Tuning of fractional order proportional integral/proportional derivative controllers based on existence conditions

2018 ◽  
Vol 233 (4) ◽  
pp. 384-391 ◽  
Author(s):  
Cristina I Muresan ◽  
Isabela R Birs ◽  
Clara M Ionescu ◽  
Robin De Keyser
Keyword(s):  
Nonlinear Equations ◽  
Fractional Order ◽  
Physical Meaning ◽  
Open Loop ◽  
Performance Criteria ◽  
Crossover Frequency ◽  
Design Constraint ◽  
Tuning Parameters ◽  
Proportional Integral ◽  
Existence Conditions

Fractional order proportional integral and proportional derivative controllers are nowadays quite often used in research studies regarding the control of various types of processes, with several papers demonstrating their advantage over the traditional proportional integral/proportional derivative controllers. The majority of the tuning techniques for these fractional order proportional integral/fractional order proportional derivative controllers are based on three frequency-domain specifications, such as the open-loop gain crossover frequency, phase margin and the iso-damping property. The tuning parameters of the controllers are determined as the solution of a system of three nonlinear equations resulting from the performance criteria. However, as with any system of nonlinear equations, it might occur that for a certain process and with some specific performance criteria, the computed parameters of the fractional order proportional integral/fractional order proportional derivative controllers do not fall into a range of values with correct physical meaning. In this article, a study regarding this limitation, as well as the existence conditions for the fractional order proportional integral/fractional order proportional derivative parameters are presented. The method could also be extended to the more complex fractional order proportional–integral–derivative controller. The aim of this research is directed toward demonstrating that when designing fractional order proportional integral/fractional order proportional derivative controllers, the choice of the performance specifications should be done based on some specific design constraints. The article shows that given a specific process and open-loop modulus and phase specifications, the gain crossover frequency (or in general, a certain test frequency used in the design), specified as a performance specification, must be selected such that the process phase fulfills an important condition (design constraint). Once this is met, the proposed approach ensures that the tuning parameters of the fractional order controller will have a physical meaning. Illustrative examples are included to validate the results.

Phase-constrained fractional order PIλ controller for second-order-plus dead time systems

2016 ◽  
Vol 39 (8) ◽  
pp. 1225-1235 ◽  
Author(s):  
Kai Chen ◽  
Rongnian Tang ◽  
Chuang Li
Keyword(s):  
Fractional Order ◽  
Dead Time ◽  
Open Loop ◽  
Second Order ◽  
Phase Constraint ◽  
Phase Margin ◽  
Crossover Frequency ◽  
Tuning Method ◽  
The Stability ◽  
Stability Line

In this paper we propose a phase-constrained fractional order [Formula: see text] controller based on a second-order-plus dead time process and a new tuning method. The design is derived in several constraints: a flat phase constraint, a gain crossover frequency and a phase margin. With the specified phase margin, it can reach the corresponding upper boundary of gain crossover frequency and the stability region. The complete surface of stabilizing controllers is achieved by guaranteeing the open-loop system to fulfil the pre-set phase margin. Afterwards, a stability line on the relative stable surface can then be obtained. For a set of controllers on the stability line, the flat phase constraint is used to make sure the uniqueness of the designed controller. The effectiveness of the proposed method is illustrated with several numerical examples.

scholarly journals Proportional-Integral Controllers Performance of a Grid-Connected Solar PV System with Particle Swarm Optimization and Ziegler–Nichols Tuning Method

Energies ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2516
Author(s):  
Klemen Deželak ◽  
Peter Bracinik ◽  
Klemen Sredenšek ◽  
Sebastijan Seme
Keyword(s):  
Particle Swarm Optimization ◽  
Distribution Network ◽  
Particle Swarm ◽  
Open Loop ◽  
Limited Area ◽  
Solar Pv ◽  
Pv System ◽  
Swarm Optimization ◽  
Proportional Integral ◽  
Tuning Method

This paper deals with photovoltaic (PV) power plant modeling and its integration into the medium-voltage distribution network. Apart from solar cells, a simulation model includes a boost converter, voltage-oriented controller and LCL filter. The main emphasis is given to the comparison of two optimization methods—particle swarm optimization (PSO) and the Ziegler–Nichols (ZN) tuning method, approaches that are used for the parameters of Proportional-Integral (PI) controllers determination. A PI controller is commonly used because of its performance, but it is limited in its effectiveness if there is a change in the parameters of the system. In our case, the aforementioned change is caused by switching the feeders of the distribution network from an open-loop to a closed-loop arrangement. The simulation results have claimed the superiority of the PSO algorithm, while the classical ZN tuning method is acceptable in a limited area of operation.

