scholarly journals Metaheuristic Optimization of PD and PID Controllers for Robotic Manipulators

2021 ◽  
Vol 54 (6) ◽  
pp. 835-845
Author(s):  
Nadia Bounouara ◽  
Mouna Ghanai ◽  
Kheireddine Chafaa
Keyword(s):  
Closed Loop ◽  
Particle Swarm Optimization Algorithm ◽  
Robotic Manipulators ◽  
Pso Algorithm ◽  
Pid Controllers ◽  
Optimal Parameters ◽  
Proportional Integral Derivative ◽  
Closed Loop System ◽  
Uniformly Bounded ◽  
Integral Gain

In this paper, the Particle Swarm Optimization algorithm (PSO) is combined with Proportional-Derivative (PD) and Proportional-Integral-Derivative (PID) to design more efficient PD and PID controllers for robotic manipulators. PSO is used to optimize the controller parameters Kp (proportional gain), Ki (integral gain) and Kd (derivative gain) to achieve better performances. The proposed algorithm is performed in two steps: (1) First, PD and PID parameters are offline optimized by the PSO algorithm. (2) Second, the obtained optimal parameters are fed in the online control loop. Stability of the proposed scheme is established using Lyapunov stability theorem, where we guarantee the global stability of the resulting closed-loop system, in the sense that all signals involved are uniformly bounded. Computer simulations of a two-link robotic manipulator have been performed to study the efficiency of the proposed method. Simulations and comparisons with genetic algorithms show that the results are very encouraging and achieve good performances.

The error-based minimal control synthesis algorithm with integral action

2003 ◽  
Vol 217 (3) ◽  
pp. 187-201 ◽  
Author(s):  
D P Stoten ◽  
S A Neild
Keyword(s):  
Closed Loop ◽  
Control Synthesis ◽  
Closed Loop System ◽  
Synthesis Algorithm ◽  
The Core ◽  
Gain Term ◽  
Integral Action ◽  
Implementation Studies ◽  
Hyperstability Theory ◽  
Integral Gain

This paper presents a new form of the direct adaptive minimal control synthesis (MCS) algorithm. As its name suggests, the error-based minimal control synthesis with integral action (Er-MCSI) algorithm is solely driven by error signals that are generated within the closed-loop system, and contains an explicit integral gain term. The purpose of this new structure is, respectively, to remove the problem of variable adaptive effort with changes in the operating set point, and to remove gain ‘wind-up’ effects due to plant disturbances and signal offsets. The core of this paper contains a proof of stability for Er-MCSI, based on hyperstability theory, together with supporting simulation and implementation studies.

scholarly journals Computational Efficiency-Based Adaptive Tracking Control for Robotic Manipulators with Unknown Input Bouc–Wen Hysteresis

Sensors ◽  
2019 ◽  
Vol 19 (12) ◽  
pp. 2776 ◽  
Author(s):  
Kan Xie ◽  
Yue Lai ◽  
Weijun Li
Keyword(s):  
Computational Efficiency ◽  
Closed Loop ◽  
Tracking Error ◽  
Control Unit ◽  
Robotic Manipulators ◽  
Lyapunov Theory ◽  
Loop System ◽  
Unknown Input ◽  
Closed Loop System ◽  
Adaptive Tracking Control

In order to maintain robotic manipulators at a high level of performance, their controllers should be able to address nonlinearities in the closed-loop system, such as input nonlinearities. Meanwhile, computational efficiency is also required for real-time implementation. In this paper, an unknown input Bouc–Wen hysteresis control problem is investigated for robotic manipulators using adaptive control and a dynamical gain-based approach. The dynamics of hysteresis are modeled as an additional control unit in the closed-loop system and are integrated with the robotic manipulators. Two adaptive parameters are developed for improving the computational efficiency of the proposed control scheme, based on which the outputs of robotic manipulators are driven to track desired trajectories. Lyapunov theory is adopted to prove the effectiveness of the proposed method. Moreover, the tracking error is improved from ultimately bounded to asymptotic tracking compared to most of the existing results. This is of important significance to improve the control quality of robotic manipulators with unknown input Bouc–Wen hysteresis. Numerical examples including fixed-point and trajectory controls are provided to show the validity of our method.

