Convergence Enhancement of Super-Twisting Sliding Mode Control Using Artificial Neural Network for DFIG-Based Wind Energy Conversion Systems

The smooth and robust injection of wind power into the utility grid requires stable, robust, and simple control strategies. The super-twisting sliding mode control (STSMC), a variant of the sliding mode control (SMC), is an effective approach employed in wind energy systems for providing smooth power transfer, robustness, inherent chattering suppression and error-free control. The STSMC has certain disadvantages of (a) less anti-disturbance capabilities due to the non-linear part that is based on variable approaching law and (b) time delay created by the disturbance and uncertainties. This paper enhances the anti-disturbance capabilities of STSMC by combining the attributes of artificial intelligence with STSMC. Initially, the STSMC is designed for both the inner and outer loop of a doubly fed induction generator (DFIG) based wind energy conversion system (WECS). Then, an artificial neural network (ANN)-based compensation term is added to improve the convergence and anti-disturbance capabilities of STSMC. The proposed ANN based STSMC paradigm is validated using a processor in the loop (PIL) based experimental setup carried out in Matlab/Simulink.

Milosavljević. The authors introduced the concept of quasi-70 sliding mode (QSM), where the system's trajectory is along 71 a surface that produces motion similar to sliding rather than 72 switching surfaces. The digitalized SMC guarantees to slide 73 at each sampling instant [14], [15]. The digital SMC are fur-74 ther studied and elaborated in [13] and [16]. Other enhance-75 ment techniques use approximation of signum function using 76 sigmoid function or continuous saturation function [17] for 77 chattering elimination at the expense of system robustness. 78 A new family of classical SMC was proposed to reduce 79 the chattering known as boundary layer SMC, whereas the 80 terminal SMC concept has been used to provide finite-time 81 convergence. Another variant of SMC known as second-82 order SMC (SOSMC) is a successful technique in removing 83 the shortcomings of SMC (i.e., chattering and infinite-time 84 convergence) while retaining the inherent robust nature of the 85 classical SMC [18]. A high order sliding mode control using 86 a super-twisting algorithm (STA) has been proposed by [19] 87 for wind energy systems. The STA-based SMC schemes are 88 easy to implement and this is implemented to make the 89 wind energy systems more robust. Various variants of super-90 twisting SMC (STSMC) are also reported in the literature. 91 For instance, the author in [20] combines the STSMC and 92 fractional order calculus to improve the performance of the 93 system with a chattering elimination approach. The author 94 in [21] uses a novel optimization method with STSMC for a 95 direct torque-controlled wind energy system and minimizes 96 the ripples in the torque and flux. The literature depicts that 97 STSMC has certain advantages of chattering elimination, 98 finite-time convergence, no knowledge of perturbations for a 99 system of relative degree one, continuous nature, and ensures 100 robustness against Lipschitz continuous disturbance having 101 bounded gradients.
improve the convergence trajectory of STSMC scheme. 149 The new control law adequately compensates the highly  163 The implementation of SMC law utilizes the dynamic model 164 of DFIG-based WECS. The DFIG-based WECS comprises 165 a hub, low and high-speed shafts, gearbox, brake, and a gen-166 erator. The model order is determined by the number of joints 167 or degrees of freedom; thus, a two-mass model is adopted in 168 this paper. The aerodynamic power from the wind speed is 169 given as follows:

II. SYSTEM DYNAMICS OF DFIG-WECS
At λ = λ opt , the C p reaches its maximum value, thus C p = 175 C p−max . In this case, the torque of the wind turbine is as 176 follows: The reference generator speed is given as follows: The reference speed is calculated using (6) when the system is 181 operating at maximum power point, whereas, it is calculated 182 from power curve data and look up tables in other cases. The 183 reference grid power is given as follows: The rotor dynamics of DFIG is given by: where the electromagnetic torque is given as follows:

189
T em = P MV s ω s L s ϕ qs I dr − ϕ ds I qr (10) 190 As per the concept of vector control, aligning the reference 191 frame to the d-axis of stator flux one gets ϕ ds = ϕ s and 192 ϕ qs = 0. The electromagnetic torque is given as follows: The DFIG rotor experiences a dynamic and variable wind 207 flow as a result of the wind's stochastic and gusty nature.

