Debbarma et al. [33] have suggested a new two-Degree-of- Freedom-**Fractional** **Order** **PID** (2-DOF-FOPID) **controller** ended up being suggested intended for automatic generation control (AGC) involving power systems. The **controller** ended up being screened intended for the ﬁrst **time** using three unequal area thermal systems considering reheat turbines and appropriate generation rate constraints (GRCs). The simultaneous optimization of several parameters as well as speed regulation parameter (R) in the governors ended up being accomplished by the way of recently produced metaheu- ristic nature-inspired criteria known as Fireﬂy Algorithm (FA). Study plainly reveals your ﬁneness in the 2-DOF- FOPID **controller** regarding negotiating moment as well as lowered oscillations. Found function furthermore explores the effectiveness of your Fireﬂy criteria primarily based mar- keting technique in locating the perfect guidelines in the con- troller as well as selection of R parameter. Moreover, the convergence attributes in the FA are generally justify when compared with its efﬁciency along with other more developed marketing technique such as PSO, BFO and ABC. Sensitivity analysis realizes your robustness in the 2-DOF-FOPID con- troller intended for distinct loading conditions as well as large improvements in inertia constant (H) parameter. Additionally, the functionality involving suggested **controller** will be screened next to better quantity perturbation as well as ran- domly load pattern.

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robustness to variations in the gain of the plant, are often used to optimize the **controller** parameters in [16–19]. However, those methods are frequency-based methods. In practice, those methods guarantee good **system** frequency response but poor **time** domain response. Two sets of **tuning** rules for FOPID based on the first Ziegler-Nichols **tuning** rules are presented in [20]. However, this method

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For analogy, the performance of **controller** **tuning** methods is compared for variations in load and set point when they undergo a step change of unit magnitude. L/T ratio is a signifi- cant factor which affects the **controller** performance and sensi- tivity of the feedback control **system**. The effect of L/T ratio on different **tuning** methods was studied by varying **time** **delay** L so that the ratio L/T varies from 0.1 to 2 covering lag dominant, balanced and **delay** significant processes. The simulations were carried out on different FOPTD processes. The main reason for varying the L/T ratio is that it affects the robustness of control- ler and performance of the closed loop **system**. For each varia- tion of L/T, new **controller** settings are calculated and closed loop response (both servo and regulatory) is observed, thus recording IAE, TV and M s . The trends of the performance

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Due to the **time** varying and switching, PI **controller** is a well known **controller** which is used in the most application. PI **controller** becomes a most popular industrial **controller** due to its simplicity and the ability to tune a few parameters automatically. The classical control methods employed to design the controllers for DC-DC Converters depend on the operating point so that the presence of parasitic elements, **time**-varying loads and variable supply voltages can make the selection of the control parameters difficult. Conventional controllers require a good knowledge of the **system** and accurate **tuning** in **order** to obtain the desired performances. PI **Controller**:

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Modeling or **System** Identification is an interactive process. From Ljung article [5], he state that modeling requires a **model** structure where mathematical **model** between input and output variable that contain unknown parameter. **System** Identification obtains Validation Data, Estimation Data, and others. This **system** build mathematical **model** of the dynamic **system** by referring to measured data. **System** Identification measure input and output **system** in **time** domain and frequency domain. The measured input and output then use to estimate value of adjustable parameter in a **model** structure as stated in [5]. Then the validation data will be used for **model** validates purpose then this process will simulate the **model** and computing the residual from the **model** when applied to the validation data. **System** Identification estimate unknown **model** parameter by minimizing the error between the **model** output and measured response. From step response obtain the FOPDT **model** can be calculated by calculating the gain, **time** constant and **time** **delay** by referring to its step response curve as stated by Thyagarajan, Shanmugam and Ponnavaikko [6]. The FOPDT **model** is commonly used in many dynamic processes.

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Multivariable **system** control is known to be more challenging to design when compared to scalar processes. This is primarily due to the presence of interactions and directionality in such systems. This limits the scope of application of most parametric **model**-based design algorithms to Single Input Single Output (SISO) applications (Huang, et al., 2003). Over the past decades, several methods of solving multivariable control issues have been proposed for conventional **PID** controllers (Loh, et al., 1993; Luyben, 1986). Niederlinski modified Ziegler-Nichol’s **tuning** rule for MIMO processes by introducing a detuning factor to meet the stability and performance of the multi-loop control **system**. Luyben introduced the Biggest Log-modulus **Tuning** (BLT) method which is a frequency domain **PID** **controller** design method. It uses a detuning factor (F) iteratively to decouple an interactive MIMO **system** (Luyben, 1986). A detailed review of some multivariable **PID** design methods was published by Shiu and Hwang (Shiu & Hwang, 1998). One common limitation of these design methods is that all the algorithms are limited to conventional **PID** controllers and do not address **fractional**- **order** controllers.

