Saptarshi Das

Saptarshi Das, Suman Saha, Shantanu Das et al.

In this paper, a comparative study is done on the time and frequency domain tuning strategies for fractional order (FO) PID controllers to handle higher order processes. A new fractional order template for reduced parameter modeling of stable minimum/non-minimum phase higher order processes is introduced and its advantage in frequency domain tuning of FOPID controllers is also presented. The time domain optimal tuning of FOPID controllers have also been carried out to handle these higher order processes by performing optimization with various integral performance indices. The paper highlights on the practical control system implementation issues like flexibility of online autotuning, reduced control signal and actuator size, capability of measurement noise filtration, load disturbance suppression, robustness against parameter uncertainties etc. in light of the above tuning methodologies.

Saptarshi Das, Indranil Pan, Shantanu Das et al.

A novel fractional order (FO) fuzzy Proportional-Integral-Derivative (PID) controller has been proposed in this paper which works on the closed loop error and its fractional derivative as the input and has a fractional integrator in its output. The fractional order differ-integrations in the proposed fuzzy logic controller (FLC) are kept as design variables along with the input-output scaling factors (SF) and are optimized with Genetic Algorithm (GA) while minimizing several integral error indices along with the control signal as the objective function. Simulations studies are carried out to control a delayed nonlinear process and an open loop unstable process with time delay. The closed loop performances and controller efforts in each case are compared with conventional PID, fuzzy PID and PIλDμ controller subjected to different integral performance indices. Simulation results show that the proposed fractional order fuzzy PID controller outperforms the others in most cases.

Anish Acharya, Saptarshi Das, Indranil Pan et al.

This paper proposes the design of Fractional Order (FO) Butterworth filter in complex w-plane (w=sq; q being any real number) considering the presence of under-damped, hyper-damped, ultra-damped poles. This is the first attempt to design such fractional Butterworth filters in complex w-plane instead of complex s-plane, as conventionally done for integer order filters. Firstly, the concept of fractional derivatives and w-plane stability of linear fractional order systems are discussed. Detailed mathematical formulation for the design of fractional Butterworth-like filter (FBWF) in w-plane is then presented. Simulation examples are given along with a practical example to design the FO Butterworth filter with given specifications in frequency domain to show the practicability of the proposed formulation.

Suman Saha, Saptarshi Das, Ratna Ghosh et al.

Phase shaping using fractional order (FO) phase shapers has been proposed by many contemporary researchers as a means of producing systems with iso-damped closed loop response due to a stepped variation in input. Such systems, with the closed loop damping remaining invariant to gain changes can be used to produce dead-beat step response with only rise time varying with gain. This technique is used to achieve an active step-back in a Pressurized Heavy Water Reactor (PHWR) where it is desired to change the reactor power to a pre-determined value within a short interval keeping the power undershoot as low as possible. This paper puts forward an approach as an alternative for the present day practice of a passive step-back mechanism where the control rods are allowed to drop during a step-back action by gravity, with release of electromagnetic clutches. The reactor under a step-back condition is identified as a system using practical test data and a suitable Proportional plus Integral plus Derivative (PID) controller is designed for it. Then the combined plant is augmented with a phase shaper to achieve a dead-beat response in terms of power drop. The fact that the identified static gain of the system depends on the initial power level at which a step-back is initiated, makes this application particularly suited for using a FO phase shaper. In this paper, a model of a nuclear reactor is developed for a control rod drop scenario involving rapid power reduction in a 500MWe Canadian Deuterium Uranium (CANDU) reactor using AutoRegressive Exogenous (ARX) algorithm. The system identification and reduced order modeling are developed from practical test data. For closed loop active control of the identified reactor model, the fractional order phase shaper along with a PID controller is shown to perform better than the present Reactor Regulating System (RRS) due to its iso-damped nature.

Indranil Pan, Saptarshi Das, Amitava Gupta

The issues of stochastically varying network delays and packet dropouts in Networked Control System (NCS) applications have been simultaneously addressed by time domain optimal tuning of fractional order (FO) PID controllers. Different variants of evolutionary algorithms are used for the tuning process and their performances are compared. Also the effectiveness of the fractional order PIλDμ controllers over their integer order counterparts is looked into. Two standard test bench plants with time delay and unstable poles which are encountered in process control applications are tuned with the proposed method to establish the validity of the tuning methodology. The proposed tuning methodology is independent of the specific choice of plant and is also applicable for less complicated systems. Thus it is useful in a wide variety of scenarios. The paper also shows the superiority of FOPID controllers over their conventional PID counterparts for NCS applications.

Saptarshi Das, Barry Juans Ajiwibawa, Shre Kumar Chatterjee et al.