208
Therefore, it is necessary to an effective paradigm should 209 be implemented to complete the challenging task of regu-210 lating a constant DC link voltage. To accomplish this task, 211 a vector control strategy will be used. The orientation of 212 reference frame is aligned with grid or stator voltage using 213 the vector control strategy. Thus when V S = V D and V Q = 214 0, active power and reactive power adapts a new structure 215 given as: As shown in (16), I d and I q directly impacts the flow of 218 electric power from grid to the converters that equalizes to 219 the DC power given as follows: Substituting (17) in (18), we get: The uncertain term g(x) is added to g(x) in (19),and is given 225 as follows:    form: The states and the non-linear dynamic function F(x) and G(x) 258 are given as follows: Once the system is defined in the desired state, the control 265 objective is defined. In the presence of system uncertainties 266 and disturbances, the control objective is the convergence of 267 the current state vector to the desired or reference state vector. 268 For this purpose, a sliding variable S is designed to achieve 269 the required dynamic of the system given in (22) during the 270 sliding mode S = S(x, t) = 0. Also, it is assumed that 271 the relative degree of the input-output (u → S) is one, 272 with stable internal dynamics. Therefore, the input-output 273 dynamics can be presented as: Also, it is assumed that: 276 A1: The uncertain function G(x, t) ∈ R exists and can be 277 shown as follows: where G 0 (x, t) > 0 is a function that is known and G(x, t) 280 is a bounded uncertainty so that ∀x ∈ R n and t ∈ [0, ∞) with an unknown boundary 1 .
with the bounded terms where the finite boundaries δ 1 , δ 2 > 0 exist but is unknown. 288 A final equation is given is follows: where µ = G 0 (x, t)u. From A1, one gets 291 A3: The objective now is to drive the sliding surface S andṠ to 294 zero under disturbance and perturbations in finite-time. SMC 295 can efficiently fulfill this objective when the boundary of the 296 disturbance is known. The surfaces that will be used in the design of first-order 299 SMC are selected as an error between the reference and actual 300 states. The surfaces are suggested based on the difference 301 between the reference and the state variable. In DFIG-based 302 WECS, the controllable state components include current, 303 speed, and DC link voltage. These controllable state compo-304 nents will be used to control the WECS in this section.

C. ROTOR SIDE CONTROL
The speed control is the first step to in the RSC control, where 308 speed error is taken given as follows: Taking its derivative asė ω =ω r −ω ref r ; and putting the values 311 from (9) we have: The surface is selected as (35) and is given as follows: Taking derivative of the above surface, one gets the following 316 relation: The SMC law consists of an equivalent terms which is 319 acquired here by selectingṠ ω = 0. The equivalent term is 320 given as follows: given as: The current control is the second step to in the RSC control 339 that takes the reference current from speed control loop and 340 uses the current error, given as follows: The next step is to take the derivative of current errors given 343 in (43). The values of variables are substituted in derivatives 344 of current errors from (12) and are given as follows: Hence (44) can be written as: The current control loop derivation is performed by select-349 ing the surface same as the dq current errors, given as follows: 350 The derivative of the above surface is given as follows: SelectingṠ = 0, and the using the SMC theory, a final 354 current control law consisting of equivalent control and dis-355 continuous control terms is derived given as follows: The third step in the control of DFIG-WECS is DC link 361 voltage control scheme derivation, that is performed by taking 362 the DC link voltage error e E shown as below: Now, to get the final control law, derivative of voltage error 365 is first taken and then values from (21) are substituted to get 366 the following equations: Now selecting the surface for GSC control law same as the 369 voltage error given as follows: The derivative of the surface for GSC control law is given as: Now using the SMC theory, the equivalent part is derived 374 from above equation equalizing to zero, and taking the dis-375 continuous term as lowing control is obtained: is deduced here using the STA structure described in [38].
where the bounded control gains, α and β, are determined 405 by the system's operating under unknown disturbances.

