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A novel approach for internet congestion control using an extended state observer 2 A novel approach for internet congestion control using an extended state observer 2 Document Transcript

  • International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN INTERNATIONAL JOURNAL OF ELECTRONICS AND 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 2, March – April (2013), © IAEMECOMMUNICATION ENGINEERING & TECHNOLOGY (IJECET)ISSN 0976 – 6464(Print)ISSN 0976 – 6472(Online)Volume 4, Issue 2, March – April, 2013, pp. 80-92 IJECET© IAEME: www.iaeme.com/ijecet.aspJournal Impact Factor (2013): 5.8896 (Calculated by GISI) ©IAEMEwww.jifactor.com A NOVEL APPROACH FOR INTERNET CONGESTION CONTROL USING AN EXTENDED STATE OBSERVER Kaliprasad A. Mahapatro1, MilindE.Rane2 1,2 Department of Electronics and Telecommunication Engineering, Vishwakarma Institute of Technology, Pune- 411019 INDIA ABSTRACT Congestion is the key factor in performance degradation of the computer networks and thus the congestion control became one of the fundamental issues in computer networks. Congestion control is the mechanism to prevent the performance degradation of the network due to changes in the traffic load in the network. Without proper congestion control mechanisms there is the possibility of inefficient utilization of resources, ultimately leading to network collapse. Hence congestion control is an effort to adapt the performance of a network to changes in the traffic load without adversely affecting user’s perceived utilities. This paper present the novel approach for internet congestion control using an Extended State Observer(ESO) along with the proportional-derivative(PD) Control, which improve the performance of congestion control on TCP/IP networks by estimating the uncertainties and disturbances, in the network. This paper also discusses the limitation of some classical observer like Disturbance Observer (DO) and how it is overcome by ESO by extending idea to practical non-linear system. The simulation shows that, the extended state observer is much superior in dealing with dynamic uncertainties and variation in network parameter. Index Terms: TCP/IP, Disturbance Observer (DO), Extended State Observer (ESO), Proportional-Derivative (PD). I. INTRODUCTION Traditionally the Internet has adopted a best effort policy while relying on an end-to- end mechanism. Complex functions are implemented by end users, keeping the core routers of network simple and scalable. This policy also helps in updating the software at the users end. Thus, currently most of the functionality of the current Internet lay within the end users protocols, particularly within Transmission Control Protocol (TCP). This strategy has worked 80