Plant electrical signals often contains low frequency drifts with or without the application of external stimuli. Quantification of the randomness in plant signals in a stimulus-specific way is hindered because the knowledge of vital frequency information in the actual biological response is not known yet. Here we design an optimum Infinite Impulse Response (IIR) filter which removes the low frequency drifts and preserves the frequency spectrum corresponding to the random component of the unstimulated plant signals by bringing the bias due to unknown artifacts and drifts to a minimum. We use energy criteria of wavelet packet transform (WPT) for optimization based tuning of the IIR filter parameters. Such an optimum filter enforces that the energy distribution of the pre-stimulus parts in different experiments are almost overlapped but under different stimuli the distributions of the energy get changed. The reported research may popularize plant signal processing, as a separate field, besides other conventional bioelectrical signal processing paradigms.

Saptarshi Das, Basudev Majumder, Anindya Pakhira et al.

Rational approximation of fractional order (FO) differ-integrators via Continued Fraction Expansion (CFE) is a well known technique. In this paper, the nominal structures of various generating functions are optimized using Genetic Algorithm (GA) to minimize the deviation in magnitude and phase response between the original FO element and the rationalized discrete time filter in Infinite Impulse Response (IIR) structure. The optimized filter based realizations show better approximation of the FO elements in comparison with the existing methods and is demonstrated by the frequency response of the IIR filters.

Saptarshi Das, Anish Acharya, Indranil Pan

Multi-wing chaotic attractors are highly complex nonlinear dynamical systems with higher number of index-2 equilibrium points. Due to the presence of several equilibrium points, randomness and hence the complexity of the state time series for these multi-wing chaotic systems is much higher than that of the conventional double-wing chaotic attractors. A real-coded Genetic Algorithm (GA) based global optimization framework has been adopted in this paper as a common template for designing optimum Proportional-Integral-Derivative (PID) controllers in order to control the state trajectories of four different multi-wing chaotic systems among the Lorenz family viz. Lu system, Chen system, Rucklidge (or Shimizu Morioka) system and Sprott-1 system. Robustness of the control scheme for different initial conditions of the multi-wing chaotic systems has also been shown.

Saptarshi Das, Indranil Pan, Shantanu Das

An optimal trade-off design for fractional order (FO)-PID controller is proposed in this paper with a Linear Quadratic Regulator (LQR) based technique using two conflicting time domain control objectives. The deviation of the state trajectories and control signal are automatically enforced by the LQR. A class of delayed FO systems with single non-integer order element has been controlled here which exhibit both sluggish and oscillatory open loop responses. The FO time delay processes are controlled within a multi-objective optimization (MOO) formulation of LQR based FOPID design. The time delays in the FO models are handled by two analytical formulations of designing optimal quadratic regulator for delayed systems. A comparison is made between the two approaches of LQR design for the stabilization of time-delay systems in the context of FOPID controller tuning. The MOO control design methodology yields the Pareto optimal trade-off solutions between the tracking performance for unit set-point change and total variation (TV) of the control signal. Numerical simulations are provided to compare the merits of the two delay handling techniques in the multi-objective LQR-FOPID design, while also showing the capability of load disturbance suppression using these optimal controllers. Tuning rules are then formed for the optimal LQR-FOPID controller knobs, using the median of the non-dominated Pareto solution to handle delays FO processes.

Saptarshi Das, Shantanu Das, Amitava Gupta

Bulk reduction of reactor power within a small finite time interval under abnormal conditions is referred to as step-back. In this paper, a 500MWe Canadian Deuterium Uranium (CANDU) type Pressurized Heavy Water Reactor (PHWR) is modeled using few variants of Least Square Estimator (LSE) from practical test data under a control rod drop scenario in order to design a control system to achieve a dead-beat response during a stepped reduction of its global power. A new fractional order (FO) model reduction technique is attempted which increases the parametric robustness of the control loop due to lesser modeling error and ensures iso-damped closed loop response with a PIλDμ or FOPID controller. Such a controller can, therefore, be used to achieve active step-back under varying load conditions for which the system dynamics change significantly. For closed loop active control of the reduced FO reactor models, the PIλDμ controller is shown to perform better than the classical integer order PID controllers and present operating Reactor Regulating System (RRS) due to its robustness against shift in system parameters.

Indranil Pan, Saptarshi Das, Avijit Routh

In this paper, synchronization of identical switched chaotic systems is explored based on Lyapunov theory of guaranteed stability. Concepts from robust control principles and switched linear systems are merged together to derive a sufficient condition for synchronization of identical master-slave switched nonlinear chaotic systems and are expressed in the form of bilinear matrix inequalities (BMIs). The nonlinear controller design problem is then recast in the form of linear matrix inequalities (LMIs) to facilitate numerical computation by standard LMI solvers and is illustrated by appropriate examples.

