Optimization of Linear Quadratic Tracking (LQT) Weight Matrices Using Simulated Annealing Applied on Planar Arm Model

Abstract

Optimal controls have been applied in this time. One of simple optimal control which will be analyzed in this research is planar arm model dynamic. The planar arm model dynamic consists of joint angles consisting of shoulder joint and elbow joint, angle velocities, and joint torquest due to passive muscle forces. There are  control inputs from six muscles in the system. In this research, from planar arm model, it will be designed optimal control using Linear Quadratic Tracking (LQT). The objective function of planar arm model is we will minimimize two angles consisting of shoulder joint and elbow joint. In LQT, the value of performance index depends on the weight matrices so that we should optimize the weight matrices. In this research, the optimization of weight matrices in planar arm model will be applied by Simulated Annealing. The Simulated Annealing method is based on the simulation of thermal annealing of critically heated solids. Based on simulation results, Simulated Annealing can optimize the weight matrices in LQT so that it results optimal performance index with angle as state solution can follow the reference and we also obtain optimal controls from six muscle forces applied.