  • International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 2, March – April (2013), © IAEMEfine to date, but networks have evolved and the traffic volume has increased many folds;hence routers need to be involved in congestion control, particularly during the period ofheavy traffic. A conventional design approach by implementing multi path Energy EfficientCongestion Control Scheme to reduce the packet loss due to congestion have been carried outin [1] by combining congestion estimation technique by taking into account queue size,contention and traffic rate. But due to this open-loop technique an efficient control cannot becarried out. In order to find effective solutions to congestion control, many feedback controlsystem models of computer networks have been proposed. The closed loop formed byTCP/IP between the end hosts, through intermediate routers, relies on implicit feedback ofcongestion information through returning acknowledgements. Active Queue Management(AQM) scheme have been proposed in recent years [2]. Two types of methodologies to dealthese issues are congestion control and congestion avoidance. In this we will deal withcongestion control because it helps in the reactive planning by applying feedback technique.A more well-known AQM scheme is probably Random Early Detection [3]. RED can detectand respond to long-term traffic patterns, but it cannot detect the short-term traffic load. [4],in most of the cases parameter adjustment in RED are performed by using heuristic functionbecause of which the probability to determine uncertainties and disturbances in networkparameters reduces. To overcome above mentioned flaws [5] shown that a proportionalcontroller plus a Smith predictor provides an exact model of the Internet flow and congestioncontrol with a guaranteed stability and efficient congestion control. Active queuemanagement (AQM) scheme based on a fuzzy controller, called hybrid fuzzy-PID controller[6] shows that, the new hybrid fuzzy PID controller provides better performance than randomearly detection (RED) and PID controllers. To improve the performance even better a robust2-DOF PID control was implemented in [4] for better congestion control. A linear gainscheduling by using PID as given by T.Alvarez in [7]stability region was well explained byusing Hobenbichlers approach. In meanwhile a well-known classical observer known as Disturbance Observer(DOB)was introduced in [8] with an artificial delay, but DOB can only work efficiently with anideal assumption of slow varying noise or constant disturbances i.e. d_ = 0, which is wellexplained in the following section III. From the aforementioned flaws in various mechanisms, a novel AQM scheme thatsupports TCP flows and avoids drastic congestion due uncertainties and disturbances innetwork parameter is introducing a modern observer known as extended state observer(ESO). ESO was carried out in various sensitive plant like nuclear-reactor, space applicationlike NASA’s flywheel [9] etc. because of its beauty controlling internal dynamics andexternal disturbances of a non-linear plant from its input-output data. Continuing the samethis paper approaches to solution of estimating disturbances in network parameter by usingESO. The composition of this paper is as follows. Section II presents the non-linearmodeling of TCP/IP protocol. Section III briefly describes the limitation of disturbanceobserver. Section IV describes the mathematical approach of non-linear extended stateobserver with its control parameter for calculating uncertainties and simulation of the same iscarried out. Extending the idea of section IV a robust control is demonstrated in Section V byintroducing feedback control i.e. ESO+PD. Finally conclusion is stated in Section VI. 81
