DC MOTOR SPEED CONTROLLER DESIGN USING POLE ASSIGNMENT TECHNIQUE FOR INDUSTRIAL APPLICATION

This paper describes DC motor speed control based on pole assignment feedback control technique. The present pole assignment technique specifies all closed-loop poles. Such a system where the reference input always zero is called a regulator system. The problem of shifting the regulator poles (closed-loop poles) at the desired location is called pole assignment problem


KEYWORDS: DC motor, Speed control, PID controllers, Pole assignment technique INTRODUCTION:
An electric motor is an electromechanical device that converts electrical energy into mechanical energy.This mechanical energy is used, for example, for rotating a pump impeller, fan or blower, driving a compressor, lifting materials etc. Electric motors are used at home (mixer, drill, fan) and in industry.
The purpose of a motor speed controller is to take a signal representing the demanded speed, and to drive a motor at that speed.The controller may or may not actually measure the speed of the motor.If it does, it is called a Feedback Speed Controller or Closed Loop Speed Controller, if not it is called an Open Loop Speed Controller.Feedback speed control is better, but more complicated.
In modern intelligent motion applications especially in industry, the demand to the accurate speed and position control is increasing.In the mean time, it is also expected that control systems should be reliable, cost effective, robust and, having with low volume weight and maintenance requirement.[Ayasun and Karbyaz, 2007] Because of the improvements in computers software packages for modeling and simulations, many authors tried to build controllers to control the speed of a DC motor.
[Ayasun and Karbyaz, 2007] describe the MATLAB/SIMULINK realization of a DC motor speed control methods, namely field resistance, armature voltage and armature resistance control methods, and feedback control system for DC motor drives.They studied the torque/speed characteristics for different field resistance, armature voltage and different armature resistance, showing how the speed of the motor vary for different PI gain values.
[Sharaf, Elbakush and Altas, 2007] present a novel PID dual loop controller for a solar photovoltaic (PV) powered industrial permanent magnet DC (PMDC) motor drive.MATLAB /SIMULINK was used in the analysis.[Silva, Carvalho, Vasconcelos and Soares, 2007] present a remote experiment for controlling a DC motor.The experiment is controlled using a PID algorithm programmed in LabView environment.[Roubal, Augusta, and Havlena, 2005] present the procedure of the control design, including a description of a system, an identification of its parameters, a simple and an advanced controller design based on optimal control.[Aung, 2007] gave an analyze how to choose DC motor to be balance with their applications of especially for Wheeled Mobile Robots (WMR).Specification of DC Motor that can be used with desire WMR is to be determined by using MATLAB Simulink model.

MOTOR MODEL
Generally, the rotational speed of a DC motor is proportional to the voltage applied to it, and the torque is proportional to the current.Speed control can be achieved by variable battery tappings, variable supply voltage, resistors or electronic controls.[speed controller,2008] A simple motor model is shown in Fig. 1.The armature is modeled as a circuit with resistance Ra connected in series with an inductance L a , e a and e b represent a voltage source and the back emf (electromotive force) in the armature when the rotor rotates respectively.[Ogata-1998, Ogata-2002, Dorf and Bishop-2005].

Fig. 1 DC Motor Model.
The motor torque T m is related to the armature current, i a , by a torque constant K i ; The back emf, e b , is relative to angular velocity by; From Fig. 1 we can write the following equations based on the Newton's law combined with the Kirchoff's law.[Ogata, 1998] There are several different ways to describe a system of linear differential equations.The plant model will be introduced in the form of state-space representation and given by the equations: According to equations from (2) to (4), the state space model will be:  In this section a design of a commonly called Pole-Placement or Pole-assignment technique will be presented.All state variables are assumed to be measurable and available for feedback.If the system is considered completely state controllable, then poles of the closed-loop system may be placed at any desired locations by means of state feedback through an appropriate state feedback gain matrix.In the conventional approach to the design of a single-input-single-output control system a designed controller (compensator) such that the dominant closed-loop poles have a desired damping ratio ζ and an undamped natural frequency ω n .In this approach, the order of the system may be raised by 1 or 2 unless pole-zero cancellation takes place.In brief the pole assignment technique is somewhat similar to the root locus method in that a closed loop poles are placed at desired locations.The basic difference is that in root locus design only the dominant closed loop poles are placed at the desired locations, while in the pole assignment technique all the closed loop poles are placed at the desired locations.[Ogata-1998, Ogata-2002, Dorf and Bishop-2005].For a control system of eq. ( 5) and depending on the pole assignment the control signal will be: Fig. 3 shows the control model that is based on the pole assignment.

Fig. 3 Closed Loop Control System
This means that the control signal uis determined by the instantaneous state, Substituting eq. ( 8) into eq.
(5) gives The solution of this equation is given by ) (t x approaches 0 as t approaches infinity.The problem of placing the regulator poles (closed-loop poles) at the desired location is called a pole assignment problem.[Ogata-1998, Ogata-2002, Dorf and Bishop-2005].

CHOOSING THE LOCATION OF DESIRED CLOSED LOOP POLES:
The first step in the pole assignment technique is to choose the location of the desired closed loop poles.The most frequently used approach is to choose such Note that if the dominant closed loop poles are placed far from the jω axis, so that the system response becomes very fast, the signals in the system become very large, with the result that the system may become nonlinear.This should be avoided.[Ogata,2002] PID TECHNIQUE: The Proportional Integral Derivative (PID) controller calculation (algorithm) involves three separate parameters; the proportional, the integral and derivative values.The proportional value determines the reaction to the current error, the integral value determines the reaction based on the sum of recent errors, and the derivative value determines the reaction based on the rate at which the error has been changing, as shown in Fig. 4.
By tuning the three constants in the PID controller algorithm, the controller can provide control action designed for specific process requirements.The response of the controller can be described in terms of the responsiveness of the controller to an error, the degree to which the controller overshoots the set point and the degree of system oscillation.[Ogata-1998, Ogata-2002, Dorf and Bishop-2005].The open loop transfer function of the DC motor according to the selected data can be given as in eq. ( 10), with two poles (-0.0575+j0) and (-1.95+j0): To examine the accurate speed and position control, the time domain specifications (Settling time; Peak amplitude, Maximum overshoot) the close loop control system should be studied.
The closed loop transfer function of the DC motor according to the selected data can be given as in eq.( 11), with two poles (-1+j1.96)and (-1-j1.96): The closed loop step response (with unity feedback control) is shown in Fig. 6, which shows that the settling time of 3.83second and peak amplitude of 1.17.

Closed Loop Step Response
Fig.2 shows the closed loop control system for the DC motor in the form of a block diagram.[Aung,2007].

Fig
Fig. 2 DC-Motor System Block Diagram initial state caused by external disturbances.The stability and transient response characteristics are determined by the eigenvalues of matrix poles.If these regulator poles are placed in the left-half s-plane, then poles based on experience in the root locus design, placing a dominant pair of closed loop poles and choosing other poles so that they are far to the left of the dominant closed loop poles.

Fig
Fig. 4 PID Controller System Block Diagram

Fig. 5
Fig.5 Flowchart for the Controller Design Procedure In many practical cases, the desired performance characteristics of control systems can be given in terms of transient-response characteristics.
Fig. 6 Closed Loop Speed Step Response

Fig. 9
Fig. 9 Pole Assignment Speed Step response

. Dr. Kais S. Ismail Dr. Firas Mohammed Tuaimah Ruba Al-Mulla Hummadi Table 1: Time response specification for three speed control systems
Table1summarizes the values of settling time, peak amplitude and overshoot for the three different control systems, which are given previously, it is clear that the pole assignment controller is better.