commands. The master is connected through a communication channel to a slave robot, in a remote location, whose purpose is to mimic the master.
Fourth International Multi-Conference on Systems, Signals & Devices March 19-22, 2007 – Hammamet, Tunisia
Volume I : Conference on Systems Analysis & Automatic Control
A Smith Predictor-Based Controller for Time Varying Delay Teleoperation Salem Belhaj1 and Moncef Tagina2 1 U.R. Analyse & Commande des Systèmes (ACS) École Nationale d’Ingénieurs de Tunis (ENIT), B.P. 37, 1002 Tunis, Tunisia. 2 École Nationale des Sciences de l’Informatique (ENSI) University of Manouba, 2010 La Manouba, Tunisia. e-mail: {Salem.Belhaj, Moncef.Tagina}@ensi.rnu.tn
Abstract— This paper aims at predicting control for long distance teleoperation with time varying delays, due to the network. Time varying delays represent a challenging problem and a few results are available. It is well known that the Smith Predictor (SP) control scheme is sensitive to time delay uncertainties and was not designed for handling variable delay. In this paper, we provide a Smith Predictor-based controller to deal with time varying delay in force reflecting interaction. The performance of the suggested predictive scheme is evaluated and confirmed through simulations of a single degree of freedom master-slave robot. Keywords— time varying delay, bilateral telecontrol, Smith Predictor, teleoperation.
I. I NTRODUCTION Time-delays introduced by the communication link in spatially distributed systems, such as network controlled systems, are examples of complex systems, although intricate, whose understanding is fundamental to prediction and control purposes. A typical teleoperation system is depicted in figure 1, where a human operator conducts a remote task by moving a master robot manipulator and thus defining motion and force commands. The master is connected through a communication channel to a slave robot, in a remote location, whose purpose is to mimic the master. Force feedback techniques matured from both conceptual and technological points-of-view. But, many problems still have to achieve a satisfactory or convincing solution. One of them is the well known major problem of time-delay caused by the introduction of the communication channel in the closed-loop system. Furthermore, the bilateral control system is greatly sensitive to uncertainty in the timedelay and the difficulty to predict the variable time-delay caused by a public network such as the Internet, the system may be unstable; this is the biggest problem of telecontrol systems. As for teleoperation, it can be stated that any small communication delays cause time-shift or signal distortion, which result in closed loop performance degradation and may destabilize any force feedback device connected either with a real system or a virtual simulator engine. Many results on the stability analysis of such systems are available in [11] and [12]. Master-slave bilateral telecontrol coupled with force feedback provide the operator with more extensive sense of telepresence, ISBN 978-9973-959-06-5 / SSD © 2007
Fig. 1: Standard bilateral teleoperation configuration. which would enable a human being to accomplish complicated remote task with the haptic information. One of the first controllers and very effective control methodology for time delayed systems, still relevant today, is the Smith Predictor [1], [2]. Three main problems in the SP schemes have been considered in the control literature: • • •
robustness (plant and/or delay) [5], [6], disturbance rejection [7], and the modified Smith predictors [8], [9], [15].
Existing results have concentrated on unknown but constant time-delays. However, SP was not designed for handling intermittent feedback with variable delays. With our SP scheme, we aim to overcome this restriction which limits existing prediction schemes. In this paper, we will show that, the use of the SP can be extended to these cases. This paper is organized as follows: a review on the use of Smith Predictors in teleoperation and their associated problems are discussed in section II. Section III briefly reviews the basics of Smith Predictors and the problem is addressed. The suggested time varying delay controller is presented in section IV. Simulation results are discussed in section V. Finally, conclusions and perspectives are presented in section VI. II. SMITH PREDICTORS IN TIME DELAYED TELEOPERATION Recently a few Smith Predictor-based teleoperation control architectures have been suggested for 2-channel forceposition teleoperation systems, in which the slave dynamics or environment are mapped at the master. Unfortunately, the performance of the controller can be very poor; the loop
may become unstable, when the dead time parameter used for designing the Smith Predictor is not equal to the time-delay of the actual teleoperator under control. This problem has been considered by Palmor [3] who discusses the stability of the scheme when there is uncertainty in the time-delay parameter. In addition to delays, the uncertainties in the slave or in the environment dynamics may cause contact instability and significant reduction in the system transparency [10]. However, it should be pointed out here that the SP is efficient only if the applied model is a perfect representation of the slave environment. In practical teleoperation, the unpredictability of the remote environment prevents the use of the SP. Indeed, it is difficult to well predict the remote environment dynamics, when contact occurred. Thus, the choice of an adequate model and the adequate tuning procedure for the bilateral control may be a serious problem when applying the SP. To deal with time-delay in teleoperation, Huang and Lewis [13] suggested a neural-network predictive based controller for non-linear systems with constant time delay. A Smith predictor controller was designed to predict slave position at the master side. This control structure provides improved stability with time-delay, but suffers from the contact transparency problems as any position-position architecture does. Smith and Zaad [14] suggested a Smith Predictor based teleoperation control architecture for systems, where the linear dynamics of the slave or environment are mapped at the master. This non-linear predictive controller use neural networks to online estimate the dynamics of the slave and environment allowing contact force replication at the master using a similar network.