406
Using the attributes of STSMC, a speed control is derived 407 using the STA and equivalent term from (39). The STSMC 408 based control paradigm is given as follows: In the similar way, the STA (54) and the equivalent 412 part in (48) are used to obtain the RSC control law given 413 as follows: To transfer power from RSC to grid, the GSC employs the 417 same surface made up of the difference between the DC link 418 voltage and its reference. The new HOSMC law for GSC 419 using (54) and equivalent law from (53) is given as follows: 420 The DFIG-based WECS is prone to certain uncertainties. 423 The ideal convergence trajectory cannot be achieved under 424 these uncertainties. The STSMC law consists of two compo-425 nents: (1) integral part − β   is given as t B in the following equation: where, t B can be seen as the convergence delay cause by the is given as under: Putting the value of sgn = S |S| = |S| S in the above expression, 442 one gets: One of the most widely used control methods for WECS 454 has been proved to be STSMC. Table 3 lists the various 455 systems using the STSMC scheme along with their surfaces, 456 errors, and system types. In [49] and [55], the author uses 457 STA to extract the most power possible while maintaining 458 robustness, chatter-free control, finite reaching time, and 459 upper bounds on externally applied disturbances. The authors 460 in [47] have found a solution to the problem with upper bound 461 presumption where an adaptive multivariable control scheme 462 with finite-time convergence and adaptive gain adjustment. 463 To demonstrate the finite-time convergence and stability of 464 the suggested control scheme, a novel Lyapunov stability the-465 ory is put forth by [47]. For floating wind turbines, an adap-466 tive super-twisting control scheme has been presented in [59]. 467 In STA algorithm-based control laws, the two controller 468 gains, α and β are fixed and selected to control performance. 469 These gains in each of the aforementioned control laws are 470 typically established by the uncertainties boundary, which 471 depends on several variables. In the process of designing 472 control laws, the uncertainty boundary is typically estimated 473 sufficiently, leading to unnecessary gains. Adaptive sliding 474 mode control (ASMC) schemes are used to address the prob-475 lems of unnecessary constant gains. The gain is adjusted to be 476 small enough to maintain the sliding motion using ASMC-477 based schemes that combine SMC theory and adaptive 478 VOLUME 10, 2022 algorithm characteristics [47]. A recent adaptive STA-based 479 SMC scheme for PMSG-based tidal stream turbine was pro-480 posed by Chen et al. [60]. The gains listed below can be used 481 to adapt the HOSMC scheme previously mentioned: The AI based part µ ANN in (63) is given as under: here y (x n ) is again the output, this time explicitly depen-517 dent on its input vector x. The Hebbian algorithm with its 518 input, i ‫ג‬ i x i , followed by a response function f () can be 519 represented as follows:

521
The synaptic weight ‫ג‬ i evolution with time is described by 522 Hebbian plasticity as under: 524 The response function y can be represented in a more 525 simpler form is given as under in (68) followed by its version 526 in matrix form in (69): The data variable x in (69), when taken as an average over 530 continuous (time) or discrete, can be written as: In eigenvectors basis form, ‫(ג‬t) is written as follows: where α * is the largest eigenvalue of C. The postsynaptic 539 neuron performs the following operation at this instant: The largest eigenvalue c * is related to the computation 542 of first principal component. Hebbian algorithm using the 543 double integrated values of the error is used to tune the 544 weights ‫ג‬ i making it adaptive. The adaptive weights are given 545 as follows:, k n=1 e,U is the control signal, and η i 548 is the learning rates. Equation (74) is implemented using 549 discontinuous projector operator shown as follows: where ζ represents the learning gain. The projection operator 552 is defined as follows: This completes the description and stability analysis of pro-556 posed loop synergized with STSMC scheme. Using the µ ANN 557 from (64). The new AISTSMC based control scheme adapts 558 the following structure: µ n = −α |S(t)| sign (S(t)) using the relation e = |e| sign(e), the above equation can 565 be further summarized to: can be written as follows: The control law in (80) Fig. 4, 593 uses a Dual Core Processor TMS320F379D integrated with 594 MATLAB/Simulink at a sampling rate of 5 × 10 −5 s in dis-595 crete time. In the adapted PIL environment, the control board 596 is physically connected to the DFIG-WECS model operat-597 ing in Simulink. The dual core processor programming is 598 done using rapid prototyping environment from Simulink. 599 The discussed controllers are discretized, and compiled from 600 MATLAB/Simulink and then hex version of these controllers 601 is programmed into the RAM of processor, where data 602 exchange takes place using high speed serial port. Two types 603 of tests are conducted for various control schemes. In the first 604 test, a deterministic wind speed waveform is used as input 605 wind with external disturbance applied as a step load to testify 606 to the robustness of the proposed control scheme. In the 607 second test, a stochastic wind speed waveform is used as input 608 wind. In this test, a lumped uncertainty d(t) commissioning 609 external and parametric uncertainty with 25% variation is 610 added to the DFIG-based WECS. Response optimization is 611 used in this paper to select the SMC and STSMC gains. 612 The Optimization toolbox in MATLAB/Simulink is used to 613 perform the optimization process where integral absolute 614 error has been used as criteria to minimize the objective func-615 tion. The introduction of ANN to STSMC can cause some 616 problems due to the Hebbian algorithm. The neurons in the 617 ANN controller updated by Hebbian algorithm are activated 618 to increase the weights, that can cause instability. Thus, the 619 weights are normalized in every iteration to limit the infinite 620 increase using the relation The outcomes of the two case studies considered are 622 explained as follows: In this test, an external disturbance is applied as a step 626 signal to testify to the chattering elimination capabilities 627 and robustness of the proposed control scheme. The DFIG 628 speed response to the deterministic wind speed waveform 629 is shown in Fig. 5. The zoomed-in view in Fig. 5(a) shows 630 the chattering phenomenon in the speed waveform due to 631 the discontinuous nature of the equivalent control law in 632 SMC.On the other hand, both the STSMC and AISTSMC 633 are of continuous nature, and successfully eliminates the 634   given in Fig. 5(b). The robust nature of SMC is evident from 637 Fig. 5(b), as it shows a little deviation in response to the step 638 uncertainty, but it loses its efficiency due to severe chattering.