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Following [5] the **PID** **controller** has been designed such that settling **time** is 0.3 sec and overshoot is 12.5%. The step response of the closed loop **system** is shown in Fig.2. The analog realization of the **PID** **controller** is shown in Fig.3 with the parameter values given in Table1. The actual realization taking into account the dielectric losses in the capacitors of the integral and derivative parts of the **controller** is shown in Fig.4 where R p and R s are the resistors representing the losses.

ABSTRACT : This new Mathematical **Model** for Auto **Tuning** of **PID** **controller** is composed of modeling of closed loop **system**, modeling of the process and **Tuning** formulas in terms of the relative damping of the transient response to set point changes. In this paper we are interested with the response of a **PID** Tuned **system** (Linear or Non-Linear) which has been subjected to step input .In conventional **PID** **Tuning** process, initially the process curve is analyzed with the help of Runge-kutta Numerical analysis method , then parameters like ( Kc , Ti and Td) are determined using Ziegler Nichols Method and finally we got a **PID** response curve. However this conventional method suffers from the disadvantage of factors like Peak-Overshoot, Rise **Time**, steady State Error and Settling **Time** etc. In **order** to improve one factor other one has to be compromised. So we need to develop a Mathematical **Model** that can overcome this difficulties as well as takes care of all the above mentioned factors very efficiently. This introduces the concept of Auto **Tuning** method in which all factors as well as parameters are adjusted and determined and compared with the results of conventional **PID** **Tuning**. To start with this Method, firstly the response curve of a Linear or Non-Linear processes are divided into four different regions and it is based on the value of the Error and the change in error which occurs in the four different regions. As we see that in the first and fourth region, error is positive , while the change in error is negative and positive respectively. Similarly in the second and third region, error is negative and the change in error is negative and positive respectively. The **system** to be undergone Auto **Tuning** may be considered as a Linear or Non-Linear complex differential equation of **order** one or two.

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Multivariable **system** control is known to be more challenging to design when compared to scalar processes. This is primarily due to the presence of interactions and directionality in such systems. This limits the scope of application of most parametric **model**-based design algorithms to Single Input Single Output (SISO) applications (Huang, et al., 2003). Over the past decades, several methods of solving multivariable control issues have been proposed for conventional **PID** controllers (Loh, et al., 1993; Luyben, 1986). Niederlinski modified Ziegler-Nichol’s **tuning** rule for MIMO processes by introducing a detuning factor to meet the stability and performance of the multi-loop control **system**. Luyben introduced the Biggest Log-modulus **Tuning** (BLT) method which is a frequency domain **PID** **controller** design method. It uses a detuning factor (F) iteratively to decouple an interactive MIMO **system** (Luyben, 1986). A detailed review of some multivariable **PID** design methods was published by Shiu and Hwang (Shiu & Hwang, 1998). One common limitation of these design methods is that all the algorithms are limited to conventional **PID** controllers and do not address **fractional**- **order** controllers.

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The idea of **fractional** **order** **PID** is proposed by Podlubny I. [1]. In 1980, Irving et al. introduced a linear parameter varying **model** in **order** to describe the steam generator dynamics over the entire operating power range and proposed a **model** reference adaptive proportional integral derivative (**PID**) level **controller** [2]. The Irving **model** and its modifications have probably been the most widely accepted steam generator models for the design of water-level controllers. On the basis of classical MPC theory for linear **time** varying **system**, Kothare and etal. established a framework to design water level **controller** for Steam Generator. In 1999, Bendotti set water-level control problem for Steam Generator as a benchmark for robust control techniques, and the evaluation of water-level control performance using six different linear control algorithms such as **PID**, etc., were also obtained [3]. The performance of these linear robust controllers is higher than that of the classical **PID**-like controllers. With the development of neural networks, fuzzy set theory and evolutionary computing, some intelligent water level controllers have also been designed which result in better transient response with comparison to those **PID** controllers.