Anindya Pakhira, Saptarshi Das, Anish Acharya et al.

Fractional order (FO) filters have been investigated in this paper, with band-pass (BP) and band-stop (BS) characteristics, which can not be achieved with conventional integer order filters with orders lesser then two. The quality factors for symmetric and asymmetric magnitude response have been optimized using real coded Genetic Algorithm (GA) for a user specified center frequency. Parametric influence of the FO filters on the magnitude response is also illustrated with credible numerical simulations.

Saptarshi Das, Kaushik Halder

This paper proposes a new strategy for missile attitude control using a hybridization of Linear Quadratic Gaussian (LQG), Loop Transfer Recovery (LTR), and Linear Quadratic Integral (LQI) control techniques. The LQG control design is carried out in two steps i.e. firstly applying Kalman filter for state estimation in noisy environment and then using the estimated states for an optimal state feedback control via Linear Quadratic Regulator (LQR). As further steps of performance improvement of the missile attitude control system, the LTR and LQI schemes are applied to increase the stability margins and guarantee set-point tracking performance respectively, while also preserving the optimality of the LQG. The weighting matrix (Q) and weighting factor (R) of LQG and the LTR fictitious noise coefficient (q) are tuned using Nelder-Mead Simplex optimization technique to make the closed-loop system act faster. Simulations are given to illustrate the validity of the proposed technique.

Sayan Saha, Saptarshi Das, Anish Acharya et al.

The paper investigates nonlinear system identification using system output data at various linearized operating points. A feed-forward multi-layer Artificial Neural Network (ANN) based approach is used for this purpose and tested for two target applications i.e. nuclear reactor power level monitoring and an AC servo position control system. Various configurations of ANN using different activation functions, number of hidden layers and neurons in each layer are trained and tested to find out the best configuration. The training is carried out multiple times to check for consistency and the mean and standard deviation of the root mean square errors (RMSE) are reported for each configuration.

Anindya Pakhira, Saptarshi Das, Indranil Pan et al.

This paper uses the Continued Fraction Expansion (CFE) method for analog realization of fractional order differ-integrator and few special classes of fractional order (FO) controllers viz. Fractional Order Proportional-Integral-Derivative (FOPID) controller, FO[PD] controller and FO lead-lag compensator. Contemporary researchers have given several formulations for rational approximation of fractional order elements. However, approximation of the controllers studied in this paper, due to having fractional power of a rational transfer function, is not available in analog domain; although its digital realization already exists. This motivates us for applying CFE based analog realization technique for complicated FO controller structures to get equivalent rational transfer functions in terms of the controller tuning parameters. The symbolic expressions for rationalized transfer function in terms of the controller tuning parameters are especially important as ready references, without the need of running CFE algorithm every time and also helps in the synthesis of analog circuits for such FO controllers.

Saptarshi Das, Sourav Das, Koushik Maharatna

In this paper, an efficient control strategy for physiological interaction based anaesthetic drug infusion model is explored using the fractional order (FO) proportional integral derivative (PID) controllers. The dynamic model is composed of several human organs by considering the brain response to the anaesthetic drug as output and the drug infusion rate as the control input. Particle Swarm Optimisation (PSO) is employed to obtain the optimal set of parameters for PID/FOPID controller structures. With the proposed FOPID control scheme much less amount of drug-infusion system can be designed to attain a specific anaesthetic target and also shows high robustness for +/-50% parametric uncertainty in the patient's brain model.

Saptarshi Das, Sayan Saha, Ayan Mukherjee et al.

Gain and order scheduling of fractional order (FO) PIλDμ controllers are studied in this paper considering four different classes of higher order processes. The mapping between the optimum PID/FOPID controller parameters and the reduced order process models are done using Radial Basis Function (RBF) type Artificial Neural Network (ANN). Simulation studies have been done to show the effectiveness of the RBFNN for online scheduling of such controllers with random change in set-point and process parameters.

Saptarshi Das, Indranil Pan, Shantanu Das et al.

Genetic Algorithm (GA) has been used in this paper for a new Nyquist based sub-optimal model reduction and optimal time domain tuning of PID and fractional order (FO) PIλDμ controllers. Comparative studies show that the new model reduction technique outperforms the conventional H2-norm based reduced order modeling techniques. Optimum tuning rule has been developed next with a test-bench of higher order processes via Genetic Programming (GP) with minimum value of weighted integral error index and control signal. From the Pareto optimal front which is a trade-off between the complexity of the formulae and control performance, an efficient set of tuning rules has been generated for time domain optimal PID and PIλDμ controllers.

Basudev Majumder, Saptarshi Das, Indranil Pan et al.