Error-based output tracking for a one-dimensional wave equation with harmonic type disturbance

2020 ◽  
Vol 37 (4) ◽  
pp. 1447-1467
Author(s):  
Ziqing Tian ◽  
Xiao-Hui Wu
Keyword(s):  
Wave Equation ◽  
Closed Loop ◽  
Tracking Error ◽  
Difficult Case ◽  
Closed Loop System ◽  
One Dimensional ◽  
Output Tracking ◽  
Planning Approach ◽  
Uniformly Bounded ◽  
Dimensional Wave

Abstract In this paper, we consider output tracking for a one-dimensional wave equation, where the boundary disturbances are either collocated or non-collocated with control. The regulated output and the control are supposed to be non-collocated with control, which represents a difficult case for output tracking of PDEs. We apply the trajectory planning approach to design an observer, in terms of tracking error only, to estimate both states of the system and the exosystem from which the disturbances are produced. An error-based feedback control is proposed by solving a standard regulator equation. It is shown that (a) the closed-loop system is uniformly bounded whenever the exosystem is bounded; (b) when the disturbance is zero, the closed-loop is asymptotically stable; and (c) the tracking error converges to zero asymptotically as time goes to infinity. Numerical simulations are performed to validate the effectiveness of the proposed control.

PID-Based Thermal Control in Heat Conduction Micro-Calorimeters

2010 ◽  
Author(s):  
Arturo Pacheco-Vega ◽  
Luis Enrique Vilchiz-Bravo ◽  
Brent E. Handy
Keyword(s):  
Heat Flow ◽  
Temperature Control ◽  
Control Strategy ◽  
Closed Loop ◽  
Thermal Control ◽  
Pid Controllers ◽  
Closed Loop System ◽  
Calvet Microcalorimeter ◽  
Control Schemes ◽  
Stable Core

Strategies based on the principle of heat flow and temperature control were implemented, and experimentally tested, to increase the sensitivity of a Tian-Calvet microcalorimeter for measuring heats of adsorption. Here, both heat-flow and temperature control schemes were explored to diminish heater-induced thermal variations within the heat sink element hence obtaining less noise in the baseline signal. PID controllers were implemented within a closed-loop system to perform the control actions in an calorimetric setup. The experimental results demonstrate that the heat flow control strategy provided a better baseline stability when compared to the temperature control. A modified control strategy is then suggested to maintain a stable core temperature and signal noise level in the system.

Internal Model Control–Proportional Integral Derivative–Fractional-Order Filter Controllers Design for Unstable Delay Systems

2015 ◽  
Vol 138 (2) ◽  
Author(s):  
Kahina Titouche ◽  
Rachid Mansouri ◽  
Maamar Bettayeb ◽  
Ubaid M. Al-Saggaf
Keyword(s):  
Fractional Order ◽  
Internal Model ◽  
Closed Loop ◽  
Control Structure ◽  
Internal Model Control ◽  
Loop System ◽  
Proportional Integral Derivative ◽  
Closed Loop System ◽  
Proportional Integral ◽  
Model Control

An analytical design for proportional integral derivative (PID) controller cascaded with a fractional-order filter is proposed for first-order unstable processes with time delay. The design algorithm is based on the internal model control (IMC) paradigm. A two degrees-of-freedom (2DOF) control structure is used to improve the performance of the closed-loop system. In the 2DOF control structure, an integer order controller is used to stabilize the inner-loop, and a fractional-order controller for the stabilized system is employed to improve the performance of the closed-loop system. The Walton–Marshall's method, which is applicable to quasi-polynomials, is then used to establish the internal stability condition of the closed-loop system (the fractional part of the controller in particular) and to seek the set of stabilizing proportional (P) or proportional-derivative (PD) controller parameters.

