Disturbance rejection FOPID controller design in v-domain

Due to the adverse effects of unpredictable environmental disturbances on real control systems, robustness of control performance becomes a substantial asset for control system design. This study introduces a v-domain optimal design scheme for Fractional Order Proportional-Integral-Derivative (FOPID) controllers with adoption of Genetic Algorithm (GA) optimization. The proposed design scheme performs placement of system pole with minimum angle to the first Riemann sheet in order to obtain improved disturbance rejection control performance. In this manner, optimal placement of the minimum angle system pole is conducted by fulfilling a predefined reference to disturbance rate (RDR) design specification. For a computer-aided solution of this optimal design problem, a multi-objective controller design strategy is presented by adopting GA. Illustrative design examples are demonstrated to evaluate performance of designed FOPID controllers. © 2020COST ActionEuropean Cooperation in Science and Technology (COST) [CA15225]; COST (European Cooperation in Science and Technology)European Cooperation in Science and Technology (COST

Optimal v-plane robust stabilization method for interval uncertain fractional order pid control systems

Robust stability is a major concern for real-world control applications. Realization of optimal robust stability requires a stabilization scheme, which ensures that the control system is stable and presents robust performance for a predefined range of system perturbations. This study presented an optimal robust stabilization approach for closed-loop fractional order proportional integral derivative (FOPID) control systems with interval parametric uncertainty and uncertain time delay. This stabilization approach, which is carried out in a v-plane, relies on the placement of the minimum angle system pole to a predefined target angle within the stability region of the first Riemann sheet. For this purpose, tuning of FOPID controller coefficients was performed to minimize a root angle error that is defined as the squared difference of minimum angle root of interval characteristic polynomials and the desired target angle within the stability region of the v-plane. To solve this optimization problem, a particle swarm optimization (PSO) algorithm was implemented. Findings of the study reveal that tuning of the target angle can also be used to improve the robust control performance of interval uncertain FOPID control systems. Illustrative examples demonstrated the effectiveness of the proposed v-domain, optimal, robust stabilization of FOPID control systems. © 2021 by the authors. Li-censee MDPI, Basel, Switzerland

Analogue Implementation of a Fractional-Order PI^{\lambda} Controller for DC Motor Speed Control

In this paper, an approach to design a fractional-order integral operator s(lambda) where -1 < lambda <0, using an analogue technique, is presented. The integrator with a constant phase angle -80.1 degree (i.e. order lambda = -0.89), bandwidth greater than 3 decades, and maximum relative phase error 1.38% is designed by cascade connection of first-order bilinear transfer segments and first-order low-pass filter. The performance of suggested realization is demonstrated in a fractional-order proportional-integral (FOPI lambda) controller described with proportional constant 1.37 and integration constant 2.28. The design specification corresponds to a speed control system of an armature controlled DC motor, which is often used in mechatronic and other fields of control theory. The behavior of both proposed analogue circuits employing two-stage Op-Amps is confirmed by SPICE simulations using TSMC 0.18 mu m level-7 LA) EN SCN018 CMOS process parameters with +/- 0.9 V supply voltages

A space charge motion simulation with FDTD method and application in negative corona electrostatic field analysis

In this paper, a finite difference time domain based simulation method is presented for the spatio-temporal analysis of space charge motion and the proposed method is applied to negative corona electrostatic field analysis. Drifting and diffusion motion equations of space charges are numerically solved and used in the simulation of corona discharges considering effects of impact ionization, electron attachment, ion–ion recombination and ion–electron recombination. The results obtained from the simulation are discussed

Optimal F-domain stabilization technique for reduction of commensurate fractional-order SISO systems

This paper presents a new approach for reduction of commensurate fractional-order single-input-single-output systems. The minimization in the frequency response error of the reduced order model (ROM) relative to the original system is carried out in the F-plane. A constrained optimization technique is introduced to satisfy the angle criteria for F-domain stability of the proposed ROM. Significant improvements in both the time- and frequency-responses over the recently published literature are illustrated using several numerical examples

An overview of FOPID controller design in v-domain: design methodologies and robust controller performance

The complex v-plane is an emerging design domain for fractional order control system design. Recently, several works demonstrated the advantages of tuning FOPID controllers in v-plane. These approaches essentially perform the minimum angle pole placement to a target angle within the stability region of the v-plane and facilitate fractional order control system design tasks because of inherently guaranteed stabilisation of fractional order transfer functions. Accordingly, the optimal FOPID controller tuning problem can be simplified to placement of minimum angle system pole to a target point within the stability region of the v-plane. After reviewing previous v-domain design works, authors investigate prominent target points that can result in improved FOPID control performance for the v-domain design task. The consideration of target points in polar coordinates can provide two design parameters (angle and magnitude), which can convey essential system knowledge associated with the stability and control performance of FOPID control systems. In this perspective, effects of minimum angle pole positions on control performance indices are investigated in detail, and some prominent target points to manage FOPID design in v-domain have been reported. The v-domain design examples are illustrated to reveal the effects of the sampled pole positions on the robust control performance