Consider a 2-D object consisting of two triangle compartments, as shown in Figure P9.4. Suppose a solution containing a 511 KeV gamma ray emitting radionuclide with concentration f = 0.5….

## Take Laplace transform for both side of equation (9) From equation (10) I_a is given as. From equ. (8 ) and (11) we get

- Speed Control of PMDC Motor using PID Controller Muaz Abdel Rahman Ismail1 , Eltahir Mohamed Heessain2 1 Juba University, Department of Electronics, College of Applied and Industrial Science. Sudan 2Department of Biomedical Engineering, Sudan university of Science and Technology, ALsahva zalt road, Khartom, Sudan Abstract: the real parameters were used for speed control PMDC motor using PID controller. PMDC Motor and Mat lab/ Simulink were used to design the transfer function and simulate PMDC Motor with and without Load, a with PID controller .The also study was discussing the performance of PMDC Motor; it found that the PI have the best perform. Keywords: PMDC Motor, PI controller, PID Controller, Ziegler – Nichols method, control speed 1. Introduction DC (Direct current) Motor is an electrical transducer that converts the electrical energy in to mechanical energy DC motor used in industrial applications, robotics application, steel rolling, mills and railways. the advantage of DC motor that are less complexity , less precise and wide range speed mode for various operate in many applications . For the operation on a wide range of speed it needs a controller to control the speed of the motor to perform the desired job and we need to eliminate the effect of disturbance that changes the speed. Many control methods have been developed to reduce the effect of disturbance such as classical control , state – space method , state feedback and optimal control but it do not give good solution for reducing the effect of disturbance. PID controller is one of the best advantage method for solving problems raised due to variation in parameter of system and environmental condition , PID controller are simply , quickly and more reliable solution over classical control and pole placement. The PID is a more robust control method then classical [4]. In this paper proposed a PID controller and it tested for various types of PID controllers. The designed Simulink model of PID controller for speed control of PMDC motor tested for various types of PID controllers, and found that for all types of PID the PI operate efficiently and gives better result to improve the speed control of PMDC motor in best time. 2. Previous Studies 2.1Prabha Malvinas (PG Student), Menka Dubey (Sr. Asst. Prof) The paper shows various method of speed control of DC Motor and many techniques for tuning PID controller [9]. 2.2 Wasif Abdel Aziz Saluos, Mohammed Abdel Karatim Alia the Gain scheduling ware implemented in PID controller to drive a DC Motor. The paper show the improved of the response system and eliminate the over shoot speed of Motor [10]. 2.3 Lokesh Kumaral The paper introduced an artificial neural network in PID controller to control DC Motor. It prepares the neural network as solution to reduce the rise time and peak over shoot. 3. The Mathematical Model of PMDC Motor A DC motor consists of electrical and mechanical equation described as: Air gap flux given as. The torque developed by the motor is given as. The back emf of the motor Taking Laplace transform will get that General equation of PMDCM is given as: Taking Laplace transform for equation (5). From equation (4 ) and (6 ) we get . The Load torque equation is given as: Take Laplace transform for both side of equation (9) From equation (10) I_a is given as. From equ. (8 ) and (11) we get