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 Influence of time delay on fractional-order PI-controlled system for a second-order oscillatory plant model with time delay

2017 ◽  
Vol 66 (4) ◽  
pp. 693-704 ◽  
Author(s):  
Talar Sadalla ◽  
Dariusz Horla ◽  
Wojciech Giernacki ◽  
Piotr Kozierski
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Open Loop ◽  
Second Order ◽  
Loop System ◽  
Tracking Performance ◽  
Controlled System ◽  
Tuning Method ◽  
Fractional Order Pi Controller ◽  
The Stability

Abstract The paper aims at presenting the influence of an open-loop time delay on the stability and tracking performance of a second-order open-loop system and continuoustime fractional-order PI controller. The tuning method of this controller is based on Hermite- Biehler and Pontryagin theorems, and the tracking performance is evaluated on the basis of two integral performance indices, namely IAE and ISE. The paper extends the results and methodology presented in previous work of the authors to analysis of the influence of time delay on the closed-loop system taking its destabilizing properties into account, as well as concerning possible application of the presented results and used models.

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.

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.

Lateral control of an Aerosonde facing tolerance in parameters and operation speed: performance robustness study

2018 ◽  
Vol 41 (8) ◽  
pp. 2319-2327 ◽  
Author(s):  
S Seyedtabaii ◽  
S Zaker
Keyword(s):  
Fractional Order ◽  
Random Systems ◽  
Open Loop ◽  
Unmanned Aircraft ◽  
Phase Margin ◽  
Operation Speed ◽  
Aerodynamic Parameters ◽  
Fractional Order Controller ◽  
High Level ◽  
Performance Robustness

The aim is to acquire low variance roll responses (performance robustness) of control of an Aerosonde despite the high level of tolerances in aerodynamic parameters and working speed. In this respect, fractional-order proportional plus integral and derivative (FOPID) is a valuable option; others are H∞ and μ synthesis. FOPID can tolerate system uncertainty by maintaining a wide open-loop flat phase margin band. All three methods are worked out using the linearized system model and deliver (at least initially) high-integer-order controllers. The uncertainty level is not explicitly considered in H∞, but it may be presented in the μ synthesis and FOPID. The uncertainty presentation in the modified fractional-order controller (mFOC) design is through a Φd curve. The Φd curve is fitted to the mean of the upper and lower bands of the phase margins distribution map of the random systems. It is shown that the mFOC design perfectly secures the desired phase margin flatness. The controllers are applied to the roll of an unmanned aircraft vehicle with a 30% tolerance in the aerodynamic parameters, and operation speed and robustness in performance is evaluated. The simulation results indicate that the mFOC design renders more coherent responses than what H∞ and µ synthesis design deliver. This is confirmed through extensive simulations.

scholarly journals PID Tuning Method Based on IMC for Inverse-Response Second-Order Plus Dead Time Processes

Processes ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1183 ◽  
Author(s):  
Duby Castellanos-Cárdenas ◽  
Fabio Castrillón ◽  
Rafael E. Vásquez ◽  
Carlos Smith
Keyword(s):  
Transfer Function ◽  
Objective Function ◽  
Dead Time ◽  
Second Order ◽  
Internal Model Control ◽  
Tuning Method ◽  
Wide Range ◽  
Model Control ◽  
Inverse Response ◽  
Tuning Rules

This work addresses a set of tuning rules for PID controllers based on Internal Model Control (IMC) for inverse-response second-order systems with dead time. The transfer function, and some time-response characteristics for such systems are first described. Then, the IMC-based methodology is developed by using an optimization objective function that mixes performance and robustness. A correlation that minimizes the objective function and that allows the user to compute the controller’s tuning parameter is found. The obtained expressions are mathematically simple, which facilitate their application in a ten-step systematic methodology. Finally, the proposed tuning method is compared to other well-known tuning rules that have been reported in literature, for a wide range of parameters of the process. The performance achieved with the proposed method is very good not only for disturbance rejection but for set-point tracking, when considering a wide-range of parameters of the process’ transfer function.

