Fractional Order Phase Shaper Design with Routh's Criterion for Iso-Damped Control System (original) (raw)
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Design of a Fractional Order Phase Shaper for Iso-Damped Control of a PHWR Under Step-Back Condition
IEEE Transactions on Nuclear Science, 2010
Phase shaping using fractional order (FO) phase shapers has been proposed by many contemporary researchers as a means of producing systems with iso-damped closed loop response due to a stepped variation in input. Such systems, with the closed loop damping remaining invariant to gain changes can be used to produce dead-beat step response with only rise time varying with gain. This technique is used to achieve an active step-back in a Pressurized Heavy Water Reactor (PHWR) where it is desired to change the reactor power to a pre-determined value within a short interval keeping the power undershoot as low as possible. This paper puts forward an approach as an alternative for the present day practice of a passive step-back mechanism where the control rods are allowed to drop during a step-back action by gravity, with release of electromagnetic clutches. The reactor under a step-back condition is identified as a system using practical test data and a suitable Proportional plus Integral plus Derivative (PID) controller is designed for it. Then the combined plant is augmented with a phase shaper to achieve a dead-beat response in terms of power drop. The fact that the identified static gain of the system depends on the initial power level at which a step-back is initiated, makes this application particularly suited for using a FO phase shaper. In this paper, a model of a nuclear reactor is developed for a control rod drop scenario involving rapid power reduction in a 500MWe Canadian Deuterium Uranium (CANDU) reactor using AutoRegressive Exogenous (ARX) algorithm. The system identification and reduced order modeling are developed from practical test data. For closed loop active control of the identified reactor model, the fractional order phase shaper along with a PID controller is shown to perform better than the present Reactor Regulating System (RRS) due to its iso-damped nature.
Design of Fractional Order Controllers Using the PM Diagram
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This work presents a modeling and controller tuning method for non-rational systems. First, a graphical tool is proposed where transfer functions are represented in a four-dimensional space. The magnitude is represented in decibels as the third dimension and a color code is applied to represent the phase in a fourth dimension. This tool, which is called Phase Magnitude (PM) diagram, allows the user to visually obtain the phase and the magnitude that have to be added to a system to meet some control design specifications. The application of the PM diagram to systems with non-rational transfer functions is discussed in this paper. A fractional order Proportional Integral Derivative (PID) controller is computed to control different non-rational systems. The tuning method, based on evolutionary computation concepts, relies on a cost function that defines the behavior in the frequency domain. The cost value is read in the PM diagram to estimate the optimum controller. To validate the con...
Simplified Fractional Order Controller Design Algorithm
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Classical fractional order controller tuning techniques usually establish the parameters of the controller by solving a system of nonlinear equations resulted from the frequency domain specifications like phase margin, gain crossover frequency, iso-damping property, robustness to uncertainty, etc. In the present paper a novel fractional order generalized optimum method for controller design using frequency domain is presented. The tuning rules are inspired from the symmetrical optimum principles of Kessler. In the first part of the paper are presented the generalized tuning rules of this method. Introducing the fractional order, one more degree of freedom is obtained in design, offering solution for practically any desired closed-loop performance measures. The proposed method has the advantage that takes into account both robustness aspects and desired closed-loop characteristics, using simple tuning-friendly equations. It can be applied to a wide range of process models, from integ...
A robust tuning method for fractional order PI controllers
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The application of fractional controller attracts more attention in the recent years. In this paper, a new tuning method for PI α controller design is proposed for a class of unknown, stable, and minimum phase plants. We are able to design a PI α controller to ensure that the phase Bode plot is flat, i.e., the phase derivative w.r.t. the frequency is zero, at a given gain crossover frequency so that the closed-loop system is robust to gain variations and the step responses exhibit an iso-damping property. Several relay feedback tests can be used to identify the plant gain and phase at the given frequency in an iterative way. The identified plant gain and phase at the desired tangent frequency are used to estimate the derivatives of amplitude and phase of the plant with respect to frequency at the same frequency point by Bode's integral relationship. Then, these derivatives are used to design a PI α controller for slope adjustment of the Nyquist plot to achieve the robustness of the system to gain variations. No plant model is assumed during the PI α controller design. Only several relay tests are needed.
International Journal of Bifurcation and Chaos, 2012
Fractional complex order integrator has been used since 1991 for the design of robust control-systems. In the CRONE control methodology, it permits the parameterization of open loop transfer function which is optimized in a robustness context. Sets of fractional order integrators that lead to a given damping factor have also been used to build iso-damping contours on the Nichols plane. These iso-damping contours can also be used to optimize the third CRONE generation open loop transfer function. However, these contours have been built using nonband-limited integrators, even if such integrators reveal to lead to unstable closed loop systems. One objective of this paper is to show how the band-limitation modifies the left half-plane dominant poles of the closed loop system and removes the right half-plane ones. Also presented are how to obtain a fractional order open loop transfer function with a high phase slope and a useful frequency response, and how the damping contours can be use...
Fractional-order PID controller design on Internet: www.PIDlab.com
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IFAC-PapersOnLine, 2018
Fractional-order PID controllers have been introduced as a general form of conventional PID controllers and gained considerable attention latterly due to the flexibility of two extra parameters (fractional integral order λ and fractional derivative order µ) provided. Designing fractional controllers in the time domain has still difficulties. Moreover, it has been observed that the techniques based on gain and phase margins existing in the literature for integer-order systems are not completely applicable to the fractional-order systems. In this study, stability regions based on specified gain and phase margins for a fractional-order PI controller to control integrating processes with time delay have been obtained and visualized in the plane. Fractional integral order λ is assumed to vary in a range between 0.1 and 1.7. Depending on the values of the order λ, and phase and gain margins, different stability regions have been obtained. To obtain stability regions, two stability boundaries have been used; RRB (Real Root Boundary) and CRB (Complex Root Boundary). Obtained stability regions can be used to design all stabilizing fractional-order PI controllers.
Design and tuning of fractional-order PID controllers for time-delayed processes
2016 UKACC 11th International Conference on Control (CONTROL), 2016
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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This paper proposes a new method to tune a fractional order PID controller. This method utilizes both the analytic and numeric approach to determine the controller parameters. The control design specifications that must be achieved by the control system are gain crossover frequency, phase margin, and peak magnitude at the resonant frequency, where the latter is a new design specification suggested by this paper. These specifications results in three equations in five unknown variables. Assuming that certain relations exist between two variables and discretizing one of them, a performance index can be evaluated and the optimal controller parameters that minimize this performance index are selected. As a case study, a third order linear time invariant system is taken as a process to be controlled and the proposed method is applied to design the controller. The resultant control system exactly fulfills the control design specification, a feature that is laked in numerical design method...
Design of Fractional Order Controllers for First Order Plus Time Delay Systems
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In this paper, a fractional order proportional integral controller (FOPI) and Fractional order[Proportional Integral] (FO[PI]) controller is designed for controlling the level of a spherical tank which is modeled as a first order plus dead time system These controllers are designed based on the same set of design specifications which will satisfy the desired given gain cross over frequency and phase margin. The performance of the designed FOPI and FO [PI] controller is compared with the Conventional integer order Proportional Integral (IOPI) controller. The simulations are done in MATLAB simulink.