Integer Order PID Controller Research Articles

Design, Analysis and Performance Evaluation of Fractional Order Proportional Integral for Three Interacting Tank Process in Frequency Domain considered as Third Order System

Conventional Integer order Proportional Integral Derivative (IOPID) are the workhorse for the control of almost 90% of the Industrial processes due to its structural simplicity. With the application of fractional calculus in the field of control engineering, Fractional Order (FO) PID controllers are gaining popularity since it requires a slight modification of the integer order PID controller. Tuning of the Integer Order PID controller parameters are by well known techniques like Ziegler Nichols method, Cohen Coon Method, etc mostly time domain based and few frequency techniques are also available. In the present research work, an attempt has been made to tune the FOPI controller using Frequency domain specifications. Frequency domain specifications considered for the design includes the Phase Margin specification, Gain crossover frequency specification and robustness to gain variations. The proposed control schemes are applied to three interacting tank process represented as third order system and verified under servo, regulatory, servo-regulatory response and robustness conditions. Comparison of the time domain performance indices are performed to guarantee the superiority of the proposed scheme.

Fractional Order Dynamic Positioning Controller

Improving the performance of Dynamic Positioning System in such applications as station keeping, position mooring and slow speed references tracking requires improving the position and heading control precision. These goals can be achieved through the improvement of the ship control system. Fractional-order calculus is a very useful tool which extends classical, integer-order calculus and is used in contemporary modeling and control applications. Fractional-order PIƛDμ controller, based on the added flexibility of fractional-order operators, are capable of superior performance compared to their integer-order counterparts. This paper presents the fractional order PIƛDμ controller designed to maintain the ship position and heading and the results were compared with classical integer order PID controller.

Robust Fractional Order Proportional Integral Control for Large Time-Delay System

In this paper, a new control method for large time delay system is proposed. Firstly, the decreasing time delay controller is used to remodel large delay time plant into small delay time plant. Then, a fractional robust proportional-integral controller (FOPI) is designed, using the phase margin and cut-off frequency at a specified point in the Bode plot of flat robust conditions, to guarantee the desired control performance and the robustness of the high order system to the gain order system. For comparison between the fractional order proportional integral controller and the traditional integer order PID (IOPID) controller, the IOPID controller is also designed following the same proposed tuning specifications. The simulation results indicates that the both designed controllers work efficiently. Furthermore, the FOPI controller makes the large time-delay system get better control effect, the system has high robustness, adaptive ability and anti-jamming ability.

Design of Fractional Order PID Controller Based Particle Swarm

Fractional order PID (FOPID) controller is a special kind of PID controller whose derivative and integral order are fractional rather than integer which has five parameters to be tuned. This paper presents study of the implementation of tuning method and performance enhancement of the closed loop system by use of the fractional order PID (PIλDμ) controller utilizing a MATLAB/Simulink. The tuning methods for these type controllers have many mixed tools of the available optimization methods and update artificial optimization methods in the design. In this paper particle swarm optimization has been implemented to design FOPID controller in which the unknown parameters are determined minimizing a given integral of time weighted absolute error (ITAE). The main specification of this paper is that the all five parameters of (PIλDμ) have been found directly without spreading the steps. It has been shown that the response and performance of the closed loop system with FOPID controller is much better than integer order PID controller for the same system and with better robustness.

Fractional Order PID Control of Railway Rescue Crane Leveling System

Aiming at the overshoot problem of electro-hydraulic position servo system used in the process of railway rescue crane hydraulic automatic leveling, and based on its characteristics such as big output power, high control accuracy, quick response speed, et al, this paper established the linear mathematical model of railway rescue crane electro-hydraulic automatic leveling system, besides, the fractional order PID control method was proposed based on the oustaloup digital filter algorithm and the working principle of fractional order PID control method was given, and then the fractional order PID controller was designed. In order to verify the effectiveness of the proposed control strategy, the MATLAB/Simulink simulation software was used. The simulation results show that the fractional order PID controller improved the speed of electro-hydraulic servo system unit step response and the capacity of resisting disturbance compared to traditional integer order PID controller, besides it can ensure the response without overshoot at the same time, so it meets the requirements for rapidity and no overshoot of railway rescue crane hydraulic automatic leveling system very well.

Design of a fractional order PID controller for hydraulic turbine regulating system using chaotic non-dominated sorting genetic algorithm II

Fractional-order PID (FOPID) controller is a generalization of traditional PID controller using fractional calculus. Compared to the traditional PID controller, in FOPID controller, the order of derivative portion and integral portion is not integer, which provides more flexibility in achieving control objectives. Design stage of such an FOPID controller consists of determining five parameters, i.e. proportional, integral and derivative gains {Kp, Ki, Kd}, and extra integration and differentiation orders {λ,μ}, which has a large difference comparing with the conventional PID tuning rules, thus a suitable optimization algorithm is essential to the parameters tuning of FOPID controller. This paper focuses on the design of the FOPID controller using chaotic non-dominated sorting genetic algorithm II (NSGAII) for hydraulic turbine regulating system (HTRS). The parameters chosen of the FOPID controller is formulated as a multi-objective optimization problem, in which the objective functions are composed by the integral of the squared error (ISE) and integral of the time multiplied squared error (ITSE). The chaotic NSGAII algorithm, which is an incorporation of chaotic behaviors into NSGAII, is used as the optimizer to search true Pareto-front of the FOPID controller and designers can implement each of them based on objective functions priority. The designed chaotic NSGAII based FOPID controller procedure is applied to a HTRS system. A comparison study between the optimum integer order PID controller and optimum fractional order PID controller is presented in the paper. The simulation and some experimental results validate the superiority of the fractional order controllers over the integer controllers.

