fractional delay compensated discrete time smc for networked control system

Digital Communications and Networks xx (xxxx) xxxx–xxxx HOSTED BY Contents lists available at ScienceDirect Digital Communications and Networks journal homepage: www.elsevier.com/locate/dcan Fractional delay compensated discrete-time SMC for networked control system☆ ⁎ D.H Shaha, , A.J Mehtab a b Gujarat Technological University, Gujarat, India Institute of Infrastructure Technology Research and Management, Gujarat, India A R T I C L E I N F O A BS T RAC T Keywords: Discrete-time sliding mode control Networked control Network delay Time-varying network induced delay in the communication channel severely affects the performance of closed loop network control systems In this paper, a novel idea of compensating the fractional time varying communication delay in the sliding surface is presented The fractional time delay in the sensor to controller and controller to actuator channel is approximated using the Thiran approximation technique to design the sliding surface A discrete-time sliding mode control law is derived using the proposed surface that compensates fractional time delay in sensor to controller and controller to actuator channels for uncertain network control systems The sufficient condition for closed loop stability of the system is derived using the Lyapunov function The efficacy of the proposed strategy is supported by the simulation results Introduction The Networked Control System (NCS) is one of the frontier areas in the field of control, both in terms of research and application The main cause of attraction is due to its lower cost, simpler installation, easier maintenance and resource sharing features Any feedback control systems, closed through some communication medium (such as CAN, Ethernet, Profibus, Profinet, DeviceNet, etc.) are classified as Networked Control Systems (NCSs) [16] Various issues such as bandwidth sharing, resource allocation, time delay, packet loss, scheduling, etc arise due to the presence of the communication medium [17] This degrades the performance of the closed loop system and even leads to instability Recently, researchers have proposed various control algorithms addressing the time delay issue Cac, Hung and Khang [1] used a pole placement method for compensating the time delay in the continuous time domain The algorithm was designed for the CAN type deterministic networked medium Yi, Kim and Choi [2] solved the time delay problem by using the Smith predictor algorithm The method was verified over wireless sensor networks (WSN) connected between the controller output and plant input Hikichi et al [3] worked on continuous time delay compensation using predictors and disturbance observer for designing a PID controller Cuellar et al [4] proposed an observer based predictor using the Pade approximation technique for time lag processes Vallabhan et al [5] have used the analytical framework approach for compensation of random time delay and packet loss Ono et al [6] designed a state feedback controller based on a modified Smith predictor which stabilized the plant in the presence of dead time Recently, Khanesar et al [8] used the Pade approximation technique for time delay compensation in a continuous time system Hu et al [23] designed a sliding mode intermittent controller for bidirectional associative memory (BAM) using neural networks with delays Saravanakumar et al [24] proved the stability using a Markovian Jump approach for neural networks having varying time interval delays Unlike the continuous time domain, very few researchers have tried to focus their work on the discrete-time domain Jacovitti and Scarano [7] proposed various time delay estimation techniques for discretetime systems Yue, Han and Lam [15] provided the model of NCSs with networked induced delay in the discrete domain Hespanha, Naghshtabrizi and Xu [10] designed a Luenberger output feedback observer based state feedback controller to deal with time delay Niu and Ho [9] designed a sliding mode control in the discrete domain in order to deal with network non-idealities such as time delay and packet loss Recently, Li et al [11] designed a sliding mode predictive control for compensation of delay in a networked control system using a Kalman Predictor They considered networked delays in an integer form Shah and Mehta [19] have designed output feedback based discrete time sliding mode control [18] to deal with delay problems in NCSs They compensated the time varying delay using a zero-order Peer review under responsibility of Chongqing