Control Design for Transient Power and Spectral Control in Optical Communication Networks Lacra Pavel1 University of Toronto, ECE Department 10 King’s College Rd., Toronto, M5S 3G4, Canada Phone: 416-946-8662, Fax: 416-978-0804
[email protected]
Abstract: This paper presents control applications to power control in optical communication networks. We consider transient power control across optical communication links, and spectral power control at composite optical amplifier sites. A decentralized network control strategy is proposed that ensures robust handling of dynamic network reconfiguration, with minimization of optical power transient excursions across network. We present control system design aspects as well as experimental results based on an actual implemented case.
transient gain control at optical amplifier sites. We propose two control schemes: based on feedback only and based on a combination of feedback and feedforward compensation. The performance of the two control schemes is compared for an optical link with 50-cascaded optical amplifiers. Then, we consider spectral power control at composite dynamic amplifier sites. A control strategy based on decoupling the control loops by using time-constant layering is presented, and two methods for handling dynamic channel count cases are discussed. Experimental results at a dynamic amplifier site are presented, based on digital implementation of the proposed controllers. 2. OPTICAL SYSTEM DESCRIPTION
1. INTRODUCTION In this paper we present applications of control system design to optical communication networks. This application area is motivated by the evolution of wavelength division multiplexed (WDM) optical communications from statically designed, point-topoint optical links towards reconfigurable optical networks. Control and management of these highly complex networks represents one of the major design challenges, [1]. Dynamics aspects in optical networks have started to be considered very recently, [2]- [4].
We consider a WDM optical system (Fig. 1) with N channels multiplexed in the wavelength domain being transmitted on a single optical fiber.
Tx Tx
l1 l2
Fiber span ~100km
l2
Rx Rx
lN
lN Tx
l1
Rx
Optical Amplifier
A flexible strategy for control of optical power is essential in reconfigurable optical communications systems, where the number of channels can change dynamically. The two components of optical power control are: transient power control at optical lineamplifier sites, and spectral power control, or equalization of channel optical powers, at dynamic composite amplifier sites.
Optical-to-electrical and electrical-to-optical conversion is done at the terminal sites only (transmitter/receiver), with signals traveling in the optical domain in between these sites.
In this paper we describe control system design aspects, simulation and experimental results for these two network control components. We describe firstly the optical communication system. Then we consider
In order to compensate for optical fiber attenuation, optical amplifiers are used every 80 km to 100 km. For long-distance optical communications systems the configuration in Fig. 1 can have tens of
1
Fig. 1. Block diagram of optical system link.
This work was done in part while the author was with Ceyba Inc.
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optical amplifier sites between terminal sites. These optical amplifiers sites can be either in-line amplifiers, or dynamic composite amplifiers, composed from optical amplifiers interconnected with dynamic gain equalizer filters. Dynamic gain equalizers (DGE) filters, [10], are optical filters with adjustable attenuation profile in the wavelength domain, that can compensate spectral non-uniformity of the optical link. Control of power across the optical link (Fig. 1) is particularly important in the context of dynamic network reconfiguration, when the number of channels changes dynamically. The optical system in Fig.1 can be regarded as a multivariable dynamical system, in a cascade configuration, having N inputs and N outputs, which correspond to the N multiplexed optical channels. Each of the elements in this cascade (the optical amplifiers) has its own individual control, resulting in a decentralized control strategy across the link. The two components of this control strategy are transient power control and spectral control, which are discussed in the next two sections. 3. TRANSIENT OPTICAL POWER CONTROL In this section we discuss transient power control at in-line optical amplifier sites (Fig. 1). The most widely used optical amplifier is the Erbium-doped fiber amplifier (EDFA), which offers a wide bandwidth suitable for WDM systems. Due to their slow-gain dynamics, [5], EDFA amplifiers do not introduce any channel cross-talk for the high bit-rates used in fiber optic communications. However in dynamically reconfigurable networks, channel add/drop are on time-scales comparable with the EDFA time-constant. Due to EDFA cross-gain saturation effects, the total gain will be varying so that the output power is constant, and hence power transients will be induced on the existent channels. These transients accumulate in amplifier cascades, their speed depending on the chain length [7], and hence very long chains require very fast compensation control. Transient power control can be realized by controlling the gain of the EDFA (transient gain control). Transient EDFA gain control has been actively studied in recent years [5]-[8], with good results for up to 16 amplifiers via electronic pump laser control. The control strategy proposed here shows good performance for very long chains of up to 50 amplifiers, as those that are typically used in ultra long-haul communications. Control is based on measurements of total input an output optical power,
