scholarly journals Discrete-Time Fractional, Variable-Order PID Controller for a Plant with Delay

Entropy ◽  
2020 ◽  
Vol 22 (7) ◽  
pp. 771 ◽  
Author(s):  
Piotr Oziablo ◽  
Dorota Mozyrska ◽  
Małgorzata Wyrwas
Keyword(s):  
Pid Controller ◽  
Step Response ◽  
Variable Order ◽  
Proportional Integral Derivative ◽  
Third Order ◽  
The Third ◽  
Squared Error ◽  
Unit Step ◽  
Weighted Error ◽  
Types Of Error

In this paper, we discuss the implementation and tuning algorithms of a variable-, fractional-order Proportional–Integral–Derivative (PID) controller based on Grünwald–Letnikov difference definition. All simulations are executed for the third-order plant with a delay. The results of a unit step response for all described implementations are presented in a graphical and tabular form. As the qualitative criteria, we use three different error values, which are the following: a summation of squared error (SSE), a summation of squared time weighted error (SSTE) and a summation of squared time-squared weighted error (SST2E). Besides three types of error values, obtained results are additionally evaluated on the basis of an overshoot and a rise time of the output signals achieved by systems with the designed controllers.

Optimal MIMO PID Controllers for the MIMO Processes

2011 ◽  
Author(s):  
Xian Hong Li ◽  
Hai Bin Yu ◽  
Ming Zhe Yuan ◽  
Chuan Zhi Zang ◽  
Zhuo Wang
Keyword(s):  
Pid Control ◽  
Pid Controller ◽  
Design Method ◽  
Pid Controllers ◽  
Proportional Integral Derivative ◽  
Nonlinear Constraint ◽  
Pid Tuning ◽  
Squared Error ◽  
Different Types ◽  
Tuning Methods

This paper focuses on the design method of the optimal multiple inputs and multiple outputs (MIMO) proportional integral derivative (PID) controllers for the MIMO processes via using Lyapunov theorems. A hybrid augmented integral squared error (HAISE) is applied to design the optimal multi-loop PID controller for the MIMO plants. The optimal multi-loop PID control problem is transformed into a nonlinear constraint optimization (NLCO) problem. The optimal PID controller parameters are obtained from solving the NLCO problem. The design method is applied to devise the multi-loop optimal PID controller for different types of MIMO plants and the optimal PID controller under different control weight is shown in this paper. The performances of different PID tuning methods are studied too. The computer simulation results are presented to demonstrate the effectiveness of the design method and good performance and robustness of the optimal multi-loop PID controllers.

scholarly journals Metode Tuning Operating Range Fuzzy PID Controller pada Sistem Orde Tiga

2020 ◽  
Vol 12 (1) ◽  
pp. 33-39
Author(s):  
Nana Sutarna ◽  
B. S. Rahayu Purwanti
Keyword(s):  
Pid Controller ◽  
Fuzzy Logic Controller ◽  
Order System ◽  
Fuzzy Pid ◽  
Third Order ◽  
Operating Range ◽  
Fuzzy Pid Controller ◽  
The Third ◽  
Fuzzy Input ◽  
Self Tuning

This research discusses the development of a model Fuzzy Proportional, Integral, Derivative (Fuzzy PID) controller models and self-tuning. This method has been implemented in the third-order system of Differential Equations, as a sample implementation of a PID controller. The methods self-tuning known are fuzzy rules, membership function (MF), and scaling factor. The focus of the discussion in this research is to introduce self-tuning to the operating range (OR) setting of MF. Previous research has succeeded in converting a PID controller to a Fuzzy Logic Controller (FLC) which is in accordance with the PID structure. The FLC has three inputs and one output as in the PID controller, hereinafter referred to as Fuzzy PID controller. Knowledgebase on the FLC structure of three inputs one output is expressed in the form of cubic fuzzy associative memory (FAM). The conversion was done by mapping errors, integrals error, derivative errors and outputs of PID controller into the OR of MF Fuzzy input/output. The size of the OR conversion value on the MF fuzzy input was set, so the response transient is set-to-point. While the OR value of the MF fuzzy output was fixed as a limitation. Improved settling time was reached up to 75.3% and percent overshoot was reduced by 57.7% in Fuzzy PID with PID controller. The output signal from the Fuzzy PID controller showed the smallest amplitude of 24.12, while the PID controller was 32.53. The amplitude unit depends on the Fuzzy PID controller parameters when it applied the real plant. The third-order Fuzzy PID controller has been successfully simulated in Simulink/Matlab.

scholarly journals CONTINUOUS FIREFLY ALGORITHM FOR OPTIMAL TUNING OF PID CONTROLLER IN AVR SYSTEM

2014 ◽  
Vol 65 (1) ◽  
pp. 44-49 ◽  
Author(s):  
Omar Bendjeghaba
Keyword(s):  
Pid Controller ◽  
Firefly Algorithm ◽  
Step Response ◽  
Voltage Regulator ◽  
Proportional Integral Derivative ◽  
Swarm Optimization ◽  
Response Characteristics ◽  
Tuning Method ◽  
Point Tracking ◽  
Avr System

