Tuning of PID controller using sigmoidal weighted error function

A Multivariate Neural Network (MNN) algorithm is proposed for the reconstruction of significant wave height time series, without any increase of the error of the MNN output with the number of modelled data. The algorithm uses a weighted error function during the learning phase, to improve the modelling of the higher significant wave height. The ability of the MNN to reconstruct sea storms is tested by applying the equivalent triangular storm model. Finally an application to the NOAA buoys moored off California shows a good performance of the MNN algorithm, both during sea storms and calm time periods.

Download Full-text

Synchronization Adaptive Fuzzy Gain Scheduling PID Controller for a Class of MIMO Nonlinear Systems

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488519500235 ◽

2019 ◽

Vol 27 (04) ◽

pp. 515-535

Author(s):

Hesam Fallah Ghavidel ◽

Ali Akbarzadeh Kalat

Keyword(s):

Nonlinear Systems ◽

Fuzzy Control ◽

Pid Controller ◽

Mimo System ◽

Error Function ◽

Adaptive Fuzzy Control ◽

Gain Scheduling ◽

Lyapunov Theory ◽

Mimo Nonlinear Systems ◽

Adaptive Fuzzy

This paper presents a new Synchronization Adaptive Fuzzy Gain Scheduling PID controller (SAFGS-PIDc) for a class of Multiple-input multiple-output (MIMO) nonlinear systems with uncertainties. To achieve better adaptation properties, weighting factor is adapted to sum together the adaptive fuzzy control scheme and Fuzzy Gain Scheduler PID control (FGS-PIDc) method, such that both controllers can be incorporated at the same time. The FGS adjusts online the parameters of the conventional PID controller, and an Indirect Adaptive Fuzzy control (IAFc) scheme that uses feedback error function as inputs is constructed. In addition, each subsystem of MIMO system is able to adaptively compensate for uncertainties and external disturbance. Also, a robust control term is designed that aims to provide added robustness in the presence of uncertainties. The proposed scheme can overcome the controller singularity problem. While the proposed controller scheme requires the uncertainties to be bounded, it does not require this bound to be known. Thus, this control law can be used for the systems that the system’s models are quite unknown. The proposed method guarantees the stability of the closed-loop system based on Lyapunov theory. Finally, simulation studies demonstrate the usefulness and effectiveness of the proposed technique for controlling nonlinear.

Download Full-text

PID Controller optimization using Metahuristic Controller with Different Nonlinearities

Turkish Journal of Computer and Mathematics Education (TURCOMAT) ◽

10.17762/turcomat.v12i2.1082 ◽

2021 ◽

Vol 12 (2) ◽

pp. 764-771

Author(s):

G. Sundari, Et. al.

Keyword(s):

Steady State ◽

Pid Controller ◽

Closed Loop ◽

Error Function ◽

Second Order ◽

Settling Time ◽

Order System ◽

Pid Controllers ◽

Dynamic Performances ◽

Conventional Methods

This paper mainly explains the application of Metaherustic controller for tuning the parameter of PID controller. The minimization of error function has been done by improving the static and dynamic performances of the system like steady state error, Peak Overshoot, and Settling Time. This could be possible by means of applying metaherustic controller like GA in tuning the PID controllers under different Nonlinearities. The main intention of this paper is to support the specifications of PID controller at various Nonlinearities such as sinusoidal and saw tooth noise. The projected scheme derives the wonderful closed-loop response of second order system and then, it provides the effectiveness of the proposed method compared to the conventional methods.

