Fractional-order PI plus D controller for second-order integrating plants: Stabilization and tuning method

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.

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

Transactions of the Institute of Measurement and Control ◽

10.1177/0142331216634427 ◽

2016 ◽

Vol 39 (8) ◽

pp. 1225-1235 ◽

Cited By ~ 7

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.

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An Adaptive Frequency-Fixed Second-Order Generalized Integrator-Quadrature Signal Generator Using Fractional-Order Conformal Mapping Based Approach

IEEE Transactions on Power Electronics ◽

10.1109/tpel.2019.2951427 ◽

2020 ◽

Vol 35 (6) ◽

pp. 5548-5552 ◽

Cited By ~ 1

Author(s):

Mohd. Afroz Akhtar ◽

Suman Saha

Keyword(s):

Conformal Mapping ◽

Fractional Order ◽

Second Order ◽

Signal Generator ◽

Quadrature Signal

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Fractional-Order PII1/2DD1/2 Control: Theoretical Aspects and Application to a Mechatronic Axis

Applied Sciences ◽

10.3390/app11083631 ◽

2021 ◽

Vol 11 (8) ◽

pp. 3631

Author(s):

Luca Bruzzone ◽

Mario Baggetta ◽

Pietro Fanghella

Keyword(s):

Fractional Order ◽

Position Control ◽

Tracking Error ◽

Experimental Tests ◽

Maximum Torque ◽

Control Effort ◽

Tuning Method ◽

Alternative Approach ◽

Remarkable Reduction ◽

Distributed Order

Fractional Calculus is usually applied to control systems by means of the well-known PIlDm scheme, which adopts integral and derivative components of non-integer orders λ and µ. An alternative approach is to add equally distributed fractional-order terms to the PID scheme instead of replacing the integer-order terms (Distributed Order PID, DOPID). This work analyzes the properties of the DOPID scheme with five terms, that is the PII1/2DD1/2 (the half-integral and the half-derivative components are added to the classical PID). The frequency domain responses of the PID, PIlDm and PII1/2DD1/2 controllers are compared, then stability features of the PII1/2DD1/2 controller are discussed. A Bode plot-based tuning method for the PII1/2DD1/2 controller is proposed and then applied to the position control of a mechatronic axis. The closed-loop behaviours of PID and PII1/2DD1/2 are compared by simulation and by experimental tests. The results show that the PII1/2DD1/2 scheme with the proposed tuning criterium allows remarkable reduction in the position error with respect to the PID, with a similar control effort and maximum torque. For the considered mechatronic axis and trapezoidal speed law, the reduction in maximum tracking error is −71% and the reduction in mean tracking error is −77%, in correspondence to a limited increase in maximum torque (+5%) and in control effort (+4%).

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