  Robotic manipulators are widely used in applications that require fast and
precise motion. Such devices, however, are prompt to nonlinear control issues
due to the flexibility in joints and the friction in the motors within the
dynamics of their rigid part. To address these issues, the Linear Matrix
Inequalities (LMIs) and Parallel Distributed Compensation (PDC) approaches are
implemented in the Takagy-Sugeno Fuzzy Model (T-SFM). We propose the following
methodology; initially, the state space equations of the nonlinear manipulator
model are derived. Next, a Takagy-Sugeno Fuzzy Model (T-SFM) technique is used
for linearizing the state space equations of the nonlinear manipulator. The
T-SFM controller is developed using the Parallel Distributed Compensation (PDC)
method. The prime concept of the designed controller is to compensate for all
the fuzzy rules. Furthermore, the Linear Matrix Inequalities (LMIs) are applied
to generate adequate cases to ensure stability and control. Convex programming
methods are applied to solve the developed LMIs problems. Simulations developed
for the proposed model show that the proposed controller stabilized the system
with zero tracking error in less than 1.5 s.