This paper analyzes a nuclear reactor power signal that suffers from network induced random delays in the shared data network while being fed-back to the Reactor Regulating System (RRS). A detailed study is carried out to investigate the self similarity of random delay dynamics due to the network traffic in shared medium. The fractionality or selfsimilarity in the network induced delay that corrupts the measured power signal coming from Self Powered Neutron Detectors (SPND) is estimated and analyzed. As any fractional order randomness is intrinsically different from conventional Gaussian kind of randomness, these delay dynamics need to be handled efficiently, before reaching the controller within the RRS. An attempt has been made to minimize the effect of the randomness in the reactor power transient data with few classes of smoothing filters. The performance measure of the smoothers with fractional order noise consideration is also investigated into.

Suman Saha, Saptarshi Das, Ratna Ghosh et al.

Phase curve of an open loop system is flat in nature if the derivative of phase with respect to frequency is zero. With a flat phase curve, the corresponding closed-loop system exhibits an iso-damped property i.e. maintains constant overshoot with the change of gain and with other parametric variations. In recent past application, fractional order (FO) phase shapers have been proposed by contemporary researchers to achieve enhanced parametric robustness. In this paper, a simple Routh tabulation based methodology is proposed to design an appropriate FO phase shaper to achieve phase flattening in a control loop, comprising a system, controlled by a classical PID controller. The method is demonstrated using MATLAB simulation of a second order DC motor plant and also a first order with time delay system.

Avijit Routh, Sourav Das, Saptarshi Das et al.

Stabilizing state feedback controller has been designed in this paper for a switched DC motor plant, controlled over communication network. The switched system formulation for the networked control system (NCS) with additional switching in a plant parameter along with the switching due to random packet losses, have been formulated as few set of non-strict Linear Matrix Inequalities (LMIs). In order to solve non-strict LMIs using standard LMI solver and to design the stabilizing state feedback controller, the Cone Complementary Linearization (CCL) technique has been adopted. Simulation studies have been carried out for a DC motor plant, operating at two different sampling times with random switching in the moment of inertia, representing sudden jerks.

Ayan Mukherjee, Anindya Pakhira, Saptarshi Das et al.

The paper presents a Stateflow based network test-bed to validate real-time optimal control algorithms. Genetic Algorithm (GA) based time domain performance index minimization is attempted for tuning of PI controller to handle a balanced lag and delay type First Order Plus Time Delay (FOPTD) process over network. The tuning performance is validated on a real-time communication network with artificially simulated stochastic delay, packet loss and out-of order packets characterizing the network.

Asmita S. Thool, Sourodeep Roy, Prahalad Kanti Barman et al.

In this study, we design a reservoir computing (RC) network by exploiting short- and long-term memory dynamics in Au/Ti/MoS$_2$/Au memristive devices. The temporal dynamics is engineered by controlling the thickness of the Chemical Vapor Deposited (CVD) MoS$_2$ films. Devices with a monolayer (1L)-MoS$_2$ film exhibit volatile (short-term memory) switching dynamics. We also report non-volatile resistance switching with excellent uniformity and analog behavior in conductance tuning for the multilayer (ML) MoS$_2$ memristive devices. We correlate this performance with trap-assisted space-charge limited conduction (SCLC) mechanism, leading to a bulk-limited resistance switching behavior. Four-bit reservoir states are generated using volatile memristors. The readout layer is implemented with an array of nonvolatile synapses. This small RC network achieves 89.56\% precision in a spoken-digit recognition task and is also used to analyze a nonlinear time series equation.

Varun Gumma, Barsha Mitra, Soumyadeep Dey et al.

In recent years, Attribute-Based Access Control (ABAC) has become quite popular and effective for enforcing access control in dynamic and collaborative environments. Implementation of ABAC requires the creation of a set of attribute-based rules which cumulatively form a policy. Designing an ABAC policy ab initio demands a substantial amount of effort from the system administrator. Moreover, organizational changes may necessitate the inclusion of new rules in an already deployed policy. In such a case, re-mining the entire ABAC policy will require a considerable amount of time and administrative effort. Instead, it is better to incrementally augment the policy. Keeping these aspects of reducing administrative overhead in mind, in this paper, we propose PAMMELA, a Policy Administration Methodology using Machine Learning to help system administrators in creating new ABAC policies as well as augmenting existing ones. PAMMELA can generate a new policy for an organization by learning the rules of a policy currently enforced in a similar organization. For policy augmentation, PAMMELA can infer new rules based on the knowledge gathered from the existing rules. Experimental results show that our proposed approach provides a reasonably good performance in terms of the various machine learning evaluation metrics as well as execution time.

Daya Shankar Pandey, Saptarshi Das, Indranil Pan et al.

