Attenuation of voltage sags effects and dynamic performance improvement of a multi-motor system

Received Sep 13, 2021 Revised Mar 20, 2022 Accepted Apr 7, 2022 In many continuous manufacturing processes such as paper, textile, winding and plastic extrusion, electric drives are frequently required to work in synchronization, often with high tolerances to ensure uniform product quality and avoid failure of the product. In a multi-motor system (MMS), voltage dips are the most common cause of the motor stoppage, and the transient loss of synchronism between motors can result in a complete system shutdown. This paper proposes a multi-motor system controlled by a Backstepping strategy to ensure servo-control and synchronization of induction motors. This technique includes indirect rotor field-oriented control (IRFOC), linear speed control, and mechanical tension control, of induction motors. Investigations of symmetrical voltage sag effects on speed, torque, and mechanical tension are also carried out. Simulation results obtained using Matlab®/SimulinkTM/SimPowerSystems® are presented to demonstrate the efficiency of the proposed control strategy.

: Electromagnetic couple and : Rotor fluxes following the axes direct and into quadratic and : Stator currents following the axes direct and into quadratic and : Stator voltage following the axes direct and into quadratic

INTRODUCTION
In many continuous manufacturing processes such as paper, textile, winding and plastic extrusion, electric drives are frequently required to work in synchronization, often with high tolerances to ensure uniform product quality and avoid failure of the product [1]. The correct functionality of these systems requires control of the mechanical tension and the speed of the winding or material transport, which requires maintaining synchronization between the motor [2], [3].
Voltage sags, as defined by the IEEE-1159 standard, are brief drops in rms voltage to between 0.1 and 0.9 pu for durations ranging from 0.5 to 1 minute [4]. Short-circuiting faults, such as single line-to-ground faults in a power system, and the start-up of large rating motors are the most common causes of voltage dips. Such issues cause significant disruptions in motor speed and material mechanical tension, resulting in massive financial production losses [5].
The main effects of voltage dips include: the decrease in dc link voltage which degrades the functionality of the r multi-motor system (MMS) and may cause it to shut down through the protection systems, the high current at the end of the dip when the dc link voltage has been reduced during the dip, which can cause significant damage to the system, and in general, sudden variations of the dc link voltage that affect the synchronism of the controllers and that can which can damage or destroy the various components of the system [5]. This problem has piqued the interest of many researchers, who are currently investigating it. Many solutions have been considered and proposed, many of which involve modifications to the traditional topology of multi-motor systems and/or incur significant costs. Mechanical or electrical auxiliary energy storage units [6], [7], unified power quality controller (UPQC) [8], [9], the application of converters with inductive elements, such as autotransformers, static power compensators (STATCOM) [10], static voltage regulator (SVR), dynamic voltage restorer (DVR) [11], [12] and energy storage devices including superconducting magnetic energy storage (SMES) [13]. These solutions, however, are still general in nature and have not been applied in multi-motor configurations.
Blaschke's field-oriented control is one of the most widely used induction motor control strategies. However, this technique is extremely sensitive to parameter changes. Sliding mode control [14], [15], for example, is one of many modified nonlinear state feedback systems. Input-output linearization control [16], passivity-based control [17], and backstepping control [18], have been presented in the literature to overcome this restriction. Backstepping control law is derived from a Lyapunov function to ensure system input-output stability and provides good performance in both steady state and transient operations, even in the presence of parameter variations and load torque disturbances [19]. In this paper, a Backstepping induction motor speed and mechanical tension controller for a multi-motor system is developed and will be evaluated by a simulation in the presence of voltage sags. This paper is organized as follows. The nonlinear model of a simple winder system powered by two 4 kW three-phase induction motors is presented in section 2. Section 3 details the principles and design of the proposed backstepping controller. Section 4 gives the simulation results of the proposed strategy, obtained using Matlab®/SimulinkTM/SimPowerSystems®/RT-Lab®. Finally, section 5 summarizes the main contributions and describes some additional research avenues.

