Adaptation of gains for a PID controller for the gradient descendent method : Design, Simulation and comparison with classic PID controller

In this document is presented the simulation of the adaptive control and obtaining of the nonlinear model of a MIPR (mobile inverted pendulum robot), this model consists of four variables (velocity and acceleration in wheels, velocity and acceleration in pendulum). The objective is to implement an adaptive PID (proportional, integral derivative) controller using the GDM (gradient descendent method), to keep the pendulum in an unstable equilibrium point, the GDM is used for to optimize the gains of the PID controller. The parameters weight and length of the nonlinear model are varying in the time. The response of adaptive control is compared with a classic PID controller of constant gains. The system with two laws of control was implemented in the Matlab software, the results are showed that classic PID controller with constant gains can not to control the MIPR, on the other hand the adaptive PID controller has good response.