Abstract This paper presents a tuning approach based on Continuous firefly algorithm (CFA) to obtain the proportional-integral- derivative (PID) controller parameters in Automatic Voltage Regulator system (AVR). In the tuning processes the CFA is iterated to reach the optimal or the near optimal of PID controller parameters when the main goal is to improve the AVR step response characteristics. Conducted simulations show the effectiveness and the efficiency of the proposed approach. Furthermore the proposed approach can improve the dynamic of the AVR system. Compared with particle swarm optimization (PSO), the new CFA tuning method has better control system performance in terms of time domain specifications and set-point tracking.

scholarly journals An Improved Analytical Tuning Rule of a Robust PID Controller for Integrating Systems with Time Delay Based on the Multiple Dominant Pole-Placement Method

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1449 ◽  
Author(s):  
Wei Zhang ◽  
Yue Cui ◽  
Xiangxin Ding
Keyword(s):  
Time Delay ◽  
Pid Controller ◽  
Second Order ◽  
Pole Placement ◽  
Tuning Parameter ◽  
Third Order ◽  
Placement Method ◽  
The Third ◽  
Dominant Pole ◽  
Fifth Order

An improved analytical tuning rule of a Proportional-Integral-Derivative (PID) controller for integrating systems with time delay is proposed using the direct synthesis method and multiple dominant pole-placement approach. Different from the traditional multiple dominant pole-placement method, the desired characteristic equation is obtained by placing the third-order dominant poles at −1/λ and placing the second-order non-dominant poles at −5/λ (λ is the tuning parameter). According to root locus theory, the third-order dominant poles and the second-order non-dominant poles are nearly symmetrically located at the two sides of the fifth-order dominant poles. This makes the third-order dominant poles closer to the imaginary axis than the fifth-order dominant poles, which means that, possibly, better performances can be achieved. Analytical formulas of a PID controller with a lead-lag filter are derived. Simple tuning rules are also given to achieve the desired robustness, which is measured by the maximum sensitivity (Ms) value. The proposed method can achieve better performances and maintain better performances when there exist parameters’ perturbation compared with other methods. Simulations for various integrating processes as well as the nonlinear continuous stirred tank reactor (CSTR) model illustrate the applicability and effectiveness of the proposed method.

Discussion: “A Simple Switching Control for Linear Systems to Assure Nonovershooting Step Responses” (Zhu, B., and Cai, K. Y., 2012, ASME J. Dyn. Syst. Meas., Control, 134, p. 034503)

2014 ◽  
Vol 136 (5) ◽  
Author(s):  
Robert Schmid
Keyword(s):  
Linear Systems ◽  
Pid Controller ◽  
State Feedback ◽  
Switching Control ◽  
Step Response ◽  
Proportional Integral Derivative ◽  
Luenberger Observer ◽  
Linear Plant ◽  
Linear State ◽  
Step Responses

This paper offers some comments on the article by Zhu and Cai (2012, “A Simple Switching Control for Linear Systems to Assure Nonovershooting Step Responses,” ASME J. Dyn. Syst. Meas., Control, 134, p. 034503). The authors offered a nonlinear switching scheme to obtain a nonovershooting step response from a linear plant, and motivated their method by showing that no linear Proportional-Integral-Derivative (PID) controller could achieve a nonovershooting response for a plant in the form of a triple integrator. In this paper, we show via an example that a linear state feedback controller in conjunction with a Luenberger observer can be found to achieve a nonovershooting response for a triple integrator.

Probe size and 5th-order aberration

1987 ◽  
Vol 45 ◽  
pp. 134-135 ◽  
Author(s):  
Zhifeng Shao
Keyword(s):  
Electron Probe ◽  
Spherical Aberration ◽  
Wave Length ◽  
Cylindrical Symmetry ◽  
Electron Wave ◽  
Third Order ◽  
The Third ◽  
Probe Radius ◽  
Small Probe ◽  
Probe Size

A small electron probe has many applications in many fields and in the case of the STEM, the probe size essentially determines the ultimate resolution. However, there are many difficulties in obtaining a very small probe.Spherical aberration is one of them and all existing probe forming systems have non-zero spherical aberration. The ultimate probe radius is given byδ = 0.43Csl/4ƛ3/4where ƛ is the electron wave length and it is apparent that δ decreases only slowly with decreasing Cs. Scherzer pointed out that the third order aberration coefficient always has the same sign regardless of the field distribution, provided only that the fields have cylindrical symmetry, are independent of time and no space charge is present. To overcome this problem, he proposed a corrector consisting of octupoles and quadrupoles.

Children’s Recall of Approximations to English

1973 ◽  
Vol 16 (2) ◽  
pp. 201-212 ◽  
Author(s):  
Elizabeth Carrow ◽  
Michael Mauldin
Keyword(s):  
Language Development ◽  
Fourth Order ◽  
Third Order ◽  
Memory Processes ◽  
The Third ◽  
General Index ◽  
General Linguistic

As a general index of language development, the recall of first through fourth order approximations to English was examined in four, five, six, and seven year olds and adults. Data suggested that recall improved with age, and increases in approximation to English were accompanied by increases in recall for six and seven year olds and adults. Recall improved for four and five year olds through the third order but declined at the fourth. The latter finding was attributed to deficits in semantic structures and memory processes in four and five year olds. The former finding was interpreted as an index of the development of general linguistic processes.

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