The Cost Function Minimization for Predictive Control by Newton-Raphson Method

The Newton-Raphson method is one of the most widely used methods for minimization. It can be easily generalized for solving non-linear differential equation systems. In this study, Generalized Predictive Controller (GPC) was applied to a 6R robot manipulator based on joint control. Newton-Raphson (N-R) method was used to minimize the cost function existing in the GPC that represents errors between reference trajectory and actual trajectory in the control of robot. The Newton-Raphson method requires less iteration numbers for convergence and reduces the calculation. This study presents a detailed derivation of the Generalized Predictive Control algorithm with Newton-Raphson minimization method. The results of angular path and position errors belonging to joints were examined and compared with Recursive Least Square (RLS) implemented Generalized Predictive Control. The simulation results showed that Newton-Raphson method improved control performance of the GPC.

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