM, and DPWM, by comparing and evaluating the results of continuous and DPWM using experimental and simulated analysis, it is suggested that 30⁰ DPWM outperforms all currently available DPWMs.Therefore, the focus of this article is on closed-loop torque control of an induction motor drive using 30⁰ DPWM.

░ 3. SPACE VECTOR PULSE WIDTH MODULATION (SVPWM)
A 3-ϕ system can distinctly be described by 2-ϕ system.As they allow for the use of the vectorial rotation attribute in a complex plane, the 2-ϕ quantities can be called as vector.The SVPWM is supposed to be a 3-ϕ sinusoidal waveform with three axes that are 120° apart in time, yielding a space vector with a constant amplitude that revolves at a constant speed.With 2 zero vectors (+++ or ---) and 6 active vectors, the two-level inverter SVPWM method creates the VREF reference voltage, that is sampled for each sub-cycle Ts.The switching sequence used in traditional SVPWM distributes the zero-vector duration (T0) evenly between the two zero states i.e., either +++ or ---in each sub-cycle.SVPWM can achieve a maximum control voltage of (1/ 3) VDC.

░ 4. 30° DPWM
In the conventional SVPWM each sector is divided into 60ᵒ but in 30ᵒ DPWM the 60ᵒ sector is divided into two intervals, that are fundamentally different from one another, such as it could be divided into width ϒ during the first quarter cycle and (60-ϒ) in the following quarter cycle.Since the clamping duration is split into two intervals, in the inverter states this is also termed as "Split Clamping PWM" in literature [22]- [25].R phase is continually clamped to the +ve DC bus for a 30ᵒ duration as shown in figure 2. and it is explained for sector I in figure 3.
Since one of the zero vector is removed, switching is reduced, which causes reduced switching losses as well as inverter losses along with the increase of switching frequency 1.5 times compared to SVPWM, as a result, it is frequently employed in high-frequency applications [26]- [28].However, conduction losses are higher than those of SVPWM for high modulation indices and higher switching frequencies.

Torque Estimator
The two-phase model given by the reference (α, β) [29]- [30] is the most appropriate model to examine the dynamic behavior and control algorithm design of the three-phase IM.The machine's three-phase representation (a, b, and c) is less complex with the help of this model.The following formulations provide the electromagnetic torque equations: The transformation known as Concordia; the three-phase reference (a, b, c) can be transformed into two-phase reference (α,β) using the below transformation: With: X could be the machine's voltage, or current.

░ 6. SIMULATION STUDIES AND RESULTS
Under varied operating circumstances, the performance of the novel constant v/f control for the IM drive based on Torque PI control has been closely reviewed.For the same 30⁰DPWM, the results have been compared with Speed PI controller.Kp = 14 and Ki = 5 are the PI controller simulation parameters.To attain the optimal performance in terms of reduced speed overshoot and undershoot, lower settling time, and no steady-state error, the PI controller was tuned using trial-and-error method.The motor is first operated in an open loop to see what must be modified so that it can reach the target speed.The values of Kp and Ki are initially assumed to be 1 and 0, respectively.The steady-state error has been eliminated after setting the value of Kp, with the optimization of rising time and overshoot, then the value of Ki has been increased which optimize steady-state error and settling time, then the value of Ki is fixed.The slip is then corrected using the torque regulator so that the desired torque is followed exactly which in turn it also reduces the THD% of current.Across the nation, electric utility vehicles are becoming more prevalent on farms, pastures, and other terrain.The closed-loop v/f control for the IMD (Induction Motor Drive) makes the suggested speed control approach reliable, simple to use, and ideal for applications requiring minimal precision.Moreover, compared to other vector control techniques, the proposed torque control technique's ease of implementation and affordable cost make it more adaptable to vehicles that do the same task, such as electric mini trucks and quad bikes, in any hilly terrain.

░ 9. CONCLUSION
This paper shows 30⁰ DPWM implementation for new closedloop v/f control of an induction motor with torque control.The speed PI and torque PI controller based on constant v/f control models have been simulated using the MATLAB/Simulink environment.In comparison to the speed PI based constant v/f control, the analytical, simulation, and experimental findings for the torque PI based constant v/f control represent a better reduction in torque ripple and harmonics in stator current.Torque is estimated with an estimator in a sensor less way, which brings about better control of torque.As a result, the performance objectives of the drive system are well met.For future scope, it is also proposed to try and implement the interval type 2 fuzzy (IT2F) method replacing PI based control, as the IT2F type phenomenally reduces torque ripples to achieve better results, as cited in contemporary articles.

Figure 4 .Figure 5 :
Figure 4. Block Diagram of 30°DPWM-based Closed-Loop v/f control of Induction Motor Drive with torque PI control Figure 9  and 10 depict the stator current THD of 2.23% and voltage THD of 0.65% with their FFT waveforms for 30° DPWM based torque control, respectively.The torque smoothing waveform for torque control approach demonstrates the least torque ripple figure 7. The addition of torque control can improve the closed-loop v/f control scheme's dynamic response.The base value of the stator voltage magnitude is determined by the first PI speed using the desired V/F characteristic, and the rotor flux regulator provides the incremental voltage needed to follow the intended rotor flux without error.The second gives the slip's base value, which is calculated using the required torque and the expected rotor flux.

Table 1
lists the empirical outcomes acquired by the FFT analysis from MATLAB/Simulink for different control techniques.It demonstrates the efficacy of the suggested torque control technique since it gives lesser THD compared to prior PI speed control.The motor starts with no load for 1.5seconds prior to getting applied with the rated load torque of 26.89Nm for 4KW induction motor are shown in figure 6.The simulation results are for 50Hz fundamental frequency and reference speed RPM of 1200RPM.