Benefiting from the great potential of the mathematical tool of fractional calculus, fractional order proportional integral (PI) controllers have been proposed as the next generations of popular PI controllers. On the other hand, the integral performance indices such as the integral square error (ISE), integral absolute error (IAE), integral time square error (ITSE), and integral time absolute error (ITAE) are commonly used in the design and evaluation of the performance of practical control systems. Considering these points, the present paper deals with the optimal tuning of the free parameters of fractional order PI controllers, to be used in control of first order plus dead time (FOPDT) processes in a unity negative control structure, on the basis of ISE performance index. Using the approach of ``tuning based on the implementable form of the controller'' instead of the approach of ``tuning based on the ideal form of the controller'' causes that no incompatibility is seen between the ideal behavior of the controller and the behavior of the implementable controller. Also, to avoid approximation error in the calculation of ISE based cost functions, algebraic relations have been used for analytically finding the values of ISE in the under study time delay control system. In fact, the main contribution of the paper is to propose simple tuning rules for implementable fractional order PI controllers with the aim of achieving an optimal control system in the viewpoint of the ISE performance criterion. These rules have been obtained by iteratively using the steepest descent (gradient descent) optimization algorithm with the constraint of optimizing the step size in each iteration. The proposed rules for tuning of the free parameters of implementable fractional order PI controllers yield in a control system whose performance is better than the control system with an optimal PI controller. This point has been successfully confirmed by some numerical and experimental examples.

This study presents a set of rules for optimal tuning a class of integer-order controllers, known as implementable fractional-order PID controllers, to be applied in control of first-order-plus-dead-time (FOPDT) processes. To this aim, the approach of so-called “, tuning based on the implementable form of the controller”,is applied instead of the common approach of “, tuning based on the ideal form of the controller”, . Consequently, no contradiction is found between the behavior of the tuned controller and that of the implemented controller. Also, algebraic relations between the values of cost functions, which are defined based on integral square error (ISE) and integral square time error (ISTE) performance indices, and free parameters of the implementable controller are established. Tuning implementable fractional-order PID controllers via the proposed rules guarantees that the values of performance indices are reduced in comparison with the case of using optimal PID controllers. In addition to numerical results, experimental results are also provided to demonstrate the effectiveness of the proposed tuning rules in practical applications.

A proper linear fuzzy PI controller is designed in order to achieve a response with specific overshoot and settling time for higher order systems. First, a new design method of this type controllers is given for a second order systems. Then, its extension is discussed for third order systems. Finally, with the ideas developed, the given design algorithm is generalized to higher order systems.

This paper proposes an optimized control policy over type one diabetes. Type one diabetes is taken into consideration as a nonlinear model (Augmented Minimal Model), which is implemented in MATLAB-SIMULINK. This Model is developed in consideration of the patient's conditions. There are some uncertainties in the regarded model due to factors such as blood glucose concentration, daily meals or sudden stresses. Moreover, there are distinct approaches toward the elimination of these uncertainties. In here, a meal is fed to the model as an input in order to omit these uncertainties. Also, different control methods could be chosen to monitor the blood glucose level. In this paper, a fractional order PID is utilized as the control method. Thereafter, the control method and parameters are tuned by conducting genetic algorithm, as a powerful evolutionary algorithm. Finally, the output of the optimized fractional order PID and traditional PID control method, which had the same parameters as the fractional PID except the fractions, are compared. At the end, it is concluded by utilizing fractional order PID, not only the controller performance improved considerably, but also, unlike the traditional PID, the blood glucose concentration is maintained in the desired range.

This paper presents a fractional-order adaptive controller based on sliding mode control for synchronization of commensurate fractional-order chaotic systems. The adaptive controller is a fractional PID controller, which the coefficients will be tuned according to a proper adaptation mechanism. fractional PID coefficients are updated using the gradient method when a proper sliding surface is chosen. To illustrate the effectiveness and performance of the controller, the proposed controller is implemented on chaotic fractional-order Genesio Tessi and Coullet systems. Performance of fractional-order PID adaptive controller (PaIlDm) based on synchronization error, and control signal is compared with the conventional adaptive controller (PID) and sliding mode controller (SMC). The simulation results show the efficiency of the proposed controller.

