Methodology of fuzzy-based tuning for sliding mode controller

Design a nonlinear controller for second order nonlinear uncertain dynamical systems is one of the most important challenging works. This thesis focuses on the design, implementation and analysis of a chattering free Mamdani’s fuzzy-based tuning error-based fuzzy sliding mode controller for highly nonlinear dynamic PUMA robot manipulator, in presence of uncertainties. In order to provide high performance nonlinear methodology, sliding mode controller is selected. Pure sliding mode controller can be used to control of partly known nonlinear dynamic parameters of robot manipulator. Conversely, pure sliding mode controller is used in many applications; it has two important drawbacks namely; chattering phenomenon which it can causes some problems such as saturation and heat the mechanical parts of robot manipulators or drivers and nonlinear equivalent dynamic formulation in uncertain dynamic parameter. In order to reduce the chattering this research is used the linear saturation function boundary layer method instead of switching function method in pure sliding mode controller and fuzzy sliding mode controller. In order to solve the uncertain nonlinear dynamic parameters, implement easily and avoid mathematical model base controller, Mamdani’s performance/error-based fuzzy logic methodology with two inputs and one output and 49 rules is applied to pure sliding mode controller. The results demonstrate that the error-based fuzzy sliding mode controller with saturation function is a model-free controllers which works well in certain and partly uncertain system. Pure sliding mode controller with saturation function and error-based fuzzy sliding mode controller with saturation function have difficulty in handling unstructured model uncertainties. To solve this problem applied fuzzy-based tuning method to error-based fuzzy sliding mode controller for adjusting the sliding surface gain (A)Since the sliding surface gain (A) is adjusted by fuzzy-based tuning method, it is nonlinear and continuous. In this research new A is obtained by the previous A multiple sliding surface slopes updating factor (A) which is a coefficient varies between half to one. Fuzzy-based tuning error-based fuzzy sliding mode controller is stable model-free controller which eliminates the chattering phenomenon without to use the boundary layer saturation function. Lyapunov stability is proved in fuzzy-based tuning fuzzy sliding mode controller based on switching (sign) function. This controller has acceptable performance in presence of uncertainty (e.g., overshoot=0%, rise time=0.8 second, steady state error = 1e-9 and RMS error=1.8e-12). Fuzzy-based tuning error-based fuzzy sliding mode controller and Guo and Woo adaptive fuzzy sliding mode controller have been comparatively evaluated through simulation, for robotic manipulator. Most of nonlinear controllers need real time mobility operation so one of the most important devices which can be used to solve this challenge is Field Programmable Gate Array (FPGA). FPGA can be used to design a controller in a single chip Integrated Circuit (IC). To have higher implementation speed with good performance SMC is implemented on Spartan 3E FPGA using Xilinx software (controller computation time=30.2 ns, Max frequency=63.7 MHz and controller action frequency=33 MHZ).

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