The uniformly distributed random number generator is normally used for the crossover and mutation operations in the standard version of the NSGA-II algorithm [30]. However since the strength of evolutionary algorithms lies in the randomness of the crossover and mutation operators, many contemporary researchers have focussed on increasing the efficiency of these algorithms by incorporating different random behaviours through various techniques like stochastic resonance and noise [33], **chaotic** maps [34] etc. In [35] it has been shown that the performance of these evolutionary algorithms increase if different types of **chaotic** maps are introduced instead of the uniform random number generator for the crossover and mutation operations. It has also been demonstrated in [35] that, in general, using **chaotic** systems for the random number generation in the crossover and mutation operations is better than using random numbers generated from a noisy sequence in terms of convergence and effectiveness of the algorithms in finding global minima. In [36] it has been shown that the **multi**-**objective** NSGA-II algorithm can be improved by using **chaotic** maps and gives better result than the original NSGA-II algorithm in terms of convergence and high efficiency in calculation. This is due to the fact that the **chaotic** process introduces diversity in the solutions. In this paper, we adopt this policy and use a **chaotic** logistic map to obtain better solutions and convergence characteristics of the NSGA-II algorithm. The logistic map is one of the simplest discrete time dynamical systems exhibiting chaos. The equation for the logistic map is given as follows:

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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.

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The population size is taken as 100 and the algorithm is run until the cumulative change in fitness function value is less than the function tolerance of 10 -4 over 100 generations. The Crossover fraction is taken as 0.8 and an intermediate crossover scheme is adopted. The mutation fraction is taken as 0.2. For choosing the parent vectors **based** on their scaled fitness values, the algorithm uses a tournament selection method with a tournament size of 2. The Pareto front population fraction is taken as 0.7. This parameter indicates the fraction of population that the solver tries to limit on the Pareto front. The **optimization** variables are the components of the active control functions, i.e. m ij ∀ ∈ i j , { 1, 2,3 } . Thus there are nine optimisation variables in total. To ensure that the solutions obtained are guaranteed to be stable, the stability criteria given by the Matignon’s theorem for commensurate and incommensurate FO **system** are incorporated in the algorithm within each **objective** function evaluation. Thus the solutions that are generated through cross-over, mutation or reproduction in each generation, is first tested to see if they satisfy the stability criteria. In case the criteria are satisfied, the **objective** function is evaluated by simulating the **chaotic** **system** with the optimum **controller** gains, provided by the NSGA-II algorithm. In case the criteria are not satisfied then a high value of **objective** function is assigned to the solution without simulating the **chaotic** **system** since that particular **controller** cannot stabilize the **system**. This automatically assigns a fitness which is worse than the others to these unstable solutions. Therefore, over the generations, the algorithm rejects the unstable solutions and converges towards those regions in the solution space, which give stable **controller** values.

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In this paper, **fractional** **order** proportional-integral-differential (FOPID) **controller** is employed in the **design** of thyristor controlled series capacitor (TCSC)-**based** damping **controller** in coordination with the secondary integral **controller** as automatic generation control (AGC) loop. In doing so, the contribu- tion of the TCSC in tie-line power exchange is extracted mathematically for small load disturbance. Adjustable parameters of the proposed FOPID-**based** TCSC damping **controller** and the AGC loop are optimized concurrently via an improved particle swarm **optimization** (IPSO) algorithm which is reinforced by **chaotic** parameter and crossover operator to obtain a globally optimal solution. The powerful FOMCON toolbox is used along with MATLAB for handling **fractional** **order** modeling and con- trol. An interconnected **multi**-source power **system** is simulated regarding the physical constraints of generation rate constraint (GRC) nonlinearity and governor dead band (GDB) effect. Simulation results using FOMCON toolbox demonstrate that the proposed FOPID-**based** TCSC damping **controller** achieves the greatest dynamic performance under different load perturbation patterns in comparison with phase lead-lag and classical PID-**based** TCSC damping controllers, all in coordination with the integral AGC. Moreover, sensitivity analyses are performed to show the robustness of the proposed **controller** under various uncertainty scenarios.

