The minimum rule base Proportional Integral Derivative (PID) Fuzzy backstepping Controller 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 PD-like fuzzy controller and a PI-like controller to have the minimum rule base. However backstepping controller is work based on cancelling decoupling and nonlinear terms of dynamic parameters of each link, this controller is work based on manipulator dynamic model and this technique is highly sensitive to the knowledge of all parameters of nonlinear robot manipulator’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 flexible robot manipulator system and testing of the quality of process control in the simulation environment of MATLAB/SIMULINK Simulator.

Both fuzzy logic and sliding mode can compensate the steady-state error of proportional-derivative (PD) control. This paper presents parallel sliding mode compensations for fuzzy PD controllers. The asymptotic stability of fuzzy PD control with first-order sliding mode compensation in the parallel structure is proven. For the parallel structure, the finite time convergence with a super-twisting second-order sliding-mode is guaranteed.

Refer to this paper, an intelligent-fuzzy feed-forward computed torque estimator for Proportional-Integral-Derivative (PID) controller is proposed for highly nonlinear continuum robot manipulator. In the absence of robot knowledge, PID may be the best controller, because it is model-free, and its parameters can be adjusted easily and separately and it is the most used in robot manipulators. In order to remove steady-state error caused by uncertainties and noise, the integrator gain has to be increased. This leads to worse transient performance, even destroys the stability. The integrator in a PID controller also reduces the bandwidth of the closed-loop system. Model-based compensation for PD control is an alternative method to substitute PID control. Computed torque compensation is one of the nonlinear compensator. The main problem of the pure computed torque compensator (CTC) was highly nonlinear dynamic parameters which related to system’s dynamic parameters in certain and uncertain systems. The nonlinear equivalent dynamic problem in uncertain system is solved by using feed-forward fuzzy inference system. To eliminate the continuum robot manipulator system’s dynamic; Mamdani fuzzy inference system is design and applied to CTC. This methodology is based on design feed-forward fuzzy inference system and applied to CTC. The results demonstrate that the model base feed-forward fuzzy CTC estimator works well to compensate linear PID controller in presence of partly uncertainty system (e.g., continuum robot).