  • International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 2, March – April (2013), © IAEMEII. TCP/AQM ROUTER DYNAMIC MODEL In this section we will be briefly discuss about the proposed non-linear model ofTCP/IP protocol and linearizing the same for controller design.A. Nonlinear modelAs in the literature, a nonlinear model of TCP/AQM [10] [8] of a single congested routerwith a transmission capacity C is given as ሶ ‫݌‬൫‫ ݐ‬െ ܴሺ‫ ݐ‬ሻ൯ ൅ ோሺ௧ሻ ௐቀ௧ିோ൫௧ିோሺ௧ሻ൯ቁ ܹሺ‫ݐ‬ሻ ൌ െ ௐሺ௧ሻ ଵ ଶ ோ൫௧ିோሺ௧ሻ൯ (1) ܹሺ‫ݐ‬ሻ െ ‫ݍ ,ܥ‬ሺ‫ݐ‬ሻ ൐ 0 ேሺ௧ሻ ‫ݍ‬ሺ‫ݐ‬ሻ ൌ ൝ோሺ௧ሻ ሶ ݉ܽ‫ݍ ,0ݔ‬ሺ‫ݐ‬ሻ ൌ 0 (2) ഥare the positive bounded quantities i.e.,ܹ ‫ א‬ሾ0, ܹ ሿ and ‫ א ݍ‬ሾ0, ‫ݍ‬ሿ. The congestion of window തwhereW& q is the maximum window size and average queue length(i.e. buffer size), theyprobability p(t) ‫ ]1 ,0[ؠ‬and output is queue velocity‫ݍ‬ሶ _ To linearize equation(1) followingsize is increased after every round-trip time R(t). p(.) denotes the (input function) packet dropassumptions are made[4] i.e. N (t) ‫ ؠ‬N. • active TCP session N(t) are time invariant i.e. C (t) ‫ؠ‬C. • transmission link capacity are time invariant • time delay argument ‫ ݐ‬െ ܴon queue length q is assumed to be fixed to ‫ ݐ‬െ ܴ଴ then the linearize model of equation(1) results into ሶߜܹ ሺ‫ݐ‬ሻ ൌ െ ோమ஼ ൫ߜܹ ሺ‫ݐ‬ሻ ൅ ߜܹ ሺ‫ ݐ‬െ ܴ଴ ሻ൯ െ ோమ ஼ ൫ߜ‫ݍ‬ሺ‫ ݐ‬ሻ ൅ ߜ‫ ݍ‬ሺ‫ ݐ‬െ ܴ଴ ሻ൯ െ ଶேమ ߜ‫ݍ‬ሺ‫ ݐ‬െ ܴ଴ ሻ (3) ே ଵ ோబ ஼ మ బ బߜ‫ݍ‬ሶ ሺ‫ݐ‬ሻ ൌ ߜܹሺ‫ݐ‬ሻ െ ߜ‫ݍ‬ሺ‫ݐ‬ሻ ே ଵ ோబ ோబ (4)f(ܴ଴ , ܹ଴ , ‫݌‬଴ , ‫ݍ‬଴ ) with a desired equilibrium queue length q0 is given bywhere W(t) and _q(t)are the incremental variables w.r.t operating point as a function of 82
  • International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 2, March – April (2013), © IAEME ܴ଴ ൌ ൅ ܶ௣ ௤బ‫ۓ‬ ஼ۖ ܹ଴ ൌ ோబ ஼ ே‫۔‬ ‫݌‬଴ ൌ మ ଶ (5)ۖ ௐబ‫ݍە‬଴ ൌ ‫ݐ݄݈݃݊݁ ݁ݑ݁ݑݍ ݐ݁݃ݎܽݐ‬This lead to a nominal model, and is given as Fig. 1. Linearized model of TCP/AQM networks‫ ܩ‬ሺ‫ݏ‬ሻ ൌ ܲ௧௖௣ ሺ‫ݏ‬ሻܲ௤௨௘௨௘ ሺ‫ݏ‬ሻ݁ ିோబ௦ (6)where‫ܩ‬ሺ‫ݏ‬ሻ is the transfer function of the plant of TCP/AQM network which includes second-Where ܲ௧௖௣ ሺ‫ݏ‬ሻ and ܲ ௤௨௘௨௘ ሺ‫ݏ‬ሻ are given asorder system and time delay element as shown in Figure: 1 ೃ೙ ಴ మܲ௧௖௣ ሺ‫ݏ‬ሻ ൌ మಿ೙మ మಿ೙ ௦ା మ (7) ೃ೙ ಴ ಿ೙ܲ௤௨௘௨௘ ሺ‫ݏ‬ሻ ൌ ೃ೙ భ ௦ା (8) ೃ೙Therefore from equation (7) (8) & figure: 1 ‫ܩ‬ሺ‫ݏ‬ሻ can be stated as ಴మ‫ ܩ‬ሺ‫ݏ‬ሻ ൌ ܲ଴ ሺ‫ݏ‬ሻ݁ ିோబ ௦ ൌ మಿ మಿ భ ݁ ିோబ௦ ൬௦ା మ ൰ቀ௦ା ቁ (9) ೃబ ಴ ೃబby taking network parameter of [4] as C = 3750packets/sec, ‫ݍ‬଴ = 175packets, ܶ௣ = 0:2sec.In order to illustrate the effectiveness of ESO method, a numerical situation will be presentedFor load of N = 60 TCP sessions, ‫݌‬଴ = 0:008& substituting the same in equation (5) we getܹ଴ = 15packets, &R ଴ = 0:246.‫ ܩ‬ሺ‫ݏ‬ሻ ൌ ሺ௦ା଴.ହଷሻሺ௦ାସ.ଵሻ ݁ ି଴.ଶସ଺ ଵ.ଵ଻ଵ଼଻ହൈଵ଴ఱ (10) 83
