Primary Resonance of Dry-Friction Oscillator With Fractional-Order Proportional-Integral-Derivative Controller of Velocity Feedback

2016 ◽  
Vol 11 (5) ◽  
Author(s):  
Yongjun Shen ◽  
Jiangchuan Niu ◽  
Shaopu Yang ◽  
Sujuan Li
Keyword(s):  
Analytical Solution ◽  
Fractional Order ◽  
Dry Friction ◽  
Primary Resonance ◽  
Proportional Integral Derivative ◽  
Velocity Feedback ◽  
Integer Order ◽  
Proportional Integral ◽  
Friction Oscillator ◽  
Dynamical Properties

The classical mass-on-moving-belt model describing friction-induced vibration is studied. The primary resonance of dry-friction oscillator with fractional-order PID (FOPID) controller of velocity feedback is investigated by Krylov–Bogoliubov–Mitropolsky (KBM) asymptotic method, and the approximately analytical solution is obtained. The effects of the parameters in FOPID controller on dynamical properties are characterized by five equivalent parameters. Those equivalent parameters could distinctly illustrate the effects of the parameters in FOPID controller on the dynamical response. The effects of dry friction on the dynamical properties are characterized in the form of the equivalent linear damping and nonlinear damping. The amplitude-frequency equation for steady-state solution associated with the stability condition is also studied. A comparison of the analytical solution with the numerical results is fulfilled, and their satisfactory agreement verifies the correctness of the approximately analytical results. Finally, the effects of the coefficients and orders in FOPID controller on the amplitude-frequency curves are analyzed, and the control performances of FOPID and traditional integer-order proportional-integral-derivative (PID) controllers are compared. The comparison results show that FOPID controller is better than traditional integer-order PID controller for controlling the primary resonance of dry-friction oscillator, when the coefficients of the two controllers are the same. This presents theoretical basis for scholars and engineers to design similar fractional-order controlled system.

Design of an integer order proportional–integral/proportional–integral–derivative controller based on model parameters of a certain class of fractional order systems

2018 ◽  
Vol 233 (3) ◽  
pp. 320-334 ◽  
Author(s):  
Erhan Yumuk ◽  
Müjde Güzelkaya ◽  
İbrahim Eksin
Keyword(s):  
Fractional Order ◽  
Design Parameter ◽  
Design Methodology ◽  
Model Parameters ◽  
Proportional Integral Derivative ◽  
Level Control ◽  
Proportional Integral Derivative Controller ◽  
Integer Order ◽  
Proportional Integral ◽  
Order Pole

In this study, we deal with systems that can be represented by single fractional order pole models and propose an integer order proportional–integral/proportional–integral–derivative controller design methodology for this class. The basic principle or backbone of the design methodology of the proposed controller relies on using the inverse of the fractional model and then approximating this fractional controller transfer function by a low integer order model using Oustaloup filter. The emerging integer order controller reveals itself either in pre-filtered proportional–integral or proportional–integral–derivative form by emphasizing on the dominancy concept of pole-zero configuration. Parameters of the proposed controllers depend on the parameters of the single fractional order pole model and the only free design parameter left is the overall controller gain. This free design parameter is determined via some approximating functions relying on an optimization procedure. Simulation results show that the proposed controller exhibits either satisfactory or better results with respect to some performance indices and time domain criteria when they are compared to classical integer order proportional–integral–derivative and fractional order proportional–integral–derivative controllers. Moreover, the proposed controller is applied to real-time liquid level control system. The application results show that the proposed controller outperforms the other controllers.

scholarly journals A new design of fractional-order dynamic matrix control with proportional–integral–derivative-type structure

2019 ◽  
Vol 52 (5-6) ◽  
pp. 567-576 ◽  
Author(s):  
Dawei Wang ◽  
Hongbo Zou ◽  
Jili Tao
Keyword(s):  
Fractional Order ◽  
Heating Furnace ◽  
Proportional Integral Derivative ◽  
Dynamic Matrix Control ◽  
Integer Order ◽  
Proportional Integral ◽  
Dynamic Matrix ◽  
Derivative Type ◽  
Matrix Control ◽  
Industrial Heating

Most dynamic systems in practice are of fractional order and often the models using fractional-order equations can grasp their intrinsic properties with more accuracy compared with conventional differential equations. In this paper, a fractional-order modeling-based proportional–integral–derivative-type dynamic matrix control is developed and tested on a typical industrial heating furnace system with fractional-order dynamics. The Oustaloup approximation method is first adopted to obtain the model approximation of the processes, which paves the way for the application of integer order dynamic matrix control to the fractional-order systems. Meanwhile, a set of proportional–integral–derivative-type operators are introduced in the cost function to further optimize the dynamic matrix control in terms of tracking and disturbance-rejection performance. The resulting controller bears both the merits of the dynamic matrix control and the proportional–integral–derivative, and thus improved control performance is obtained. In addition, an industrial heating furnace process system is given to test the performance of the proposed method in comparison with traditional integer order model-based dynamic matrix control, and results show that the proposed method gives improved system performance.