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Traditionally the PID **controller** has been used in the **AVR** loop due to its simplicity and ease of implementation [5]. However, recently the **fractional** **order** PID (FOPID) **controller** have been used in the **design** of **AVR** systems and have been shown to outperform the PID in many cases [6], [7]. In Zamani et al. [8], the FOPID has been tuned for an **AVR** **system** using the Particle Swarm Optimisation (PSO) algorithm employing time domain criterion like the Integral of Absolute Error (IAE), percentage overshoot, rise time, settling time, steady state error, **controller** effort etc. In Tang et al. [6], the optimal parameters of the FOPID **controller** for the **AVR** **system**, has been found using a **chaotic** ant swarm algorithm. In [6] a customised **objective** function has been designed using the peak overshoot, steady state error, rise time and the settling time. The above mentioned literatures perform optimisation considering only a single **objective**. But in a practical control **system** **design** multiple objectives need to be addressed. In the study by Pan and Das [9], the **AVR** **design** problem has been cast as a **multi**- **objective** problem and the efficacy of the PID and the FOPID controllers are compared with respect to different contradictory **objective** functions like the Integral of Time Multiplied Squared Error (ITSE) and the **controller** effort etc. However, the optimisation is done in the time domain and the obtained **controller** values are checked for robustness against gain variation by varying different parameters of the control loop. All these above mentioned literatures which employ time domain optimisation techniques cannot guarantee a certain degree of gain or phase margins which are important for the plant operator. These margins are useful from a control practitioner’s view point as they can give an estimate of how much uncertainty the **system** can tolerate before

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We extended the benefits of P ⋋ **controller** for **AVR** **system**. In Particular, a masked P ⋋ **controller** is developed in matlab by programming to optimize the parameters **based** on the recently developed **optimization** techniques instead of using toolbox which was restrained for using advanced **optimization** techniques. Genetic Algorithm (GA) technique has already been used to determine optimal solution to several power engineering problems and we employed these algorithms to **design** an FOPID **controller** for Automatic voltage regulator (**AVR**) problem. The proposed **controller** is simulated within various scenarios and its performance is compared with those of an optimally-designed PID **controller**. Transient response and performance robustness characteristics of both controllers are studied and superiority of the proposed **controller** in all two respects is illustrated.

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The present scenario running in the electricity market is about interconnected power grid. Renewable power sources are more economical to meet the load requirement of consumers and industries that too pollute the enironment. So many markets are looking forward for the inegration of Non- renewable power sources to the interconnection of power grid [4]. Wind and solar energies are being more preferable energy sources.In addition to these sources ther are many more sources such as Bio mass, MHD, tidal energy, wave energy etc., which can be used for integrated but the major drawback is about it can produce only a minimum amout of elecrical energy compared with other sources. The main aim of the AGC is to balance load demand and generation maintaing frequency at an acceptable range. But in the interconnection of power grid there occurs load fluctuations due to many transients etc., which may lead to the frequecny deviations [2]. İn **order** to regain the power **system** to the normal operating condition a **controller** action is necessary.

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In 1996, Jung and Dorf proposed a new structure of con- troller and termed as proportional- integral-derivative and ac- celeration (PIDA) **controller** [2]. It consists of three numbers of zeros and poles but two poles may be neglected in the de- sign process. It is addition of a zero in the standard PID struc- ture to derive the PIDA structure of the controller.The intro- duction of an extra zero to the PID **controller** is to change the root locus of the third **order** plant in **order** to make dom- inant roots more dominant by eliminating the effects of non- dominant roots [4].

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By constructing two scaling matrices, i.e., a function matrix (t) and a constant matrix W which is not equal to the identity matrix, a kind of W – (t) synchronization between **fractional**-**order** and integer-**order** **chaotic** (hyper-**chaotic**) systems with diﬀerent dimensions is investigated in this paper. **Based** on the **fractional**-**order** Lyapunov direct method, a **controller** is designed to drive the synchronization error convergence to zero asymptotically. Finally, four numerical examples are presented to illustrate the eﬀectiveness of the proposed method.

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However, to the best of the authors’ knowledge, to this day, still less scholars consider the adaptive impulsive synchronization of delay **fractional**-**order** **chaotic** systems. Motivated by the above works, the adaptive impulsive synchronization for a class of **fractional**-**order** **chaotic** systems with an unknown Lipschitz constant and time delay is discussed. The rest of this paper is organized as follows: In Section 2, some preliminaries of **fractional** derivative are briefly introduced. A new adaptive impulsive synchronization method of delay **fractional**-**order** **chaotic** systems is proposed in Section 3, **based** on the theory of Lyapunov stability and impulsive differential equations. Finally, conclusions are addressed in Section 4.

