In this assignment solution, we delve into the realm of continuous models by simulating a 2-link SCARA robot. The focus is on understanding the dynamics of the system and implementing PID control to govern its behavior. We develop the Lagrangian equations, linearize the system, and employ Simulink for simulation. This exploration sheds light on the challenges and intricacies of controlling a robotic system with precision.
The SCARA robot is a mainstay in production assembly lines, known for its versatility and efficiency. It is often controlled using Proportional-Integral-Derivative (PID) compensators, which ensure precise and controlled movements. In this assignment solution, our focus narrows down to a 2-link SCARA robot, equipped with an end effector, where we explore the core principles governing its operation.
Assignment 1
Abstract
Continuous models are models that simulate a continuous time system. In this model, we
simulate a 2 link SCARA robot. The model simulates the position of the second link when the
first link is moved. We simulate Lagrangian system of equations for the robot. This is done to
get the dynamics of the system. Then we linearize it to introduce a PID control.
Introduction
SCARA robot or Selective Compliance Assembly Robot Arm is a production assembly line
robot. The SCARA robot is usually controlled by PID compensators. In this simulation, we try to
control a SCARA robot with two links and an end effector.
Let us develop the Lagrangian equations for the robot system.
The coordinates of the centre of gravity of the robot link are given by
The coordinates of the position of arm is given by
The kinetic energy function is given by
Using these equations, the final system equation is given by
Here,
Here,
Modeling
The transfer function of the motor is given by
This system can be represented by
Approach
The system equation is nonlinear. We have to linearize the equation to be able to control the
system. This linearized system is then controlled using a PID controller.
The PID control for the robot is given by
In PID Controller,
P- Current error
I-Sum of error
D- Corrective error
This is one of the simplest controller models. Using this model, we can minimize the postion
error of the end effect. One way of tuning this method is to use Ziegler Nichols tuning method.
The transfer function for this system is given by
Simulation
The Simulink model for one motor and link is given
by
Assumptions
1. The inductance is negligible in comparison to the resistance.
2. There is no potential energy
3. The two links are parallel
Conclusion
The robot system is simulated using a Simulink model. A PID controller is implemented. It is
seen that further tuning is required to reduce the error in the system.