Proceedings of the 2011 IEEE International Conference on Mechatronics

April 13-15,2011, Istanbul, Turkey

Compensation of Time-varying Delay Acting in Networked Control Systems Using Adaptive Smith

Predictor and Parallel Fuzzy-PI Controller Edin Dragol/\ Aida Brankovic#2, Jasmin Velagic#3 and Nedim Osmic#4

#Department of Automatic Control and Electronics

Faculty of Electrical Engineering, University of Sarajevo

Sarajevo, Bosnia and Herzegovina

ledindragolj@hotmail.com, 2eiapapei@hotmail.com, 3jasmin.velagic@etf.unsa.ba

Abstract- This paper focuses on problems which arise from

network controlled systems within master-slave type of communications. Since the master and slave are connected over the network, network-induced time-varying delay has negative impact on system stability and control system performance. In order to compensate an influence of delay in NCS we proposed the improvement of two control strategies, Smith predictive and parallel fuzzy-PI controllers. Design of parallel fuzzy-PI controller has no demands for mathematical model of controlled system. Parameters of PI controller are adjusted adaptively depending on the delay. Adaptive Smith predictor is based on the adaptive loop that decreases influence of network-induced delay. It requires a mathematical model of the controlled system. Furthermore, simulations and practical experiments are given to illustrate the effectiveness and robustness of the proposed methods.

Keywords- Networked control systems (NCS), time-varying delay, adaptive Smith predictor, parallel fuzzy-PI controller

I. INTRODUCTION

In recent years, considerable attention has been paid to networked control systems (NCSs) in which the control loops are closed via communication network. The interest for NCS is motivated by many benefits they offer such as the reduced system wiring, the ease of maintenance and installation, the increased system flexibility and the low cost [1]-[4].

Many modem industrial systems are hierarchical organized and distributed over the communication network with decentralized control [5]. NCS concept provides the decentralized control, and further more gives advantages like modularity, possibility of quick and appropriate responses and ensures the interaction between separated systems. Since the output of the system is feedback through a communication network, network-induced delay makes design of network control system quite complex. The delays, either constant or time-varying, can degrade the performance of the control loop significantly and can even lead to instability [6], [7]. Central issues studied in NCSs are the influence of network delays on the control performance and stability analysis [8], [9]. There are the three main directions in approaching the problem of network-induced delays in NCS. One way is to design a controller irrespective of the delay, and then to design a

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network scheduling procedure so that the delay is minimized. The second approach is to study the NCS problem as an integration of network and control design. In the third approach the control strategy is designed so that it compensates a priori the networked-induced delay [10]. Lately there are a few main delay compensation strategies that applies ideas of fuzzy control where it is not necessary any more to know exact mathematical model of the system [11], [12], modified Smith predictor [13]-[15], gain scheduling and robust control [16]. In optimal stochastic control methodology, controller is designed to guarantee the stability and performance criterion of NCS, assuming the probability distributions of delay is known [9]. In robust control method, the network delays are modeled as simultaneous multiplicative perturbation, and controller is given in frequency domain [17]. Intelligent control techniques such as fuzzy logic modulation and genetic algorithm are also presented in some literatures [18], [19].

In this paper we are studying different controllers design problems for systems with unknown or time-varying delays. Networked delay is considered in both forward and feedback loops. We expose study and comparison of experimental results of Smith and fuzzy-based controllers tested on the DC motor, where adaptive Smith predictor has been used as referent model for comparison of obtained results.

The paper is organized as follows. In Section II the networked control system for DC motor is described with brief explanation of its main components. Section III presents the modified Smith like approach to NCSs. Design of parallel fuzzy-PI networked-based controller is given in Section IV. Simulation and experimental results are demonstrated in Section V to verify the effectiveness of proposed control strategies and conclusions are drawn in the last Section.

II. CONTROL SYSTEM DESCRIPTION

The block structure of the proposed control system is shown in Fig. 1. The communication between master and slave node has been established using Ethernet protocol. In this paper we used UDP protocol for transferring data using binary encoding from master to slave node and opposite. Nodes are implemented as Simulink models and compiled

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using Real Time Windows Target for real-time execution. Slave node receives data, forward to DC motor drive using NI 6024E DAQ card, collect output data and provides feedback.