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the proposed method generates a solution very near to the global optimum solution. Ying-Tung Hsiao presents an optimum approach for designing of PID controllers using ACO to minimize the integral absolute control error. The experiment results demonstrate that better control performance can be achieved in comparison with conventional PID method.[6] Duan Hai-bin presented a parameter **optimization** strategy for PID **controller** using ACO Algorithm. The algorithm has been applied to the combinatorial **optimization** problem, and the results indicate high precision of control and quick response. Mohd. Rozely Kalil, Ismail Musirin proposed Ant Colony **Optimization** (ACO) technique for searching the optimal point of maximum loadability point at a load bus.. Hamid Boubertakh, Mohamed Tadjine, Pierre-Yves Glorennec and Salim Labiod has proposed theory that although conventional PID controllers are the most used in the industrial process, their performance is often limited when it is poorly tuned and/or used for controlling highly complex processes with nonlinearities, complex dynamic behaviors.[3] Ing-Tung Hsiao proposed a solution algorithm **based** on the ant colony **optimization** technique to determine the parameters of the PID **controller** for getting a well performance for a given plant. Simulation results demonstrate that better control performance can be achieved in comparison with known methods.[4] Kiarash , Mehrdad Abedi,(2011) Shuffled frog leaping and particle swarm **optimization** this two algoritm are used to determine optimal PID **controller** in **AVR** **system** and also shows that for tuning PID **controller** using various **optimization** technique reduces complexity and find more realistic result than trial and error method.[4] Hany M. Hasanien (2013) propose **optimization** of PID **controller** in **AVR** **system** shows that minimize the maximum percentage overshoot, the rise time, the settling time and oscillation and step response of **AVR** **system** can be changed. Richa Singh (IEEE 2016)-ACO is popular technique which shows behavior of real ant colonies to find solutions to discrete **optimization** problems.[13]

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Automatic voltage regulator plays a crucial role in power **system** so as to regulate the output voltage at a nominally constant desired voltage level. In power generator, the function of **AVR** is to ensure the voltage from the power generators to be running smoothly and also to maintain the stability of the voltage from the generators. The stability of the **AVR** control **system** is an important issue since it can critically impinge on the security of the power **system**. The excitation **system** ought to responsible for the effective voltage control and improvement of the **system** stability [1]. The excitation **system** not only controls the output voltage of the generator and also controls the power factor and magnitude of the current. In most of the exciter **system** a thyristor-**based** **system** is employed to provide a controlled output voltage to the exciter. In most of the industrial applications the proportional-integral-derivative (PID) **controller** has been commonly used because of its simple configuration, trouble-free implementation and good performance in a large range of operating conditions. Nevertheless, effective and suitable tuning of the PID controller’s parameters has been relatively difficult because many industrial processes are frequently affected by problems such as higher **order**, time delays and nonlinearities [2-4].

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Abstract: Weather information plays significant role in agriculture as well as in green house projects. So monitoring of weather parameter is very essential. The present **system** is designed to monitor weather parameters like temperature and humidity with digital display. The stored data can be transmitted to personal computer (PC). Micro-**controller** **AVR**-Atmega 32 is the heart of the weather monitoring **system**. Temperature sensor used is LM-35 and humidity sensor used is SY-HS-220.Software programming has been done by using embedded-C programming. The system’s experimental results show that the present weather monitoring **system** is more accurate to measure temperature and humidity.

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Improving the dynamic performance of an automobile suspension **system** is considered as the main demand for comfortable and safe passenger travelling. From all previously proposed and implemented works, it is noticed that there are other factors that need to be considered to raising the car holding and stability in the road for improved passenger comfort when travelling. The minimization of car body displacement and oscillation time after exposure to road disturbances have been adopted in this work due to their contribution in raising the car holding and stability. The improvement in these features was maintained via a robust control methodology. The **Fractional** **Order** PID **controller** tuned by the Whales **Optimization** Algorithm (WOA) and Particle Swarm **Optimization** (PSO) algorithm is suggested in this work as a robust **controller** to reduce the effect of these demerits. In this paper, an active quarter car suspension nonlinear **system** is designed for the presented goals using a robust **controller**. Minimizing the displacement of the car body and reducing the damping frequency are achieved via a nonlinear control strategy using the **fractional** **order** PID **controller**, which can maintain the required characteristics. Tuning the parameters of the FOPID **controller** is performed by using the Whales **Optimization** Algorithm (WOA). Robustness of the FOPID **controller** is examined and proved to withstand a **system** parameter variation of ±12 % in all **system** parameters and a maximum of ±80 % in **controller** parameter variation. Simulation outcomes also indicate a considerably improved performance of the active suspension **system** with the **fractional** **order** PID **controller** over the traditional PID. Keywords

