A geometric description of the set of stabilizing PID controllers

2021 ◽  
Author(s):  
Keqin Gu ◽  
Qian Ma ◽  
Huiqing Zhou ◽  
Salma Mahzoon ◽  
Xingzi Yang
Keyword(s):  
Pid Controllers ◽  
Geometric Description

scholarly journals A geometric description of the set of stabilizing PID controllers

2020 ◽  
Vol 53 (2) ◽  
pp. 4481-4486
Author(s):  
Keqin Gu ◽  
Qian Ma ◽  
Huiqing Zhou ◽  
Salma Mahzoon ◽  
Xingzi Yang
Keyword(s):  
Pid Controllers ◽  
Geometric Description

Development of a Jacobian Module for Advanced Pulp and Paper Simulation and Control

TAPPI Journal ◽  
2009 ◽  
Vol 8 (1) ◽  
pp. 4-11
Author(s):  
MOHAMED CHBEL ◽  
LUC LAPERRIÈRE
Keyword(s):  
Control System ◽  
Nonlinear Behavior ◽  
Simulation Software ◽  
Pulp And Paper ◽  
Pid Controllers ◽  
Tuning Parameters ◽  
Pid Tuning ◽  
Fixed Set ◽  
And Control ◽  
Operating Points

Pulp and paper processes frequently present nonlinear behavior, which means that process dynam-ics change with the operating points. These nonlinearities can challenge process control. PID controllers are the most popular controllers because they are simple and robust. However, a fixed set of PID tuning parameters is gen-erally not sufficient to optimize control of the process. Problems related to nonlinearities such as sluggish or oscilla-tory response can arise in different operating regions. Gain scheduling is a potential solution. In processes with mul-tiple control objectives, the control strategy must further evaluate loop interactions to decide on the pairing of manipulated and controlled variables that minimize the effect of such interactions and hence, optimize controller’s performance and stability. Using the CADSIM Plus™ commercial simulation software, we developed a Jacobian sim-ulation module that enables automatic bumps on the manipulated variables to calculate process gains at different operating points. These gains can be used in controller tuning. The module also enables the control system designer to evaluate loop interactions in a multivariable control system by calculating the Relative Gain Array (RGA) matrix, of which the Jacobian is an essential part.

An Adjustment of Reference Tracking PID Controllers for a First-order System with a Dead Time

2016 ◽  
Vol 136 (5) ◽  
pp. 676-682 ◽  
Author(s):  
Akihiro Ishimura ◽  
Masayoshi Nakamoto ◽  
Takuya Kinoshita ◽  
Toru Yamamoto
Keyword(s):  
Dead Time ◽  
Order System ◽  
Pid Controllers ◽  
Reference Tracking ◽  
First Order

OAT GEOMETRIC DESCRIPTION OF THE GRAIN OF HULLESS OAT VARIETIES IN THE NORTHERN TRANS-URAL ZONE

2018 ◽  
Author(s):  
Yu. S. Ivanova ◽  
◽  
I. G. Loskutov ◽  
M. N. Fomina ◽  
E. V. Blinova ◽  
...  
Keyword(s):  
Geometric Description

Grasshopper Algorithm Optimized Fractional Order Fuzzy PID Frequency Controller for Hybrid Power Systems

2019 ◽  
Vol 12 (6) ◽  
pp. 519-531
Author(s):  
Deepak Kumar Lal ◽  
Ajit Kumar Barisal
Keyword(s):  
Power Systems ◽  
Power System ◽  
Fractional Order ◽  
Pid Controller ◽  
Load Frequency Control ◽  
Pid Controllers ◽  
Fuzzy Pid ◽  
Fuzzy Pid Controller ◽  
Hybrid Power ◽  
Increasing Demand

