Authors N.K.Poddar 1, R.P.Gupta 2 1,2 Electrical Engineering Department, B.I.T Sindri Dhanbad, India

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1 Volume 4 Issue 07 July-2016 Pages ISSN(e): Website: DOI: Position Control And Delay Analysis of DC Servo Motor Using Conventional Controller Authors N.K.Poddar 1, R.P.Gupta 2 1,2 Electrical Engineering Department, B.I.T Sindri Dhanbad, India - nirmaltheocean@gmail.com, ramjee_gupta@yahoo.com ABSTRACT- Position control study of DC-servo motor is very important, since it is extensively deployed in various servomechanisms. In the present paper position control and delay analysis of DC-servo motor using different controller has been discussed. In any control application, controller design is the most important part. There are different types of controller architectures available in control literature. The controllers used here are PID, FOPID and IMC. By PID-ZN tune the value of, and to obtain the output at desired level, by FOPID Optimize the value of the power s of PID controller to control the system better than PID-ZN, and by using IMC controller control the system better than PID-ZN and FOPID. Keyword-Ziegler Nichols (ZN), Fractional order PID (FOPID), Internal Module Controller (IMC). I. INTRODUCTION This work proposed to position control and delay analysis of DC-servo motor using different controller. PID widely used in many industrial and domestic applications, to control the parameter variable which makes system unstable. So it is used to control the undesired response such as overshoot, settling time. The function of PID controller is to maintain the system response at desired level so that there is no difference between process variable and set point value and to minimize time domain performance measure such as rising time, settling time and overshoot. PID controller is very popular because of its Generation of this type of controller is given By the fraction of P and was introduce first F.Wobbe. It is based on solving a set of nonlinear equation, it gives better result compare of PID- ZN. IMC philosophy relies on Internal Model Principle which states that control can be achieved only if control system encapsulates, either implicitly or explicitly, some representation of process to be controlled. If control scheme has been developed based on exact model of process, simplicity, robustness and reliability with some limitations. A PID controller improves system response both transient as well as steady state response. Ziegler and Nichols proposed first method in 1940 for the tuning of PID parameters. But in some cases it has been difficult to tune the parameters with conventional techniques consist some issues such as nonlinearities, time delays so to overcome such type of difficulties control engineers are working on more conventional controller such as FOPID and IMC give the better output compare of PID. The FOPID ideas first proposed by J. Liouvile in 1832.A then perfect control is theoretically possible. By using IMC the system output taken better than PID and FOPID. II. MODELLING OF DC-SERVO MOTOR Consider schematic diagram of armature controlled DC servo motor as shown in Figure 1. The control can be archived either by controlling the field current or armature current. Generally it have separate DC source for armature winding N.K.Poddar, R.P.Gupta IJSRE Volume 4 Issue 7 July 2016 Page 5630

2 and field winding. DC servo motor is a linear SISO plant model having third order transfer function. Let us voltage apply to the armature terminal, due to it exciting current in armature winding. This armature current induces mutual flux Ф in the field winding. The effect of exciting current and mmf generate torque on shaft as shown in Figure 1. Figure-1 (Schematic diag. of DC-servo motor) Mathematical relationship between the shaft angular position and voltage input to DC servo motor can be derived from the physical laws. This work focuses on the design of such a controller for DC servo motor which can guarantee stability of system and can give an optimal PID FOPID and IMC controller. A design by mathematical model of DC servo motor is given by equation = [1] Where is armature inductance is armature resistance is moment of inertia of shaft is viscous friction co-efficient is motor constant is back emf constant Ѳ is angular position of shaft is electromotive force constant II(a). Modelling in Disturbance Figure 2 (Block diag. of DC-servo motor) Here = =electromotive force constant. Here the disturbance is modefying function of this work taken as Td= [2] Now put the value of k=1,5,50,100,500,1000,5000,10000 in [2]. At the initial disturbance system found unstable but at k=10000 the system bcomes stable. Hence the Td modefied as T d = [3] II(b). Modelling in Delay Consider the delay of one second thn new modefied transfer function written as = Approximate transfer function calculated as = [4] Put the value of H, =1 ohm, =0.01 Kg/, B=01 n.m.s, Km=0.01Nm/amp, Kb=0.02v/rad/sec then transfer function before modelling equation [1] becomes G(s)= = [5] After moelling equation [4] becomes G(s) = (1-s) [6] III PID CONTROLLER DESIGN Controller in any system plays very significant role and helps in taking remedial control action. The essential function of controller is to maintain the output at that level so that there is no difference between the measured output and set point value. PID controllers are the predominant type of controllers which are used in almost every process industry. PID controller is widely used in industries due to its simplicity and easy to implement. A PID controller calculates an error and tries to minimize it by adjusting the control N.K.Poddar, R.P.Gupta IJSRE Volume 4 Issue 7 July 2016 Page 5631

inputs. It improves the transient response of the system by reducing overshoot and by shortening the settling time and also has the ability to eliminate steady state offset through integral action.

