Finite Element Based Modelling and Vibration Suppression of Flexible Link Manipulator Using Linear Quadratic Gaussian Controller

Abstract

Flexible link robot manipulators have potential advantages over traditional heavy and bulky robots like rigid link manipulators (RLM), including lower cost, a greater work volume, higher operational speed, a higher payload-to manipulator weight ratio, smaller actuators, lower energy consumption, better manoeuvrability, improved transportability, and safer operation due to less inertia. These FLM benefits are more significant in areas where energy efficiency is important, particularly in the space industry. On the other hand, because of their innate structural flexibility, they experience vibrations and take some time to reach the proper position after the actuating force has been released. The oscillating reaction at the tip significantly restricts the performance of these manipulators as a result. Furthermore, from a mathematical perspective, we can state that the dynamics of the rigid link robot can be determined on the assumption that the body's centre of gravity holds the majority of the mass, in which case the robot's dynamics would be expressed in terms of differential equations. On the other hand 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 modelled using Finite Element Method to generate a mathematical model of the manipulator. Then the models subsequently controlled by two types of controllers a normal PID controller tuned with particle swarm optimization and a linear quadratic gaussian controller (LQG) tuned with PSO. The TLFM system performance improvement with each of the controller against disturbance and payload variations is evaluated discussed and compared. The simulation results show that the developed strategies perform satisfactorily in terms of precise and reliable vibration suppression without steady state error and that LQG controller has a significant overshoot reduction compared to PID controllers and a good transient response with a rise time and settling time has been achieved for linear quadratic gaussian controller. Then particle swarm optimization tuned linear quadratic gaussian controller methods are better when compared with PID conventional methods.

Flexible link robot manipulators have potential advantages over traditional heavy and bulky robots like rigid link manipulators (RLM), including lower cost, a greater work volume, higher operational speed, a higher payload-to manipulator weight ratio, smaller actuators, lower energy consumption, better manoeuvrability, improved transportability, and safer operation due to less inertia. These FLM benefits are more significant in areas where energy efficiency is important, particularly in the space industry. On the other hand,because of their innate structural flexibility, they experience vibrations and take some time to reach the proper position after the actuating force has been released. The oscillating reaction at the tip significantly restricts the performance of these manipulators as a result. Furthermore, from a mathematical perspective, we can state that the dynamics of the rigid link robot can be determined on the assumption that the body's centre of gravity holds the majority of the mass, in which case the robot's dynamics would be expressed in terms of differential equations. On the other hand flexible robot position is not constant and hence partial differential equation is used to represent the distributed nature of position, whichresults in large number of equations increasing the computational effort. In this work a two-link flexible manipulator modelled using Finite Element Method to generate a mathematical model of the manipulator. Then the models subsequently controlled by twotypes of controllers a normal PID controller tuned with particle swarm optimization and a linear quadratic gaussian controller (LQG) tuned with PSO. The TLFM system performance improvement with each of the controller against disturbance and payload variations is evaluated discussed and compared. The simulation results show that the developed strategies perform satisfactorily in terms of precise and reliable vibration suppression without steady state error and that LQG controller has a significant overshoot reduction compared to PID controllers and a good transient response with a rise time andsettling time has been achieved for linear quadratic gaussian controller. Then particle swarm optimization tuned linear quadratic gaussian controller methods are better when compared with PID conventional methods.