Fig. 2: A classical feedback control system incorporating a Smith Predictor. C(s) = K). It is also assumed that the time-delay parameter (e−sτ ) is exactly known. In this case the signal v contains a prediction of the output y, τ units in the future. The presence of a large dead-time in the process (E(s)e−sτ ) causes the feedback of y(t) to be delayed and forces conventional controllers to operate with a low gain. The Smith Predictor improves the closed-loop performance by introducing a minor feedback loop around the primary controller to produce v(t), which is an estimation of the variation of y(t) during the last n units of time. This variation v(t) added to the delayed measurement constitutes an estimation of the current value of y, which will become available as the later measurement y(t + τ n). This is subtracted form the requested value r to produce the error 0 that is fed into the controller, as: 0 = − (E(s) − E0 (s)e−sτ )u
(3)
Assuming a perfectly matched model, E(s) = E0 (s), (eq. 3) simplifies to
III. SMITH PREDICTOR DESIGN Smith [1] proposed a delay compensation method, for SISO stable systems with a pure transport lag, which allowed for a high loop gain in order to provide a better accuracy. The SP (figure 2) uses a model of the plant and the precisely known time-delay in the feedback loop around a proportional controller. It is useful to reexamine how the Smith Predictor operates in order to extend its use to time varying delay case.
0 = − E(s)(1 − e−sτ )u
The idea behind Smith Predictors is to use a controller structure which takes the delay out of the control loop and allows a feedback design based on E(s) only. In the classical Smith Predictor [2], a controller of the form C0(s) =
A. Definition and basic properties For simplicity we shall use E(s) instead of the transfer function of the whole system in the slave side. The classical configuration of a Smith Predictor is shown in figure 2. Consider the plant: G(s, τ ) = E(s)e−sτ
(1)
C(s) 1 + C(s)E(s) − C(s)E(s)e−sτ
(5)
is used, which gives the following closed-loop transfer function Hcl (s) =
C(s)E(s) −sτ e 1 + C(s)E(s)
(6)
B. Model description In this paper, the following dynamics of the single degree of freedom master-slave robot is considered:
And its associated nominal model: G0 (s) = E0 (s)e−sτ
(4)
(2)
Where E(s) and E0 (s) are strictly proper rational transfer functions which denote respectively the undelayed part of the plant and its model, τ ≥ 0 is the time-delay parameter. Assume that the controller C(s) is a proportional controller (i.e.
Mm x ¨m (t) + Bm x˙ m (t) + Km = Fh (t) − Fm (t) ¨s (t) + Bs x˙ s (t) + Ks = Ms x
Fs (t)
(7)
Where Mm , Ms are the respective inertias. The subscripts “m” and “s” stands for master and slave respectively. Bm ,
Bs represent the master and the slave damping respectively and Km , Ks are the respective gain. Fh (t) is the operator force, Fm (t) is the force feedback received at the master side. The force Fs (t), reflected from the slave to the master, can be written as: Fs (t) = Fc (t) − Fe (t)
(8)
Where Fe (t) is the force exerted on the slave by its environment and Fc (t) is a force applied by the P.D. controller in the slave side and is given by: Fc (t) = B(x˙ sd (t) − x˙ s (t)) + K(xsd (t) − xs (t))
(9)
Where K, B are positive constants which represent respectively the proportional and the derivative gain. This force drives velocity tracking error between master and slave to zero. C. Problem formulation We aim to predict the delayed force feedback at the master side using a Smith Predictor. The expression of this force is given by: F (t − τ (t))
(10)
In the case of constant time-delay (i.e. τ (t) = τ ), the expression of the predictive controller is given by: E(s)(1 − e−sτ )
(11)
Whereas when the delay is time varying, in most practical cases, the expression of the force (eq. 10), in the Laplace domain, is expressed in the integral form by: Z∞
Fs (t − τ (t))e−st dt
(12)
0
Where s denotes the Laplace variable. In order to design a discrete controller, the main difficulty is the discretization, or a good approximation, of E(s) e−sτ (t) for digital implementations. IV. T IME VARYING DELAY CONTROLLER The improvements of the Internet-based telecontrol systems make, significantly more interesting, rapidly and possibly random varying transmission delays. This is the case, for instance, in teleoperation over the Internet. Information is transmitted in small packets and is routed in real time through a possibly large number of intermediate routers, depending on the distance between the master and the slave sites. While average latencies may be low, the instantaneous delays may increase suddenly due to QoS (Quality of Service) factors such as rerouting, congestion, bandwidth limitation, packet losses or other network problems. In the extreme, the connection may
Fig. 3: Smith Predictor for time varying delay teleoperation.