In this paper, multi-layer feed forward neural networks are used to predict the lower heating value of gas (LHV), lower heating value of gasification products including tars and entrained char (LHVp) and syngas yield during gasification of municipal solid waste (MSW) during gasification in a fluidized bed reactor. These artificial neural networks (ANNs) with different architectures are trained using the Levenberg-Marquardt (LM) back-propagation algorithm and a cross validation is also performed to ensure that the results generalise to other unseen datasets. A rigorous study is carried out on optimally choosing the number of hidden layers, number of neurons in the hidden layer and activation function in a network using multiple Monte Carlo runs. Nine input and three output parameters are used to train and test various neural network architectures in both multiple output and single output prediction paradigms using the available experimental datasets. The model selection procedure is carried out to ascertain the best network architecture in terms of predictive accuracy. The simulation results show that the ANN based methodology is a viable alternative which can be used to predict the performance of a fluidized bed gasifier.

Saptarshi Das, Kaushik Halder, Amitava Gupta

This paper derives new formulations for designing dominant pole placement based proportional-integral-derivative (PID) controllers to handle second order processes with time delays (SOPTD). Previously, similar attempts have been made for pole placement in delay-free systems. The presence of the time delay term manifests itself as a higher order system with variable number of interlaced poles and zeros upon Pade approximation, which makes it difficult to achieve precise pole placement control. We here report the analytical expressions to constrain the closed loop dominant and non-dominant poles at the desired locations in the complex s-plane, using a third order Pade approximation for the delay term. However, invariance of the closed loop performance with different time delay approximation has also been verified using increasing order of Pade, representing a closed to reality higher order delay dynamics. The choice of the nature of non-dominant poles e.g. all being complex, real or a combination of them modifies the characteristic equation and influences the achievable stability regions. The effect of different types of non-dominant poles and the corresponding stability regions are obtained for nine test-bench processes indicating different levels of open-loop damping and lag to delay ratio. Next, we investigate which expression yields a wider stability region in the design parameter space by using Monte Carlo simulations while uniformly sampling a chosen design parameter space. Various time and frequency domain control performance parameters are investigated next, as well as their deviations with uncertain process parameters, using thousands of Monte Carlo simulations, around the robust stable solution for each of the nine test-bench processes.

Indranil Pan, Saptarshi Das

In a recent paper, we presented an intelligent evolutionary search technique through genetic programming (GP) for finding new analytical expressions of nonlinear dynamical systems, similar to the classical Lorenz attractor's which also exhibit chaotic behaviour in the phase space. In this paper, we extend our previous finding to explore yet another gallery of new chaotic attractors which are derived from the original Lorenz system of equations. Compared to the previous exploration with sinusoidal type transcendental nonlinearity, here we focus on only cross-product and higher-power type nonlinearities in the three state equations. We here report over 150 different structures of chaotic attractors along with their one set of parameter values, phase space dynamics and the Largest Lyapunov Exponents (LLE). The expressions of these new Lorenz-like nonlinear dynamical systems have been automatically evolved through multi-gene genetic programming (MGGP). In the past two decades, there have been many claims of designing new chaotic attractors as an incremental extension of the Lorenz family. We provide here a large family of chaotic systems whose structure closely resemble the original Lorenz system but with drastically different phase space dynamics. This advances the state of the art knowledge of discovering new chaotic systems which can find application in many real-world problems. This work may also find its archival value in future in the domain of new chaotic system discovery.

Shre Kumar Chatterjee, Saptarshi Das, Koushik Maharatna et al.

Plants monitor their surrounding environment and control their physiological functions by producing an electrical response. We recorded electrical signals from different plants by exposing them to Sodium Chloride (NaCl), Ozone (O3) and Sulfuric Acid (H2SO4) under laboratory conditions. After applying pre-processing techniques such as filtering and drift removal, we extracted few statistical features from the acquired plant electrical signals. Using these features, combined with different classification algorithms, we used a decision tree based multi-class classification strategy to identify the three different external chemical stimuli. We here present our exploration to obtain the optimum set of ranked feature and classifier combination that can separate a particular chemical stimulus from the incoming stream of plant electrical signals. The paper also reports an exhaustive comparison of similar feature based classification using the filtered and the raw plant signals, containing the high frequency stochastic part and also the low frequency trends present in it, as two different cases for feature extraction. The work, presented in this paper opens up new possibilities for using plant electrical signals to monitor and detect other environmental stimuli apart from NaCl, O3 and H2SO4 in future.

