Methodology of FPGA-Based Mathematical Error-Based Tuning Sliding Mode Controller

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).Design a nonlinear controller for second order nonlinear uncertain dynamical systems is one of the most important challenging works. This paper focuses on the design of a FPGAbased chattering free mathematical error-based tuning sliding mode controller (MTSMC) for highly nonlinear dynamic 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 an important drawback namely; chattering phenomenon which it can causes some problems such as saturation and heat the mechanical parts of robot manipulators or drivers. In order to reduce the chattering this research is used the switching function in presence of mathematical error-based method instead of switching function method in pure sliding mode controller. The results demonstrate that the FPGA-based sliding mode controller with switching function is a model-based controllers which works well in certain and partly uncertain system. Pure sliding mode controller has difficulty in handling unstructured model uncertainties. To solve this problem applied mathematical model-free tuning method to FPGA-based sliding mode controller for adjusting the sliding surface gain ( ). Since the sliding surface gain ( ) is adjusted by mathematical model free-based tuning method, it is nonlinear and continuous. In this research new is obtained by the previous multiple sliding surface slopes updating factor . FPGA-based Chattering free mathematical errorbased tuning sliding mode controller is stable controller which eliminates the chattering phenomenon without to use the boundary layer saturation function. Lyapunov stability is proved in mathematical error-based tuning sliding mode controller with 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). To have higher implementation speed with good performance TVSC 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).