be temporarily blocked. Such effects distort the signals, can introduce high frequency data, and can lead to instability if left untreated. The Smith Predictor was developed for dealing with deadtime problems common to industrial process where feedback from the processes is continuous, i.e. in each control cycle a new delayed feedback is available. However, in telecontrol, the feedback is intermittent. This is due to the communication link. Further, the delay is variable. Therefore, the original Smith Predictor is not suited for applications with variable delay. The modifications proposed in this section show how these limitations can be removed. We have used the Smith Predictor principle to design the time varying delay controller as it is shown in figure 3. The main idea of designing the SP to deal with time varying delay in teleoperation is to design the compensator according to the characteristic of time-delay, which exists in both forward and feedback path. The main principle of our Smith Predictor framework is, firstly, to estimate the dynamic model of the slave and to parallel estimator with the time-delay of the communication channel, to ensure the master to act ahead by trying to send the delayed control signal into the slave as early as possible, so the effect of time-delay in forward path can be eliminated. Secondly, to remove the dead-time from the characteristic equation of the closed-loop system, this will ensure that the response of the telecontrol system is equal to the original system. V. SIMULATIONS In this section we verify the efficiency of the suggested architecture. The simulations were carried out on a single degree of freedom master-slave robot whose dynamics are given by (eq. 7, 8 and 9) where: Mm = Ms = 0.1kg , Bm = Bs = 1N/m, Km = Ks = 5, B = 3N/m and K = 10. We assumed that the master and the slave start with the same initial position and velocity, it means there is no initial position/velocity offset between the two robots. We have modeled c using the block the teleoperated system (figure 3) in Matlab° diagrams of Simulink, particularly “Variable Transport Delay” block to model the variable time-delay. Network delays are time varying as depicted in figure 4. The operator is supposed to apply a sinusoidal force Fh to the master.
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system becomes instable (figure 7). Whereas, in the Smith Predictor-based teleoperation, the slave position tracks the master (figure 8) until the contact occurs, slave position steps aside the master position. This position discrepancy (shift) appears when the contact made due to the physical time delay, is unavoidable whatever the controller is. Besides, position drift is a well known problem in such systems.
We have also simulated the case where the slave contacts the remote environment at t = 30sec. This force (unit step) is reflected to the master as seen in figure 6. Furthermore, we observe (figure 5), in the scheme without prediction, that master and slave forces can not follow the operation force as the time goes on, the system turned to be unstable. Whereas in the prediction based configuration, the slave force faithfully tracks the master until it impacts the environment at t = 30sec, as seen in figure 6.
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A. Comparison with the scheme without prediction
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Fig. 7: Unstable behavior of master and slave Position on contact with the remote environment at t = 30s: without SP. As depicted in figure 10, the SP ensures good velocity tracking even in contact, compared to the scheme without prediction (figure 9). The suggested predictive control strategy can cancel the delay effect in the closed-loop system. We also notice that the slave velocity presents a peak due to the
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Fig. 8: Master and slave Position on contact with the remote environment at t = 30s: with SP.
Fig. 10: Master and slave Velocity on contact with the remote environment at t = 30s: with SP.
physical time delay when the contact is reached.
Note that the racking errors of the suggested scheme are smaller than that of the scheme with estimated delays.
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Fig. 9: Unstable behavior of master and slave Velocity on contact with the remote environment at t = 30s: without SP. B. Robustness with respect to time-delay uncertainties We further study the robustness of the proposed scheme on the time-delay uncertainties. Two estimated delays are considered here τˆ1 (t) and τˆ2 (t). These measured delays (figure 11) are different from the real ones (figure 4). As shown in figures 12 and 13, the suggested scheme is robust on the time-delay estimation, the system is still stable and hence the proposed scheme seems to be robust with respect to time-delay uncertainties. The theoretical proof of robustness is under study.