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GA is an optimization technique inspired by the mechanisms of natural selection.GA starts with an initial population containing a number of chromosomes where each one represents a solution of the problem in which its performance is evaluated based on a fitness function. Based on the fitness of individual and defined probability, a group of chromosomes is selected to undergo three common stages: selection, crossover and mutation. The application of these three basic operations will allow the creation of new individuals to yield better solutions than the parents, leading to the optimal solution. The features of GA illustrated in the work by considering the problem of designing a control **system** for a plant of a first **order** **system** with **time** **delay** and obtaining the possible results. The future scope of this work is aimed at providing a self-**tuning** **PID** **controller** with proposed algorithm (Particle Swarm Optimization - PSO) so as to solve the complex issues for real **time** problems.

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Stephanopoulos, G.[2] process design and control has been referred. Transfer function for the pressure process which is a (SISO) **system** is obtained from the response of the above process which is obtained until the process settles without the effect of the **PID** **controller** action. The response is taken for open loop process without the effect of **controller**. From the response gain of the process is determined and by two point method the values of **delay** **time** and **time** constant are calculated. **Model** validation is done by using two point method the basic formulae for calculating **time** constant and **delay** **time** is given below

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This section represents the development of a **tuning** method of PI D **controller** for first **order** plus **time** **delay** **system** with gain parameter uncertainty structure. All parameters of the PI D **controller** are calculated to satisfy the performance of the plant. Five unknown parameters of the PI D **controller** are estimated solving five non-linear equations that satisfy five design criteria [12]. Bode plot of FOPTD systems with gain parameter uncertainty structure are successfully combined with five design criteria to obtain the PI D **controller**. The phase and amplitude of the plant in frequency domain taken as,

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In this paper , **Fractional** **order** PI **controller** is used to add more flexible to the speed control BLDC motor **system**. FOPI parameters are optimal **tuning** using Evolutionary Algorithms. From the simulation results, it can be concluded that the proposed FOPID **controller** improves the overshoot, the rising **time**, settling **time**, steady state error and provides flexibility and robust stability as compared to the same **system** using conventional **PID** **controller**.

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From classical control engineering perspective the stress has always been to obtain linearized **model** of a process and the **controller** as the control theory for these types of systems are already well formulated. With the advent of fuzzy set-theory there is perhaps some more flexibility in designing systems and expressing the observations in a more easy to follow linguistic notation. The fuzzy logic **controller** in a closed loop control **system** is basically a static non-linearity between its inputs and outputs, which can be tuned easily to match the desired performance of the control **system** in a more heuristic manner without delving into the exact mathematical description of the modeled nonlinearity. Traditional **PID** controllers work on the basis of the inputs of error, the derivative and the integral of error. An attempt can be made to justify the logic of incorporating a **fractional** rate of error as an input to a **controller** instead of a pure derivative term. Assuming that a human operator replaces the automatic **controller** in the closed loop feedback **system**, the human operator would rely on his intuition, experience and practice to formulate a control strategy and he would not do the differentiation and integration in a mathematical sense. However the **controller** output generated as a result of his actions may be approximated by appropriate mathematical operations which have the required compensation characteristics. Herein lies the applicability of FO derivatives or integrals over their IO counterparts as better approximation of such type of control signals, since it gives additional flexibility to the design. The rationale behind incorporating **fractional** **order** operators in the FLC input and output can be visualized like an heuristic reasoning for an observation of a particular rate of change in error (not in mathematical sense) by a human operator and the corresponding actions he takes over **time** which is not static in nature since the **fractional**

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To obtain optimal **controller** gains experimentally, the initial TF **Model** must be specified to generate better parameters Kp, Ki, Kd. The performance evaluation of **controller** includes the estimation of responses criteria such as Rise **time**, Settling **time**, Steady state response and Overshoot. In this test, the optimization of the **PID** parameters based on proposed strategies which were implemented with closed loop **tuning**. Different gains obtained from different plant models were used, as described in Table 5. Output response **time** with Overshoot was captured and the **PID** parameters gains were calculated. A few representative results from a deferent **order** **model** were extracted in three cases to show the validation of performance comparing with Matlab **PID** toolbox tune. The aim is to find the optimal set of **PID** gains for second and third **order** models. The response of produced results was analysed in terms of Response criteria with Overshoot. It was found that the optimal values of the proportional gains can be obtained within 37 iterations. Figure 4 shows Case 1 simulation results comparison in response **time** for both proposed **tuning** and toolbox tune. Obviously, as it can be seen that case 1 based proposed **tuning** can track the given references with better minimization responses, compared with Matlab **PID** toolbox tune. The analysis of the performance-based proposed **tuning** from Figure 4 to Figure 6 shows that the enhancement was influenced by the behavioral **system** much better than toolbox tune. It shows that by the proposed **tuning** based **PID** **controller**, control accuracy throughout the process can be improved.

