Nonlinear pd controllers with gravity compensation for robot manipulators

Abstract

A Nonlinear Proportional-Derivative (NPD) controller with gravity compensation is proposed and applied to robot manipulators in this paper. The proportional and derivative gains are changed by the nonlinear function of errors in the NPD controller. The closed-loop system, composed of nonlinear robot dynamics and NPD controllers, is globally asymptotically stable in position control of robot manipulators. The comparison of the simulation experiments in the position control (the step response) of a robot manipulator with two degrees of freedom is also presented to illustrate that the NPD controller is superior to the conventional PD controller in a position control system. The experimental results show that the NPD controller can obtain a faster response velocity and higher position accuracy than the conventional PD controller in the position control of robot manipulators because the proportional and derivative gains of the NPD controller can be changed by the nonlinear function of errors. The NPD controller provides a novel approach for robot control systems.

Adaptive Controller Algorithm for 2-DOF Humanoid Robot Arm

“…Nevertheless, the control properties can only be achieved by manual tuning of the PD controller gains by using various tuning methods such as the Ziegler-Nichols method or by just trial-and-error approach. However, although this type of controller is widely used in the field of robotics [22], implementing this type of control strategy is not practical to model human control. This is because, the manual tuning of the PD controller gains would require exhaustive computational time in searching the optimal values for the gains to achieve the desired trajectory, and also would be harmful to the patient if during the learning process, inadequate torque is exerted by the controller that could damage the patient's arm rather than improving them.…”

Investigation on the influence of parameter uncertainties in the position tracking of robot manipulators

“…The fixed PID parameters in these controllers may often deteriorate control performances, and while these controllers are enough for the general control, they usually result in weak robustness and poor performances due to the nonlinearity characteristics of robot arms. Research works on nonlinear PD or PID controllers of robot arms such as [4][5][6] were proposed for these purposes. Huang et al [6] proposed a nonlinear PD controller with gravity compensation that is globally asymptotically stable in position control and a comparison was made between their proposed controller and the conventional PD controller, which showed that a faster response velocity and higher position accuracy were obtained by the former.…”

“…Research works on nonlinear PD or PID controllers of robot arms such as [4][5][6] were proposed for these purposes. Huang et al [6] proposed a nonlinear PD controller with gravity compensation that is globally asymptotically stable in position control and a comparison was made between their proposed controller and the conventional PD controller, which showed that a faster response velocity and higher position accuracy were obtained by the former. Davoud et al [7] proposed fractional order PID controllers by applying evolutionary algorithms (particle swarm optimization (PSO), the genetic algorithm and estimations of the distribution algorithm) and better tracking results were obtained compared to the normal PID controllers.…”

Análise de Desempenho de Técnicas de Controle de Ganhos Variáveis na Tarefa de Controle de Posição de Manipuladores Robóticos

“…. Controladores não lineares procuram modificar os valores dos ganhos através de funções não lineares que são, normalmente, dependentes de uma variável do sistema [9], [7], já os do tipo fuzzy utilizam funções de pertinência para fazer as mudanças necessárias nos ganhos.…”

“…A comparação realizada representa uma contribuição para preencher lacunas deixadas nas análises apresentadas em [7] que compara o controlador NPD com o controlador PD e [2] que realizou uma comparação entre um controlador fuzzy e um controlador PID, ambos comparando técnicas de ganhos dinâmicos somente com técnicas clássicas, bem como para verificar a capacidade destes controladores em manter o desempenho em trajetórias para as quais não foram projetados, além disso, busca-se averiguar o desempenho da linguagem Julia com relação a simulações de sistemas dinâmicos e em algoritmos de inteligência computacional.…”