3 inputs. It improves the transient response of the system by reducing overshoot and by shortening the settling time and also has the ability to eliminate steady state offset through integral action. The transfer function for the PID controller can be written as, Where is proportional gain = + + s is integral gain is differential gain To tune the PID using ZN controller put 1+G(s)H(s) =0 For without delay s+10 =0 Put s=jw results J( w)+( )=0 [7] Comparing real and imaginary to zero of the equation [7] w=4.086, =116.9 Use =0.6Kc, Ti=0.5T, Td=0.125T Where T=2π/w, =1/Ti, =1/Td Resulting =70.26, =1.3, =5.2For with delay = 5.46, =0.36, =1.45 IV. FOPID DESIGNING One of the primary controllers is PID controller, which is widely used. Fractional controller is denoted by P was proposed by Igor Podlubny in 1997, here λ and μ have non-integer values. Figure 3 shows the block diagram of fractional order PID controller = ( ) [8] Where is the equivalent taken common constant after putting the Ziegler-Nichols value, and. Figure 3 (Block diag. of FOPID) Where λ and μ are an arbitrary real numbers, amplification (gain), is integration constant and is differentiation constant. Taking λ=1 and μ=1, a classical PID controller is obtained. For further practical digital realization, the derivative part has to be complemented by first order filter. The table for selective λ and μ for without delay Table 1 for selection of λ and μ λ >1 and μ >1 λ =1.5, μ =1.5 λ<1 and μ>1 λ =0.2, μ =2 λ >1 and μ<1 λ =0.7, μ =0.7 λ <1 and μ<1 λ =0.5, μ =0.5 Best output observe at λ =1.5, μ =1.5 for without delay. Best output observe at λ=1.2, μ=1.2 for with delay V. IMC CONTROLLER DESIGN IMC philosophy relies on Internal Model Principle which states that control can be achieved only if control system encapsulates, either implicitly or explicitly, some representation of process to be controlled. If control scheme has been developed based on exact model of process, then perfect control is theoretically possible. The main feature of internal model controller is that the process model is in parallel with the actual process. Fig. 4 shows the scheme of IMC. The plant parameter comprises of servo motor system. With the help of transfer function of these systems, model can be predicted. is N.K.Poddar, R.P.Gupta IJSRE Volume 4 Issue 7 July 2016 Page 5632

Figure 4 (Block diagram of IMC) Plant gain without delay (s)= [9] Plant gain with delay same as [8] (s)= [10] The process model is factored into two parts, that is invertible part and noninvertible

4 Figure 4 (Block diagram of IMC) Plant gain without delay (s)= [9] Plant gain with delay same as [8] (s)= [10] The process model is factored into two parts, that is invertible part and noninvertible part.the non-invertible part consists of RHP zeros and time delays. This term if inverted, will lead to instability and reliability problem.this factorization is performed so as to make the resulting internal model controller stable. Additionally, to improve robustness, the effect of process model mismatch should be minimized. Since discrepancy between process and model behavior usually occur at the high frequency end of frequency response, a low pass filter is usually added to attenuate the effects of processmodel mismatch. Thus, the internal model controller is usually designed as the inverse of process model in series with a low pass filter. Next we set [11] Where is a low pass function defined as [12] Where λ is closed loop time constant. A good rule of thumb is to choose λ to be twice fast as Put denominator zero of [12] to check the condition of poles =0 S=0, -9.99,-1.67 Since all pole lies in LHP or at zero Therefore we have to take =, and take λ=1, n=4 results equation [11], [12] becomes = [13] Equation [13] valid for with and without delay VI. SIMUATION AND RESULT COMPARISION The simulation of PID-ZN, FOPID and IMC Using without delay shown in Figure 5, 6, 7 Figure 5 (Simulation of PID-ZN without Figure 6 (Simulation of FOPID without N.K.Poddar, R.P.Gupta IJSRE Volume 4 Issue 7 July 2016 Page 5633

