A novel global asymptotic stable set-point fuzzy controller with bounded torques for robot manipulators

Sliding Mode Control of Robot Manipulators via Intelligent Approaches

“…When the tracking error would be less than predefined value then a sectorial fuzzy controller (SFC), (Calcev, 1998), is responsible for control action. Designing of this kind of fuzzy controller is exactly the same as in which has performed in (Santibanez et al, 2005). This proposed controller has following advantages.…”

“…This proposed controller has following advantages. 1) There are less tracking errors versus traditional SMC in condition that the control input is limited, 2) the chattering is avoided, 3) convergence of tracking error is more rapid than fuzzy controller designed in (Santibanez et al, 2005) and modeling uncertainty is considered here (Shafiei & Sepasi, 2010).…”

“…In this section, the SFC class of fuzzy controller studied in (Santibanez et al, 2005) is considered which has two-input one-output rules used in the formulation of the knowledge base. These IF-THEN rules have following form: The fuzzy system considered here has following specifications: Singleton fuzzifier, triangular membership functions for each inputs, singleton membership functions for the output, rule base defined by (51), (see Table. 2), product inference and center average defuzzifier.…”

“…Special properties of this input-output mapping ( ) y x for x 1 , x 2 are given in (Santibanez et al, 2005). Lemma 2.3.…”

“…Proof: the stability analysis is based on the study performed in (Calcev 1998) and is fully discussed in (Santibanez et al, 2005), so it is omitted here. Note that for constant set-point we have 0 d q = , hence q q = − .…”