New Results on PID Stabilization of Integral Process with Time Delay

2015 ◽  
Vol 775 ◽  
pp. 339-346
Author(s):  
Yu Dong
Keyword(s):  
Time Delay ◽  
Pid Controller ◽  
Imaginary Axis ◽  
Stability Region ◽  
Closed Loop ◽  
Closed Loop System ◽  
Double Pole ◽  
Integral Process ◽  
The Stability ◽  
Integral Gain

This paper considers the problem of stabilizing an integral process with time delay by a PID controller. As the proportional gain reaches the extreme value, the closed-loop system contains a double pole on the non-negative imaginary axis. Using this property, the admissible range of the proportional gain is derived, also the corresponding integral gain and derivative gain are obtained. For a fixed value of the proportional gain, the stability region in the plane of the integral and derivative gains is determined analytically. Moreover, the admissible ranges of the integral and derivative gains are computed and found to be non-convex. A numerical example illustrates the method presented.

A Robustly Stable Multiestimation-Based Adaptive Control Scheme for Robotic Manipulators

2005 ◽  
Vol 128 (2) ◽  
pp. 414-421 ◽  
Author(s):  
A. Ibeas ◽  
M. de la Sen
Keyword(s):  
Adaptive Systems ◽  
Closed Loop ◽  
Sudden Change ◽  
Robotic Manipulators ◽  
Adaptive Controller ◽  
Time Instant ◽  
Loop System ◽  
System Stability ◽  
Closed Loop System ◽  
Control Scheme

A multiestimation-based robust adaptive controller is designed for robotic manipulators. The control scheme is composed of a set of estimation algorithms running in parallel along with a supervisory index proposed with the aim of evaluating the identification performance of each one. Then, a higher-order level supervision algorithm decides in real time the estimator that will parametrize the adaptive controller at each time instant according to the values of the above supervisory indexes. There exists a minimum residence time between switches in such a way that the closed-loop system stability is guaranteed. It is verified through simulations that multiestimation-based schemes can improve the transient response of adaptive systems as well as the closed-loop behavior when a sudden change in the parameters or in the reference input occurs by appropriate switching between the various estimation schemes running in parallel. The closed-loop system is proved to be robustly stable under the influence of uncertainties due to a poor modeling of the robotic manipulator. Finally, the usefulness of the proposed scheme is highlighted by some simulation examples.

Adaptive neural sliding mode control with prescribed performance of robotic manipulators subject to backlash hysteresis

2021 ◽  
pp. 095440622110145
Author(s):  
Huaizhen Wang ◽  
Lijin Fang ◽  
Junyi Wang ◽  
Tangzhong Song ◽  
Hesong Shen
Keyword(s):  
Sliding Mode Control ◽  
Closed Loop ◽  
Sliding Mode ◽  
Nonlinear Function ◽  
Robotic Manipulators ◽  
Loop System ◽  
Closed Loop System ◽  
Terminal Sliding Mode ◽  
Prescribed Performance ◽  
Mode Control

Robust and precise control of robot systems are still challenging problems due to the existence of uncertainties and backlash hysteresis. To deal with the problems, an adaptive neural sliding mode control with prescribed performance is proposed for robotic manipulators. A finite-time nonsingular terminal sliding mode control combined with a new prescribed performance function (PPF) is developed to guarantee the transient and steady-state performance of the closed-loop system. Based on the sliding mode variable, an adaptive law is presented to effectively estimate the bound of system uncertainties where the prior knowledge of uncertainties is not needed. To approximate nonlinear function and unknown dynamics, the Gaussian radial basis function neural networks(RBFNNs) is introduced to compensate the lumped nonlinearities. All signals of the closed-loop system are proven to be uniformly ultimately bounded (UUB) by Lyapunov analysis. Finally, comparative simulations are conducted to illustrate superiority and reliability of the proposed control strategy.

An Improved Design for PID Controller Based on Viere Theorem

2013 ◽  
Vol 303-306 ◽  
pp. 1167-1170
Author(s):  
Zhi Yi Xu ◽  
Xiang Jun Zhang ◽  
Zhen Liu
Keyword(s):  
Pid Controller ◽  
Closed Loop ◽  
Controller Design ◽  
New Method ◽  
Optimal Parameters ◽  
Closed Loop System ◽  
Pid Controller Design ◽  
Search Speed ◽  
Improved Design ◽  
The Stability

The paper proposes a new method based on the Viere theorem to decide the range containing the optimal parameters. The method can accelerate the parameters search speed on the computer and avoid some unnecessary job for PID controller design. It can be acted as a criterion to judge the stability of the closed loop system.

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