University of Posts and Telecommunication ⁎ Corresponding author E-mail address: dipeshshah.ic@gmail.com (D.H Shah) http://dx.doi.org/10.1016/j.dcan.2016.09.006 Received 18 February 2016; Received in revised form 22 September 2016; Accepted 30 September 2016 Available online xxxx 2352-8648/ © 2016 Chongqing University of Posts and Telecommuniocations Production and hosting by Elsevier B.V This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by/4.0/) Please cite this article as: Shah, D.H., Digital Communications and Networks (2016), http://dx.doi.org/10.1016/j.dcan.2016.09.006 Digital Communications and Networks xx (xxxx) xxxx–xxxx D.H Shah, A.J Mehta Assumption The disturbance are bounded in nature which is represented as: hold technique Recently, Argha et al designed a discrete time sliding mode control to handle the random delays occurring in NCSs [20] They treated delays as stochastic variables due to the random behavior Guo et al [21] considered the state estimation problem for wireless NCS The sliding mode observer was designed to solve the state estimation problem considering stochastic uncertainty and time delay Yao et al [22] designed a robust model predictive control (RMPC) and state observer for a class of time varying systems under input constraints and packet loss situations Although lot of work is done, time delay compensation in the discrete domain is still under investigation Most of the researchers [8,11,12,19], have assumed the values of network delays in terms of an integer But, in real time the delays may have non-integer type values So, as per the authors best knowledge till date none of the researchers in the discrete domain have tried to study the effect of fractional delay in NCSs The compensation of fractional delays occurring within the network is still an open research problem in NCSs in discrete domain Apart from these, the controllers were designed based on the time delay approximation technique without considering the effect of uncertainty Further, the control algorithm is implemented through digital processor and the communication is also carried out in digital signal form This motivates the authors to explore the Discrete-Time SMC algorithm which compensates the fractional delay occurring within the network even in the presence of system uncertainties and disturbances In this work, the fractional time delay is compensated at the sliding surface instead of compensating at the control law In the proposed method, the sliding gain will change according to the networked delay and force the system states to slide along the predetermined surface Based on the proposed sliding surface, the control law is derived This law provides faster convergence without increasing the amplitude of the quasi-sliding band Once the sliding surface and the control law are designed in SMC, the next step is to design the band which guarantees the stability of the designed sliding surface and causes the system states to remain within that band for a finite interval of time The paper is organized as follows: Section describes the Problem Statement The main part of the paper, design of the compensated sliding surface is presented in Section Section discusses about discrete time sliding mode control for NCS with time delay Results and discussion are enclosed in Section followed by the conclusion in Section dl ≤ d (k ) ≤ du, where dl and du denote the lower and upper bounds of the disturbances, respectively The network induced delay is the combination of the sensor to controller delay (τsc ) and controller to actuator delay (τca ) which is represented as: τ = τsc + τca, Remark In this paper it is considered that both network delays τlsc and τlca are considered as a fractional part of τsc and τca respectively Both represent the positive scalar quantities having the same properties Thus, both the delays reach their maximum values at the same interval Assumption Network induced delay varies with time and satisfies the given condition Rn (8) τl ≤ τ ≤ τu, where τl and τu indicate the lower bound and upper bound of the networked delay The objective is to design a robust DSMC algorithm which stabilizes the system (3), in the presence of a sensor controller delay τsc and controller to actuator delay τca satisfying the condition (8) and matching the uncertainty satisfying condition (6) Design of sliding surface for NCS Fig represents the schematic diagram of NCS with time delay compensator The sensor samples the data packets at regular sampling interval h The data signals in the closed loop system will experience sensor to controller