which are typical real-time measurements used in the industry at amplifier sites. As a dynamic system, the EDFA is a plant with two sets of inputs: control input, which is represented by the optical power of the pump laser, pp(t), and signal input, which is the N-dimensional input vector represented by the optical powers of the multiplexed channels (wavelengths), pin,,i(t), i = 1..N, pin = [pin,1 … pin,N]T Starting from the rate-equations [5], the EDFA optical amplifier can be described in state-space representation as a nonlinear multivariable system: dx /dt
=
- t-1 x(t) -
S1 N
g [e(bi x – ai)l - 1]pin,i (t) + + [e(bp x – a p)l - 1] pp(t)
pout,1(t)= e(b1 x – a1)l pin,1(t) … pout,N(t)= e(bN x – a N)l pin,N(t)
(1)
where the EDFA output is defined as the Ndimensional signal output power vector pout = [pout,1 … pout,N]T In equations (1), x(t) is the average inversion level [5], representing the internal state of the EDFA, while ai, bi, g and t are parameters specific to the optical fiber and Erbium, respectively. The EDFA total input and respectively total output power are: pin,T = S1N pin,i(t)
(2)
N
pout,T = S1 pout,i(t) while the EDFA total gain is defined as GainT = pout,T /pin,T Note from (1) that the output power per channel depends directly on corresponding input power per channel and on the current state x(t). This shows that cross-saturation effects at sudden changes on a group of channels are due to the time-variation of x(t) (see the state equation in (1)). It can be shown that the total gain is a weighted average of the gain coefficients of each channel in (1), so that controlling the total gain to remain constant will ensure (approximately) that each component of the pout remains constant. From (1), (2), after linearization around a nominal point and normalization, we can write the linearized model in state-space form as dx /dt Pout(t) yGain(t)
= A x(t) + B1 Pin(t) + B2 u(t) = C1 x(t) + D11 Pin (t) = C2 x(t) + D21 Pin (t)
(3)
2
where Pin(t), Pout(t) and yGain(t) are the linearized input, output power vectors and the total gain, respectively.
Pout
Pin G (EDFA)
y
u K
Fig. 2. Block diagram of one stage EDFA – control framework.
The model in (3) corresponds to the generalized plant in Fig.2, where the optical input power vector, Pin, can be regarded as a disturbance signal, and the pump power is the control input, u. For step like changes on Pin, the control objective is to adjust the pump power u(t) such that disturbances are rejected on Pout. Notice that the only measurement available for feedback is the total gain (scalar), denoted yGain in (3), while control is intended to be effective on all the N channels. For N = 10 channels the numerical values of the parameters in (3) are: A = - 4202.1 B 1 = [-2.728 -4.136 -4.715 -4.979 -5.167 -5.252 -5.198 -5.165 -5.418] B2 = 65 C1= [120.773 93.236 75.858 62.63 53.903 47.187 T 40.707 36.168 31.399 27.284] D11 = I10x10 C2 = 59.023 D21 =0.1*[-1.004 -0.335 -0.058 0.069 0.16 0.203 … 0.179] For an uncontrolled case (u=0), the time response of a cascade of 50 two-section optical EDFA amplifiers, each section modeled as in (3), is shown in Fig. 3 for a step drop of optical power on 50% of the channels. It can be seen that the power transients become faster as more amplifiers are cascaded. This is due to the dynamic response being determined by the repeated pole and the zeros distribution of the multivariable cascaded system. In order to design a controller for (3) we consider the subsystem from control u(t) to measurement yGain(t), which is formed from the first and last equation in (3). Since this is a SISO plant (see also Fig.2) we use a typical PID controller:
Fig. 3. Step response of a 50 EDFA cascade (uncontrolled) for drop in power on 50% channels.
K(s) = Kr (1+t1 s)( 1+t2 s) t1 s (1+0.1t2 s)
(4)
Notice that even though a PI type would have been sufficient for adequate steady-state performance, we have included a derivative component for improved phase margin and transient response [9]. We have selected the parameters such that optimized performance is achieved with infinite gain margin and good phase margin (56o): Kr = 2.5 t1 = 4.76e-05, t2 = 1.438e-05. This is particularly important since the final controller will be based on gain scheduling, requiring good robustness margin. The discrete-time state-space representation of the feedback controller (4), amenable for digital implementation, is given in (5) for a sampling rate of Fs = 100 kHz: xc (k+1) = Ac xc(k) + Bc y (k) u (k) = Cc xc(k) + Dc y (k) where: Ac = Cc =
|1 –0.306 | |0 0.0009 | | 1.035 –1.674|
(5)
Bc = | 1.035| | 167.4| Dc = 5.655
In order to improve the transient response (smaller overshoot and faster response), we have added a direct feedforward component for disturbance rejection, [9]. Since the disturbance appears at the plant input (see (3), a simple static feedforward component was used, based on directly measuring the change in signal input power. We used pre-filtering by a low pass filter with a time-constant of 1 microsecond in order to limit too abrupt changes
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in pump power. The resulting feedforward controller is given as: Kffw (s) = 2.607 / (10-6 s + 1)
(6)
component greatly improves the performance: overshoot is reduced from 0.15dB to 0.05dB, while settling time is reduced from 600 msec to 300 msec.
