adaptive fuzzy sliding mode control

Authors: Seonghyeon Jo([email protected])

Date: Jan 20, 2022

This repository is a MATLAB simulation of adaptive fuzzy sliding mode control for robot manipulator. The robot manipulator uses sawyer 4-dof manipulator and prototype 3-dof manipulator. we compare to simple PID Controller, Sliding Mode Control(SMC), Fuzzy Silding Mode Control(FSMC), Adaptive Fuzzy Sliding Mode Control(AFSMC).

"Adaptive fuzzy sliding mode control using supervisory fuzzy control for 3 DOF planar robot manipulators."

Description of robot manipulator model

In general, the dynamic of a robotic manipulator can be expressed as follows: where denote the joint position vector, velocity vector, acceleration, the vector of control torques, and the vector of disturbance torques, respectively, and denotes the symmetric positive definite inertia matrix, denotes the Coriolis matrix, denotes the gravity vector and is the friction matrix.

Multiplying $M^{-1}(q)$ by both sides in Equation (1), we have

The sliding proportional-integral-derivative PID surface in the space of tracking error can be defined as:

where kp is positive proportional gain matrix, ki is positive integral gain matrix, kd is positive derivative gain.

Take the derivative of sliding surface with respect to time, then

The control effort being derived as the solution of s˙(t) = 0 without considering uncertainty (d(t) = 0) is to achieve the desired performance under nominal model, and it is referred to as equivalent control effort , represented by ueq(t)

sawyer 4-dof manipulator

RMSE

Method	joint 1	joint 2	joint 3	joint 4	sum
PID	0.0394	0.0339	0.0044	0.0083	0.0860
SMC-SIGN	0.0078	0.0349	0.0003	0.0039	0.0469
SMC-SAT	0.0078	0.0358	0.0004	0.0019	0.0460
FSMC	0.0111	0.0146	0.0017	0.0043	0.0317
AFSMC	0.0105	0.0141	0.0013	0.0042	0.0301

Figure

pid controller

smc using sign function

smc using sat function

smc using sat function

fsmc

afsmc