Multi Loop PID Controller Robotic Arm Manipulator
Department of Electrical and computer Engineering, WPI
Email:gkodumudisrichan@wpi.edu

ABSTRACT
The precise control upon each degree of freedom of a robotic arm is a great challenge in implementing industrial work.
This paper aims to design a novel controller for an automated robotic arm. A discrete Proportional Integral Derivative
(PID) control technique is being used to replace the complex electronic circuitry, which would greatly reduce the cost and size of the controller. Function is derived for mathematical modeling of the system through which the stability of the system can be evaluated prior to fabrication.looptune to tune a multi-loop controller for a 4-DOF robotic arm manipulator.

1. Introduction
The recent rapid progress in robotic technologies has led to great expectations for robots to be applied in various fields such as industrial robots, guard robots and home robots [1]. Robotic arms find vast applications in several industrial automation processes such as manufacturing tasks, assembly lines etc. [2]. Motion control of a robotic arm can be classified into many categories. Lygorouas et al. [3] developed a computer-controlled light weight mechanical arm. This mechanical arm was a self-contained, autonomous system capable of executing high-level commands from a supervisory computer. The actuators of the joints were permanent magnet type DC motors driven by servo amplifiers via Pulse Width Modulation. Aung [4] designed and implemented a controller circuit based on
PIC microcontroller and H bridge circuit to control the motion of a Wheeled Mobile Robot (WMR). He used
MATLAB software for the modeling of the total system.
Silva [5] applied fuzzy logic at several hierarchical levels of a typical robotic control system. For controlling robotic manipulators, Moosavian [6] used Transpose Jacobian (TJ) control. Arciniegas et al. [7] developed neural network based adaptive control system to control the flexible robotic arm. Tseng [8] developed a DSP based instantaneous torque controller to control the manipulator.
Rogers [9] designed a microcontroller circuit for interfacing joint sensor to control robotic arm. In this text a unique computed torque technique is being used to actuate the various joints. Given the dynamic equation of a

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robotic arm, the basic problem is to determine the various torque/forces to drive all the joints of the arm in real time. This is done in order to track a desired time based trajectory as closely as possible. The motor current/ voltage characteristics and the computed torque are converted into an applied motor current/voltage which actuates the dc motors.
A closed loop PID controller is being used to reduce the overshoot, rise time and the steady state error. A PID controller usually comprises of a Proportional, Integral and Derivative circuitry but here the whole PID controller is implemented through programming which greatly reduces the electronic circuitry as well as cost of the system. This approach also simplifies tuning of the proportional (Kp), integral (Ki) and derivative (Kd) gains. The computed voltage from the error signal is applied to the motor by Pulse Width Modulation (PWM) technique.
A function is a mathematical expression which relate
. This can be modeled via MATLAB (SIMULINK) to obtain the vario teristics of the whole system which may be in the form of graphs. Here an approximate transfer function is derived considering the parameters such as damping, moment of inertia, gear ratio etc.
It is followed by the concepts of PID.
Then, the advantage of implementing a discrete PID controller is highlighted by using an atmega 16/32 bit microcontroller.

2. Transfer Function
The transfer function of a single joint can be well approximated by Equation (1.1) using the following variables:
Va = Armature voltage (Volts)
La = Armature inductance (Henry)
Ra =