delay (τsc ) and controller to actuator delay (τca ) These delayed signals must be compensated using approximation techniques to avoid the degradation of the output In this work, the Thiran approximation technique [25] is used for compensating the networked delay occurring due to the presence of the network For designing the DSMC, the sliding surface using the Thiran Approximation rule in the form of Lemma as under: (1) Lemma The sliding variable for the given system (3) with sensor to controller network delay satisfying Assumptions (1) and (2) is given as: (2) sc(k ) = 2Csx (k ) − αCsx (k − 1), Let us consider the continuous LTI system in normal form as: y(t ) = Cx (t ) + Du(t − τ ), Rm represents the system state vector, u ∈ represents the where x ∈ control input, y ∈ Rp represents the system output, A ∈ R n × n , B ∈ R n × m , Bd ∈ R n × m , C ∈ Rp × n , D ∈ Rp × m are the matrices of appropriate dimensions, d (t ) presents the matched disturbances and τ represents the total networked induced delay The discrete form of Eqs (1) and (2) is given by: x (k + 1) = Fx (k ) + Gu(k − τl ) + Gdd (k ), (3) y(k ) = Cx (k ) + Du(k − τl ), e Ah , h e AhBdh (4) Rn indicates the plant state, where F = x (k ) ∈ G=∫ u(k ) ∈ R m defines the control input, y(k ) ∈ Rp represents the plant output, d (k ) represents the matched disturbances applied at the control input, τl is the fractional part of network induced delay occurring within the network Mathematically it is represented as, τl = τ / h , (7) where τsc = τlsc*h and τca = τlca*h Problem statement x (̇ t ) = Ax (t ) + Bu(t − τ ) + Bd d (t )), (6) (5) where τ is the total network induced delay and h is the sampling interval Fig Block diagram of NCS with time delay compensation (9) Digital Communications and Networks xx (xxxx) xxxx–xxxx D.H Shah, A.J Mehta where α = + 8τl + 8τlsc sc + 6τl + 4τlsc sc u(k ) = − (2CsG )−1[Hx (k ) − Ix (k ) − Jsc(k ) − dc(k ) + d1 − 2CsGdd (k )] and Cs represent the sliding gain (19) Proof Let the sliding variable with network delay from sensor to controller τsc is given by: sc(k ) = Csx (k − τlsc ), where H = 2CsF , I = αCs , J = [1 − q(sc(k ))] (10) Proof The reaching law proposed in [13] is used to derive the control law since it provides faster convergence The reaching law is given by: where Cs indicates the sliding gain, x (k − τlsc ) indicates the delayed state vector The value of the sliding gain Cs is calculated using LQ method with proper selection of Q and R matrices Applying Z transform to Eq (10) we get: sc(z ) = Csx (z )z−τlsc , where {q[s(k )]} = (11) z−τlsc z−τlsc d (k ) represents the disturbance, d1 = value of d (k ), d2 = constant satisfying: (21) The compensated reaching law considering the network delay is given by: (12) sc[(k + 1)] = {1 − q[sc(k )]}sc(k ) − dc(k ) + d1, (13) (23) dc(k ) = 2d (k ) − αd (k − 1), ⎡ ⎛1⎞ ⎛ ⎞⎧ 2τl 2τl + ⎫ ⎬z +( − 1)1⎜ ⎟ z−τlsc = ⎢( − 1)0 ⎜ ⎟⎨ sc + sc ⎝1⎠ ⎠ ⎝ ⎩ ⎭ τ τ + l l ⎣ sc sc 2x (k + 1)Cs − αCsx (k ) = [1 − q(s(k ))]sc(k ) − dc(k ) + d1, Substituting the value of x (k + 1), (25) (14) Further simplification gives, 2CsFx (k ) + 2Cs(Gu(k ) + Gdd (k )) − αCsx (k ) = [1 − q(sc(k ))]sc(k ) − dc(k ) (15) + d1, + 8τl + 8τlsc sc + 6τl + 4τlsc sc u(k ) = − (2CsG )−1[Hx (k ) − Ix (k ) − Jsc(k ) − dc(k ) + d1 − 2CsGdd (k )] (16) (27) further solving, sc(z ) = 2x (z )Cs − αz−1x (z )Cs where H = 2CsF , I = αCs , J = [1 − q(sc(k ))] This completes the proof.□ The next step is to prove the stability such that any trajectory of the system (3) will be driven onto the sliding surface and maintained on it within a finite interval of time So, using the sliding surface (18) and control law (27), a stability condition is derived such that the system states shall remain within the band in the presence of varying network time delay Stability: The trajectory of the closed loop system can be driven using the sliding surface in finite time with the controller designed in (27) under varying networked time delay (8) and matched uncertainty (6) such that for any κ ≥ d2 and γ≻0 the following condition should hold true: (17) Applying the inverse Z transform we have, sc(k ) = 2Csx (k ) − αCsx (k − 1) (26) Eq (26) further can be expressed in terms of control law as: Substituting Eq (15) in Eq (11) we get, sc(z ) = [2 − αz−1]x (z )Cs, (24) 2Cs[Fx (k ) + Gu(k ) + Gdd (k )] − αCsx (k ) = [1 − q(sc(k ))]sc(k ) − dc(k ) + d1, Further solving we get, where α = (22) where sc(k ) represents the compensated sliding surface and dc(k ) represents the compensated disturbance which is given as: Using Eq (18), Eq (22) can be rewritten as: z−τlsc = − αz−1, mean deviated value of d (k ) and κ is the designer's The above equation can be further expanded as: ⎧ 2τlsc 2τl + ⎫ −1⎤ ⎨ ⎬z ⎥ , + sc ⎩ 2τlsc + 2τlsc + ⎭ ⎦ du + dl , κ ≥ d2, where n indicates the order of approximation Considering n = and taking the first order approximation we have, ⎛ n ⎞ 2τlsc + i −k = Σk1=0( − 1)k ⎜ ⎟ Π z ⎝ k ⎠i =0 2τlsc + k + i κ , κ + | s(k )| du − dl , where τlsc = τsc / h Using the Thiran approximation, the discrete time delay is represented as: ⎛n⎞ n 2τlsc + i −k = Σkn=0( − 1)k ⎜ ⎟∏ z , ⎝ k ⎠ i =0 2τlsc + k + i (20) s[(k + 1)] = {1 − q[s(k )]}s(k ) − d (k ) + d1, (18) This completes the proof.