Automatic Generation Control of Single Area Thermal Power System with Fractional Order PID (PIλDμ) Controllers

This paper proposes a fractional order PID (FOPID) controller for the supplementary automatic generation control (AGC) of a single area thermal power system having non-reheat turbines. The parameters of fractional PID controller are determined using genetic algorithm (GA). The effectiveness of the proposed controller is established by comparing its performance with the conventional integer order integral, PI and PID controllers based AGC. The investigations reveal that the proposed fractional order controller is better than the integer order controllers in terms of settling time, peak overshoot, steady state error and mean of sum of squared errors (MSSE).

Realization of Fractional Order Controllers by Using Multiple Tuning-Rules

Fractional order PID controller has two degrees of freedom more than the integer order PID controller,and it has better control performance. The paper briefly describes the fractional order PID controller, and through Ziegler-Nichols type tuning rules, Padula & Visioli tuning rules and tuning by minimization methods to achieve fractional order PID controllers respectively. Additionally, the Oustaloup approximation methods are both introduced. Based on these methods, we have considered the steam pressure model and the vehicle wire control system. The simulation result shows that control system stability can be obtained by using the tuning-rules proposed in this paper.

The Fractional Brownian Motion Approach to Analysis of Fractional Control System with Non-Stationary Plant

In this study a fractional Brownian motion model is used to randomize integer-and fractional-order plant parameters. The analysis of these plants in systems with integer-order PID and fractional-order PIλDδ controllers is shown. The aim of the analysis is to compare robustness of both controllers. The quality of control system is measured by integral quality parameter. The fractional Brownian motion gives much flexibility in modeling non-stationary plants, the volatility and standard deviation of fractional Brownian motion can be easily adjusted.

Fuzzy Logic Based Set-Point Weighting for Fractional Order PID Control

Differentiation and integration of non-integer order have drawn increasing attention in research community. Fractional order dynamic systems have been recognized as effective tool for characterizing the real world phenomena. This may be implemented by using different control structures in which a fuzzy mechanism is adopted to tune the parameters by using Ziegler-Nichols method. Fractional-order PID control is the development of general integer-order PID controller. This paper proposes the basic framework of fractional order dynamic system with fuzzy weighted set-point. Comparisons are made with PID and FOPID controllers for first and second order systems. The response shows the superiority of the fuzzy set-point weighting methodology over the other methods.

The Frequency Research of Fractional Order PIλDμ Controller

Since most of the control systems in real industrial production are fractional，there is necessery to propose fractional order PIλDμ controller, which extend the traditional integer-order PID controller to fractional order, it has increased two free degree: Integral-order λ and differential-order μ, to more accurately control those complex systems. At the same time analysis the performance of fractional order PIλDμ controller in frequency domain. Especially,the two degrees’ effect to controller.

Pareto optimal robust design of fractional-order PID controllers for systems with probabilistic uncertainties

In this paper, a multi-objective optimization approach is used for Pareto optimum design of robust integer-order and fractional-order PID controllers for both integer-order and fractional-order plants with parametric uncertainties. The aim of this paper is to compare the performances of those optimally-designed controllers dealing with parametric uncertainties of both integer-order and fractional-order plants. In this way, four combinations of plants and controllers have been considered in which five conflicting objective functions in both time and frequency domains are used in the Pareto design of both integer-order and fractional-order PID controllers. The results clearly show that effective trade-off design points can be compromisingly explored among the optimal robust integer-order and fractional-order PID controllers obtained using the methodology of this work. Furthermore, the superior robust stability and robust performance of the fractional-order PID controllers will be demonstrated in comparison with those of the integer-order PID controllers.

Automated design of fractional PI QFT controller using interval constraint satisfaction technique (ICST)

In this paper, a fractional-order proportional-integral (FOPI) controller is proposed and designed for a class of nonlinear integer-order (IO) systems. For fair comparison, the proposed FOPI and the traditional integer-order PID (IOPID) controllers are designed following the same set of imposed tuning constraints, which can guarantee the desired control performance and the robustness of the designed controllers to the loop gain variations. This proposed design scheme offers a practical and systematic way of controller design for the nonlinear IO plant. We also propose a new and efficient method for automated synthesis of a fixed structure Quantitative Feedback Theory (QFT) FO controller. This is achieved by solving QFT quadratic inequalities of robust stability and performance specifications. The controller synthesis problem is posed as interval constraint satisfying problem (ICSP) and solved with interval constraint solver. The main feature of this method is that it guarantees to find all feasible controllers of given structure in the specified search domain. The designed FOPI and the traditional IOPID controllers are tested on the experimental setup designed by Educational Control Product (ECP) Magnetic Levitation Setup ECP 730. From the experimental results presented, it is observed that the designed FO controllers work more efficiently, with improved performance compared with the designed stabilizing IOPID controller.