  • International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 2, March – April (2013), © IAEMEIII. CHEN’S DISTURBANCE OBSERVER For simplicity of analysis of Disturbance Observer let us consider a linear time-invariant,continuous-time dynamic system of TCP/AQM in equation (9) model as.x = Ax + Bu+Bd (11)y= Cx (12)Where, A,B are the nominal system matrices considering no uncertainties and d is a constant or slowvarying input disturbance which is to be estimated.A. Mathematical modelingConstant DisturbanceConsidering z1 to estimate of d the equation (35 in [11]) can be written as .z1 = ξ + c1x 1= & ξ + c1 x (13) .1 = ξ + c1 (Ax +Bu +Bd) ……. from eqn8 (14) .Choosing ξ as - c1 (Ax+Bu) - c1Bd and sub in 10 we get....... 1= − c1 (Ax + Bu) − c1Bz1 + c1 (Ax + Bu) + c1Bd (15) = (d- z1) c1B (16)whered - z1 disturbance estimation error, denoting the same by η Equation 15 reduces to1= C1 η ................ where C1 = c1B (17)Thus, under the assumption that d˙= 0 we can write,ߟ ൌ െ‫ݖ‬ଵ ൌ െ‫ܥ‬ଵ ߟ ሶ (18)ߟ ൅ ‫ܥ‬ଵ ߟ ൌ 0 ሶ ሺ19ሻorC1 ≫ 0 or C1→∞Thus by the property of linear differential equation If C1>0 thenߟ →0. Thus error→0 as we increasesThis is well explained in Figure: 7.The problem with this observer is that it fails when the assumption of ݀ሶ = 0 is violated. Thus, underB. Limitation of Disturbance Observerthe assumption that ݀ሶ ് 0 we can write,ߟ ൌ ݀ሶ െ ‫ݖ‬ଵ ሶ ሶ (20) = ݀ሶ െ ‫ܥ‬ଵ η ሶ (21)ߟ ൅ ‫ܥ‬ଵ ߟ ൌ ݀ሶ ሶOr (22)Thus by the property of linear differential equation ifC1 >0 then ߟ →݀ሶ , which state that errordynamics never reduces to zero under condition݀ሶ ് 0 which is rather a practical case. 84
  • International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 2, March – April (2013), © IAEMEIV. NONLINEAR EXTENDED STATE OBSERVER As seen from previous section the attention was restricted to constant or slow varyingdisturbances which never occur or can be achieved practically. Extending the idea to practicalnon-linear system on of the famous modern observer known as Extended State observer was introduced bya Chinese scientist J.Han. Extended state observers offer a unique theoretical fascination. Theassociated theory is intimately related to the linear as well as non-linear system concepts ofcontrollability, observability, dynamic response, and stability, and provides a setting[11][12] in whichall of these concepts interact. Extended state Observer can estimate the uncertainties and state of theplant [13].A. Mathematical Modeling of ESOIn general the 2nd order non-linear equation is represented asÿ = ሺ‫ݕ ,ݕ‬ሶ , ‫ݓ‬ሻ+ b0u (23)Where f (.) represent the dynamics of theplant+ disturbance,w- is the unknown disturbance,u -is the control signal,y -is the measured output,b0 -is assumed to be given.The Equation 19 was augmented as  x1 & = x2 x  &2 = x3 + b0 u  &  x3 =h y  = x1 (24)Here ݂ሺ‫ݕ ,ݕ‬ሶ , ‫ݓ‬ሻ and its derivative hൌ ݂ሶሺ‫ݕ ,ݕ‬ሶ , ‫ݓ‬ሻare assumed to be unknown, it is now possible to݂ሺ‫ݕ ,ݕ‬ሶ , ‫ݓ‬ሻby using state estimator for equation 20. HAN proposed a non-linear observer.estimate  z1 & = z2 +β1 g1 (e) z +β2 g2 (e) +b0u  &2 = z3   z3 = β3 g3 (e) & where e=y-‫ݖ‬ଵ ‫ݖ‬ଷ is the estimate of the uncertain function f (.).  (25)݃ଵ (.)is modified exponential function given as...... e ai sign ( e ) , e > δ g i (e, ai , δ ) =   e  1-a ,e <δ  δ i (26) ߙ is chosen between 0 & 1Where....... ݃ଵ is the gain. • ߜis the small number used to limit the gain. • ߚ is the observer gain • • 85
