Real time implementation of anti-windup PI controller for speed control of induction machine based on DTC strategy

Lahcen Ouboubker, Jawad Lamterkati, Mohamed Khafallah, Aziz El Afia Faculty of Applied Sciences of Ait Melloul, Ibn Zohr University, Agadir, Morocco LGEMS Laboratory, National School of Applied Sciences of Agadir, Ibn Zohr University, Agadir, Morocco RITM Laboratory, High School of Technology, Hassan II University, Casablanca, Morocco Energy and Electrical Systems Laboratory, ENSEM, Hassan II University, Casablanca, Morocco ENSAM, Hassan II University, Casablanca, Morocco


INTRODUCTION
Traditionally, DC motors are used for speed variation of electric machines, because the magnetic flux and electromagnetic torque are easily controlled by the stator and rotor current, respectively [1]. In the last two decades, AC motors are replacing DC motors. The induction machine (IM) is the most robust and responsive AC motor in the industry. However, its nonlinear and highly coupled structure presents a limitation to the performance of the control of this induction machine [2]. In the last decade, a new control method called DTC has been introduced. DTC has received considerable attention in industrial motor drive applications. The main reason for its popularity is due to its simple structure, robustness to rotor parameter variations and fast dynamic response [3].
Direct torque control (DTC) has been developed to replace traditional PWM drives of the open-and closed-loop type used in FOC [4]. DTC has several advantages: torque response, torque repeatability, motor dynamic and static speed accuracy [5]. The DTC method is characterized by a switching table that determines the voltage vector to be applied for controlling the switches of the voltage inverter [6]. This control method is very simple. It allows decoupled control to flux and torque without resorting to use the technique of width modulation and pulse current regulators [6]. This type of control is based on non-linear correctors of the hysteresis type which present limitations in case of large switching and uncontrollable frequency [6].

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On the other hand, the design of the speed controller greatly affects the performance of the drive. Vector control generally uses proportional-integral (PI) speed controller as inner speed loop to generate torque current [7], [8]. PI speed controller is often used because it can reduce steady state error and easy to implement. To get fast dynamic response, high PI gains cause undesirable system behavior such as high overshoot and slow settling time. On the other hand, integral-proportional (IP) speed controller has been presented in [8], [9], [10] that provide better performance in reducing or eliminating overshoot, but still gives fast dynamic response.
Both speed controller schemes on conventional PI and conventional IP are designed without considering the limit of controller output. Whereas, in real condition, a control system will find the saturation problem. When it saturated, the feedback loop can be damaged and the system works like an open loop system. In addition, the existence of integral action that responds to accumulated errors from the past can lead to large overshoot, delayed response, slow settling time, even system instability. This problem is called windup effect. Anti-windup strategies are available in order to solve the problem of windup effect [11], [12].
The conventional antiwindup methods include: (i) conditional integration [13]- [15], where the integral action is activated or deactivated depending on certain conditions, the integration being suspended in case of saturation and the control error is of the same sign as the control signal; (ii) the use of a limited integrator [16], where the integrator value is limited to the linear range of the actuator by hard feedback via a high-gain dead zone; (iii) in [17]- [19] a classical method for computing feedback in which the difference between the saturated and unsaturated control signal is used to generate a feedback signal that acts on the integrator input is presented [20]. Unified anti-doubling strategies that combine the tracking back calculation and conditional integration approaches are presented in [20], [21].
In this work we present an anti-windup PI speed control for an induction machine based on a direct torque control strategy, in order to eliminate the undesirable side effect known as integrator windup. The proposed anti-windup controller has some advantages: almost zero overshoot and very simple implementation in existing PI controllers. To validate our approach, the Anti-windup PI controller performances for induction machine speed control based on direct torque control strategy have been investigated by simulations under MATLAB/Simulink and the validity of the proposed control scheme is proved by the experimental results on dSPACE system with DS1104 controller board. Figure 1 shows a simplified circuit diagram of a conventional two-level voltage inverter feeding an induction machine. The delivered voltage vector depends on the state of the switches S a , S b , S c and the DC voltage E.

Modeling of the three-phase inverter
The function of the inverter is to convert the direct voltage into alternating one. The DC-AC converter is composed of 6 insulated gate bipolar transistors (IGBTs) to control the three-phase induction machine. The aim of this kind of system is to manage the amplitude and frequency of the stator voltages. The three-phase inverter model contains eight switching states. Figure 2 shows the representation of each IGBT state based on a vector presentation. The stator phase voltages are described in (1) using literature [22], where V(a,b,c) are the three phase stator voltages, E is the DC link voltage and S(a,b,c) are the switching functions that can take two logic values 0 or 1.
The output voltage of the inverter is defined in (2) and (3) using the vector presentation.
Then, can be expressed using (4). The (4) allows the determination of the voltage for each sector using the vector presentation.