Quadrotors are types of Unmanned Aerial Vehicles (UAVs) which have unique features compared to conventional aircraft because of its vertical take-off and landing capability, flying in small areas and its high maneuverability. Also the relatively simple, economical and easy flight system of quadrotors, allows it to be widely used as a good platform for development, implementation and testing a variety of control methods. One of the robust control methods is sliding mode control. In spite of the high capabilities of this approach, it has one main problem which is high frequency switching of the control signal which is known as the chattering phenomenon. In the past several decades, fractional order differential equations have been implemented in engineering application field, including controller design and provides the possibility of using controllers for improving the performance of system. In this paper, a fractional order sliding surface has been employed for designing sliding mode control rule for quadrotors. The main objective of this study is to improve the performance and reduce the chattering phenomenon in sliding mode method. In this regard, by introducing sliding PDa surface, the control rule is designed in two different modes of 0<a£1 and 1<a<2 and the effect of a in the performance of the system is evaluated. Based on conducted simulations, it can be inferred that using an optimal value for a in fractional order sliding surface decreases the chattering in control input.

In this paper, a new comparative approach was proposed for reliable controller design. Scientists and engineers are often confronted with the analysis, design, and synthesis of real-life problems. The first step in such studies is the development of a 'mathematical model' which can be considered as a substitute for the real problem. The mathematical model is used here as a plant. fractional integrals and derivatives have found wide application in the control of dynamical systems when the controlled system and the controller are described by a set of fractional order differential equations. Here the stability and robustness of fractional order system is checked at the different level and it is found that the stability region is large in the complex plane. This large stability region provides the more flexibility for system implementation in the control engineering. Generally, an analytically or experimentally approaches are used for designing the controller. If a fractional order controller design approach used for a given plant then the controlled parameter gives the better result.

The EVs battery has the ability to enhance the balance between the load demand and power generation units. The EV aggregators to manage the random behaviour of EV owners and increasing EVs participation in the ancillary services market are employed. The presence of aggregators could lead to time-varying delay in load frequency control (LFC) schemes. The effects of these delays must be considered in the LFC controller design. Due to the dependency of controller effectiveness on its parameters, these parameters should be designed in such a way that the LFC system has desired performance in the presence of time-varying delay. Therefore, a Sine Cosine Algorithm (SCA) is utilized to adjust the fractional-order PID (FOPID) controller coefficients. Also, some evaluations are performed about the proposed LFC performance by integral absolute error (IAE) indicator. Simulations are carried out in both single and two area LFC system containing EV aggregators with time-varying delay. According to results, the proposed controller has fewer frequency variations in contrast to other controllers presented in the case studies. The obtained output could be considered as a solution to evaluate the proposed controller performance for damping the frequency oscillations in the delayed LFC system.

Most of our power requirements are fulfilled by coal-fired power plants. This paper aims to improve its efficiency by designing a fractional order Proportional Derivative controller (FOPD).  A mathematical model is developed from the real-time data from the fossil-fueled power plant in Tuticorin India.  The optimal tuning parameters for the FOPD controller are chosen from a selection of widely popular Optimization Algorithms (OA) [Sine Cosine OA (SCOA), Ant Lion OA (ALOA), Moth Flame OA (MFOA), and Whale OA (WOA)]. The analysis evaluates the controller's performance with time domain specifications like settling time, undershoots, and overshoots, and the superiority is highlighted.  The operational efficiency of the power plant is evaluated against The efficiency values were calculated by the proposed controller using various OAs. The plant's operational efficiency is determined to be 37.2%. An increase in efficiency of 23.5% is achieved while using the intelligent controllers. Improvement in efficiency is also highlighted.