□ According to Eq (18), the compensated sliding variable sc(k ) depends on the difference of the present and past state variables The past state variable is multiplied with the parameter ‘α ’ approximated through the Thiran approximation rule So, the delay in the sliding surface at each sampling instant k is compensated by past state variables multiplied over the parameter ‘α ’ which is approximated equal to the networked delay Now, we are ready to propose the control law using the sliding surface (9) 0⪯M ≺scT (k )sc(k ) (28) Proof Let the sliding surface be given by: Design of the discrete time networked sliding mode control under time delay compensation sc(k + 1) = 2Csx (k + 1) − αCsx (k ), In this section, the derivation of the discrete time sliding mode control law along with its stability using the compensated sliding surface (18) is represented in the form of Theorem (29) Let the Lyapunov function be given by: Vs(k ) = scT (k )sc(k ), Theorem The discrete-time sliding surface (9) is reached within a finite time in the presence of varying time delays (8) and matched uncertainty (6) provided the control law is designed as: (30) Taking the forward difference of the above equation ΔVs(k ) = scT (k + 1)sc(k + 1) − scT (k )sc(k ), (31) Digital Communications and Networks xx (xxxx) xxxx–xxxx D.H Shah, A.J Mehta Substituting the value of sc(k + 1) from Eq (18) we get, ΔVs(k ) = [2Csx (k + 1) − αCsx (k )]T [2Csx (k + 1) − αCsx (k )] − scT (k )sc(k ), (32) Substituting the value of x (k + 1) we get, ΔVs(k ) = [2Cs[Fx (k ) + Gu(k ) + Gdd (k )] − αCsx (k )]T [2Cs[Fx (k ) + Gu(k ) + Gdd (k )] − αCsx (k )] − scT (k )sc(k ), (33) Substituting the value of u(k ) and further solving it we have, ΔVs(k ) = [[1 − q(sc(k ))]sc(k ) − dc(k ) + d1]T *[[1 − q(sc(k ))]sc(k ) − dc(k ) + d1] − scT (k )sc(k ), (34) Fig Time varying disturbance d(k) versus time We see that the term [[1 − q(sc(k ))]sc(k ) − dc(k ) + d1] contains the disturbance term in ΔVs(k ) Let M = [[1 − q(sc(k ))]sc(k ) − dc(k ) + d1]T *[[1 − q(sc(k ))]sc(k ) − dc(k ) + d1] Then we have, ΔVs(k ) = M − scT (k )sc(k ) (35) The term M is tuned to zero by appropriately selecting the parameter κ If M is closed to zero, then scT (k )sc(k ) will be larger than M Thus, for any constant parameterγ , we have M − scT (k )sc(k )≺ − γscT (k )sc(k ) Therefore, by tuning the parameterκ , we have, ΔVs(k )≺ − γscT (k )sc(k ) which guarantees the convergence of ΔVs(k ) This completes the proof.□ The control signal u(k ), will also experience controller to actuator delay (τca ) which results in the delayed control signal u(k − τlca ) To avoid the degradation of the plant response, the time delay compensation is done from the controller to actuator Using the same approach of the Thiran approximation as discussed in the earlier section the compensated control signal is represented as: Fig Total networked delay τ versus time (36) ua(k ) = 2u(k ) − βu(k − 1), where β= + 8τl + 8τlca ca + 6τl + 4τlca ca and τlca = τca / h It is noted from Eq (36) that the control signal ua(k ) depends on the difference of the present and past control signals The past control signal is multiplied over the parameter ‘ β ’ approximated through the Thiran approximation This compensated control signal is further applied to the plant Results and discussion To prove the efficiency of the proposed method an example from [14] is simulated in the MATLAB environment Consider the continuous LTI system as, ⎡ ⎤ A = ⎢−0.7 ⎥ , ⎣ −1.5⎦ ⎡ ⎤ B = ⎢−0.03⎥ , C = [1 ], ⎣ −1 ⎦ Fig x1 versus time with initial condition x1=1 D = [ ] Discretizing the above system parameters at the sampling interval of h = 30 ms : ⎡ ⎤ F = ⎢ 0.9792 0.05805⎥ , 0.956 ⎦ ⎣ ⎡ ⎤ G = ⎢−0.001771⎥ , C = [1 ], ⎣ −0.02934 ⎦ D = [ ] Figs 2–11 show the nature of the system under a networked environment In order to check the robustness of the derived control law, a slow time varying disturbance is applied to the system shown in Fig Fig presents the time