MODELING OF THE STUDIED SYSTEM
The control of multi-motor systems in the presence of voltage sags will be evaluated by simulation. Figures 1 and 2 shows a drive system consisting of two three-phase motors with a common DC bus, which are mechanically coupled by an elastic band with an adjustable mechanical tension. Motor IM1 performs unwinding whereas motor IM2 performs winding. This system is composed of two different parts, the mechanical part and the electrical part [5], [20], [21].

Electric drive
The model consists of two three-phase asynchronous motors; the drives are connected to DC bus, to which an adjustable capacitor bank is connected, allowing the energy, allowing the energy characteristics of the system to be modified, Figure 2. The motors (IM1, IM2) are powered by PWM inverters in order to vary the speed. The electrical converter that connects the input power to the DC bus is a three-phase rectifier bridge with diodes. A model based on motor equivalent circuit equations is usually sufficient to synthesize the control law [22]- [25]. In the d-q synchronously rotating frame, the electrical dynamic model of a three-phase Yconnected induction motor IMi can be expressed as: With: The electromagnetic torque is given by (2).

= .
. . (2) Where the parameters of the induction motor are defined in Table 1 and the different physical variables are defined in the nomenclature.

Electrical and mechanical models
The web-transport system's model is based on three laws, Hooke's law, Coulomb's law and mass conservation law, which enable to calculate the web tension between the two rolls [5], [26]. Where the dynamical equation of mechanical web tension T in (3) is a function of induction motor linear speeds V1 and V2 and web length .
Model of the mechanical of the system is given by, Using this equation, it is easy to see that the tension force in the section studied (T) is produced by the coupling of several variables in the system. Indeed, it depends on the length ( ), the band section (S), the Young modulus (E) of the band and the rollers radius 1 and 2 .

Control structure
The strategy control structure shown in Figures 2 and 3 are implemented using backstepping speed controllers (BSC) combined with IRFOC. The mechanical tension control can be realized with a classical controller PI this controller generates the speed reference for IM1 in a cascade control loop structure [5], [19], [23], [27]. Backstepping control strategy development steps are: Step 1: Calculating stator currents and torque references: Let us introduce the rotor speed and the flux tracking errors with their derivatives: So, the dynamic equations of the errors are: Using (5), the derivative of (6) is written as: This can be rewritten as: In order to ensure stable tracking, 1 and 3 should be positive parameters. This results in: The stator current and torque references can then be deduced as: Step 2: Set-point computation of stator voltages This step proposes a method for obtaining the current references generated by the first step. Consider the following current errors: As a result, the error (12) can be written as: The time derivative of (13) is as: In (15), the control input Stator voltages and appeared. New Lyapunov function based on errors in speed, rotor flux, and stator currents, such that: The derivative of (16) is given by: By setting (13) in (17), one can obtain: The stator voltages are then determined by the inputs as: where 2 and 4 are positive parameters chosen to ensure a faster dynamic of the rotor speed, rotor flux, and stator currents. Then (15) can be written as: This can be rewritten as: The closed loop error system is expressed as: It is interesting to note that the speed of convergence of the error signals to the reference signals depends on the dynamics of the matrix A in (22), in other words, the values of the gains 1 , 2 , 3 , and 4 depend on the desired position of the poles in closed loop.