5 Figure 7 (Simulation of IMC without Fig 8(Response of PID, FOPID and IMC without Fig 9(Simulation of PID, FOPID, IMC with The response of Fig 9 Table 2(Comparison of time domain without TYPE OF Mp(%) Tr(sec) Ts(sec) CONTROLLER PID-ZN FOPID IMC The simulation of PID-ZN, FOPID, IMC using delay shown in Fig 7 Fig 10(Response of PID, FOPID, and IMC with N.K.Poddar, R.P.Gupta IJSRE Volume 4 Issue 7 July 2016 Page 5634

6 Table 3 (Comparison of time domain with CONTROLLR Mp(%) Tr(sec) Ts(sec0 PID-ZN FOPID IMC It is observe from the Table 2 and Table 3 even delay is provided to the system used controller shows the ability to control the system with some time domain difference. VII CONCLUSION In this work, a comparative study of different conventional controller studied. The aim of the proposed controller is even delay is provided to the system, the position of DC-servo motor system respond to a desired position in the shortest possible time and minimum or no overshoot irrespective of step change in load and process disturbances, equipment saturation and non-linearity of different control equipment s. MATLAB software tool is used for finding the controller parameters for the PID controller used in the DC servo motor. A computer simulation is done to illustrate the results for ZN-PID, FOPID and IMC. After time response analysis carried out on different controllers it is observed that IMC controller gives the better response compare of PID-ZN and FOPID. Finally the robustness and better performance indices of used controller is achieved even delay is provided to the system REFERENCES 1. Astrom, K.J., Introduction to stochastic control theory, Academic Press, New York, B. Nagraj, S. Subha, and B. Rampriya, Tuning algorithm for PID controller using soft commuting techniques, IJCSNS International journal of computer science and network security, Vol.8, No. 4, April Neenu Thomas, Dr. P. Poongodi Position Control of DC Motor Using Genetic Algorithm Based PID Controller Proceedings of the World Congress on Engineering 2009 Vol II WCE 2009, July 1-3, 2009, London, U.K. 4. Mohd Fua ad Rahamat & Mariam md Ghazaly, Performance Comparison between PID and Fuzzy Logic Controller in 5. K. W. Song, G. S. Choi, G. H. Choi, and J. S. Kim, Integration of distributed control networks with IP networks for remote control and monitoring, Proc. of ICMIT, pp , Yamaguchi, Japan, December W. S. Levine, Control System Fundamentals, CRC Press, pp , R. E. Bethel and R. G. Rahikka, Optimum time delay detection and tracking, IEEE Trans. on Aerospace and Electronic Systems, vol. 26, no. 5, pp , September [8] K. W. Song, G. S. Choi, G. H. Choi, and J. S. Kim, Lon Works-based virtual device network (VDN) for predictive maintenance, Int. J. of Applied Electro-magnetic and Mechanics, vol. 18. no. 1-3, pp , Dongmei Yu, Qingding Guo and Qing Hu, Position Control of Linear Servo System Using Intelligent Feedback Controller, Sixth IEEE International Conference on Intelligent Systems Design and Applications (ISDA 06), Xiaodiao Huang and Liting Shi, Simulation on a Fuzzy-PID Position Controller of the CNC Servo System, Sixth IEEE International Conference on Intelligent Systems Design and Applications (ISDA 06), Xiaodiao Huang and Liting Shi, Simulation on a Fuzzy-PID Position Controller of the CNC Servo System, Sixth IEEE International Conference on Intelligent Systems Design and Applications (ISDA 06), N.K.Poddar, R.P.Gupta IJSRE Volume 4 Issue 7 July 2016 Page 5635

7 12. M. Maeda and S. Murakami, Fuzzy Gain Scheduling of PID Controllers, Fuzzy Sets Syst., 51, 29 40, I. J. Nagrath and M.Gopal, Control System Engineering. Fifth Edition. 14. Zuo Yusheng, Compared with PID, Fuzzy, PID Fuzzy Controller Hohai University, Nanking in Jiangsu Province. VIII NOMENCLATURE Armature current Field current in ampear Motor torque constant Back emf constant B Viscous friction co-efficient Back emf in volts J Moment of inertia of motor Ѳ Angular displacement of shaft in radians Armature inductance in hennery Armature resistance in ohm Controlled model Process model Proportional gain Integral gain Derivative gain N.K.Poddar, R.P.Gupta IJSRE Volume 4 Issue 7 July 2016 Page 5636

Position Control of DC Motor by Compensating Strategies

Position Control of DC Motor by Compensating Strategies S Prem Kumar 1 J V Pavan Chand 1 B Pangedaiah 1 1. Assistant professor of Laki Reddy Balireddy College Of Engineering, Mylavaram Abstract - As the