Model Predictive Control of a Two-Link Flexible Manipulator

Abstract

Flexible manipulators are widely used because of the many advantages it provides like low weight, low power consumption leading to low overall cost. However due to the inherent structural flexibility they undergo vibrations and take time to come to the desired position once the actuating force is removed .The most crucial problems associated while designing a feedback control system for a flexible-link are that the system being non-minimum phase, under-actuated and non-collocated because of the physical separation between the actuators and the sensors. Moreover from mathematical point of view we can say that the dynamics of the rigid link robot can be derived assuming the total mass to be concentrated at centre of gravity of the body hence dynamics of the robot would result in terms of differential equations. On contrary flexible robot position is not constant and hence partial differential equation is used to represent the distributed nature of position which results in large number of equations increasing the computational effort. In this work a two link flexible manipulator is modelled using Assumed Mode Method considering two modes of vibration. Further fuzzy identification is also performed using T-S modelling approach which minimises the computation and takes into account higher modes of vibration. The input spaces consists of the torque inputs to the link and membership function of Gaussian form is chosen. The consequent parameters are calculated using Least Square Algorithm. For controlling the tip vibration a controller is designed using Model Predictive Control. The Model Predictive Control is an optimal control method in which the control law is calculated using the system output. MPC is widely used in the industry due to its better performance. The results are compared with another controller based on Linear Quadratic Regulator.