VIEWS: 0 PAGES: 13 CATEGORY: Business POSTED ON: 4/2/2013 Public Domain
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), © IAEME COMMUNICATION 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.asp Journal Impact Factor (2013): 5.8896 (Calculated by GISI) ©IAEME www.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), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 2, March – April (2013), © IAEME fine 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 of heavy traffic. A conventional design approach by implementing multi path Energy Efficient Congestion Control Scheme to reduce the packet loss due to congestion have been carried out in [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 be carried out. In order to find effective solutions to congestion control, many feedback control system models of computer networks have been proposed. The closed loop formed by TCP/IP between the end hosts, through intermediate routers, relies on implicit feedback of congestion information through returning acknowledgements. Active Queue Management (AQM) scheme have been proposed in recent years [2]. Two types of methodologies to deal these issues are congestion control and congestion avoidance. In this we will deal with congestion 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 detect and 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 function because of which the probability to determine uncertainties and disturbances in network parameters reduces. To overcome above mentioned flaws [5] shown that a proportional controller plus a Smith predictor provides an exact model of the Internet flow and congestion control with a guaranteed stability and efficient congestion control. Active queue management (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 random early detection (RED) and PID controllers. To improve the performance even better a robust 2-DOF PID control was implemented in [4] for better congestion control. A linear gain scheduling by using PID as given by T.Alvarez in [7]stability region was well explained by using 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 an ideal assumption of slow varying noise or constant disturbances i.e. d_ = 0, which is well explained in the following section III. From the aforementioned flaws in various mechanisms, a novel AQM scheme that supports TCP flows and avoids drastic congestion due uncertainties and disturbances in network parameter is introducing a modern observer known as extended state observer (ESO). ESO was carried out in various sensitive plant like nuclear-reactor, space application like NASA’s flywheel [9] etc. because of its beauty controlling internal dynamics and external disturbances of a non-linear plant from its input-output data. Continuing the same this paper approaches to solution of estimating disturbances in network parameter by using ESO. The composition of this paper is as follows. Section II presents the non-linear modeling of TCP/IP protocol. Section III briefly describes the limitation of disturbance observer. Section IV describes the mathematical approach of non-linear extended state observer with its control parameter for calculating uncertainties and simulation of the same is carried out. Extending the idea of section IV a robust control is demonstrated in Section V by introducing feedback control i.e. ESO+PD. Finally conclusion is stated in Section VI. 81 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 2, March – April (2013), © IAEME II. TCP/AQM ROUTER DYNAMIC MODEL In this section we will be briefly discuss about the proposed non-linear model of TCP/IP protocol and linearizing the same for controller design. A. Nonlinear model As in the literature, a nonlinear model of TCP/AQM [10] [8] of a single congested router with a transmission capacity C is given as (1) (2) whereW& q is the maximum window size and average queue length(i.e. buffer size), they are the positive bounded quantities i.e., and . The congestion of window size is increased after every round-trip time R(t). p(.) denotes the (input function) packet drop probability p(t) [0, 1] and output is queue velocity _ To linearize equation(1) following assumptions are made[4] • active TCP session N(t) are time invariant i.e. N (t) N. • transmission link capacity are time invariant i.e. C (t) C. • time delay argument on queue length q is assumed to be fixed to then the linearize model of equation(1) results into (3) (4) where W(t) and _q(t)are the incremental variables w.r.t operating point as a function of f( ) with a desired equilibrium queue length q0 is given by 82 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 2, March – April (2013), © IAEME (5) This lead to a nominal model, and is given as Fig. 1. Linearized model of TCP/AQM networks (6) where is the transfer function of the plant of TCP/AQM network which includes second- order system and time delay element as shown in Figure: 1 Where and are given as (7) (8) Therefore from equation (7) (8) & figure: 1 can be stated as (9) In order to illustrate the effectiveness of ESO method, a numerical situation will be presented by taking network parameter of [4] as C = 3750packets/sec, = 175packets, = 0:2sec. For load of N = 60 TCP sessions, = 0:008& substituting the same in equation (5) we get = 15packets, & = 0:246. (10) 83 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 2, March – April (2013), © IAEME III. 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 slow varying input disturbance which is to be estimated. A. Mathematical modeling Constant Disturbance Considering 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 to 1= C1 η ................ where C1 = c1B (17) Thus, under the assumption that d˙= 0 we can write, (18) or C1 ≫ 0 or C1→∞ Thus by the property of linear differential equation If C1>0 then →0. Thus error→0 as we increases This is well explained in Figure: 7. B. Limitation of Disturbance Observer The problem with this observer is that it fails when the assumption of = 0 is violated. Thus, under the assumption that we can write, (20) = η (21) Or (22) Thus by the property of linear differential equation ifC1 >0 then → , which state that error dynamics never reduces to zero under condition which is rather a practical case. 84 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 2, March – April (2013), © IAEME IV. NONLINEAR EXTENDED STATE OBSERVER As seen from previous section the attention was restricted to constant or slow varying disturbances 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 by a Chinese scientist J.Han. Extended state observers offer a unique theoretical fascination. The associated theory is intimately related to the linear as well as non-linear system concepts of controllability, observability, dynamic response, and stability, and provides a setting[11][12] in which all of these concepts interact. Extended state Observer can estimate the uncertainties and state of the plant [13]. A. Mathematical Modeling of ESO In general the 2nd order non-linear equation is represented as ÿ= + b0u (23) Where f (.) represent the dynamics of the plant+ 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 and its derivative h are assumed to be unknown, it is now possible to estimate by using state estimator for equation 20. HAN proposed a non-linear observer. z1 & = z2 +β1 g1 (e) z +β2 g2 (e) +b0u &2 = z3 z3 = β3 g3 (e) & (25) where e=y- is the estimate of the uncertain function f (.). (.)