  • International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 2, March – April (2013), © IAEMEB. State space representation of TCP/IP protocolAs seen from equation (28) &(25)for simplicity in simulation of ESO it is better to represent transferfunction of TCP/AQM plant in the form of state space. Therefore equation (9) can be represented inthe form‫ ݔ‬ൌ ‫ݔܣ‬ሶ ൅ ‫ݑܤ‬as ‫ݔ‬ሶ 0 1 ‫ݔ‬ଵ 0൤ ଵ൨ ൌ ቂ ቃ ቂ‫ ݔ‬ቃ ൅ ቂ ቃ‫ݑ‬ ‫ݔ‬ሶ ଶ െ2.173 െ4.63 ଶ 133.91 ൈ 10ଷ (27)writing Equation (27) in the form (28) we get ‫ݔ‬ሶ ଵ ൌ ‫ݔ‬ଶ ‫ ݔ‬ൌ െ૛. ૚ૠ૜࢞૚ െ ૝. ૟૜࢞૛ ൅ 133.91 ൈ 10ଷ ሶ Plant൞ ଶ ‫ݔ‬ሶ ଷ ൌ ݄ (28) ‫ ݕ‬ൌ ‫ݔ‬ଵC. Estimation of unknown functionIn this section we will estimate the unknown function as stated in equation (28). To make thesimulation more practical we added random number to the o/p of the plant which is treated as noise inthe network parameter. Fig. 2. Block diagram of ESO for estimation of unknown function in presence of dynamic noise 86
  • International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 2, March – April (2013), © IAEMEIn figure: 2gives the detail block diagram of estimating state, which is simulated inSIMULINKMATLAB and resulted are provided in Figure: 3. the profile generator istaken during the simulation initially as step input. The input is feeded to the usualThe difference of output of the plant ‫ݔ‬ଵ and ‫ݖ‬ଵ which is derived ultimately from ‫ݖ‬ଷ as ሶ ሶ ሶplant and to ESO s as a reference input.seen from Equation:25 is taken as input by ESO block, together with o/p difference,input and algorithm proposed in equation:25 & 26 the estimation z3 is carried out andplotted on scope along with output of plant. The detail description of parameters andplant and ESO is carried out in following subsection.D. Adjustment of parameters α, β, δCalculation of ߙScale ߙ௜ is chosen in between 0& 1, because it yields ݃௜ high gain [14] [6]. In our case- ߙଵ = 1.00we consider for Equation: 26 as.........-ߙଶ = 0.750-ߙଷ = 0.625Calculation of ߚ Gain bi is adjusted by using pole-placement method. In our case byusing matlab simulation by using place (A’ B’ p) command.ߚ௜ for Equation: 25- ߚଵ = 109as.........- ߚଶ = 3858- ߚଷ = 44640Calculation of ߜߜis the small number used to limit the gain in the neighborhood of origin. In our case- ߜ = 10ିଷit is taken as for Equation: 26 as.........25& 26 estimation is carried out in matlab for step in Figure: 3, its seen that ‫ݖ‬ଷ (Z inConsidering values in above subsection and substituting the same in Equation: 28,Fig) converges to unknown functionf (.).V. ROBUST CONTROL Based on their open loop performance, NESO from figure: 1 is evaluated in agenerator provides the desired state trajectory in both y and ‫ ,ݕ‬in simulation we have ሶclosed-loop feedback setting, such as that shown in Figure: 4 for NESO. The profileused step and sine profile. Based on 87
  • International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 2, March – April (2013), © IAEME Fig. 3. Estimation of unknown function in presence of dynamic noisethe separation principle, the controller is designed independently(PD block in figure:4),state information, ‫ݖ‬ଷ , which converges to ‫ݔ‬ଷ ൌ ݂ሺ‫ݓ ,ݕ ,ݕ‬ሻis used to compensate for the ሶassuming that all states are accessible in the control law. In the case of NESO, the extendedunknown ݂ሺ‫ݓ ,ݕ ,ݕ‬ሻ. In particular, the control law is given as ሶ‫ݑ‬ൌ ି௭య ା௄௘ ௕బ (29)where e = ሾ‫ݒ‬ଵ െ ‫ݖ‬ଵ , ‫ݒ‬ଶ െ ‫ݖ‬ଶ ሿ் and K is the state feedback gain that is equivalent to aproportional derivative (PD) controller design, and ‫ݒ‬ଵ ൌ ‫ݔ‬ଵ ‫ כ‬and ‫ݒ‬ଶ ൌ ‫ݔ‬ଶ ‫ כ‬where ‫ݔ‬ଵ ‫ כ‬is a planti/p as shown in figure:4 Substituting (29) in (23)‫ݕ‬ሷ ൌ ሺ݂ ሺ‫ݓ ,ݕ ,ݕ‬ሻ െ ‫ݖ‬ଷ ሻ ൅ ‫݁ܭ‬ ሶ (30)K matrix can be determined via pole-placement [8][15] determining K matrix as ݇ଵ െ10൤ ൨ൌቂ ቃ ݇ଶ െ05 (31) 88
