Fuzzy Self-Tuning PID Semiglobal Regulator for Robot Manipulators

Abstract

In this paper, we present a semiglobal asymptotic stability analysis via Lyapunov theory for a new proportionalintegral-derivative (PID) controller control scheme, proposed in this work, which is based on a fuzzy system for tuning the PID gains for robot manipulators. PID controller is a well-known set point control strategy for industrial manipulators which ensures semiglobal asymptotic stability for fixed symmetric positive definite (proportional, integral, and derivative) gain matrices. We show that semiglobal asymptotic stability attribute also holds for a class of gain matrices depending on the manipulator states. This feature increases the potential of the PID control scheme to improve the performance of the transient response and handle practical constraints in actual robots such as presence of actuators with limited torque capabilities. We illustrate this potential by means of a fuzzy self-tuning algorithm to select the proportional, integral, and derivative gains according to the actual state of a robotic manipulator. To the best of the authors' knowledge, our proposal of a fuzzy self-tuning PID regulator for robot manipulators is the first one with a semiglobal asymptotic stability proof. Real-time experimental results on a two-degree-of-freedom robot arm show the usefulness of the proposed approach.

Approximation grid evaluation-based PID control in cascade with nonlinear gain

“…However, setting up a direct self-tuning PID control system requires time-consuming tuning [11], [12], exact plant models [11], a highly specialized mathematical background [13], [14], [15], substantial computing power [11], [12], and very often the presence of expensive experts and one or more microcomputers and computers [14], [16]. Besides the limited availability of reductions of online computation load in other adaptive control [17], the studies reported in [2], [7], [8], [9], [18], [19], [20], [21], [22], [23], [24], [25] used a class of simple nonlinear self-tuning PID controllers (NPID, for short) that helps to make a conventional linear fixed-gain PID controller an adaptive controller, where nonlinear control encountered in various practical systems, which is frequently one of the main causes of poor performance, oscillation, or even instability [26], is envisioned for linear systems with the aim to improve performance [27]. For example, on the occasion where the error generated is high, the self-tuned nonlinear function will automatically amplify the gain in order to correct the error until the desired output has been achieved.…”

Regulación Saturada con Ganancia Variable Derivativa de Robots Manipuladores

“…Los controladores auto sintonizables (self tuning controllers) existen desde hace tiempo con diferentes concepciones Åström and Wittenmark (1973), reglas de sintonía en función del error de posición con lógica difusa y redes neuronales para las ganancias proporcional K p y derivativa K v se encuentran en Llama et al (2000Llama et al ( , 2001; Santibáñez et al (2002Santibáñez et al ( , 2004; Meza et al (2009) ;Llama et al (2010); Meza et al (2012); Armendariz et al (2012). El concepto de ganancias variables se discute en Salas and Llama (2010); Salas et al (2012bSalas et al ( , 2013.…”

Design and Implementation of FFPIV Scheme for Closed Loop Motion Controller

“…Recently, several topics of advanced control are applied in motion controller such as a modified fuzzy logic control in automotive system [8], fuzzy PID with feed-forward control strategy in CNC machine [9] [10], fuzzy PI/PD-based control scheme in tracking applications including disturbance rejection and external loading [11] [12], self-tuning fuzzy PID through continuous updating approach of output scaling factor [13], a hybrid fuzzy bang-bang controller to improve the motor behavior [14] [15] or fuzzy PID with a class of gain matrices depending on the manipulator states [16].…”