639
The lack of robustness described insection 3.3 is visible from 640 the speed waveform in Fig. 5(b). It can be seen that the speed waveform for STSMC loses its tracking at t = 5 s and 642 converges very slowly to the reference value. The ANN-based 643 AISTSMC compensates for the STSMC problem and gives 644 improved performance when step disturbance is applied. 645 The speed deviation for STSMC is 158.1545 rad s −1 from 646 reference value, whereas AISTSMC gives much lesser devi-647 ation of 158.154 rad s −1 . Similarly, the AISTSMC shows 648 The reactive power deviation for STSMC is 0.807 k VAR 689 from zero value, whereas AISTSMC gives much lesser devi-690 ation of 0.0013 kVAR. Similarly the AISTSMC converges 691 back to the zero value after t = 0.05 s, whereas STSMC 692 convergence to zero after t = 1 s.

693
A similar analysis is also made for grid-side control. The 694 DC link response to the deterministic wind speed waveform is 695 shown in Fig. 8. A constant voltage of 760 V is selected as ref-696 erence voltage (E * ). It can be observed that SMC is showinga 697 fast convergence of 0.97 s, but it suffers from severe chatter-698 ing in the V DC . The SMC shows an overshoot 18.1 V, STSMC 699 offers a larger overshoot of 40 V, whereas the AISTSMC has 700 a lesser overshoot of 23 V with improved and much smoother 701 V DC . Similarly, at t = 5 s, where a step uncertainty is applied, 702 the SMC offers good robustness followed by AISTSMC with 703 an overshoot of 8 V. The STSMC, due to less robustness, 704 offers a high overshoot of 106 V compared to the proposed 705 AISTSMC scheme that offers an overshoot of 80 V. Thus, 706 it is validated that the STSMC exhibits inherent chattering 707 elimination feature due to its continuous nature, whereas the 708 AISTSMC enjoys both the robustness and chattering elimina-709 tion features and proves itself to be a viable option for DFIG-710 based WECS. The error waveform for the V DC is shown in 711 Fig. 8 (b) where it is clear that the AISTSMC provides less 712 error than the STSMC scheme. 713 VOLUME 10, 2022   The DFIG speed response to the stochastic wind waveform 724 is shown in Fig. 9. The zoomed-in view in Fig. 9 shows 725 that the SMC has robust performance as compared to the 726 STSMC scheme under lumped uncertainties. The total devi-727 ation for SMC is 0.02 rad s −1 , whereas the deviation for 728 STSMC is 0.03 rad s −1 , which is much higher than the SMC 729 scheme. On the other hand, the AISTSMC shows a negligible 730 deviation under lumped uncertainties. It can be seen from 731 Fig. 10 that the active power waveform for STSMC deviates 732 at a large scale as compared to the active power under the 733 normal condition at t = 5 s. The ANN-based AISTSMC 734 compensates for the STSMC problem and gives improved 735 performance when step disturbance is applied. The active 736 power deviation as compared to power under normal conditions, shown in Fig. 10 (b), is 0.01 kW for SMC, 0.018 kWfor The DFIG reactive power response to the stochastic wind  To eliminate the lack of robustness in STSMC, the signum 779 function is initially replaced by a super-twisting algorithm. 780 Then, to improve the robustness of the STSMC-based system, 781 the ANN theory is introduced which increases the robustness 782 against external disturbances and parametric uncertainties. 783 Under uncertain situations, the performance of the ANN-784 based STSMC approach is compared with the SMC and 785 STSMC benchmarks. The suggested technique outperforms 786 the SMC and STSMC in terms of lowest chattering, quick 787 dynamic response, higher accuracy, and disturbance rejec-788 tion. It is evident from the DC link voltage that the SMC 789 offers an overshoot of 8 V, STSMC offers a high overshoot 790 of 106 V, and the proposed AISTSMC scheme offers 80 V. 791 In summary, the results show that the ANN-based control 792 method established in this study is a viable and desired option 793 for DFIG-based WECS. Pakistan. He is currently an Associate Profes-1065 sor of electrical engineering with Taif Univer-1066 sity, Saudi Arabia. His research interests include 1067 renewable energy, flight control systems, integer 1068 and fractional order modeling of dynamic sys-1069 tems, integer/fractional order adaptive robust con-1070 trol methods, fuzzy/NN, hydraulic and electrical servos, epidemic, and 1071 vaccination control strategies. analysis and optimal design of next-generation electrical machines using 1090 smart materials, such as electromagnets, piezoelectric, and magnetic shape 1091 memory alloys.