Download Full-text

Speed Control Optimization for Autonomous Vehicles with Metaheuristics

Electronics ◽

10.3390/electronics9040551 ◽

2020 ◽

Vol 9 (4) ◽

pp. 551 ◽

Cited By ~ 3

Author(s):

José Eugenio Naranjo ◽

Francisco Serradilla ◽

Fawzi Nashashibi

Keyword(s):

Autonomous Vehicles ◽

Pid Controller ◽

Error Function ◽

Absolute Error ◽

Optimization Methods ◽

Research Area ◽

Point Of View ◽

Fine Tuning ◽

Cruise Control ◽

Pid Tuning

The development of speed controllers under execution in autonomous vehicles within their dynamic driving task (DDT) is a traditional research area from the point of view of control techniques. In this regard, Proportional – Integral – Derivative (PID) controllers are the most widely used in order to meet the requirements of cruise control. However, fine tuning of the parameters associated with this type of controller can be complex, especially if it is intended to optimize them and reduce their characteristic errors. The objective of the work described in this paper is to evaluate the capacity of several metaheuristics for the adjustment of the parameters Kp, 1/Ti, and 1/Td of a PID controller to regulate the speed of a vehicle. To do this, an adjustment error function has been established from a linear combination of classic estimators of the goodness of the controller, such as overshoot, settling time (ts), steady-state error (ess), and the number of changes of sign of the signal (d). The error obtained when applying the controller has also been compared to a computational model of the vehicle after estimating the parameters Kp, Ki, and Kd, both for a setpoint sequence used in the adjustment of the system parameters and for a sequence not used during the adjustment, and therefore unknown by the system. The main novelty of the paper is to propose a new global error function, a function that enables the use of heuristic optimization methods for PID tuning. This optimization has been carried out by using three methods: genetic algorithms (GA), memetics algorithms (MA), and mesh adaptive direct search (MADS). The results of the application of the optimization methods using the proposed metric show that the accuracy of the PID controller is improved, compared with the classical optimization based on classical methods like the integral absolute error (IAE) or similar metrics, reducing oscillatory behaviours as well as minimizing the analysed performance indexes.

Download Full-text

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

Entropy ◽

10.3390/e22070771 ◽

2020 ◽

Vol 22 (7) ◽

pp. 771 ◽

Cited By ~ 2

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.

Download Full-text

Lagrangian Modeling and Optimal MIMO PID Control of a Manipulator Using Tabu Search Algorithm

10.47890/jadct/2020/seahosseini/10123451 ◽

2020 ◽

Vol 1 (1) ◽

Author(s):

Seyed Ehsan Aghakouchaki Hosseini ◽

Mohammad Dashti Javan

Keyword(s):

Tabu Search ◽

Pid Controller ◽

Error Function ◽

Optimization Techniques ◽

Surface Finishing ◽

Main Role ◽

Final Position ◽

Optimal Position ◽

Lagrangian Modeling ◽

And Control

Robot manipulators, given their promising features and capabilities, have found a variety of applications in many fields including construction, nuclear, car, manufacturing and surgical industries, among others, which has turned them to a large and diffuse industry. In construction, use of robots has automated many tasks and risky jobs, including multitask road construction and maintenance processes based on ergonomic and economic analyses, surface finishing, concreting, excavating and backfilling, to name but a few. Hence, manipulators have progressively replaced human labor to meet strict health regulations, productivity gains, and control goals. Movement of an effector tool into a proper location and orientation required for a work object is the main role of a manipulator. In this research dynamic modeling and control of a 2-DOF planar robotic manipulator is presented using a PID controller to obtain optimal position of final operator of the manipulator. Considering nonlinearity of the system under consideration, to optimize final position of the manipulator, parameters of PID controller were tuned using Tabu Search (TS) algorithm as one of meta-heuristic optimization techniques. Numerical results obtained from simulations in this study demonstrated robustness and efficiency of the selected approach for optimizing the final position of the manipulator, minimizing oscillations and fast convergence of the error function to zero, compared to that of uncontrolled state as well as controlled system by PID controller with empirically adjusted factors. Efficiency of the proposed method was verified for different angular positions of joints in the manipulator. Keywords:Lagrangian Modeling; Manipulator; MIMO PID Controller; Evolutionary Algorithms

Download Full-text