Indranil Pan, Saptarshi Das, Shantanu Das

In this paper, an active control policy design for a fractional order (FO) financial system is attempted, considering multiple conflicting objectives. An active control template as a nonlinear state feedback mechanism is developed and the controller gains are chosen within a multi-objective optimization (MOO) framework to satisfy the conditions of asymptotic stability, derived analytically. The MOO gives a set of solutions on the Pareto optimal front for the multiple conflicting objectives that are considered. It is shown that there is a trade-off between the multiple design objectives and a better performance in one objective can only be obtained at the cost of performance deterioration in the other objectives. The multi-objective controller design has been compared using three different MOO techniques viz. Non Dominated Sorting Genetic Algorithm-II (NSGA-II), epsilon variable Multi-Objective Genetic Algorithm (ev-MOGA), and Multi Objective Evolutionary Algorithm with Decomposition (MOEA/D). The robustness of the same control policy designed with the nominal system settings have been investigated also for gradual decrease in the commensurate and incommensurate fractional orders of the financial system.

Shre Kumar Chatterjee, Saptarshi Das, Koushik Maharatna et al.

Plants sense their environment by producing electrical signals which in essence represent changes in underlying physiological processes. These electrical signals, when monitored, show both stochastic and deterministic dynamics. In this paper, we compute 11 statistical features from the raw non-stationary plant electrical signal time series to classify the stimulus applied (causing the electrical signal). By using different discriminant analysis based classification techniques, we successfully establish that there is enough information in the raw electrical signal to classify the stimuli. In the process, we also propose two standard features which consistently give good classification results for three types of stimuli - Sodium Chloride (NaCl), Sulphuric Acid (H2SO4) and Ozone (O3). This may facilitate reduction in the complexity involved in computing all the features for online classification of similar external stimuli in future.

Indranil Pan, Saptarshi Das

This paper investigates the operation of a hybrid power system through a novel fuzzy control scheme. The hybrid power system employs various autonomous generation systems like wind turbine, solar photovoltaic, diesel engine, fuel-cell, aqua electrolyzer etc. Other energy storage devices like the battery, flywheel and ultra-capacitor are also present in the network. A novel fractional order (FO) fuzzy control scheme is employed and its parameters are tuned with a particle swarm optimization (PSO) algorithm augmented with two chaotic maps for achieving an improved performance. This FO fuzzy controller shows better performance over the classical PID, and the integer order fuzzy PID controller in both linear and nonlinear operating regimes. The FO fuzzy controller also shows stronger robustness properties against system parameter variation and rate constraint nonlinearity, than that with the other controller structures. The robustness is a highly desirable property in such a scenario since many components of the hybrid power system may be switched on/off or may run at lower/higher power output, at different time instants.

Indranil Pan, Saptarshi Das

Fractional order proportional-integral-derivative (FOPID) controllers are designed for load frequency control (LFC) of two interconnected power systems. Conflicting time domain design objectives are considered in a multi objective optimization (MOO) based design framework to design the gains and the fractional differ-integral orders of the FOPID controllers in the two areas. Here, we explore the effect of augmenting two different chaotic maps along with the uniform random number generator (RNG) in the popular MOO algorithm - the Non-dominated Sorting Genetic Algorithm-II (NSGA-II). Different measures of quality for MOO e.g. hypervolume indicator, moment of inertia based diversity metric, total Pareto spread, spacing metric are adopted to select the best set of controller parameters from multiple runs of all the NSGA-II variants (i.e. nominal and chaotic versions). The chaotic versions of the NSGA-II algorithm are compared with the standard NSGA-II in terms of solution quality and computational time. In addition, the Pareto optimal fronts showing the trade-off between the two conflicting time domain design objectives are compared to show the advantage of using the FOPID controller over that with simple PID controller. The nature of fast/slow and high/low noise amplification effects of the FOPID structure or the four quadrant operation in the two inter-connected areas of the power system is also explored. A fuzzy logic based method has been adopted next to select the best compromise solution from the best Pareto fronts corresponding to each MOO comparison criteria. The time domain system responses are shown for the fuzzy best compromise solutions under nominal operating conditions. Comparative analysis on the merits and de-merits of each controller structure is reported then. A robustness analysis is also done for the PID and the FOPID controllers.

Wasifa Jamal, Saptarshi Das, Koushik Maharatna et al.