Fractional Order Modeling of a PHWR Under Step-Back Condition and Control of Its Global Power With a Robust ${\rm PI}^{\lambda} {\rm D} ^{\mu}$ Controller

Bulk reduction of reactor power within a small finite time interval under abnormal conditions is referred to as step-back. In this paper, a 500MWe Canadian Deuterium Uranium (CANDU) type Pressurized Heavy Water Reactor (PHWR) is modeled using few variants of Least Square Estimator (LSE) from practical test data under a control rod drop scenario in order to design a control system to achieve a dead-beat response during a stepped reduction of its global power. A new fractional order (FO) model reduction technique is attempted which increases the parametric robustness of the control loop due to lesser modeling error and ensures iso-damped closed loop response with a PI{\lambda}D{\mu} or FOPID controller. Such a controller can, therefore, be used to achieve active step-back under varying load conditions for which the system dynamics change significantly. For closed loop active control of the reduced FO reactor models, the PI{\lambda}D{\mu} controller is shown to perform better than the classical integer order PID controllers and present operating Reactor Regulating System (RRS) due to its robustness against shift in system parameters.

Tuning fractional order proportional integral controllers for fractional order systems

In this paper, two fractional order proportional integral controllers are proposed and designed for a class of fractional order systems. For fair comparison, the proposed fractional order proportional integral (FOPI), fractional order [proportional integral] (FO[PI]) and the traditional integer order PID (IOPID) controllers are all designed following the same set of the imposed tuning constraints, which can guarantee the desired control performance and the robustness of the designed controllers to the loop gain variations. This proposed design scheme offers a practical and systematic way of the controllers design for the considered class of fractional order plants. From the simulation and experimental results presented, both of the two designed fractional order controllers work efficiently, with improved performance comparing with the designed stabilizing integer order PID controller by the observation. Moreover, it is interesting to observe that the designed FO[PI] controller outperforms the designed FOPI controller following the proposed design schemes for the class of fractional order systems considered.

Designing fractional-order PI<SUP align=right>λ</SUP>D<SUP align=right>μ</SUP> controller using differential harmony search algorithm

Harmony Search (HS) has recently emerged as an efficient metaheuristic algorithm that draws inspiration from the music improvisation process. This article describes the design of fractional-order proportional-integral-derivative (FOPID) controllers, using a newly developed variant of HS, known as differential harmony search (DHS). Design of FOPID controllers is more complex than that of conventional integer-order PID controller since the latter involves only three parameters while the former involves five parameters to tune. Controller synthesis is based on user specifications like peak overshoot and, rise time; which are used to formulate a single objective optimisation problem. Tustin operator-based continuous fraction expansion (CFE) scheme was used to digitally realise fractional-order closed loop transfer function of the designed plant-controller setup. Experimental results of comparison between DHS and a few established optimisation techniques [particle swarm optimisation (PSO) and genetic algorithm (GA)] over different instantiations of the design problem reflect the superiority of the proposed methodology.

Fractional order [proportional derivative] controller for a class of fractional order systems

Recently, fractional order systems (FOS) have attracted more and more attention in various fields. But the control design techniques available for the FOS suffer from the lack of direct systematic approaches. In this paper, we focus on a given type of simple model of FOS. A fractional order [proportional derivative] (FO-[PD]) controller is proposed for this class of FOS, and a practical and systematic tuning procedure has been developed for the proposed FO-[PD] controller synthesis. The fairness issue in comparing with other controllers such as the traditional integer order PID (IO-PID) controller and the fractional order proportional derivative (FO-PD) controller has been addressed under the same number of design parameters and the same specifications. Fair comparisons of the three controllers (i.e., IO-PID, FO-PD and FO-[PD]) via the simulation tests illustrate that, the IO-PID controller designed may not always be stabilizing to achieve flat-phase specification while both FO-PD and FO-[PD] controllers designed are always stabilizing. Furthermore, the proposed FO-[PD] controller outperforms FO-PD controller for the class of fractional order systems.

Design of optimal fractional-order PID controllers

In this paper we are concerned with the design of a Fractional-order PID controller which involves noninteger-order integrator and differentiator. The three controller gains and two real orders of the fractional-order PID controller are determined to minimize an integral square error (ISE)performance index while satisfying the specified gain and phase margins. We formulate the design problem as a constrained parametric optimization and apply a differential evolution algorithm to search globally the optimal controller parameters. Due to the problem lack of analytic time-domain analysis methods for fractional-order systems, and effective numerical method is utilized to compute the ISE performance index as well as to check the stability in the frequency domain. Design examples are given to compare the performance of the optimal fractional-order PID controller with the optimal integer-order PID controller in controlling integer-order as well as fractional-order processes.