Robust Fractional Order Controller Research Articles

Vaccination controllers for SEIR epidemic models based on fractional order dynamics

Abstract This article proposes a novel fractional order robust vaccination controller based on the fractional order SEIR epidemic model which is subject to the parametric uncertainties. Classical sliding mode controller is robust but due to the high frequency chattering phenomena, it is not feasible for practical implementation. To reduce the chattering phenomena, a new fractional order sliding manifold is proposed and a low gain fractional order robust vaccination control law is formulated with same robustness as classical sliding mode control. Effectiveness of the proposed vaccination control strategy is shown through numerical simulations.

Robust Fractional Order Controllers for Distributed Systems

Robust Fractional Order Controllers for Distributed Systems

Fractional sliding mode control of underwater ROVs subject to non-differentiable disturbances

Some hydrodynamic phenomena of an underwater Remotely Operated Vehicle (ROV), such as turbulence, cavitation, and multi-phase fluidic regimes, are associated to continuous but nowhere differentiable functions. These disturbances stand as complex forces potentially influencing the ROVs during typical navigation tasks. In this paper, the tracking control of a ROV subject to nonsmooth Holder disturbances is proposed based on a fractionalorder robust controller that ensures exponential tracking. Notably, the controller gives rise to a closed-loop system with the following characteristics: a) continuous control signal that alleviates chattering effects; b) the fractional sliding motion is substantiated on a proposed resetting memory principle; c) the control is robust to model uncertainties; and d) exact rejection of Holder disturbances in finite-time. A representative simulation study reveals the feasibility of the proposed scheme.

Design of robust fractional‐order lead–lag controller for uncertain systems

In this study, a new method for designing fractional-order robust lead–lag controllers in order to ensure robust stability in uncertain systems with unstructured uncertainty, has been presented. In this method, at first by the use of pole placement and solving Diophantine equation, a fractional-order controller, which has a new form, is designed in order to stabilise the nominal system. Then a constrained optimisation problem is solved, in which, the cost function consists of the numerator and denominator coefficients of the proposed fractional-order controller and the constraints are the robust stability conditions. Finally, the parameters of the robust fractional-order controller are acquired. This method is implemented on an unstable system and simulation results are presented.

A new fractional-order sliding mode controller via a nonlinear disturbance observer for a class of dynamical systems with mismatched disturbances

This paper investigates the stabilization and disturbance rejection for a class of fractional-order nonlinear dynamical systems with mismatched disturbances. To fulfill this purpose a new fractional-order sliding mode control (FOSMC) based on a nonlinear disturbance observer is proposed. In order to design the suitable fractional-order sliding mode controller, a proper switching surface is introduced. Afterward, by using the sliding mode theory and Lyapunov stability theory, a robust fractional-order control law via a nonlinear disturbance observer is proposed to assure the existence of the sliding motion in finite time. The proposed fractional-order sliding mode controller exposes better control performance, ensures fast and robust stability of the closed-loop system, eliminates the disturbances and diminishes the chattering problem. Finally, the effectiveness of the proposed fractional-order controller is depicted via numerical simulation results of practical example and is compared with some other controllers.

Robust Fractional Order Controller for Chaotic Systems

In this paper, we propose a robust fractional controller structure to control chaotic systems. The fractional controller structure is based on the predictive control of chaotic systems. The parameters of the controller are obtained by minimizing the error state energy.Simulation results on Chen and Lorenz chaotic systems show the effectiveness of the proposed controller to reject the noise and the disturbance injected to these systems states. These results show also that the proposed controller gives better results than the standard predictive control.

Adaptive fuzzy fractional-order sliding mode controller for a class of dynamical systems with uncertainty

A sliding mode control (SMC) strategy is proposed for a second-order non-linear system using fractional calculus and adaptive fuzzy compensator, named fuzzy fractional-order SMC (FFOSMC). The major contribution of this research includes the formulation of a robust fractional-order controller based on a novel non-integer sliding manifold. The proposed controller utilizes reduced discontinuous switching gain using a fuzzy logic system. A fractional-order adaptation law is derived to update the fuzzy logic system, which has more degrees of freedom to achieve the desired performance. The stability of the closed-loop system is guaranteed using fractional-order Lyapunov theory. The parameters of the proposed control method are optimized using Simulink response optimization. Finally, the performance of the FFOSMC is fully investigated and compared with a conventional SMC controller and an integral SMC controller. From simulation results, it is concluded that the proposed algorithm is effective and more robust.