varying network induced delay with a range of ms ≤ τ ≤ 35 ms under which the system shows a stable response satisfying (8) In this work, the networked delay is considered as the time required for the data packets to travel from sensor to controller and controller to actuator The amount of time required for data packets to travel from sensor to controller is 1.5 ms ≤ τsc ≤ 17.5 ms and for controller to actuator is 1.5 ms ≤ τca ≤ 17.5 ms respectively Fig x2 versus time with initial condition x1=1 Digital Communications and Networks xx (xxxx) xxxx–xxxx D.H Shah, A.J Mehta Fig 10 Response of SNR Fig sc(k) versus sampling instants k Fig 11 Nature of state variables for different SNR Figs and show the plant variables with the initial condition x(k ) = [11] Both the states converge to zero from the given initial condition in the presence of network delay The sliding gain Cs is calculated using the discrete LQ optimal method with Q = diag(1000, 1000) and R = The computed values of the optimal sliding gain are Cs = [ − 1.77 − 2.766] Fig shows the compensated sliding surface calculated using the Thiran approximation rule We observe that the compensated sliding variable is computed from the first sampling instant in the presence of the sensor to controller fractional delay Fig shows the control signal u(k ) which is computed using the proposed compensated sliding surface sc(k ) This control signal is further applied to the plant through the network The same approach of time delay compensation is used to compute the compensated control signal ua(k ) These results are shown in Fig Fig shows the results of stability It is observed from Fig that for the given κ = 10 and d2 = 0.2 that guarantees the convergence of ΔVs(k ) and implies that the trajectories of system (3) will be driven on the sliding surface and maintained on it under the specified network delay and matched uncertainty The algorithm is also examined for different SNRs as shown in Fig 10 It is observed from Fig 11 that the system states converge to zero for different SNRs Thus, from the above results it is justified that the Thiran approximation provides better compensation within the specified band The control law derived using Thiran approximation is more robust than [8,11,12,19] because it generates less chattering even in the presence of network delay and matched uncertainty Fig u(k) versus time Fig ua(k) versus time Conclusion In this paper, a new concept for compensating the network delay having fractional behavior in sliding surface was introduced The Thiran approximation technique is used to compensate the networked delay The sliding surface is designed in such a manner that it slides on the predetermined surface according to the network delay Using this novel approach, control law for discrete-time networked sliding mode is designed to compute the control sequences in the presence of a variable time delay and matched uncertainty Stability is checked using Fig Result of stability Digital Communications and Networks xx (xxxx) xxxx–xxxx D.H Shah, A.J Mehta Trans Ind Electron 57 (7) (2010) [18] A Mehta, B Bandyopadhyay, Frequency-Shaped and Observer-Based DiscreteTime Sliding Mode Control, Springer, 2015 [19] D Shah, A Mehta, Output feedback discrete-time networked sliding mode control, in: IEEE Proceedings of Recent Advances in Sliding Modes, 2015, pp 1–7 http:// dx.doi.org/10.1109/RASM.2015.7154635 [20] A Argha, L Li, W Su, H Nguyen, Discrete-time sliding mode control for networked systems with random communication delays, in: IEEE Proceedings of American Control Conference, 2015, 6016–6021 [21] P Guo, J Zhang, H Karimi, Y Liu, M Lyu, Y Bo, State estimation for wireless network control system with stochastic uncertainty and time delay based on sliding mode observer, Abstr Appl Anal (2014) (2014) 1–8 [22] D Yao, H Karimi, Y Sun, Q Lu, Robust model predictive control of networked control systems under input constraints and packet dropouts, Abstr Appl Anal (2014) (2014) 1–11 [23] J Hu, J Liang, H Karimi, J Cao, Sliding intermittent control for bam neural networks with delays, Abstr Appl Anal (2013) (2013) 1–15 [24] R Saravanakumar, M Syed Ali, C Ahn, H Karimi, P Shi, Stability of Markovian jump generalized neural networks with interval time-varying delays, IEEE Trans Neural Netw Learn Syst 99 (2016) 1–11 [25] J Thiran, Recursive digital filters with maximally flat group delay, IEEE Trans Circuit Theory 18 (6) (1971) 659–663 the Lyapunov function such that the system states would remain within that band in finite interval of time even in the presence of network delay and