The Frequency Research of Fractional Order PIλDμ Controller

2013 ◽  
Vol 278-280 ◽  
pp. 1521-1524
Author(s):  
Hai Qun Wang ◽  
Ling Meng
Keyword(s):  
Complex Systems ◽  
Frequency Domain ◽  
Control Systems ◽  
Fractional Order ◽  
Industrial Production ◽  
Pid Controller ◽  
Time Analysis ◽  
Integer Order ◽  
Integral Order

Since most of the control systems in real industrial production are fractional，there is necessery to propose fractional order PIλDμ controller, which extend the traditional integer-order PID controller to fractional order, it has increased two free degree: Integral-order λ and differential-order μ, to more accurately control those complex systems. At the same time analysis the performance of fractional order PIλDμ controller in frequency domain. Especially,the two degrees’ effect to controller.

Exploiting Fractional Order PID Controller Methods in Improving the Performance of Integer Order PID Controllers: A GA Based Approach

2009 ◽  
Author(s):  
Bijoy K. Mukherjee ◽  
Santanu Metia ◽  
Sio-Iong Ao ◽  
Alan Hoi-Shou Chan ◽  
Hideki Katagiri ◽  
...  
Keyword(s):  
Fractional Order ◽  
Pid Controller ◽  
Pid Controllers ◽  
Integer Order ◽  
Fractional Order Pid ◽  
Fractional Order Pid Controller

Optimal fractional-order PID control design for time-delayed multi-input multi-output seismic-excited structural system

2021 ◽  
pp. 107754632110531
Author(s):  
Abbas-Ali Zamani ◽  
Sadegh Etedali
Keyword(s):  
Time Delay ◽  
Control Systems ◽  
Design Process ◽  
Fractional Order ◽  
Seismic Performance ◽  
Pid Control ◽  
Pid Controller ◽  
Control Design ◽  
Structural System ◽  
Fractional Order Pid

The application of the fractional-order PID (FOPID) controller is recently becoming a topic of research interest for vibration control of structures. Some researchers have successfully implemented the FOPID controller in a single-input single-output (SISO) control structural system subjected to earthquake excitations. However, there is a lack of research that focuses on its application in multi-input multi-output (MIMO) control systems to implement it in seismic-excited structures. In this case, the cross-coupling of the process channels in the MIMO control structural system may result in a complex design process of controllers so that each loop is independently designed. From an operational point of view, the time delay and saturation limit of the actuators are other challenges that significantly affect the performance and robustness of the controller so that ignoring them in the design process may lead to unrealistic results. According to the challenges, the present study proposed an optimal fractional-order PID control design approach for structural control systems subjected to earthquake excitation. Gases Brownian motion optimization (GBMO) algorithm is utilized for optimal tuning of the controller parameters. Considering six real earthquakes and seven performance indices, the performance of the proposed controller, implemented on a ten-story building equipped with an active tendon system (ATS), is compared with those provided by the classical PID controller. Simulation results indicate that the proposed FOPID controller is more efficient than the PID in both terms of seismic performance and robustness against time-delay effects. The proposed FOPID controller can maintain suitable seismic performance in small time delays, while a significant performance loss is observed for the PID controller.

The Inverted Decoupling Based Fractional Order Two-Input-Two-Output IMC Controller

2017 ◽  
Author(s):  
Dazi Li ◽  
Xingyu He
Keyword(s):  
Frequency Domain ◽  
Fractional Order ◽  
Disturbance Rejection ◽  
Internal Model ◽  
Design Method ◽  
Internal Model Control ◽  
Order System ◽  
Single Input Single Output ◽  
Integer Order ◽  
Model Control

Many processes in the industry can be modeled as fractional order, research on the fractional order become more and more popular. Usually, controllers such as fractional order PID (FOPID) or fractional active disturbance rejection control (FADRC) are used to control single-input-single-output (SISO) fractional order system. However, when it comes to fractional order two-input-two-output (TITO) processes, few research focus on this. In this paper, a new design method for fractional order control based on multivariable non-internal model control with inverted decoupling is proposed to handle non-integer order two-input-two-output system. The controller proposed in this paper just has two parameters to tune compared with the five parameters of the FOPID controller, and the controller structure can be achieved by internal model control (IMC) method which means it is easy to implement. The parameters tuning method used in this paper is based on frequency domain strategy. Compared with integer order situation, fractional order method is more complex, because the calculation of the frequency domain characteristics is difficult. The controller proposed in this paper is robust to process gain variations, what’s more, it provides ideal performance for both set point-tracking and disturbance rejection. Numerical results are given to show the performance of the proposed controller.

