Review, Design, Optimization and Stability Analysis of Fractional-Order PID Controller

Soukkou, Ammar; BELHOUR, M.C.; Leulmi, Salah

doi:10.5815/ijisa.2016.07.08

Cited by 26 publications

(22 citation statements)

References 66 publications

(78 reference statements)

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“…The gain matrix K can be obtained using equation (14). (14) where the matrix P is derived from Riccati equation according to equation (15).…”

Section: B Lqr Methodsmentioning

confidence: 99%

“…Some researchers have tried to apply different types of flight control methods to an aircraft, in particular, the quadrotor series. They consist of PID (Proportional, Integral and Derivative) methods [14] [15], LQ (Linear Quadratic) [16] [17] [18], utilising fusion and filter methods such as complementary methods, DCM (Direct Cosine Matrix) filters, and the Kalman filter method [19]. LQ methods, such as LQR (Linear Quadratic Regulator) and LQG (Linear Quadratic Gaussian) utilising HJB (Hamilton-Jacobi-Bellman) equations in managing cost functions to achieve optimal control.…”

Section: Introductionmentioning

confidence: 99%

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Translation Movement Stability Control of Quad Tiltrotor Using LQR and LQG

Dharmawan¹,

Ashari²,

Putra³

2018

IJISA

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Quadrotor as one type of UAV (Unmanned Aerial Vehicle) is a system that underactuated. It means that the system has a signal control amount is lower than the degrees of freedom or DOF (Degree Of Freedom). This condition causes the quadrotor have limited mobility. If quadrotor is made to have 6 DOF or more (overactuated system), the motion control system to optimise the flight will be different from before. We need to develop overactuated quadrotor control. Quadtiltrotor as the development of quadrotor has some control signal over its DOF. So we call it as an overactuated system. Based on the type of manoeuvre to do, the transition process when the quad tiltrotor performs a translational motion using the tilting rotor need special treatment. The tilt angle change is intended that the quad tiltrotor can perform translational motion while still maintaining its orientation angle near 0°. This orientation angle can change during the undesirable rotational movement as the effect of the transition process. If additional rotational movements cannot be damped, the quad tiltrotor can experience multi overshoot, steady-state error, or even fall. Because of this matter, we need to develop flight control system to handle it. The flight control system of quad tiltrotor can be designed using a model of the system. Models can be created using quad tiltrotor dynamics by the Newton-Euler approach. Then the model is simulated along with the control system using the method of control. Several control methods can be utilised in a quad tiltrotor flight systems. However, with the implementation of LQG control method and Integrator, optimal translational control of the quad tiltrotor can be achieved.

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“…The gain matrix K can be obtained using equation (14). (14) where the matrix P is derived from Riccati equation according to equation (15).…”

Section: B Lqr Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Translation Movement Stability Control of Quad Tiltrotor Using LQR and LQG

Dharmawan¹,

Ashari²,

Putra³

2018

IJISA

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“…Autotuning methods for fractional order PID controllers were also proposed [21][22][23]. Some rather recent review papers on fractional order controllers can be found in [24][25][26] and provide an insight into fractional order control of different types. An excellent review paper on fractional order controllers, including their most widely used continuous and discrete approximation methods, as well as their digital and analogue implementation methods.…”

Section: Introductionmentioning

confidence: 99%

Event-Based Implementation of Fractional Order IMC Controllers for Simple FOPDT Processes

2020

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Fractional order calculus has been used to generalize various types of controllers, including internal model controllers (IMC). The focus of this manuscript is towards fractional order IMCs for first order plus dead-time (FOPDT) processes, including delay and lag dominant ones. The design is novel at it is based on a new approximation approach, the non-rational transfer function method. This allows for a more accurate approximation of the process dead-time and ensures an improved closed loop response. The main problem with fractional order controllers is concerned with their implementation as higher order transfer functions. In cases where central processing unit CPU, bandwidth allocation, and energy usage are limited, resources need to be efficiently managed. This can be achieved using an event-based implementation. The novelty of this paper resides in such an event-based algorithm for fractional order IMC (FO-IMC) controllers. Numerical results are provided for lag and delay dominant FOPDT processes. For comparison purposes, an integer order PI controller, tuned according to the same performance specifications as the FO-IMC, is also implemented as an event-based control strategy. The numerical results show that the proposed event-based implementation for the FO-IMC controller is suitable and provides for a smaller computational effort, thus being more suitable in various industrial applications.

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“…Integer order system control by posing it as a fractional order system has been proposed in [38], wherein parameter  acts as input to the fuzzy controller, and µ as output. A review of physicalfractional and biological-genetic operators for modeling and control of industrial process by using multi objective genetic algorithm to optimize the parameters of the FOPID is analyzed in [39]. In [40], authors have presented fractional-order feedback controller for control and synchronization of fractional-order chaotic systems.…”

Section: Introductionmentioning

confidence: 99%

A Genetic Algorithm based Fractional Fuzzy PID Controller for Integer and Fractional order Systems

Kumar¹,

Sharma²

2018

IJISA

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This work aims at designing a fractional Proportional-Integral-Derivative controller wherein we hybridize a genetic algorithm based fractional Proportional-Integral-Derivative controller with a fuzzy logic Proportional-Integral-Derivative controller. We attempt at optimizing the fractional order Proportional-Integral-Derivative controller parameters by incorporating a Genetic Algorithm based mechanism. Thereafter, the optimized genetic algorithm based fractional Proportional-Integral-Derivative control is further fine tuned and hybridized to a fuzzy Proportional-Integral-Derivative control. Here, fuzzy logic based inference mechanism is used to tackle system uncertainties and use of rule firing strengths produces an adaptive control. Genetic Algorithm has been used to generate the most optimal controller by a natural selection of the fittest. Amalgamating Genetic Algorithm and fuzzy control approaches on fractional order systems produces a highly efficient and noise tolerant control regime. We give simulation results and compare our hybrid approach against conventional and fractional Proportional-Integral-Derivative approaches on various integer and fractional order systems (with dead time) to elucidate its superiority and effectiveness.

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Review, Design, Optimization and Stability Analysis of Fractional-Order PID Controller

Cited by 26 publications

References 66 publications

Translation Movement Stability Control of Quad Tiltrotor Using LQR and LQG

Translation Movement Stability Control of Quad Tiltrotor Using LQR and LQG

Event-Based Implementation of Fractional Order IMC Controllers for Simple FOPDT Processes

A Genetic Algorithm based Fractional Fuzzy PID Controller for Integer and Fractional order Systems

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