  • International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 2, March – April (2013), © IAEME Fig. 4. Complete Robust control block.A control o/p of network can be seen in figure: 5 for step input and to explain the beauty ofESO+PD for compensating o/p, a smooth control o/p can been seen in figure: 6 when sine i/pis applied and keeping the parameters same as that of step input. 89
  • International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 2, March – April (2013), © IAEME Fig. 5. O/p of proposed congestion controller ESO + PD when i/p is step signal Fig. 6. O/p of proposed congestion controller ESO + PD when i/p is sine wave 90
  • International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 2, March – April (2013), © IAEMEVI. CONCLUSION1) As seen from section (III), Disturbance Observer only estimates the disturbances and notdisturbance is not constant i.e. ݀ሶ ് 0. Therefore Disturbance Observer works fails tothestate of the plant. As seen from equation: 22 DO fail to estimate the disturbances whenworksunder practical application.2) To overcome the disadvantages of DOB and PID controller this paper presents a novelAQM scheme supporting TCP flows to avoid congestion. ESO could estimate the plantdynamics in presence of variation in network parameters from figure: 3.3) ESO along with PD control helps to compensate the plant of TCP/AQM. From the figure:5 asymptotic stability is assured for the dynamic system. Tuning of PD control is muchsimpler when ESO is introduced.4) From figure:2 and 4 it can observed that robust control is achieved by just feeding o/p ofthe plant along with reference i/p to ESO. So practically even if plant knowledge is notknown, robust control can be achieved as shown in o/p figure: 3, 5 & 6.poses transfer function as unity, i.e.‫ܩ‬௦ ሺ‫ݏ‬ሻ ൌ 1. But practically sensor causes phase lag,5) Sensor which is used as a feedback to the controller to control the plant should ideallyattenuation and electromagnetic interference which makes ‫ܩ‬௦ ሺ‫ݏ‬ሻ ് 1 a small change in ‫ܩ‬௦ ሺ‫ݏ‬ሻcan misguide the controller and corrupt the o/p of the plant and also causes wastage of power.From figure:4 it can been seen that, sensor o/p is not directly feeded to the controller insteadit has been feeded to ESO and o/p of ESO generated by correcting the deviation between themodel and actual o/p i.e. an observe state is feeded to controller proves to be more superiorthan sensor o/p.ACKNOWLEDGMENT The authors would like to thank to Prof: VattiRambabuArgunrao from VishwakarmaInstitute of Technology and Prof: Prasheel V. Suryawanshi from MIT Academy ofEngineering for many fruitful discussions.REFERENCES[1] B. Chellaprabha and S. C. Pandian, “A multipath energy efficient congestion controlscheme for wireless sensor network,” Journal of Computer Science, vol. 8, no. 6, pp. 943 –950, 2012.[2] D. T. C. V. Hollot, Vishal Misra and W. Gong, “Analysis and design of controllers foraqm routers supporting tcp flows,” IEEE Transaction on Automatic Control, vol. 47.