Modeling and PDC fuzzy control of planar parallel robot

Abstract

Many works in the literature have studied the kinematical and dynamical issues of parallel robots. But it is still difficult to extend the vast control strategies to parallel mechanisms due to the complexity of the model-based control. This complexity is mainly caused by the presence of multiple closed kinematic chains, making the system naturally described by a set of differential-algebraic equations. The aim of this work is to control a two-degree-of-freedom parallel manipulator. A mechanical model based on differential-algebraic equations is given. The goal is to use the structural characteristics of the mechanical system to reduce the complexity of the nonlinear model. Therefore, a trajectory tracking control is achieved using the Takagi-Sugeno fuzzy model derived from the differential-algebraic equation forms and its linear matrix inequality constraints formulation. Simulation results show that the proposed approach based on differential-algebraic equations and Takagi-Sugeno fuzzy modeling leads to a better robustness against the structural uncertainties.

State-Difference Feedback Control for Discrete-Time Takagi–Sugeno Fuzzy Descriptor Systems with Parameter Uncertainties and External Noises

“…Control Method Performance [11] Sliding mode control Dissipativity constraint [12] PID control No [13] State feedback method control Robust constraint [14] Observer-based Output feedback control Robust constraint [23] Observer-based control No Present work…”

“…T-S FS are used in many fields, including robotic arms, pattern recognition, and power systems [9,10]. In the growing field of control systems and mathematical modeling, T-S FS have been extended to descriptor systems [11,12]. Through the combination of fuzzy rules, difference equations, and algebraic equations, the T-S fuzzy descriptor system (T-S FDS) can solve complex problems in various applications and interrelated phenomena [13].…”

“…In addition, we can combine linear control theory to make the analysis and control of complex nonlinear systems more effective. (2) Compared with existing control methods [11][12][13], the proposed state difference feedback control method can effectively solve the algebraic equation limitation problem in DA systems. (3) Compared with the controller proposed in [14,15], this paper uses the passivity constraints to suppress the impact of external noise on the system, making the modeling system more suitable for actual engineering.…”

“…where Q 1 and Q 2 are free-weighting function matrices. Substituting free-weighting function (12) into the first forward difference of (11) yields…”