Indranil Pan

Frequency domain design of fractional order PID controller for AVR system using chaotic multi-objective optimization

Abstract A fractional order (FO) PID or FOPID controller is designed for an Automatic Voltage Regulator (AVR) system with the consideration of contradictory performance objectives. An improved evolutionary Non-dominated Sorting Genetic Algorithm (NSGA-II), augmented with a chaotic Henon map is used for the multi-objective optimization based design procedure. The Henon map as the random number generator outperforms the original NSGA-II algorithm and its Logistic map assisted version for obtaining a better design trade-off with an FOPID controller. The Pareto fronts showing the trade-offs between the different design objectives have also been shown for both the FOPID controller and the conventional PID controller to enunciate the relative merits and demerits of each. The design is done in frequency domain and hence stability and robustness of the design is automatically guaranteed unlike the other time domain optimization based controller design methods.

Fractional order fuzzy control of hybrid power system with renewable generation using chaotic PSO

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.

Extending the concept of analog Butterworth filter for fractional order systems

This paper proposes the design of fractional order (FO) Butterworth filter in complex w-plane (w=s^q; 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. First, 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.

Fractional Order AGC for Distributed Energy Resources Using Robust Optimization

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 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 controllers to highlight the merits and demerits of each scheme.

Multi-gene genetic programming based predictive models for municipal solid waste gasification in a fluidized bed gasifier.

A multi-gene genetic programming technique is proposed as a new method to predict syngas yield production and the lower heating value for municipal solid waste gasification in a fluidized bed gasifier. The study shows that the predicted outputs of the municipal solid waste gasification process are in good agreement with the experimental dataset and also generalise well to validation (untrained) data. Published experimental datasets are used for model training and validation purposes. The results show the effectiveness of the genetic programming technique for solving complex nonlinear regression problems. The multi-gene genetic programming are also compared with a single-gene genetic programming model to show the relative merits and demerits of the technique. This study demonstrates that the genetic programming based data-driven modelling strategy can be a good candidate for developing models for other types of fuels as well.

Multi-objective active control policy design for commensurate and incommensurate fractional order chaotic financial systems

Abstract In this study, an active control policy design is proposed for a fractional order financial system, which considers multiple conflicting objectives. An active control template is used as a nonlinear state feedback mechanism and the controller gains are selected within a multi-objective optimization (MOO) framework to satisfy the conditions of asymptotic stability, which are derived analytically. The MOO obtains a set of solutions on the Pareto optimal front for the multiple conflicting objectives that are considered. We demonstrate that there is a trade-off between the multiple design objectives where better performance for one objective can only be obtained at the cost of degrading the performance for the other objectives. The multi-objective controller design was compared using three different MOO techniques, i.e., non-dominated sorting genetic algorithm-II, epsilon variable multi-objective genetic algorithm, and multi-objective evolutionary algorithm with decomposition. The robustness of the same control policy designed with the nominal system settings was also investigated with gradual decrease in the commensurate and incommensurate fractional orders of the financial system.

Artificial neural network based modelling approach for municipal solid waste gasification in a fluidized bed reactor

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.

Multi-objective LQR with optimum weight selection to design FOPID controllers for delayed fractional order processes.

An optimal trade-off design for fractional order (FO)-PID controller is proposed with a Linear Quadratic Regulator (LQR) based technique using two conflicting time domain objectives. A class of delayed FO systems with single non-integer order element, exhibiting both sluggish and oscillatory open loop responses, have been controlled here. The FO time delay processes are handled within a multi-objective optimization (MOO) formalism of LQR based FOPID design. A comparison is made between two contemporary approaches of stabilizing time-delay systems withinLQR. The MOO control design methodology yields the Pareto optimal trade-off solutions between the tracking performance and total variation (TV) of the control signal. Tuning rules are formed for the optimal LQR-FOPID controller parameters, using median of the non-dominated Pareto solutions to handle delayed FO processes.

Robust optimization of subsurface flow using polynomial chaos and response surface surrogates

This study employs an inclusive framework for surrogate model-based optimization in the presence of parametric and spatial uncertainties. The framework is applied to optimize water injection rate for optimal hydrocarbon recovery from a synthetic subsurface model with uncertainty in the geological and fluid relative permeability properties. In one model of parametric uncertainty, geological properties such as the channel’s absolute permeability and the fault transmissibility multiplier and the fluid relative permeability parameters such as the residual oil saturation to water and the water relative permeability at residual oil are assumed to be non-informative. In another model, the channels positions are assumed uncertain and various realizations of the channelized permeability are parameterized and the spatial uncertainty is accounted for in the optimization. The uncertainty is quantified in each evaluation of the objective function via polynomial chaos expansions. The coefficients of polynomial chaos expansion are solved by probabilistic collocation method. The objective function is assigned with a risk-averse net present value computed from a distribution of values obtained from the probabilistic proxies. The proxies are updated for each round of objective function evaluation. Monte-Carlo simulations are also conducted to verify accuracy and to demonstrate the computational efficiency of the probabilistic collocation approach. The optimization is conducted in various random input cases (depending on the number of uncertain parameters) and for each case net present value is successfully maximized and optimal solutions of the water injection rates are determined.

Robust optimization of well location to enhance hysteretical trapping of CO2: Assessment of various uncertainty quantification methods and utilization of mixed response surface surrogates

The paper aims to solve a robust optimization problem (optimization in presence of uncertainty) for finding the optimal locations of a number of CO2 injection wells for geological sequestration of carbon dioxide in a saline aquifer. The parametric uncertainties are the interfacial tension between CO2 and aquifer brine, the Lands trapping coefficient and the boundary aquifers absolute. The spatial uncertainties are due to the channelized permeability field which exhibits a binary channel-non-channel system. The objective function of the optimization is the amount of residually trapped CO2 due to the hysteresis of the relative permeability curves. A risk-averse value derived from the cumulative density function of the distribution of the amount of trapped gas is chosen as the objective function value. In order to ensure that the uncertainties are effectively taken into account, Monte Carlo simulation and Polynomial Chaos Expansion (PCE)-based methods are used and compared with each other. For different cases of parametric and spatial uncertainties, the most accurate uncertainty quantification (UQ) method is chosen to be integrated within the optimization algorithm. While for parametric uncertainty cases of up to two uncertain variables, PCE-based methods computationally outperform Monte Carlo simulations, it is shown that for the multimodal distributions of the function of trapped gas occurring for the spatial uncertainty case, Monte Carlo simulations are more reliable than PCE-based UQ methods. For the discrete (integer) optimization problem, various mixed response surface surrogate models are tested and the robust optimization resulted in optimal CO2 injection well locations. This article is protected by copyright. All rights reserved.