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Fig. 11: Estimated time-delay. VI. CONCLUSION A new Smith Predictor-based control structure for time varying delay in bilateral teleoperation is developed. Compared with the scheme without predictors, the suggested configuration can achieve satisfactory tracking performance despite the time varying delay, and the amplitude of the control signal is kept within 2. This method is suitable for long distance teleoperation with variable time-delay caused by communication channels, but requires precise knowledge
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R EFERENCES
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[1] Smith, O.J.M. Closer Control of Loops with Dead Time. Chemical Engineering Progress, Vol. 53, No. 5, pp. 217-219, May 1957. [2] Smith, O.J.M. A Controller to overcome Dead Time. ISA Journal, Vol. 0.25 6, No. 2, pp. 28-33, 1959. [3] Palmor, Z. J. and Powers, D. V. Improved Dead Time Compensator 0.2 Controllers. AIChE J., Vol. 31, No. 2, pp. 215-221, 1985. [4] Michiels, W. and Niculescu, S.-I. On Delay Sensitivity of Smith 0.15 Predictors. Macmillan, New York, 1992. [5] Adam, E.J., Latchman, H.A. and Crisalle, O.D. Robustness of the Smith 0.1 Predictor with Respect to Uncertainty in the Time-Delay Parameter. in the Proceedings of the American Control Conference, Chicago, IL, Vol. 0.05 2, pp. 1452-1457, June 2000. [6] Santacesaria, G. and Scattolini, R. Easy Tuning of Smith Predictor in 0 Presence of Delay Uncertainty. Automatica, Vol. 29, pp. 1595-1597, 1993. −0.05 [7] Watanabe, K. and Ito, M. A process-Model Control for Linear Systems with Delays. IEEE Transactions on Automatic Control, Vol. 26, No. 6, −0.1 pp. 1261-1269, December 1981. 0 5 10 15 20 25 30 35 40 45 50 [8] Arioui, H., Mamar, S., and Hamel, T. A Smith Prediction Based Haptic Time (s) Feedback Controller for Time Delayed Virtual Environments Systems. in the Proceedings of the American Control Conference, pp. 4303-4308, May 2002. [9] Saghir, M. and Book, W. Wave-Based Teleoperation with Prediction. Fig. 12: Master and slave Position on contact with the remote in the Proceedings of the American Control Conference, Arlington, pp. environment at t = 30s: with SP and estimated delay1. 4605-4611, June 2001. [10] Lawrance, D. A. Stability and Transparency in Bilateral Teleoperation. IEEE Transaction on Robotics and Automation,Vo. 9, No. 5, pp. 624637, 1993. 0.5 [11] Gu, K., Kharitonov, V. L. and Chen, J.Stability of Time Delay Systems. Master Birkhauser, Boston, 2003. Slave [12] Niculescu, S-I. Delay Effects on Stability, A Robust Control Approach. 0.4 LNCIS 269 Springer-Verlag, London Limited, 2001. [13] Huang, J-Q. and Lewis, F. L. Neural-Network Predictive Control for 0.3 Nonlinear Dynamic Systems With Time-Delay. IEEE Transactions on Neural Networks, Vol. 14, No. 2, pp. 377-389, March 2003. [14] Smith, A. C. and Hashtrudi-Zaad, K. Neural Network-Based Teleop0.2 eration using Smith Predictors. Proceedings of the IEEE International Conference on Mechatronics & Automation, Niagara Falls, Canada, pp. 0.1 1654-1659, July 2005. [15] Sourdille, P. and O’Dwyer, A.A New Modified Smith Predictor Design. in the Proceedings of the 1st International Symposium on Information 0 and Communication Technologies, Dublin, Ireland, pp. 385-390, 2003. Position (m)
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Fig. 13: Master and slave Position on contact with the remote environment at t = 30s: with SP and estimated delay2.
of the model and the time-delay parameter. As noticed before, the Smith Predictor is sensitive to dead-time mismatch, and if the delay is varying significantly with time, the dynamic performance of the Smith Predictor can be damaged. Whereas, in the case where the estimation of time varying delay is not accurate, the system can maintain stability which further shows the robustness of the scheme. Our current work focuses on estimating the dead-time online; the Smith Predictor could then be used easily with large improvement. Future work entails such adaptive Smithlike predictors, where the predictive controller uses recurrent neural networks to online estimate the variable delay.
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