Fractional Order Proportional Derivative (FOPD) and FO[PD] Controller Design for Networked Position Servo Systems

2009 ◽  
Author(s):  
Yongshun Jin ◽  
YangQuan Chen ◽  
Chunyang Wang ◽  
Ying Luo
Keyword(s):  
Fractional Order ◽  
Controller Design ◽  
Phase Margin ◽  
Crossover Frequency ◽  
Pd Controller ◽  
Servo Systems ◽  
Integer Order ◽  
Simulation Results ◽  
Position Servo ◽  
The Given

This paper considers the fractional order proportional derivative (FOPD) controller and fractional order [proportional derivative] (FO[PD]) controller for networked position servo systems. The systematic design schemes of the networked position servo system with a time delay are presented. It follows from the Bode plot of the FOPD system and the FO[PD] that the given gain crossover frequency and phase margin are fulfilled. Moreover, the phase derivative w.r.t. the frequency is zero, which means that the closed-loop system is robust to gain variations at the given gain crossover frequency. However, sometimes we can not get the controller parameters to meet our robustness requirement. In this paper, we have studied on this situation and presented the requirement of the gain cross frequency, and phase margin in the designing process. For the comparison of fractional order controllers with traditional integer order controller, the integer order proportional integral differential (IOPID) was also designed by using the same proposed method. The simulation results have verified that FOPD and FO[PD] are effective for networked position servo. The simulation results also reveal that both FOPD controller and FO[PD] controller outperform IO-PID controller for this type of system.

Practical Tuning Rule Development for Fractional Order Proportional and Integral Controllers

2008 ◽  
Vol 3 (2) ◽  
Author(s):  
YangQuan Chen ◽  
Tripti Bhaskaran ◽  
Dingyü Xue
Keyword(s):  
Fractional Order ◽  
Dynamic Systems ◽  
Disturbance Rejection ◽  
Dead Time ◽  
Pi Controller ◽  
First Order ◽  
Tuning Method ◽  
Peak Sensitivity ◽  
Practical Nature ◽  
Tuning Rules

This paper presents a new practical tuning method for fractional order proportional and integral (FO-PI) controller. The plant to be controlled is mainly first order plus delay time (FOPDT). The tuning is optimum in the sense that the load disturbance rejection is optimized yet with a constraint on the maximum or peak sensitivity. We generalized Ms constrained integral (MIGO) based controller tuning method to handle the FO-PI case, called F-MIGO, given the fractional order α. The F-MIGO method is then used to develop tuning rules for the FOPDT class of dynamic systems. The final developed tuning rules only apply the relative dead time τ of the FOPDT model to determine the best fractional order α and at the same time to determine the best FO-PI gains. Extensive simulation results are included to illustrate the simple yet practical nature of the developed new tuning rules. The tuning rule development procedure for FO-PI is not only valid for FOPDT but also applicable for other general class of plants.

Stability of radical anions derived from substituted 5-nitrofurans investigated by ESR spectroscopy

1985 ◽  
Vol 50 (7) ◽  
pp. 1594-1601 ◽  
Author(s):  
Jiří Klíma ◽  
Larisa Baumane ◽  
Janis Stradinš ◽  
Jiří Volke ◽  
Romualds Gavars
Keyword(s):  
Radical Anion ◽  
High Stability ◽  
Esr Spectroscopy ◽  
Reaction Path ◽  
Order Reaction ◽  
Second Order ◽  
Radical Anions ◽  
Second Order Reaction ◽  
Unpaired Electron Density ◽  
The Stability

It has been found that the decay in dimethylformamide and dimethylformamide-water mixtures of radical anions in five of the investigated 5-nitrofurans is governed by a second-order reaction. Only the decay of the radical anion generated from 5-nitro-2-furfural III may be described by an equation including parallel first- and second-order reactions; this behaviour is evidently caused by the relatively high stability of the corresponding dianion, this being an intermediate in the reaction path. The presence of a larger conjugated system in the substituent in position 2 results in a decrease of the unpaired electron density in the nitro group and, consequently, an increase in the stability of the corresponding radical anions.

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