which is implemented as a digital controller at a fast sampling rate of Fs,fast = 10 MHz. Notice that feedforward compensation normally requires N direct coefficients (each per channel) for perfect compensation of any channel being dropped. Since only the total signal input power can be measured, instead of N coefficients a single (averaged) coefficient is used. As a result there will be some sensitivity to which channels are being dropped/added. A typical configuration for high-performance EDFA amplifiers has two or more fiber sections (stages), each modeled as in (1) or (3), with the first section being uncontrolled for better noise figure. A variable optical attenuator (VOA) can also be included between the two sections. The control diagram for such a typical configuration is shown in Fig. 4. The various measurement points at the input/output of the two EDFA sections are denoted by PIN1 to PIN4. The first section has a feedforward component Kffw1 used only for transient detection. For a constant gain of the overall EDFA amplifier, the feedback controller on the second section, Kfbk2, (Fig. 2) has to satisfy both disturbance rejection and reference tracking. As the first section experience gain increase, the gain reference of the second EDFA section is adjusted dynamically, such that the overall EDFA gain remains constant. PIN1
PIN2
Gcoil1 Kffw1
PIN3
PIN4
LVOA up +
-
Kfbk2
+
-
Gt,coil2
EDFA block
Gcoil11
(b) Fig. 5. Step response of an EDFA for drop in power on 20% channels: (a) feedback only, (b) feedback + feedforward.
Gcoil2 Kffw2
(a)
_..
G0both
Fig. 4. Two stage EDFA amplifier: feedback/feedforward control.
In the following we present simulation results for the two control strategies: feedback only and combined feedback/feedforward. We plot the power variation of an arbitrary selected surviving channel for a drop in power (step) on a group of channels. Fig. 5 (a) shows results for a drop in power on 20% of channels (2 out of 10) for feedback control only, (a), and for combined feedforward/feedback control, (b). As seen, the addition of the feedforward
This improvement is particularly relevant for very long chains of EDFAs. In Fig.6 we have compared the performance of the two control schemes for the case of 50 EDFA cascaded amplifiers (see Fig. 3 for the no control case): (a) feedback only, and (b) combined feedback/feedforward. In both Fig. 6(a) and Fig. 6(b), the top plots show the surviving channel power variation after the first section (uncontrolled) (PIN2 point in Fig. 4), for all amplifiers on the same graph. The bottom plots in Fig. 6(a) and (b) show the surviving power excursions at the output of all EDFA amplifiers for a drop in power on half the channels. Both schemes provide good compensation with fast time response (less than 1ms settling time). However the combined feedback/feedforward scheme has an overshoot of about 1.5 dB only, with a reduction of about 1.5 dB compared to the feedback only case.
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Due to an averaged feedfoward coefficient being used, there is some sensitivity to the group of channels being dropped (see Fig.7, for same conditions as in Fig. 6(b), but for a different dropped channel group). 4. DYNAMIC SPECTRAL CONTROL In this section we consider dynamic spectral control at composite amplifier sites (see Fig. 1). Such sites are composed by multiple interconnected elements, such as optical amplifiers (described in the previous section) and dynamic optical filters, as described in the following.
(a)
Dynamic optical filters are used as dynamic power or gain equalizers (DGE) for equalizing wavelength channel powers. For such an optical filter, the input and the output optical power for wavelength channel l i, i.e., u(l i) and y(l i), respectively, are related by: y(li)= F(li) u (li)
i=1..N
(7)
where F(li) is the corresponding filter attenuation per channel, or attenuation profile. The attenuation profile, functionally dependent on optical technology parameters, can be adjusted in real-time, resulting in dynamic optical filters.
(b) Fig. 6. Step response of a 50 EDFA cascade for drop in power on 50% channels: (a) feedback only, (b) feedback + feedforward.