Design and Implementation of Fractional Order Controller for Service Robots

In this paper, the fractional order motion control is designed basing on the Leader IDX service robotic platform, where the implementation of robust fractional order controller is introduced in details. The fractional order PDμ control is analyzed in frequency domain by using an FIR/IIR method. The system model of the motor of Leader I-DX is established in MATLAB so that the influence of μ to the whole control system can be verified, and the comparisons of PD and PDμ controllers are shown as well. Motivated by the better performance of fractional order controllers, a digital implementation of fractional order PDμ controllers using PRONY technique is applied so that the incremental fractional order controllers can be realized. The real experiments on Leader I-DX platform are illustrated to validate the above concepts.

Tuning of robust FO[PI] plus fractional lead controller for integrating time-delay systems

This paper presents the design of a robust fractional-order controller consisting of FO[PI] controller and fractional lead compensator, for the generalised, known and minimum-phase integrating time-delay plants. The fractional-order controller is designed to satisfy design specifications of phase margin, gain crossover frequency and flat phase constraint. Using Bode's integral relationship, a FO[PI] controller is designed to satisfy the flat phase constraint which ensure that phase bode plot of the compensated system is flat at gain crossover frequency. Then, the design of fractional lead compensator is done to satisfy design specifications of phase margin and gain crossover frequency. The simulation results illustrate the effectiveness and simplicity of presented method for robust controller design with an iso-damping property.

Robust fractional-order control of PMSG-based WECS

This paper presents some novel fractional-order nonlinear sliding mode controllers for maximum power extraction of a grid-connected wind energy conversion system. Two similar fractional-order controllers with nonlinear sliding manifolds are proposed for generator-side and grid-side converters. The main role of the generator-side controller is regulating the mechanical speed of wind turbine to follow an optimum speed. On the other hand, the grid-side controller main goal is governing the active and reactive power by tuning DC-link voltage. Practical stability of both controllers is achieved by fractional-order nonlinear stability theorems. Comparative simulations are presented to show the effectiveness of the proposed controllers.

A robust fractional order controller for an EAF electrode position system

This paper proposes a simple fractional-order controller with a PI α structure for controlling the position of the electrodes of an electric arc furnace (EAF). The dynamics of one of the three electrodes of an industrial EAF process was experimentally identified. Models of the electrode position system and the furnace electrical system (electric arc impedance model) were obtained. This identification procedure yielded an equivalent fourth order plus time delay transfer function, and showed strong plant parameter variations and measured and unmeasured disturbances. We therefore propose a new methodology for the design of fractional-order robust controllers for this system. By carrying out a partial inversion of the dynamics, a method for fractional-order robust control of first order plus time delay plants was developed and applied to this process. It was shown that the attained controllers significantly outperformed the robustness achieved with PI and PID controller (also combined with the partial dynamics inversion term), while adding only moderate complexity to the control structure.

Simplified Optimization Routine for Tuning Robust Fractional Order Controllers

Fractional order controllers have been used intensively over the last decades in controlling different types of processes. The main methods for tuning such controllers are based on a frequency domain approach followed by optimization routine, generally in the form of the Matlab fminsearch, but also evolving to more complex routines, such as the genetic algorithms. An alternative to these time consuming optimization routines, a simple graphical method has been proposed. However, these graphical methods are not suitable for all combinations of the imposed performance specifications. To preserve their simplicity, but also to make these graphical methods generally applicable, a modified graphical method using a very straightforward and simple optimization routine is proposed within the paper. Two case studies are presented, for tuning fractional order PI and PD controllers.

Robust fractional order controller based on improved particle swarm optimization algorithm for the wind turbine equipped with a doubly fed asynchronous machine

In this paper, an improvement of the particle swarm optimization algorithm is proposed. The aim of this algorithm is to determine the optimal parameters of a robust fractional order controller which guarantees stability and robustness of required nominal performances. Controllers with fractional order are first obtained by a previous transformation of the multi-objective optimization problem into an equivalent single-optimization problem, and then solved by the proposed improved particle swarm optimization algorithm. In order to examine the stability and performance robustness, this controller is applied on an ill-conditioned wind turbine equipped with a doubly fed asynchronous machine, where the system dynamics is modeled by an unstructured output multiplicative uncertainty model. The simulation results show the effectiveness of the proposed synthesis method, where the control is compared (for the same design frequency-domain specifications) for both the robust fractional order controller such as that designed through the standard particle swarm optimization algorithm and that obtained by resolving the multi-objective optimization problem.