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) Where....... • is chosen between 0 & 1 • is the gain. • is the small number used to limit the gain. • is the observer gain 85 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 2, March – April (2013), © IAEME B. State space representation of TCP/IP protocol As seen from equation (28) &(25)for simplicity in simulation of ESO it is better to represent transfer function of TCP/AQM plant in the form of state space. Therefore equation (9) can be represented in the form as (27) writing Equation (27) in the form (28) we get Plant (28) C. Estimation of unknown function In this section we will estimate the unknown function as stated in equation (28). To make the simulation more practical we added random number to the o/p of the plant which is treated as noise in the 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), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 2, March – April (2013), © IAEME In figure: 2gives the detail block diagram of estimating state, which is simulated in SIMULINKMATLAB and resulted are provided in Figure: 3. the profile generator is taken during the simulation initially as step input. The input is feeded to the usual plant and to ESO s as a reference input. The difference of output of the plant and which is derived ultimately from as 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 and plotted on scope along with output of plant. The detail description of parameters and plant and ESO is carried out in following subsection. D. Adjustment of parameters Calculation of Scale is chosen in between 0& 1, because it yields high gain [14] [6]. In our case we consider for Equation: 26 as......... - = 1.00 - = 0.750 - = 0.625 Calculation of Gain bi is adjusted by using pole-placement method. In our case by using matlab simulation by using place (A’ B’ p) command. for Equation: 25 as......... - = 109 - = 3858 - = 44640 Calculation of is the small number used to limit the gain in the neighborhood of origin. In our case it is taken as for Equation: 26 as......... - = Considering values in above subsection and substituting the same in Equation: 28, 25& 26 estimation is carried out in matlab for step in Figure: 3, its seen that (Z in Fig) converges to unknown functionf (.). V. ROBUST CONTROL Based on their open loop performance, NESO from figure: 1 is evaluated in a closed-loop feedback setting, such as that shown in Figure: 4 for NESO. The profile generator provides the desired state trajectory in both y and , in simulation we have used step and sine profile. Based on 87 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 2, March – April (2013), © IAEME Fig. 3. Estimation of unknown function in presence of dynamic noise the separation principle, the controller is designed independently(PD block in figure:4), assuming that all states are accessible in the control law. In the case of NESO, the extended state information, , which converges to is used to compensate for the unknown . In particular, the control law is given as (29) where e = and K is the state feedback gain that is equivalent to a proportional derivative (PD) controller design, and and where is a plant i/p as shown in figure:4 Substituting (29) in (23) (30) K matrix can be determined via pole-placement [8][15] determining K matrix as (31) 88 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 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 of ESO+PD for compensating o/p, a smooth control o/p can been seen in figure: 6 when sine i/p is applied and keeping the parameters same as that of step input. 89 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 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), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 2, March – April (2013), © IAEME VI. CONCLUSION 1) As seen from section (III), Disturbance Observer only estimates the disturbances and not thestate of the plant. As seen from equation: 22 DO fail to estimate the disturbances when disturbance is not constant i.e. . Therefore Disturbance Observer works fails to worksunder practical application. 2) To overcome the disadvantages of DOB and PID controller this paper presents a novel AQM scheme supporting TCP flows to avoid congestion. ESO could estimate the plant dynamics 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 much simpler when ESO is introduced. 4) From figure:2 and 4 it can observed that robust control is achieved by just feeding o/p of the plant along with reference i/p to ESO. So practically even if plant knowledge is not known, robust control can be achieved as shown in o/p figure: 3, 5 & 6. 5) Sensor which is used as a feedback to the controller to control the plant should ideally poses transfer function as unity, i.e. . But practically sensor causes phase lag, attenuation and electromagnetic interference which makes a small change in can 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 instead it has been feeded to ESO and o/p of ESO generated by correcting the deviation between the model and actual o/p i.e. an observe state is feeded to controller proves to be more superior than sensor o/p. ACKNOWLEDGMENT The authors would like to thank to Prof: VattiRambabuArgunrao from Vishwakarma Institute of Technology and Prof: Prasheel V. Suryawanshi from MIT Academy of Engineering for many fruitful discussions. REFERENCES [1] B. Chellaprabha and S. C. Pandian, “A multipath energy efficient congestion control scheme 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 for aqm 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 aqm routers,” IEEE Transaction on Automatic Control, vol. 51. [4] V. M. A. R. Vilanova, “Robust 2-dof pid control for congestion control of tcp/ip networks,” 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 input shaping,” IFAC 03 Workshop on Time -delay Systems, p. CR 2179, 2003. [6] M. N. Hossein ASHTIANI, HamedMoradi POUR, “Active queue management in tcp networks 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), ISSN 0976 – 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 the World 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 a disturbance observer,” IEEE, pp. 1 – 5, 2008. [9] L. D. B. X. S. Alexander, Richard Rarick, “A novel application of an extended state observer 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 routers supporting 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,” American Control Conference, pp. 4989 – 4996, June 2003. [13] X. Yang and Y. Huang, “Capabilities of extended state observer for estimating uncertainties,” American Control Conference, pp. 3700 – 3705, June 2009. [14] S. P. Luis L_opez, Gemma del Rey Almansa and A. Fern_andez, “A mathematical model 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 design techniques,” 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