matched uncertainty The simulation results show that the Thiran approximation enhanced the response under network nonidealities The proposed algorithm is valid for deterministic or time varying network delays It can be valid for those applications whose bandwidths are fixed and network delays are deterministic in nature In the future, the work can be extended for single as well as multiple packets drop out conditions The same approach can be extended for wireless NCS having random types of communication delays as well as with random dropout conditions References [1] N Cac, N Hung, N Khang, CAN-based networked control systems: a compensation for communication time delays, Am J Embed Syst Appl (3) (2014) 13–20 [2] H Yi, H Kim, J Choi, Design of networked control system with discrete-time state predictor over WSN, J Adv Comput Netw (2) (2014) 106–109 [3] Y Hikichi, K Sasaki, R Tanaka, H Shibasaki, K Kawaguchi, Y Ishida, A discrete PID control system using predictors and an observer for the influence of a time delay, Int J Model Optim (1) (2013) 1–4 [4] B Cuellar, M Villa, G Anaya, O Ramirez, J Ramirez, Observer-based prediction scheme for time-lag processes, in: Proceedings of American Control Conference, 2007, pp 639–644 [5] M Vallabhan, S Srinivasan, S Ashok, S Ramaswamy, R Ayyagari, An analytical framework for analysis and design of networked control systems with random delays and packet losses, in: Proceedings of IEEE Canadian Conference on Electrical and Computer Engineering, 2012 [6] M Ono, N Ban, K Sasaki, K Matsumoto, Y Ishida, Discrete modified Smith predictor for an unstable plant with dead time using a plant predictor, Int J Comput Sci Netw Secur 10 (9) (2010) 80–85 [7] G Jacovitti, G Scarano, Discrete time techniques for time delay estimation, IEEE Trans Signal Process 41 (2) (1993) 525–533 [8] M Khanesar, O Kaynak, S Yin, H Gao, Adaptive indirect fuzzy sliding mode controller for networked control 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robust Hinf control of systems with uncertainty, Automatica 41 (1) (2005) 999–1007 [16] D Shah, A Mehta, Design of robust controller for networked control system, in: Proceedings of the IEEE International Conference on Computer, Communication and Control Technology, 2014, pp 385-390 http://dx.doi.org/10.1109/I4CT 2014.6914211 [17] R Gupta, M Chow, Networked control system: overview and research trends, IEEE Dipesh Shah born in India and obtained B.E Instrumentation and Control (2007) and M.E Applied Instrumentation (2010) from Gujarat University Ahmedabad Currently, he is working as an Assistant Professor at Sardar Vallabhbhai Patel Institute of Technology, Vasad, Gujarat, India He is pursuing Ph.D from Gujarat Technological University, Ahmedabad, Gujarat, India His research interest is robust controllers, sliding mode control, networked control system and communication networks Axay Mehta obtained B.E Electrical (1996), M.Tech (2002) and Ph.D (2009) degree from Gujarat University Ahmedabad, IIT Kharagpur and IIT Mumbai, respectively He has worked as various faculty positions at various Institutions including Associate Faculty at Indian Institute Technology, Gandhinagar He also acted as Professor; Director at Gujarat Power Engineering and Research Institute, Mehsana, Gujarat, India, during 2012–2014 Currently, he is an Associate Professor at the Institute of Infrastructure Technology Research and Management, Ahmedabad, Gujarat His research interest is non-linear sliding mode control and observer, sliding mode control application in electrical engineering and networked control system He has published 35 research papers in peer reviewed international journals and conferences of repute He is Senior Member IEEE, Life Member of Institution of Engineers (India), Life Member of Indian Society for Technical Education and Member of Systems Society of India He is conferred the Best research paper award at NSC 2002 by Systems Society of India and Pedagogical Innovation award 2014 by GTU ... [20] A Argha, L Li, W Su, H Nguyen, Discrete- time sliding mode control for networked systems with random communication delays, in: IEEE Proceedings of American Control Conference, 2015, 6016–6021... systems: a compensation for communication time delays, Am J Embed Syst Appl (3) (2014) 13–20 [2] H Yi, H Kim, J Choi, Design of networked control system with discrete- time state predictor over... techniques for time delay estimation, IEEE Trans Signal Process 41 (2) (1993) 525–533 [8] M Khanesar, O Kaynak, S Yin, H Gao, Adaptive indirect fuzzy sliding mode controller for networked control systems