scholarly journals μ-Synthesis for Fractional-Order Robust Controllers

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 911
Author(s):  
Vlad Mihaly ◽  
Mircea Şuşcă ◽  
Dora Morar ◽  
Mihai Stănese ◽  
Petru Dobra
Keyword(s):  
Control Problem ◽  
Fractional Order ◽  
Design Procedure ◽  
High Order ◽  
Numerical Control ◽  
Performance Criteria ◽  
Iteration Algorithm ◽  
Optimization Approach ◽  
Cnc Machine ◽  
Bee Colony

The current article presents a design procedure for obtaining robust multiple-input and multiple-output (MIMO) fractional-order controllers using a μ-synthesis design procedure with D–K iteration. μ-synthesis uses the generalized Robust Control framework in order to find a controller which meets the stability and performance criteria for a family of plants. Because this control problem is NP-hard, it is usually solved using an approximation, the most common being the D–K iteration algorithm, but, this approximation leads to high-order controllers, which are not practically feasible. If a desired structure is imposed to the controller, the corresponding K step is a non-convex problem. The novelty of the paper consists in an artificial bee colony swarm optimization approach to compute the nearly optimal controller parameters. Further, a mixed-sensitivity μ-synthesis control problem is solved with the proposed approach for a two-axis Computer Numerical Control (CNC) machine benchmark problem. The resulting controller using the described algorithm manages to ensure, with mathematical guarantee, both robust stability and robust performance, while the high-order controller obtained with the classical μ-synthesis approach in MATLAB does not offer this.

On Robust Control of Fractional Order Plants: Invariant Phase Margin

2015 ◽  
Vol 10 (5) ◽  
Author(s):  
Mohammad Hossein Basiri ◽  
Mohammad Saleh Tavazoei
Keyword(s):  
Robust Control ◽  
Fractional Order ◽  
Phase Margin ◽  
Crossover Frequency ◽  
Large Uncertainty ◽  
Robust Controller ◽  
Numerical Examples

Recently, a robust controller has been proposed to be used in control of plants with large uncertainty in location of one of their poles. By using this controller, not only the phase margin and gain crossover frequency are adjustable for the nominal case but also the phase margin remains constant, notwithstanding the variations in location of the uncertain pole of the plant. In this paper, the tuning rule of the aforementioned controller is extended such that it can be applied in control of plants modeled by fractional order models. Numerical examples are provided to show the effectiveness of the tuned controller.

A novel fractional order PID plus derivative (PIλDµDµ2) controller for AVR system using equilibrium optimizer

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Abdulsamed Tabak
Keyword(s):  
Fractional Order ◽  
Transient Response ◽  
Superior Performance ◽  
Control Performance ◽  
Proportional Integral Derivative ◽  
Content Type ◽  
Proportional Integral ◽  
Avr System ◽  
Optimization Parameters ◽  
Fractional Order Pid

Purpose The purpose of this paper is to improve transient response and dynamic performance of automatic voltage regulator (AVR). Design/methodology/approach This paper proposes a novel fractional order proportional–integral–derivative plus derivative (PIλDµDµ2) controller called FOPIDD for AVR system. The FOPIDD controller has seven optimization parameters and the equilibrium optimizer algorithm is used for tuning of controller parameters. The utilized objective function is widely preferred in AVR systems and consists of transient response characteristics. Findings In this study, results of AVR system controlled by FOPIDD is compared with results of proportional–integral–derivative (PID), proportional–integral–derivative acceleration, PID plus second order derivative and fractional order PID controllers. FOPIDD outperforms compared controllers in terms of transient response criteria such as settling time, rise time and overshoot. Then, the frequency domain analysis is performed for the AVR system with FOPIDD controller, and the results are found satisfactory. In addition, robustness test is realized for evaluating performance of FOPIDD controller in perturbed system parameters. In robustness test, FOPIDD controller shows superior control performance. Originality/value The FOPIDD controller is introduced for the first time to improve the control performance of the AVR system. The proposed FOPIDD controller has shown superior performance on AVR systems because of having seven optimization parameters and being fractional order based.

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