A New Speed Control Technique for a Separately Excited Direct Current Motor by PID Controller

In this study, by deriving electro-mechanic mathematical model of separately excited direct current motor (SEDCM) via equivalent circuit, a new control block diagram has been formed. By using this block diagram, state space model of SEDCM has been created and block diagram of motor has been formed in Matlab Simulink environment. Steady state and transient values of armature current, emf, produced torque, speed and position angle have been obtained using this new model. By adding PID controller to block diagram, SEDCM has been remodeled. Finally, results of steady state and transient analysis of SEDCM have examined through speed control of the proposed model. It is reported that the suggested modeling technique is able to analyze the speed control of the SEDCM.


I. INTRODUCTION
HIS DOCUMENT is in parallel to rapid development of technology, from toy production to industry even from robots to space devices, many products contain motors powered by electrical energy.One of them is Direct Current motor.In comparison to alternating current motor, speed control of direct current motor is easier [1,2].Therefore, as it used to be, today they still take their place in industrial applications.Day by day, by the development of technology, their use in new products increases.High power DC motors are generally used in paper factories, weaving machines, ship propellers, printing machines and elevators and, low power DC motors are frequently used with motor controllers for the parts which especially require speed and position control in robotics, 3D printers, copying machines, moving parts of computers, radar tracking systems [3,4].
There are many types of DC motors which can be classified according to their winding and connection types and purpose of usage.The constant increase in the number of direct current motors and their dependence on the technology has made the development of the control of these motors important.In parallel to developing technology, the variety of DC motors and continuous increase of their usage area have made the development of the control of these motors important.

II. DIRECT CURRENT MOTORS AND PID CONTROLLER
The Electrical motors can be classified as alternating current motors and direct current motors.Direct current motors among themselves also can be classified in two groups according to their excitation type and connection type.According to excitation type, there are separately excited and self-excited direct current motors and, according to connection type there are shunt, serial and compound direct current motors.Except these, there are step and servo motors driven with DC [5].

A. Separately Excited DC Motors
Armature and excitation windings of SEDCM are independent from each other.They need to be excited by two different DC source.These are called separately excited DC motors [5].As known, DC motors consist of two electrical parts which are armature and excitation circuit and one mechanical part which transmits torque.As known, DC motors consist of two electrical parts which are armature and excitation circuit and one mechanical part which transmits torque.While DC machine works as generator, torque is applied to DC machine, but while DC machine works as motor, torque is applied to load which is coupled to shaft.A dc machine which works as motor is represented with general equivalent electromechanic system given in Fig. 1 [3].

B. Proportional-integral and derivative (PID) controller
PID controller is built up by using three controllers as seen in Fig. 2. In system, by using proportional, integral and derivative controls, control signal is generated.The system works with K P , K I and K D constants.A low pass filter is used to reduce noise of derivative control [8-10]

IV. MATLAB SIMULINK ENVIRONMENT AND SIMULATION OF CONTROL SYSTEM
A. Simulation model in Matlab Simulink Environment for SEDCM Motor parameters of SEDCM are given in Table 1.Bu using these values, Matlab/Simulink model of system which is shown in Fig. 4 is formed.Display modules are inserted to the certain points to monitor the results of steady state and transient analysis.The graphs of some values such as armature current, emf, armature current, produced torque, excitation current and position angle vs time are given below before PID controller is added to system in Matlab/Simulink environment for SEDCM.When Fig. 7 is examined, it is figured out that with excitation current of 1.614 A emf reaches 409.781V in a few hundred milliseconds and then gets stable.Fig. 8. Graphs of speed and position angle vs time of SEDCM When Fig. 8 is examined, it is figured out that speed of motor reaches approximately 600 rad/s in a few hundred milliseconds and after 1 second, it gets stable and takes value of 623.87 rad/s.Position angle increases logarithmically in a few hundred milliseconds and after that it keeps increasing linearly and get value of 6052.17 rad at 10th second.
The speed value of motor is measured as 623.87 rad/s which is equal to 5957.33 rpm and this value is used as a reference value for control models.

B. Simulation model in Matlab Simulink Environment with PID controller for SEDCM
The model of control system with PID controller in the Matlab/Simulink environment can be seen in Fig. 9. Since the speed of motor is normally 623.87 rad/s, reference value is fixed to this value.After that, by varying resistance and capacity values in related layers of control circuit control parameters K P , K I , K D and K P1 , K I1 and K D1 are adjusted and it is ensured that the output speed is 653,87 rad/s.When Fig. 12 is examined, it is figured out that with excitation current of 1.615 A, emf increases logarithmically and reaches 409.781V in 3 seconds.Later on, then gets stable.When Fig. 13 is examined, it is figured out that speed of motor reaches approximately 623.87 rad/s in 3 seconds, it gets stable and takes value of 623.87 rad/s.Position angle increases logarithmically in 3 seconds and after that it keeps increasing linearly and get value of 5043.14 rad at 10th second.
The speed value of motor is measured as 623.87 rad/s which is equal to 5957.33 rpm and this value is used as a reference value for control models.

Fig. 5 .
Fig.5.Graphs of armature current and emf vs time of SEDCM When Fig. 5 is examined, it is figured out that armature current increases logarithmically approximately up to 1150 A in a few hundred milliseconds and after 1 second, it gets stable and takes value of 38.755 A. Emf reaches 409.781V in a few hundred milliseconds and gets stable.

Fig. 6 .
Fig.6.Graphs of armature current and produced torque vs time of SEDCM

Fig. 7 .
Fig.7.Graphs of excitation current and emf vs time of SEDCM

Fig. 10 .
Fig.10.Graphs of armature current and emf vs time of SEDCM with PID controllerWhen Fig.10is examined, it is figured out that armature current increases logarithmically approximately up to 500 A in a few seconds and decreases logarithmically approximately up to 38.755 A. Later on, it gets stable.Emf reaches 409.781V in a few seconds and gets stable.

Fig. 11 .
Fig.11.Graphs of armature current and produced torque vs time of SEDCM with PID controller When Fig. 11 is examined, it is figured out that armature current increases logarithmically approximately up to 500 A in a few seconds and decreases logarithmically approximately up to 38.759 A. Later on, it gets stable.Produced torque logarithmically increases up to 150Nm in a 2.2 seconds and decreases logarithmically up to 25.464 Nm in 3.5s.Later on, it gets stable with value of 25.464 Nm.

Fig. 12 .
Fig.12.Graphs of excitation current and emf vs time of SEDCM with PID controller

Fig. 13 .
Fig.13.Graphs of speed and position angle vs time of SEDCM with PID controller figured out that SEDCM with proposed speed control technique has lower startup current in shorter duration and reaches stable sooner.
: Position angle;   : An angular velocity of rotor; J m : Rotational inertia of motor bearing; b m : Friction constant; K: EMF-Torque constant.These types of motor are not preferred in industry because they are separately excited.Even if they are used, excitation windings are connected in parallel with armature and it is used as shunt DC motor.Apart from this, they are used for experimental purposes in the organizations provided with technical training.
f : Field inductance; i f : Field current; V f : Field voltage; T e : Motor torque;

TABLE II
Fig.4.Matlab/Simulink simulation model of SEDCM