Depending on technology and implementation configurations different resolutions in the wavelength (spectral) domain can be achieved, [11]-[13]. For example such a dynamic optical filter can be realized as a cascade of M sections of Mach-Zender interferometer, [10], for which the attenuation profile versus wavelength is given as: F(li) = P1M [(1+Aj) – (1 –Aj) sin (2p liTj+ fj)] i =1..N, j =1..M
(8)
where Aj , f j are the adjustable amplitude and phase parameters. These parameters can be varied such that the output channel powers, y(l i), (7), approximate a desired spectral profile, ytgt(li), which is typically flat (power equalization). For a mean-square type cost criteria: J = S1N ei2
(9)
where ei = (y(li) - ytgt(li)/ ytgt(li), i=1..N, a simplified adaptive LMS algorithm can be used for coefficient adaptation. The resulting update equations are:
Fig. 7. Sensitivity of feedforward scheme to dropped channel set.
aj (m) bj (m) Aj fj
= = = =
aj(m-1) – m S1N ei cos (2p l iTj) bj(m-1) – m S1N ei sin (2p l iTj) [1+ √(aj2 (m) + bj2 (m))]-1 p/2 - atan(bj (m) / aj (m))
(10)
5
where m is the update rate. The DGE filter parameters are updated at discrete times, t = mTosa, based on realtime measurements of channel powers y(li), obtained every Tosa from an optical spectrum analyzer. Such a DGE filter is typically used together with optical amplifiers (required to compensate DGE insertion loss) resulting in a composite dynamic optical amplifier site as shown in Fig. 8. The two optical amplifiers, pre-EDFA and post-EDFA, respectively, are each operating with its own controller as described in the previous section, decentralized one from another, based on individual total power measurements. pre-EDFA
are almost decoupled. The EDFA reaches steady state very fast, and overall stability is determined as for a static gain in the feedback path of the DGE. Fig. 9 shows the results of equalizing a tilted spectral profile of about 3 dB across 100 data points. The two EDFAs are controlled in total (average) power mode (APC) and the DGE is updated (10) with M =8, m =1. The successive DGE attenuation profiles are shown in Fig.9(a), while the spectral plot of optical powers is shown in (b) for 30 iterations. The last iteration (bottom plot) shows very good residual error of maximum 0.1 dB peak-to-peak.
post-EDFA
OSA
DGEQ
OSA
DCM
OSA
u
y
Kdgeq Amp/DGE block Target profile
Fig. 8. Block diagram of composite dynamic amplifier.
Typically in normal operation the pre-EDFA and post-EDFA optical amplifiers are controlled in total (average) power control mode (APC), so that constant average power per channel is launched after each such site (see Fig. 1). This satisfies the link budget requirements by compensating the optical fiber loss in between amplifier sites, such that the same power is launched after each site. The APC control can be designed as an outer control loop around the gain controller described in the previous section. This is the normal EDFA control mode with transition to the gain control mode (transient control) being done only at detection of channel power sudden add/drop. In Fig. 8, we denoted with OSA measurement points for the optical channel powers. These are taken by an optical spectrum analyzer and used as feedback for adjusting the DGE, and also for updating, the power targets for the EDFA control. The dynamic composite amplifier (Fig. 8) is a complex interconnected system, with coupling on the feedback path due to the varying gain of post-EDFA. Resorting to layering of the time-constants can ensure stability of this system. If the DGE time-constant (outer loop) is much longer than the EDFA control time-constant (inner loop), then the two control loops
(a)
(b) Fig. 9. Spectral Control for 30 steps: (a) DGE attenuation profile evolution; (b) Optical power spectral profile at various steps and last step.
In addition to target tracking, good performance for dynamically changing channel count is very important. As shown in the previous section, sudden channel drop/add can be handled at the EDFA level on a very fast time-scale by transitioning to the gain control mode. Based on the updated channel number information from the OSA (much slower time-scale), the EDFAs can then return to power control mode,
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with target properly updated. In the meantime DGE controller operates continuously, performing spectral equalization on the existent channels.
5. EXPERIMENTAL RESULTS Experimentally obtained results are shown in Fig.11, for a practical implementation of the control strategy at the dynamic amplifier site (Fig. 8). Both EDFAs are operated in power control mode and DGE is adjusted continuously. The plot in Fig. 11(a) shows the initial optical power spectral profile for 68 channels, while Fig. 11(b) shows the flattened profile. An average residual error of 0.5 dB is achieved, limited by the accuracy of power measurements (via OSA), and DGE device. Due to the resolution of the DGE, high frequency components in the spectral profile are not removed.
(a)
(a)
(b) Fig. 10. Spectral Control - Drop/Add middle channels: DGE attenuation profile evolution: (a) use only existent; (b) interpolate over dropped channels.