SIMULATION RESULTS AND DISCUSSION
Elastic band and two induction motors coupled structures are used to validate, by simulation, the dynamic performances, effectiveness and robustness of the backstepping proposed control strategy in the presence of type A symmetrical voltage dips. These results are compared to PI control that has been presented in [2] and the sliding mode control (SMC) that has been presented in [14], [28]. All parameters are listed in Tables 1 and 2. The models in Figures 2 and 3 were implemented in the Matlab/Simulink environment. Furthermore, we used models from the "SimPowerSystems" Blockset for induction motors and associated electrical converters, which provides comprehensive models that are close to reality. The system was set to run at a speed of 35 m/s, with a mechanical tension set-point of 4 N for the mechanical tension. The simulation results for the proposed structure system for a two three-phase IM fed by PWM voltage source inverters (Vdc= 281 V) with a rated speed of 35 m/s were obtained using PI indirect rotor flux-oriented control (PI-IRFOC), (SMC), and (BSC). When there are type A voltage dips at time t=4 s, the rectifier bridge blocks, zero DC link current shown in Figure 4, the DC link voltage drops shown in Figure 5, and both motors decelerate at their own rate shown in Figure 6(a). The motors are constrained to maintain similar speeds due to the stress associated with the mechanical link between the motors via elastic band. Following the disappearance of the voltage dip at time t=5 s, there is a sudden change in the difference between the voltage available on the network and the voltage on the DC link, resulting in a strong current. This results in a high-current call (overcurrent) that charges the DC link capacity. This will also cause an overvoltage on the DC link due to inductances in the system. When the DC link voltage is restored, both motors can accelerate with a high current draw to the speed set point. Table 3 provides a brief comparison of the various performances obtained from simulation results for the three-control strategy.
The resulting for BSC, PI-IRFOC, and SMC are shown side by side in Figure 6, along with linear speeds and mechanical tension. The performance of the three control methods is compared using various criteria such as dynamic response, stability properties, ease of controller design, and robustness to voltage sags. These criteria are examined individually below: − Dynamic response: Figure 6 shows the system response; (a) speed evolution using PI-IRFOC, (b) mechanical tension using PI-IRFOC, (c) speed evolution using SMC, (d) mechanical tension using SMC, (e) speed evolution using BSC, and (f) mechanical tension using BSC. In comparison to the PI-IRFOC, SMC and non-linear BSC provide better tracking responses and faster speed response for multimotor systems. Before and after the voltage sag, the mechanical tension of the material web is maintained constant, Moreover, compared to PI-IRFOC and SMC, BSC has small oscillations during the sag. − Stability proprieties: For PI-IRFOC, the stability analysis is performed using a pole placement or full state feedback (FSF) and pole compensation, whereas for BSC and SMC, the Lyapunov stability method is used. It can be seen that all methods have stable performances, but BSC and SMC have faster convergence. − Robustness to voltage sags: BSC proposed control strategy ensures good voltage dip immunity. In addition, due to a voltage drop at t=4 seconds, the DC link voltage has decreased by 50% and remain at this level for 1 second. Figure 6 highlights the impact of the grid voltage dip on the mechanical tension. BSC shown in Figure 6(f) ensures low oscillations on the elastic material compared to SMC shown in Figure 6(d) and PI-IRFOC shown in Figure 6(b). − Ease of controller's design: The PI-IRFOC is characterized by two parameters. The pole placement technique was used to determine these parameters in a closed-loop. Achievable dynamics are constrained; one obvious limitation is that the poles must be placed on the complex plane's left half to ensure closed loop stability. The dynamic response of the system is improved by BSC and SMC, which are based on a system model. Furthermore, Hurwitz is used to determine the parameters of the BSC controller in closedloop. Nonetheless, the real parts of the eigenvalues of the previously given matrix A are all negative.

CONCLUSION
In this paper, we compare three control laws for controlling the speed and mechanical tension of a multi-motor system. The investigated system is made up of two induction motors connected by an elastic band. In order to design an improved control law for the linear speed of the web based on the Backstepping strategy, we evaluated the system's behavior in the presence of voltage sags. Simulation was used to assess the effectiveness of the proposed control scheme. This nonlinear control method was compared to existing SMC and PI-IRFOC techniques.
This work allowed us to make a technological contribution to high performance multi-motors systems. Simulation results clearly showed the problems created in drives with variable and coupled speeds/mechanical tension. The advantages of the three investigated control structures are that they compensate the effects of nonlinearity and voltage dips and that they ensure a good internal stability of the system. The obtained results confirm the proposed Backstepping control strategy's high performance in terms of rise time, faster transient response, and robustness to voltage sags when compared to SMC and PI-IRFOC. Note that the mechanical tension oscillations observed at start-up with the Backstepping control law are due to the excitation of the system by discontinuous set-points (step) and the presence of derivates blocs in the controller. These oscillations could be significantly damped by filtering the set-points. For future works, we are planning to develop a multi-motors system management strategy to mitigate other types of voltage sags.