Phase synchronisation in multichannel EEG is known as the manifestation of functional brain connectivity. Traditional phase synchronisation studies are mostly based on time average synchrony measures hence do not preserve the temporal evolution of the phase difference. Here we propose a new method to show the existence of a small set of unique phase synchronised patterns or "states" in multi-channel EEG recordings, each "state" being stable of the order of ms, from typical and pathological subjects during face perception tasks. The proposed methodology bridges the concepts of EEG microstates and phase synchronisation in time and frequency domain respectively. The analysis is reported for four groups of children including typical, Autism Spectrum Disorder (ASD), low and high anxiety subjects - a total of 44 subjects. In all cases, we observe consistent existence of these states - termed as synchrostates - within specific cognition related frequency bands (beta and gamma bands), though the topographies of these synchrostates differ for different subject groups with different pathological conditions. The inter-synchrostate switching follows a well-defined sequence capturing the underlying inter-electrode phase relation dynamics in stimulus- and person-centric manner. Our study is motivated from the well-known EEG microstate exhibiting stable potential maps over the scalp. However, here we report a similar observation of quasi-stable phase synchronised states in multichannel EEG. The existence of the synchrostates coupled with their unique switching sequence characteristics could be considered as a potentially new field over contemporary EEG phase synchronisation studies.

Indranil Pan, Saptarshi Das

The applicability of fractional order (FO) automatic generation control (AGC) for power system frequency oscillation damping is investigated in this paper, employing distributed energy generation. The hybrid power system employs various autonomous generation systems like wind turbine, solar photovoltaic, diesel engine, fuel-cell and aqua electrolyzer along with other energy storage devices like the battery and flywheel. The controller is placed in a remote location while receiving and sending signals over an unreliable communication network with stochastic delay. The controller parameters are tuned using robust optimization techniques employing different variants of Particle Swarm Optimization (PSO) and are compared with the corresponding optimal solutions. An archival based strategy is used for reducing the number of function evaluations for the robust optimization methods. The solutions obtained through the robust optimization are able to handle higher variation in the controller gains and orders without significant decrease in the system performance. This is desirable from the FO controller implementation point of view, as the design is able to accommodate variations in the system parameter which may result due to the approximation of FO operators, using different realization methods and order of accuracy. Also a comparison is made between the FO and the integer order (IO) controllers to highlight the merits and demerits of each scheme.

Wasifa Jamal, Saptarshi Das, Ioana-Anastasia Oprescu et al.

This paper proposes a stochastic model using the concept of Markov chains for the inter-state transitions of the millisecond order quasi-stable phase synchronized patterns or synchrostates, found in multi-channel Electroencephalogram (EEG) signals. First and second order transition probability matrices are estimated for Markov chain modelling from 100 trials of 128-channel EEG signals during two different face perception tasks. Prediction accuracies with such finite Markov chain models for synchrostate transition are also compared, under a data-partitioning based cross-validation scheme.

Wasifa Jamal, Saptarshi Das, Ioana-Anastasia Oprescu et al.

Objective. The paper investigates the presence of autism using the functional brain connectivity measures derived from electro-encephalogram (EEG) of children during face perception tasks. Approach. Phase synchronized patterns from 128-channel EEG signals are obtained for typical children and children with autism spectrum disorder (ASD). The phase synchronized states or synchrostates temporally switch amongst themselves as an underlying process for the completion of a particular cognitive task. We used 12 subjects in each group (ASD and typical) for analyzing their EEG while processing fearful, happy and neutral faces. The minimal and maximally occurring synchrostates for each subject are chosen for extraction of brain connectivity features, which are used for classification between these two groups of subjects. Among different supervised learning techniques, we here explored the discriminant analysis and support vector machine both with polynomial kernels for the classification task. Main results. The leave one out cross-validation of the classification algorithm gives 94.7% accuracy as the best performance with corresponding sensitivity and specificity values as 85.7% and 100% respectively. Significance. The proposed method gives high classification accuracies and outperforms other contemporary research results. The effectiveness of the proposed method for classification of autistic and typical children suggests the possibility of using it on a larger population to validate it for clinical practice.

Valentina Bono, Wasifa Jamal, Saptarshi Das et al.

In order to reduce the muscle artifacts in multi-channel pervasive Electroencephalogram (EEG) signals, we here propose and compare two hybrid algorithms by combining the concept of wavelet packet transform (WPT), empirical mode decomposition (EMD) and Independent Component Analysis (ICA). The signal cleaning performances of WPT-EMD and WPT-ICA algorithms have been compared using a signal-to-noise ratio (SNR)-like criterion for artifacts. The algorithms have been tested on multiple trials of four different artifact cases viz. eye-blinking and muscle artifacts including left and right hand movement and head-shaking.

Indranil Pan, Saptarshi Das

In this paper, we propose a novel methodology for automatically finding new chaotic attractors through a computational intelligence technique known as multi-gene genetic programming (MGGP). We apply this technique to the case of the Lorenz attractor and evolve several new chaotic attractors based on the basic Lorenz template. The MGGP algorithm automatically finds new nonlinear expressions for the different state variables starting from the original Lorenz system. The Lyapunov exponents of each of the attractors are calculated numerically based on the time series of the state variables using time delay embedding techniques. The MGGP algorithm tries to search the functional space of the attractors by aiming to maximise the largest Lyapunov exponent (LLE) of the evolved attractors. To demonstrate the potential of the proposed methodology, we report over one hundred new chaotic attractor structures along with their parameters, which are evolved from just the Lorenz system alone.