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Rhythmic processes are common and very important to life: cyclic behaviors are found in heart beating, breath, and circadian rhythms [1]. The biological systems are always exposed to external perturbations, which may produce alterations on these rhythms as a consequence of coupling synchronization of the autonomous oscillators with pertur- bations. Coupling of therapeutic perturbations, such as drugs and radiation, on biologi- cal systems result in biological rhythms, which is known as chronotherapy. Cancer [2,3], rheumatoid arthritis [4], and asthma [5,6] are a number of the diseases under study in this field because of their relation with circadian cycles. Mathematical models and numerical simulations are necessary to understand the functions of biological rhythms, to comprehend the transition from simple to complex behaviors, and to delineate their conditions [7]. **Chaotic** behavior is a usual phenomenon in these sys- tems, which is the main focus of this article.

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The **multi**-**objective** **optimization** of the mathematical model was carried out by the method of Exploration of Nonlinear Programming with restrictions. The computational simulation, according to the model of the Tchebycheff Program, was implemented. A series of optimal variants of the efficiency indicators and the variables that govern the process were obtained for the **design** of the spiral pump. Figure-1 shows the front of Pareto of the not inferior solutions.

All basic ideas of **fractional** calculus, the stability of **fractional** **order** **system**, sensitivity, robustness and MATLAB function are presented here. The robustness and sensitivity analysis is investigated for the given real-time example. The main purpose of the paper is to draw attention to **fractional** **order** **system** stability and analysis over a conventional way. Here an integer **order** plant is controlled by full **order** **controller** and **fractional** **order** **controller**. It concludes here that the **fractional** **order** **system** has robustness and a large region for

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This paper provides an efficient Grid connected PV MPPT method with reducedcomponents. It computes the instantaneous and junction array conductances.The first one is done using the array current andvoltage, whereas the second one uses the array junction current,which is estimated using ANFIS cell model presented ina recent paper of the authors [17]. Still, it requires informationon the climatic parameters. Hence, it is proposed ANFIS control as ananalytical model with a denoising **based** wavelet algorithm toestimate them, which helps reducing the hardware using onlyone voltage sensor. The simulation results areprovided to validate the proposed ANFIS - PV **based** MPPT scheme capabilities.This paper is organized as follows: Section II provides an overview of Modeling of PV **system**. The proposedthree phase PV **system** is developed and explained in Section III.Section IV shows in detail the estimation of environmentalparameters. The simulation results **based** on MATLAB arepresented in Section V and Section VII gives a conclusion.

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many applications. So far, several definitions of **fractional** **order** derivatives have been presented [6]. Recently, conformable **fractional** **order** derivative as a new definition of **fractional** **order** derivative is introduced. One of important its advantages is having simple calculation [7]. Various papers have been presented **based** on conformable **fractional** **order** derivatives. In [8], some important laws and definitions **based** on conformable **fractional** **order** derivative are presented. **Fractional** Newtonian mechanics **based** on conformable **fractional** calculus are studied in [9]. Stability of **fractional** differential systems is discussed using conformable **fractional** **order** derivative in [10]. Sliding mode **controller** is an effective strategy to control systems with uncertainties and disturbances. In [11], two new nonlinear sliding mode controllers are developed. In [12], a chattering-free full-**order** nonlinear sliding mode **controller** is developed. In **order** to control type I diabetes in presence uncertainties and disturbances, a **fractional** **order** sliding mode **controller** and adaptive **fractional** **order** sliding mode **controller** are designed in [13]. For an uncertain manipulator, a fuzzy robust **fractional** **order** **controller** is developed in [14]. **Fractional** sliding mode schemes are presented to track and stabilize some nonlinear **fractional**-**order** systems with uncertainty in [15].

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[7] A. Mujumdar, S. Kurode, B. Tamhane, "**Fractional** **Order** Sliding mode control for Single Link Flexible Manipulator", 2013 IEEE International Conference on Control Applications (CCA) Part of 2013 IEEE **Multi** Conference on Systems and Control Hyderabad, India, pp. 288-293, August 28-30, 2013. [8] C. Yin, Y. Q. Chen, S. Zhong, "**Fractional**-**order** sliding mode **based** extremum seeking control of a class of nonlinear systems", Automatica , Vol. 50, No. 12, pp. 3173-3181, December 2014. [9] S. Pashaei, M. Badamchizadeh, "A new **fractional**-**order** sliding mode **controller** via a nonlinear disturbance observer for a class of dynamical systems with mismatched disturbances", ISA Transactions, Vol. 63, pp. 39-48, 2016.

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