Convergence speed for system identification and estimation is a popular topic for determining the kinematics and dynamic identification/estimation of the parameters of robot manipulators. In this paper, adaptive fuzzy inverse dynamic system estimation is used to improve robust modeling, especially for a serial links robot manipulator. The Lyapunov technique is used to analyze the convergence rate of the tracking error and increase the accuracy response of the parameter estimation. Performance of robot estimation is conducted, and the results show fast convergence of the proposed finite time technique for a 6-DOF robot manipulator.

In practical applications, modeling of real systems with unknown parameters such as distillation columns are typically complex. To address issues with distillation column estimation, the system is identified by a proposed intelligent, auto-regressive, exogenous-Laguerre (AI-ARX-Laguerre) technique. In this method, an intelligent technique is introduced for data-driven identi?cation of the distillation column. The Laguerre method is used for the removal of input/output noise and decreases the system complexity. The fuzzy logic method is proposed to reduce the system’s estimation error and to accurately optimize the ARX-Laguerre parameters. The proposed method outperforms the ARX and ARX-Laguerre technique by achieving average estimation accuracy improvements of 16% and 9%, respectively.

The minimum rule base Proportional Integral Derivative (PID) Fuzzy backstepping Controller for three dimensions spherical motor is presented in this research. The popularity of PID Fuzzy backstepping controller can be attributed to their robust performance in a wide range of operating conditions and partly to their functional simplicity. The process of setting of PID Fuzzy backstepping controller can be determined as an optimization task. Over the years, use of intelligent strategies for tuning of these controllers has been growing. PID methodology has three inputs and if any input is described with seven linguistic values, and any rule has three conditions we will need 7 × 7 × 7 = 343 rules. It is too much work to write 343 rules. In this research the PID-like fuzzy controller can be constructed as a parallel structure of a PI-like controller and a PD-like fuzzy controller to have the minimum rule base. However backstepping controller is work based on cancelling decoupling and nonlinear terms of dynamic parameters of each dimension, this controller is work based on spherical motor dynamic model and this technique is highly sensitive to the knowledge of all parameters of nonlinear three dimension spherical motor’s dynamic equation. This research is used to reduce or eliminate the backstepping controller problem based on minimum rule base fuzzy logic theory to control of spherical motor system and testing of the quality of process control in the simulation environment of MATLAB/SIMULINK Simulator.