Top PDF Regression model for tuning the PID controller with fractional order time delay system

Regression model for tuning the PID controller with fractional order time delay system

Regression model for tuning the PID controller with fractional order time delay system

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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Satisfactory optimization design for fractional order PID controller

Satisfactory optimization design for fractional order PID controller

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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A comparative study of fractional order PIλ /PIλ Dμ tuning rules for stable first order plus time delay processes

A comparative study of fractional order PIλ /PIλ Dμ tuning rules for stable first order plus time delay processes

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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Fractional Order PID Controller Based Bidirectional Dc/Dc Converter

Fractional Order PID Controller Based Bidirectional Dc/Dc Converter

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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PID Controller Design With Different Tuning Methods

PID Controller Design With Different Tuning Methods

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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On fractional-order PID controllers

On fractional-order PID controllers

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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Fractional Order Modeling and GA Based Tuning for Analog Realization with Lossy Capacitors of a PID Controller

Fractional Order Modeling and GA Based Tuning for Analog Realization with Lossy Capacitors of a PID Controller

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.

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Mathematical Model for Auto Tuning of PID Controller

Mathematical Model for Auto Tuning of PID Controller

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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On fractional-order PID controllers

On fractional-order PID controllers

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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A Robust Fractional Order PID Controller for Liquid Level system

A Robust Fractional Order PID Controller for Liquid Level system

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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Comparison of PID Controller Tuning Methods with Genetic  Algorithm for FOPTD System

Comparison of PID Controller Tuning Methods with Genetic Algorithm for FOPTD System

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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Design of Model Based PID Controller Tuning for Pressure Process

Design of Model Based PID Controller Tuning for Pressure Process

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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Analysis of Fractional order PID controller for Ceramic Infrared Heater

Analysis of Fractional order PID controller for Ceramic Infrared Heater

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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Speed Control of Brushless DC Motor based on Fractional Order PID Controller

Speed Control of Brushless DC Motor based on Fractional Order PID Controller

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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A Novel Fractional Order Fuzzy PID Controller and Its Optimal Time Domain Tuning Based on Integral Performance Indices

A Novel Fractional Order Fuzzy PID Controller and Its Optimal Time Domain Tuning Based on Integral Performance Indices

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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A Novel Method for Tuning PID Controller

A Novel Method for Tuning PID Controller

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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Evolutionary algorithms based tuning of PID controller  for an AVR system

Evolutionary algorithms based tuning of PID controller for an AVR system

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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Design and tuning of fractional-order PID controllers for time-delayed processes

Design and tuning of fractional-order PID controllers for time-delayed processes

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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Tuning of a 2DOF PI-PID Controller for use with Second-order-like Processes

Tuning of a 2DOF PI-PID Controller for use with Second-order-like Processes

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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Comparison of Fractional Order PID Controller and Sliding Mode Controller with Computational Tuning Algorithm

Comparison of Fractional Order PID Controller and Sliding Mode Controller with Computational Tuning Algorithm

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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