Robust Fractional Order Control of a DC Motor Based on Particle Swarm Optimization

his paper presents a robust stable controller for speed control of a linear permanent magnet DC motor. A fractional controller is presented and the optimal parameters of this controller are obtained using Particle Swarm Optimization (PSO) technique. Interval uncertainty is considered in the parameters of the DC motor. Stability of the closed loop system with the proposed controller in presence of interval uncertainty is verified through the extension of Kharitanov’s theorem for fractional order systems. Simulation results demonstrate the successful performance of the proposed controller.

Robust fractional order controller for irrigation main canal pools with time-varying dynamical parameters

A new method is proposed with which to design a class of robust fractional order controllers – which we denote as FPI controllers since they can be regarded as a generalization of standard PI controllers – for the effective control of water distribution in irrigation main canal pools characterized by time-varying dynamical parameters. The closed loop behavior of the nominal plant is defined by using frequency specifications, which are combined with an optimization procedure that minimizes the IAE ( Integral of Absolute Error) – a cost related to the closed loop time response specifications – in the whole range of plant parameter variations. Interest in such robust fractional order controllers is justified by the fact that dynamical parameters of irrigation main canal pools may change drastically according to their operational regimes. Equivalent FPI, PI and PID controllers – in the sense of their exhibiting the same closed loop dynamics for the nominal plant specifications – were simulated for several working conditions, and their behaviors were compared. Additional issues, such as noise rejection or robustness to unmodelled high frequency dynamics have also been considered.

Fractional order robust control for cogging effect compensation in PMSM position servo systems: Stability analysis and experiments

Fractional calculus is a generalization of the integration and differentiation to the fractional (non-integer) order. In this paper, for the first time, a fractional order robust control (FO-RC) method is devised for cogging effect compensation on permanent magnetic synchronous motors (PMSM) position and velocity servo system. In this FO-RC scheme, a fractional order robust controller is designed to compensate the cogging effect, and guarantee the boundedness of all signals. Stability properties have been proven for the systems with the traditional integer order robust control method and the proposed fractional order robust control scheme, respectively. Simulation illustration and experimental validation are presented to show the advantage of the proposed FO-RC scheme for cogging effect compensation over the conventional integer order method.

Fractional order robust control based on Bode's ideal transfer function

Robust control based on fractional order calculus is gaining more and more interests from the control community. It was known that the open-loop transfer function of a good control system shows a fractional order integral form with a fractional order between 1 and 2. This fractional order integral form is called the Bode's ideal loop transfer function. In this paper, a new conception method of a controller which will guarantee that the open-loop transfer function of a unity feedback control will be the Bode's ideal transfer function is considered. The basic ideas and the derived formulations are presented. A numerical example is also reported to validate the introduced conception strategy.

Smith predictor based robust fractional order control: Application to water distribution in a main irrigation canal pool

This paper proposes a new methodology to design fractional integral controllers combined with Smith predictors, which are robust to high frequency model changes. In particular, special attention is paid to time delay changes. These controllers show also less sensitivity to high frequency measurement noise and disturbances than PI or PID controllers. This methodology is applied to design controllers for water distribution in a main irrigation canal pool. Simulated results of standard PI and PID controllers plus a Smith predictor, and the controller developed in this paper are compared when applied to the dynamical model of a real main irrigation canal pool showing that our controller exhibits better and more robust features than these. Moreover our controller is compared with other more complex control techniques as predictive control and robust H ∞ controllers, exhibiting better or similar performances than these.

Fractional robust control of main irrigation canals with variable dynamic parameters

A new method is proposed for controlling main irrigation canals with variable dynamical parameters based on robust fractional order controllers. A methodology for designing PID controllers robust to changes in the time delay and the gain is presented first. Then this method is generalized to design fractional controllers that exhibit the same robustness as the previous PID to time delay and gain changes, but are noticeably more robust to variations in the dominant time constant of the process. This method is applied to control main irrigation canals. Extensive numerical simulations using the dynamic model of a real canal were carried out. Then experimental results were obtained in a prototype canal that proved the effectiveness of the proposed control method in terms of performance and robustness.

On Fractional-Order QFT Controllers

We propose the synthesis of robust fractional-order controllers using the principles of quantitative feedback theory (QFT). The resulting controllers are called as fractional-order QFT controllers. To demonstrate the synthesis method, we synthesize proportional-integral-derivative (PID) and more general types of fractional-order QFT controllers for a fractional-order plant, a DC motor, and a multistage flash desalination process.