Modeling of the three-phase induction machine
The induction machine is a nonlinear and unsymmetrical system. As reported in literature, the stator and rotor voltage equations can be represented in a stationary reference frame using (5) and (6) [23]- [25]. The (7) and (8)

BASIC DTC OF INDUCTION MACHINE DRIVE
DTC is a vector control method used to control the torque and therefore the speed of the induction machine by controlling the switching sequence of the inverter transistors. The Figure 3 shows the basic DTC principle. The DTC provides direct and independent the control of the flux and torque of an induction machine by selecting the optimal switching modes of the voltage inverter. it allows the flux and torque to be maintained within their hysteresis bands. Thus, DTC provides very fast torque response without using coordinate transformation, current controllers and PWM generator. In the DTC, the machine torque control is achieved with two hysteresis controllers, one for stator flux magnitude error and the other for the torque magnitude error. The selection of one switching vector per sampling time depends on the sign of these two controllers [6]. By using a ( , ) stationary stator reference frame, the stator flux linkage and electromagnetic torque Г e are calculating by using (9) and (10): The stator flux linkage phasor is given by (11): The angle is equal to: The estimated electromagnetic torque is given by (13): The error between the estimated torque Г and the reference torque Г * is the input of a three level hysteresis comparator, whereas the error between the estimated stator flux magnitude and his reference stator flux magnitude * is the input of a two level hysteresis comparator. Figure 4 (a) and Figure 4   To determine the stator voltage vector to be applied, the circular stator flux path is first divided into six symmetrical sectors ( Figure 5) [6]. Then, the effect of each stator vector voltage on the flux and torque is studied. The selection of the adequate voltage vector is based on the switching table given in Table 1. The inputs quantities are the flux sector and the outputs of the two hysteresis comparators.

ANTI-WINDUP PI CONTROLLER
The structure of the anti-windup PI controller based on the back-calculation method is presented in Figure 6. The saturation error u e and anti-windup gain K are the main parameters for the integral action correction, where: A feedback signal is generated from the difference between the saturated and unsaturated control signals and is used to reduce the integrator input when the controller output exceeds the actuator limits. The saturation in Figure 6 can either be a model used in the controller or the actual saturation of the actuator if its output is measurable. Figure 6. Anti-windup PI controller based on back calculation method

SIMULATION RESULTS AND DISCUSSION
In order to evaluate the performance of the proposed control strategy, simulation tests were carried out in MATLAB/Simulink environment for a 1.5 kW induction machine. Table 2 shows the regroups the electrical and mechanical parameters values. Different simulation tests were carried out under the conditions, DC voltage E=150V; Reference stator flux = 0.35 ; = 0.01 , Г = 0.02 . ; and the sampling time = 1 4 . The first test aims to evaluate the speed tracking efficiency. In fact, as shown in Figure 7, starting from a steady state of 600 rpm, 400 rpm acceleration and deceleration steps were applied respectively at t=1,2 s and t=3 s. We remark that the Anti-windup PI speed controller has achieved the test goals: no over/under-shoots, faster time response and better constancy in steady state. Figure 8 presents electromagnetic torque.
The stator currents Figure 9 and Figure 10 are sinusoidal and present less harmonics. The stator flux Figure 11 tracks its reference with good performance. The second test is to evaluate the disturbances rejection effectiveness. In fact, during this test, the speed was maintained at 600 rpm and a disturbance (80% of load torque ( )) was inserted at = 1.5 and removed at t=3s . As shown in Figure 12, the proposed PI Anti-windup controller has significant improvements; the rejection of load disturbances was done quickly. In addition, as schown in Figure 13, the developed torque follows the load torque. The compensations for disturbance are achieved by developed electromagnetic torque automatically.   The first test aims to evaluate practically the speed tracking efficiency. In fact, as shown in Figure 16, starting from a steady state of 600 rpm, 400 rpm acceleration and deceleration steps were applied. We remark that the Anti-windup PI speed controller has achieved the test goals: no over/undershoots, faster time response and better constancy in steady state. Figure 17 presents practical electromagnetic torque. Figure 18 and Figure 19 shows that the stator currents of the machine have a sinusoidal waveform and present less harmonics. The stator flux Figure 20 tracks its reference with good performance. the experimental results confirm the simulation results. The second test is to evaluate the disturbances rejection effectiveness. In fact, during this test, the speed was maintained at 600 rpm and a disturbance (80% of ) was inserted at = 13.4 and removed at t=20s. As shown in Figure 21, the proposed anti-windup PI controller offers significant improvements; load disturbance rejection was achieved quickly with the proposed controller. Moreover, as schown in Figure 22, the developed torque can follow the load torque. The compensations for disturbance are achieved by developed electromagnetic torque automatically. The experimental results confirm the simulation results.

CONCLUSION
In this paper, we presented a simulation and real time implementation study of anti-windup PI controller in order to improve induction machine speed control based on direct torque control strategy. A model of proposed control scheme, based on the Matlab-Simulink simulation tool, has been proposed and validated through-out experimental test results. The experimental results show that the DTC method applied to an induction machine using an Anti-windup PI controller of speed present most interest and contribute to improvement the performance of system.