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The Automatic Voltage Regulator (AVR) is a very important module to maintain the terminal voltage of any power generators since it adjusts the exciter voltage of the power generators. The AVR **system** is to continuously observe the terminal voltage of power generator under various loading conditions at all times by ensuring that the generator's voltage operates within the predetermined limits. The AVR **system** consists of four main parts, namely amplifier, exciter, generator and sensor. The real **model** of AVR **system** [20] is illustrated in Figure 1. In **order** to **model** the four aforesaid components and determine their transfer functions, each component must be linearized by ignoring the saturation and other nonlinearities and also considering the major **time** constant. The estimated transfer functions of these components may be represented by mathematical as follows [12]:

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Abstract— Frequency domain based design methods are investigated for the design and **tuning** of **fractional**-**order** **PID** for scalar applications. Since Ziegler-Nichol’s **tuning** rule and other algorithms cannot be applied directly to **tuning** of **fractional**-**order** controllers, a new algorithm is developed to handle the **tuning** of these **fractional**-**order** **PID** controllers based on a single frequency point just like Ziegler-Nichol’s rule for inter **order** **PID**. Critical parameters of the **system** are obtained at the ultimate point and the **controller** parameters are calculated from these critical measurements to meet design specifications. Thereafter, **fractional** **order** is obtained to meet a specified robustness criteria which is the phase-invariability against gain variations around the phase cross-over frequency. Results are simulated on second –**order** plus dead **time** plant to demonstrate both performance and robustness.

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Araki and Taguchi (2003) in their paper about 2DOF **PID** controllers presented a structure of the 2DOF **PID** **controller** with a PD sub-**controller** in a feedforward loop and a **PID** sub-**controller** in the forward path of the control **system**. They tuned the **controller** for seven types of processes [1]. Viteckova and Vitecek (2008) studied the **tuning** process of 2DOF **controller** used with integral plus **time** **delay** plants. They used a second **order** filter receiving the reference input signal and a **PID** sub- **controller** in the feed forward path receiving the error signal [2]. Alfaro, Vilanova and Arrieta (2009) presented some considerations on set-point weight choice for 2DOF **PID** controllers. The 2DOF **controller** structure they used consisted of a PI sub- **controller** receiving the reference input signal and a **PID** sub-**controller** with derivative filter in the feedback path. Their analysis considered the robustness of the control **system** [3]. Viteckova

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An EHA **system** is well-known to be widely applied in various applications, for instance aircraft and vehicle pressing machine. These applications usually involve the processes that demanded high force, high precision, and flexible response which require the assistance of the high-performance control **system**. However, the high-performance **controller** designs usually require an expert in the related field. Besides, the cost and the **time** spend will be the defects in the complex or high-performance **controller** design. In the industrial field, the **PID** **controller** is usually used, which is much easier and simple to be designed. Depending on the required outcome, if the high precision result is required, the **PID** **controller** might be unable to achieve the required objective. This paper intends to assess the performance of the common use **PID** **controller**, the improved **PID** **controller** named **fractional** **order** **PID** **controller**, and also the SMC **controller** during the changes of supply pressure in the EHA **system**. The parameters of each **controller** are obtained using the PSO **tuning** algorithm. By referring to the robustness numerical analysis, although the FO-**PID** **controller** is capable to outperform the conventional **PID** **controller**, with the robustness index value of 0.0764, the robustness index value of the SMC is even smaller which is 0.0617. As the robustness index value represents the error occurred during the changes in the operating condition, the SMC is able to perform better without discarding the important properties of the EHA **system** during the occurrence of the variation. Apart from using the PSO computational **tuning** method, the performance of these controllers might be enhanced through different computational **tuning** methods. Therefore, further investigation regarding the computational **tuning** algorithm which can be applied in the practical **system** will be carried out.

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