Indranil Pan, Daya Shankar Pandey, Saptarshi Das

In this paper, a nonlinear symbolic regression technique using an evolutionary algorithm known as multi-gene genetic programming (MGGP) is applied for a data-driven modelling between the dependent and the independent variables. The technique is applied for modelling the measured global solar irradiation and validated through numerical simulations. The proposed modelling technique shows improved results over the fuzzy logic and artificial neural network (ANN) based approaches as attempted by contemporary researchers. The method proposed here results in nonlinear analytical expressions, unlike those with neural networks which is essentially a black box modelling approach. This additional flexibility is an advantage from the modelling perspective and helps to discern the important variables which affect the prediction. Due to the evolutionary nature of the algorithm, it is able to get out of local minima and converge to a global optimum unlike the back-propagation (BP) algorithm used for training neural networks. This results in a better percentage fit than the ones obtained using neural networks by contemporary researchers. Also a hold-out cross validation is done on the obtained genetic programming (GP) results which show that the results generalize well to new data and do not over-fit the training samples. The multi-gene GP results are compared with those, obtained using its single-gene version and also the same with four classical regression models in order to show the effectiveness of the adopted approach.

Sayan Saha, Saptarshi Das, Anindya Pakhira et al.

Decentralized PID controllers have been designed in this paper for simultaneous tracking of individual process variables in multivariable systems under step reference input. The controller design framework takes into account the minimization of a weighted sum of Integral of Time multiplied Squared Error (ITSE) and Integral of Squared Controller Output (ISCO) so as to balance the overall tracking errors for the process variables and required variation in the corresponding manipulated variables. Decentralized PID gains are tuned using three popular Evolutionary Algorithms (EAs) viz. Genetic Algorithm (GA), Evolutionary Strategy (ES) and Cultural Algorithm (CA). Credible simulation comparisons have been reported for four benchmark 2x2 multivariable processes.

Saptarshi Das, Indranil Pan, Khrist Sur et al.

This paper investigates typical behaviors like damped oscillations in fractional order (FO) dynamical systems. Such response occurs due to the presence of, what is conceived as, pseudo-damping and meta-damping in some special class of FO systems. Here, approximation of such damped oscillation in FO systems with the conventional notion of integer order damping and time constant has been carried out using Genetic Algorithm (GA). Next, a multilayer feed-forward Artificial Neural Network (ANN) has been trained using the GA based results to predict the optimal pseudo and meta-damping from knowledge of the maximum order or number of terms in the FO dynamical system.

Indranil Pan, Saptarshi Das

In this paper, a fractional order (FO) PIλDμcontroller is designed to take care of various contradictory objective functions for an Automatic Voltage Regulator (AVR) system. An improved evolutionary Non-dominated Sorting Genetic Algorithm II (NSGA II), which is augmented with a chaotic map for greater effectiveness, is used for the multi-objective optimization problem. The Pareto fronts showing the trade-off between different design criteria are obtained for the PIλDμand PID controller. A comparative analysis is done with respect to the standard PID controller to demonstrate the merits and demerits of the fractional order PIλDμcontroller.

Saptarshi Das, Indranil Pan, Shantanu Das et al.

Genetic Algorithm (GA) has been used in this paper for a new approach of sub-optimal model reduction in the Nyquist plane and optimal time domain tuning of PID and fractional order (FO) PIλDμ controllers. Simulation studies show that the Nyquist based new model reduction technique outperforms the conventional H2 norm based reduced parameter modeling technique. With the tuned controller parameters and reduced order model parameter data-set, optimum tuning rules have been developed with a test-bench of higher order processes via Genetic Programming (GP). The GP performs a symbolic regression on the reduced process parameters to evolve a tuning rule which provides the best analytical expression to map the data. The tuning rules are developed for a minimum time domain integral performance index described by weighted sum of error index and controller effort. From the reported Pareto optimal front of GP based optimal rule extraction technique a trade-off can be made between the complexity of the tuning formulae and the control performance. The efficacy of the single-gene and multi-gene GP based tuning rules has been compared with original GA based control performance for the PID and PIλDμ controllers, handling four different class of representative higher order processes. These rules are very useful for process control engineers as they inherit the power of the GA based tuning methodology, but can be easily calculated without the requirement for running the computationally intensive GA every time. Three dimensional plots of the required variation in PID/FOPID controller parameters with reduced process parameters have been shown as a guideline for the operator. Parametric robustness of the reported GP based tuning rules has also been shown with credible simulation examples.