Background: Due to the increasing demand for the electrical power and limitations of conventional energy to produce electricity. Methods: Now the Microgrid (MG) system based on alternative energy sources are used to provide electrical energy to fulfill the increasing demand. The power system frequency deviates from its nominal value when the generation differs the load demand. The paper presents, Load Frequency Control (LFC) of a hybrid power structure consisting of a reheat turbine thermal unit, hydropower generation unit and Distributed Generation (DG) resources. Results: The execution of the proposed fractional order Fuzzy proportional-integral-derivative (FO Fuzzy PID) controller is explored by comparing the results with different types of controllers such as PID, fractional order PID (FOPID) and Fuzzy PID controllers. The controller parameters are optimized with a novel application of Grasshopper Optimization Algorithm (GOA). The robustness of the proposed FO Fuzzy PID controller towards different loading, Step Load Perturbations (SLP) and random step change of wind power is tested. Further, the study is extended to an AC microgrid integrated three region thermal power systems. Conclusion: The performed time domain simulations results demonstrate the effectiveness of the proposed FO Fuzzy PID controller and show that it has better performance than that of PID, FOPID and Fuzzy PID controllers. The suggested approach is reached out to the more practical multi-region power system. Thus, the worthiness and adequacy of the proposed technique are verified effectively.

scholarly journals Design of Optimal PID Controller withɛ-Routh Stability for Different Processes

2013 ◽  
Vol 2013 ◽  
pp. 1-22 ◽  
Author(s):  
XianHong Li ◽  
HaiBin Yu ◽  
MingZhe Yuan
Keyword(s):  
Pid Controller ◽  
Design Method ◽  
Optimization Methods ◽  
Pid Controllers ◽  
Water Tank ◽  
Nonlinear Constraint ◽  
Order Error ◽  
Interior Method ◽  
Tank System ◽  
Tuning Methods

This paper presents a design method of the optimal proportional-integral-derivative (PID) controller withɛ-Routh stability for different processes through Lyapunov approach. The optimal PID controller could be acquired by minimizing an augmented integral squared error (AISE) performance index which contains control error and at least first-order error derivative, or even may containnth-order error derivative. The optimal control problem could be transformed into a nonlinear constraint optimization (NLCO) problem via Lyapunov theorems. Therefore, optimal PID controller could be obtained by solving NLCO problem through interior method or other optimization methods. The proposed method can be applied for different processes, and optimal PID controllers under various control weight matrices andɛ-Routh stability are presented for different processes. Control weight matrix andɛ-Routh stability’s effects on system performances are studied, and different tuning methods’ system performances are also discussed.ɛ-Routh stability’s effects on disturbance rejection ability are investigated, and different tuning methods’ disturbances rejection ability is studied. To further illustrate the proposed method, experimental results of coupled water tank system (CWTS) under different set points are presented. Both simulation results and experiment results show the effectiveness and usefulness of the proposed method.

Optimal tuning of PID controller in time delay system: a review on various optimization techniques

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Thomas George ◽  
V. Ganesan
Keyword(s):  
Time Delay ◽  
Pid Control ◽  
Pid Controller ◽  
Optimization Techniques ◽  
Operating Conditions ◽  
Delay Systems ◽  
Pid Controllers ◽  
Time Delay Systems ◽  
Process Industries ◽  
First Order

AbstractThe processes which contain at least one pole at the origin are known as integrating systems. The process output varies continuously with time at certain speed when they are disturbed from the equilibrium operating point by any environment disturbance/change in input conditions and thus they are considered as non-self-regulating. In most occasions this phenomenon is very disadvantageous and dangerous. Therefore it is always a challenging task to efficient control such kind of processes. Depending upon the number of poles present at the origin and also on the location of other poles in transfer function different types of integrating systems exist. Stable first order plus time delay systems with an integrator (FOPTDI), unstable first order plus time delay systems with an integrator (UFOPTDI), pure integrating plus time delay (PIPTD) systems and double integrating plus time delay (DIPTD) systems are the classifications of integrating systems. By using a well-controlled positioning stage the advances in micro and nano metrology are inevitable in order satisfy the need to maintain the product quality of miniaturized components. As proportional-integral-derivative (PID) controllers are very simple to tune, easy to understand and robust in control they are widely implemented in many of the chemical process industries. In industries this PID control is the most common control algorithm used and also this has been universally accepted in industrial control. In a wide range of operating conditions the popularity of PID controllers can be attributed partly to their robust performance and partly to their functional simplicity which allows engineers to operate them in a simple, straight forward manner. One of the accepted control algorithms by the process industries is the PID control. However, in order to accomplish high precision positioning performance and to build a robust controller tuning of the key parameters in a PID controller is most inevitable. Therefore, for PID controllers many tuning methods are proposed. the main factors that lead to lifetime reduction in gain loss of PID parameters are described in This paper and also the main methods used for gain tuning based on optimization approach analysis is reviewed. The advantages and disadvantages of each one are outlined and some future directions for research are analyzed.

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