Tuning PID and PI<sup>¿</sup>D<sup>¿</sup> Controllers using the Integral Time Absolute Error Criterion

AbstractIn this paper, a sliding mode controller (SMC) with PID surface is designed for the trajectory tracking control of a robot manipulator using different optimization algorithms such as, Antlion Optimization Algorithm (ALO) Sine Cosine Algorithm (SCA) Grey Wolf Optimizer (GWO) and Whale Optimizer Algorithm (WOA). The aim of this work is to introduce a novel SMC-PID-ALO to control nonlinear systems, especially the position of two of the joints of a 2DOF robot manipulator. The basic idea is to determinate four optimal parameters (Kp, Ki, Kd and lamda) ensuring the best performance of a robot manipulator system, minimizing the integral time absolute error criterion (ITAE) and the integral time square error criterion (ISTE). The robot manipulator is modeled in Simulink and the control is implemented using the MATLAB environment. The obtained simulation results prove the robustness of ALO in comparison with other algorithms.

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Improved Backstepping Control of a DFIG based Wind Energy Conversion System using Ant Lion Optimizer Algorithm

Periodica Polytechnica Electrical Engineering and Computer Science ◽

10.3311/ppee.18716 ◽

2021 ◽

Author(s):

Zoubir Zeghdi ◽

Linda Barazane ◽

Youcef Bekakra ◽

Abdelkader Larabi

Keyword(s):

Fitness Function ◽

Harmonic Distortion ◽

Absolute Error ◽

Optimization Method ◽

Backstepping Control ◽

Ant Lion Optimizer ◽

Integral Time ◽

Distortion Minimization ◽

Ant Lion ◽

Doubly Fed

In this paper, an improved Backstepping control based on a recent optimization method called Ant Lion Optimizer (ALO) algorithm for a Doubly Fed Induction Generator (DFIG) driven by a wind turbine is designed and presented. ALO algorithm is applied for obtaining optimum Backstepping control (BCS) parameters that are able to make the drive more robust with a faster dynamic response, higher accuracy and steady performance. The fitness function of the ALO algorithm to be minimized is designed using some indexes criterion like Integral Time Absolute Error (ITAE) and Integral Time Square Error (ITSE). Simulation tests are carried out in MATLAB/Simulink environment to validate the effectiveness of the proposed BCS-ALO and compared to the conventional BCS control. The results prove that the objectives of this paper were accomplished in terms of robustness, better dynamic efficiency, reduced harmonic distortion, minimization of stator powers ripples and performing well in solving the problem of uncertainty of the model parameter.

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Fixed Points- Noncontractive Functions

Optimal Solution of Nonlinear Equations ◽

10.1093/oso/9780195106909.003.0007 ◽

2001 ◽

Author(s):

Krzysztof A. Sikorski

Keyword(s):

Fixed Points ◽

Absolute Error ◽

Small Error ◽

Homotopy Continuation ◽

Average Case Analysis ◽

Error Criterion ◽

Worst Case ◽

Average Case ◽

Worst Case Complexity ◽

Exponential Complexity

In this chapter we consider the approximation of fixed points of noncontractive functions with respect to the absolute error criterion. In this case the functions may have multiple and/or whole manifolds of fixed points. We analyze methods based on sequential function evaluations as information. The simple iteration usually does not converge in this case, and the problem becomes much more difficult to solve. We prove that even in the two-dimensional case the problem has infinite worst case complexity. This means that no methods exist that solve the problem with arbitrarily small error tolerance for some “bad” functions. In the univariate case the problem is solvable, and a bisection envelope method is optimal. These results are in contrast with the solution under the residual error criterion. The problem then becomes solvable, although with exponential complexity, as outlined in the annotations. Therefore, simplicial and/or homotopy continuation and all methods based on function evaluations exhibit exponential worst case cost for solving the problem in the residual sense. These results indicate the need of average case analysis, since for many test functions the existing algorithms computed ε-approximations with polynomial in 1/ε cost.

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Compatibility of objective functions with simplex algorithm for controller tuning of HVDC system

Ingeniería e Investigación ◽

10.15446/ing.investig.v39n3.70221 ◽

2020 ◽

Vol 39 (3) ◽

pp. 34-43

Author(s):

Haaris Rasool ◽

Aazim Rasool ◽

Ataul Aziz Ikram ◽

Urfa Rasool ◽

Mohsin Jamil ◽

...

Keyword(s):

Optimization Technique ◽

Absolute Error ◽

Simplex Algorithm ◽

Control Parameters ◽

Objective Functions ◽

Simulation Design ◽

Hvdc System ◽

Integral Time ◽

Time Simulation ◽

Simulation Based

This work aims to tune multiple controllers at the same time for a HVDC system by using a self-generated (SG) simulation-based optimization technique. Online optimization is a powerful tool to improve performance of the system. Proportion integral (PI) controllers of Multi-infeed HVDC systems are optimized by the evaluation of objective functions in time simulation design (TSD). Model based simulation setup is applied for rapid selection of optimal PI control parameters, designed in PSCAD software. A multiple objective function (OF), i.e. Integral absolute error (IAE), integral square error (ISE), integral time absolute error (ITAE), integral time square error (ITSE), and integral square time error (ISTE), is assembled for testing the compatibility of OFs with nonlinear self-generated simplex algorithm (SS-SA). Improved control parameters are achieved after multiple iterations. All OFs generate optimum responses and their results are compared with each other by their minimized numerical values. Disturbance rejection criteria are also proposed to assess the designed controller performance along with robustness of system. Results are displayed in form of graphs and tables in this paper.

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