[3] G. P. Liansheng Tan, Wei Zhang and G. Chen, “Stability of tcp/red systems in aqmrouters,” IEEE Transaction on Automatic Control, vol. 51.[4] V. M. A. R. Vilanova, “Robust 2-dof pid control for congestion control of tcp/ipnetworks,” Int. J. of Computers, Communications & Control, vol. V, no. 5, pp. 968 – 975,2010.[5] S. Mascolo, “Modeling the internet congestion control using a smith controller with inputshaping,” IFAC 03 Workshop on Time -delay Systems, p. CR 2179, 2003.[6] M. N. Hossein ASHTIANI, HamedMoradi POUR, “Active queue management in tcpnetworks based on fuzzy-pid controller,” Applied Computer Science & Mathematics, vol. 6,no. 12, pp. 9 – 14, 2012. 91
  • International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 2, March – April (2013), © IAEME[7] T. Alvarez, “Design of pid controllers for tcp/aqm wireless networks,” Proceedings of theWorld Congress on Engineering, vol. 2, pp. 01 – 08, WCE 2012, July 4 - 6, 2012, London,U.K.[8] J. K. Ryogo Kubo and Y. Fujimoto, “Advanced internet congestion control using adisturbance observer,” IEEE, pp. 1 – 5, 2008.[9] L. D. B. X. S. Alexander, Richard Rarick, “A novel application of an extended stateobserver for high performance control of NASAs HSS flywheel and fault detection,”American Control Conference, pp. 5216 – 5221, June 11-13, 2008.[10] W. G. V. Misra and D. Towsley, “Fluid-based analysis of a network of aqm routerssupporting tcp flows with an application to red,” ACM SIGCOMM Comp. Commun.Review, vol. 30, no. 04, pp. 151 – 160, October 2000.[11] A. Radke and Z. Gao, “A survey of state and disturbance observers for practitioners,”American Control Conference, pp. 5183 – 5188, June 2006.[12] Z. Gao, “Scaling and bandwidth-parameterization based controller tuning,” AmericanControl Conference, pp. 4989 – 4996, June 2003.[13] X. Yang and Y. Huang, “Capabilities of extended state observer for estimatinguncertainties,” American Control Conference, pp. 3700 – 3705, June 2009.[14] S. P. Luis L_opez, Gemma del Rey Almansa and A. Fern_andez, “A mathematicalmodel for the tcp tragedy of the commons,” ELSIVER Theoretical Computer Science, pp. 4 –26, 2005.[15] W. Wang and Z. Gao, “A comparison study of advanced state observer designtechniques,” American Control Conference, pp. 4754 – 4759, June 2003.AUTHORS’ INFORMATION KaliprasadA.Mahapatro He received his Bachelors of engineering in Electronics & Telecommunication from University of PUNE, INDIA in 2010. His basic area of interest is in control system & embedded system Design, Robotics. He worked as a Junior Research Fellow (JRF) for Department of Atomic Energy-Board of Research in Nuclear Science. His research is carried designing a Control Scheme for a class of Non-Linear System. Currently he currently is pursuing his Master’s degree in Signal Processing from Vishwakarma Institute of Technology, Pune University MilindE.Rane. He received his BE degree in Electronics engineering from University of Pune and M.Tech in Digital Electronics from Visvesvaraya Technological University, Belgaum, in 1999 and 2001 respectively.His research interest includes image processing, pattern recognition and Biometrics Recognition 92