A novel fractional order PID plus derivative (PIλDµDµ2) controller for AVR system using equilibrium optimizer

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Abdulsamed Tabak
Keyword(s):  
Fractional Order ◽  
Transient Response ◽  
Superior Performance ◽  
Control Performance ◽  
Proportional Integral Derivative ◽  
Content Type ◽  
Proportional Integral ◽  
Avr System ◽  
Optimization Parameters ◽  
Fractional Order Pid

Purpose The purpose of this paper is to improve transient response and dynamic performance of automatic voltage regulator (AVR). Design/methodology/approach This paper proposes a novel fractional order proportional–integral–derivative plus derivative (PIλDµDµ2) controller called FOPIDD for AVR system. The FOPIDD controller has seven optimization parameters and the equilibrium optimizer algorithm is used for tuning of controller parameters. The utilized objective function is widely preferred in AVR systems and consists of transient response characteristics. Findings In this study, results of AVR system controlled by FOPIDD is compared with results of proportional–integral–derivative (PID), proportional–integral–derivative acceleration, PID plus second order derivative and fractional order PID controllers. FOPIDD outperforms compared controllers in terms of transient response criteria such as settling time, rise time and overshoot. Then, the frequency domain analysis is performed for the AVR system with FOPIDD controller, and the results are found satisfactory. In addition, robustness test is realized for evaluating performance of FOPIDD controller in perturbed system parameters. In robustness test, FOPIDD controller shows superior control performance. Originality/value The FOPIDD controller is introduced for the first time to improve the control performance of the AVR system. The proposed FOPIDD controller has shown superior performance on AVR systems because of having seven optimization parameters and being fractional order based.

Fractional order frequency proportional-integral-derivative control of microgrid consisting of renewable energy sources based on multi-objective grasshopper optimization algorithm

2021 ◽  
pp. 014233122110346
Author(s):  
Abdulsamed Tabak
Keyword(s):  
Fractional Order ◽  
Optimization Algorithm ◽  
Frequency Control ◽  
Frequency Deviation ◽  
Control Signal ◽  
Proportional Integral Derivative ◽  
Proportional Integral ◽  
Multi Objective ◽  
Grasshopper Optimization Algorithm ◽  
Grasshopper Optimization

In recent years, fractional order proportional-integral-derivative (FOPID) controllers have been applied in different areas in the academy due to their superior performance over conventional proportional-integral-derivative (PID) controllers. When the literature is reviewed, it has been observed that lack of studies that use swarm-based and multi-objective optimization algorithms together with FOPID controllers in frequency control of micro-grid. The load frequency control (LFC) problem is considered as two objectives in order to eliminate the complications that occur when only the frequency deviation is minimized. In our study, a method called MOGOA-FOPID in which both the frequency deviation and the control signal are minimized together for the frequency control in the microgrid is proposed. By using the multi-objective grasshopper optimization algorithm (MOGOA), both the frequency deviation and the control signal are minimized together, and thus, it is aimed to limit the battery capacity, reduce the flywheel jerk and avoid high diesel fuel consumption as well as an effective frequency control. In order to obtain a more realistic system, not only the photovoltaic (PV) solar and wind power but also the load demand is taken in a stochastic structure. Then, the results of the proposed MOGOA-FOPID are compared with the results of multi-objective genetic algorithm (MOGA)-based PID/FOPID and MOGOA-PID and its superiority is demonstrated. Finally, robustness tests of the system are performed under the perturbed parameters and outperform of MOGOA-FOPID over other methods is seen.

Sliding mode observer-based fractional-order proportional–integral–derivative sliding mode control for electro-hydraulic servo systems

2020 ◽  
Vol 234 (10) ◽  
pp. 1887-1898 ◽  
Author(s):  
Cheng Cheng ◽  
Songyong Liu ◽  
Hongzhuang Wu
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Sliding Mode ◽  
Lyapunov Theory ◽  
Sliding Mode Observer ◽  
Proportional Integral Derivative ◽  
Servo Systems ◽  
Proportional Integral ◽  
Mode Control ◽  
Hydraulic Servo

This paper proposes an observer-based sliding mode control method for electro-hydraulic servo systems with uncertain nonlinearities, external disturbances, and immeasurable states. The mathematical model is built based on the principle of electro-hydraulic servo systems. Owing to its highly robustness and finite time properties, the sliding mode observer is chosen and designed to estimate the velocity and the equivalent pressure online only using the position feedback. Then, in order to tackle the chattering problem of conventional sliding mode control and increase the control accuracy, a novel second-order sliding mode control scheme is proposed based on the fractional-order proportional–integral–derivative sliding surface and the state observer. The stability of the overall system is proved by Lyapunov theory. Finally, the detailed simulations are conducted, which include the comparative analysis of control performance with other methods and the study of observation performance.

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