scholarly journals Absorptive Repetitive Filters with Operators of Generalized Fractional Calculus

2013 ◽  
Vol 13 (4) ◽  
pp. 42-53 ◽  
Author(s):  
Nina Nikolova ◽  
Emil Nikolov
Keyword(s):  
Comparative Analysis ◽  
Fractional Calculus ◽  
Control Systems ◽  
Fractional Order ◽  
Fractional Integration ◽  
Frequency Characteristics ◽  
Rational Approximations ◽  
Integer Order ◽  
New Class ◽  
Generalized Fractional Calculus

Abstract : An essentially new class of repetitive fractional disturbance absorptive filters in disturbances absorbing control systems is proposed in the paper. Systematization of the standard repetitive fractional disturbance absorptive filters of this class is suggested. They use rational approximations of the operators for fractional integration in the theory of fractional calculus. The paper discusses the possibilities for repetitive absorbing of the disturbances with integer order filters and with fractional order filters. The results from the comparative analysis of their frequency characteristics are given below.

Frequency Constrained Adaptive PID Laws for Motion Control Systems

2017 ◽  
Author(s):  
Tesheng Hsiao ◽  
Chung-Chiang Cheng
Keyword(s):  
Frequency Domain ◽  
Control Systems ◽  
Motion Control ◽  
Time Domain ◽  
Pid Controller ◽  
Tracking Performance ◽  
Tracking Errors ◽  
Pid Tuning ◽  
The Time Domain ◽  
Tuning Methods

The proportional-integral-derivative (PID) controller is widely used in motion control systems due to its simplicity and effectiveness. To achieve satisfactory performance, the PID parameters must be properly tuned. Although numerous PID tuning methods were investigated in the past, most of them were based on either time-domain or frequency-domain responses, while integration of features in both domains for PID tuning was less addressed. However, many industrial practitioners still found it difficult to compromise multiple conflicting control objectives, such as fast responses, small overshoot and tracking errors, and good robustness, with PID controllers. Moreover, it is desirable to adjust PID parameters online such that plant variations and unexpected disturbances can be compensated for more efficiently. In view of these requirements, this paper proposes an adaptive PID control law that updates its parameters online by minimizing the time-domain tracking errors subject to frequency-domain constraints that are imposed for loop shaping. By combining optimization criteria in both time and frequency domains for online parameter adjustment, the proposed PID controller can achieve good tracking performance with adequate robustness margin. Then the proposed PID law is applied to control an XZ-table driven by AC servo motors. Experimental results show that the tracking performance of the proposed controller is superior to that of a constant-gain PID controller whose parameters were tuned by the commercial Matlab/Simulink PID tuner.

An Enhanced Robust Fractional Order PID Controller for Electric Machinery System: Tuning Rules and Simulations

2015 ◽  
Author(s):  
Chunyang Wang ◽  
Meng Wu ◽  
Nianchun Cai ◽  
Xuelian Liu ◽  
Chengjun Tian
Keyword(s):  
Fractional Order ◽  
Pid Controller ◽  
Optimal Parameter ◽  
Design Method ◽  
Open Loop ◽  
Electrical Machinery ◽  
Integer Order ◽  
Fractional Order Pid ◽  
Fractional Order Pid Controller ◽  
Machinery System

A design method of enhanced robust fractional order PID controller is proposed to control electrical machinery system. Magnitude margin constraint, phase margin constraint and the gain robustness constraints of partly flat phase in specified dots around crossover frequency are adopted to design enhanced robust fractional order PID controller which has stronger robustness to open-loop gain variation compared with integer order PID controller. Besides, nonlinear optimization function is adopted to hunt for optimal parameter solutions of enhanced robust fractional order PID controller, so the five parameters of enhanced robust fractional order PID controller can be solved. The electrical machinery control system models are simulated and tested by MATLAB/SIMULINK, and the results show that the proposed fractional order PID controller has stronger robustness and smaller overshoot, compared with integer order PID controller.

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