For handling such dynamic channel count cases, we have considered two control strategies for the DGE update equations (10): firstly, (a), DGE uses only data of the existent (surviving) channels, and secondly, (b) DGE uses data for existent channels plus data obtained by interpolation over the dropped channels. The two strategies are compared in Fig. 10, which shows results for a sudden drop of the middle channels, followed by adding back the same channels. It can be seen that the strategy with interpolation performs better, resulting in less perturbation on the spectral profile of the DGE (8).
(b) Fig. 11. Spectral Control – experimental results: (a) initial optical power spectral profile; (b) final equalized profile.
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Fig. 12 shows experimental results for a channel drop case. The initial flattened profile is shown in Fig.12(a), while Fig. 12(b) shows the spectral profile after the middle group of channels have been dropped. Good performance is achieved, with the surviving channels maintaining about the same flat level. Note that EDFAs (Fig. 8) have returned to power control mode with the power target being updated based on the reduced channel count.
(a)
(b)
composite dynamic amplifier sites was considered. A control strategy based on decoupling the control loops by using time-constant layering was presented. Two strategies for handling dynamic channel count cases have been discussed. Based on a digital implementation of the proposed controllers, experimental results at a dynamic amplifier site were presented indicating good performance. REFERENCES [1]
S. Barnes, “All-Optical networks: principles, solutions and challenges”, in Proceedings OFC 2002, Optical Fiber Communic. Conf., Anaheim, CA, pp.98-99, 2002.
[2]
S. J. B. Yoo, W. Xin, L. D. Garrett, et al., “Observation of prolonged power transients in a reconfigurable multiwavelength network and their suppression by gain-clamping of optical amplifiers”, IEEE Photon. Tech. Lett., vol.10, 1659-1661, 1998.
[3]
P. Kim, S. Bae, S. Joon Ahn, N. Park, “Analysis on the channel power oscillation in the closed WDM ring network with the channel power equalizer”, IEEE Photon. Tech. Lett, vol 12, 1409-1411, 2000.
[4]
L. Pavel, “Effect of equalization strategy on dynamic response of optical networks”, Proc. IEEE LEOS 2002, IEEE Laser and Electro-Optics Soc. Ann. Meeting, Glasgow, Nov. 2002.
[5]
A. K. Srivastava, Y. Sun, J. L. Zyskind and J.W Sulhoff, “EDFA transient response to channel loss in WDM transmission systems”, IEEE Photon. Tech. Lett, vol. 9, 386-388, 1997.
[6]
Y. Sun, J. L. Zyskind, and A. K. Srivastava, “Average inversion level, modeling, and physics of Erbium-doped fiber amplifiers”, IEEE J. Sel. Topics in Quantum Electronics, vol. 3, 991-1007, 1997.
[7]
Y. Sun, A. K. Srivastava, J. L. Zyskind, J.W Sulhoff, C. Wolf and R. W. Tkach, “Fast power transients in WDM optical networks with cascaded EDFAs”, Electronics Letters, 33 (4), 313-314, 1997.
[8]
H. Suzuki, N. Takachio, O. Ishida, M. Koga, “Power excursion suppression in cascades of optical amplifiers with automatic maximum level control”, IEEE Photon. Tech. Lett., vol.11, 1051-1053, 1999.
[9]
S. Skogestad and Ian Postlethwaite, “Multivariable feedback control – analysis and control”, John Wiley & Sons, 1996.
Fig. 12. Spectral Control: channel drop case - experimental results: (a) initial equalized power spectral profile; (b) final spectral profile (after channel drop, EDFA back in power mode).
[10] C. K. Madsen, J. H. Zhao, “Optical Filter Design and analysis - a signal processing approach”, John Wiley & Sons, 1999.
6. CONCLUSIONS
[11] C. R. Doerr, L. W. Stultz, et al., “An automatic 40wavelength channelized equalizer”, IEEE Photon. Tech. Lett, vol. 12, 1195-1197, 2000.
In this paper we presented control design applied to optical power transient control and spectral power control in optical communication systems. A transient control strategy was proposed based on a combination of feedback and feedforward control, with good results for very long (up to 50) cascaded optical amplifiers. Spectral control design at
[12] K. Inoue, T. Kominato and H. Toba, “Tunable gain equalization using a Mach-Zender optical filter in multistage fiber amplifiers”, IEEE Photon. Tech. Lett., vol. 3, 718-720, 1991. [13] J. E. Ford and J. A. Walker, “Dynamic spectral power equalization using micro-optomechanics”, I E E E Photon. Tech. Lett., vol.10, 1440-1442, 1998.
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