Network

Master node Slave node

Fig. 1. Block structure of the proposed control system

The hardware block structure of analyzed system is shown in Fig. 2. In the rest of this section the main components of this system will be described in brief.

A. Master Node

Simulink model on the master node implements controller and sends setpoint and control signal.

B. Network and Network-Induced Delay

Connection between master and slave PC can be established using different types of networks (LAN, WLAN, WAN, CAN etc.). In this study we used the Ethernet and UDP protocol that is supported by Real Time Windows Target. Since the output data is as already mentioned, feedback through a communication network, network induces delay. Network induced delays are 7:sc and 7:ca, the 7:sc is sensor-to­controller delay and the 7:ca is controller-to-actuator delay. Both network delays are considered random, have the same value and are uniform distributed. The total network delay (7:

=7:sc + 7:ca) is much larger than sample period.

C. Slave Node

This node consists of Slave PC that receives and transmits data to Master PC, actuator, plant and sensor. PC is connected to the control system using NI 6024E DAQ Card. NI 6024E DAQ card was used for identification of DC motor drive and later for connecting slave PC to DC motor drive. It alouds real time data collecting. Card was used for transferring control signals from the master to the motor drive and for collecting motor speed data.

D. Controlled Object - DC Motor Drive

Controlled object is at large explained in [20], it contains three main parts: first quadrant PWM controller, DC motor and incremental encoder. Mathematical model of object was obtained by identification using NI 6024E DAQ card for collecting data and Matlab System Identification Toolbox. Parameters were identified by method of step response identification (k=10.334, T=0.68582 [s)). Obtained transfer function of object is:

Ethemet :r.,'laster PC

Fig. 2. Hardware block structure of analyzed control system

III. DESIGN OF ADAPTIVE SMITH PREDICTOR

Structure of adaptive Smith predictor (ASP) was proposed in [13], and it is shown in Fig. 3. The predictor consists of the ordinary controller, process model, plant, estimation and adaptation of delay loop and a filter.

Fig. 3. Adaptive Smith predictor

In this figure Gp(s) is the controlled plant, Gm(s) is the acquired model of controlled plant by conducting identification of the process. The C(s) is ordinary controller, the Gis) is the first order low pass filter which improves robustness of Smith predictor. The r and y are the input and output of the system, respectively. The 7:est represents estimated total network delay (7:est ;::: 7:) . The closed loop transfer function is given by:

y(s) = C(s)e-roaSGp(s)/(1+ C(s)Gm(s)

r(s) (2) + (e -rsosC(s)e -roasGp(s) - C(s)Gm (s)e -rests)Gf (s»

From (2) it can be seen that effects of network-induced delay are presented in denominator of closed loop transfer function. Its influence can degrade performance of control system and in some cases lead to system instability. It is important to minimize these undesired effects by achieving condition:

Equation (3) can be satisfied if the prediction model can accurately approximate the actual model (Gm(s) =Gp(s». Also, if estimated total communication delay is equal to real total communication delay, 7:est;:::7:, then (2) can be reduced to:

y(s) C(s)e-roasGp(s)

r(s) 1+ C(s)Gm (s) (4)

The adaptive Smith predictor can minimize effects of

Gm(s) = Q(s) =

_k

_ U(s) I+ Ts

(1) network-induced delay in closed loop as shown in (4). Additional ramp signal is transmitted across network in order to estimate the total network delay in adaptation loop. Theoretically it would go to infmity because it maps time into The controlled variable is the speed of motor drive.

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amplitude, but in this case its amplitude is fmite and it depends of simulation time.

"(est is calculated as difference between transmited and received ramp signal in each time sample. The transfer function of the PI controller is given by:

ki C(s)=kp +­

S

The transfer function of the filter is expressed as:

I Gf(s)=-­

I+ Tfs

(5)

(6)

where Tf is a time constant of the filter. Controller parameters kp, ki and Ii were tuned by a genetic algorithm. This algorithm is implemented within Genetic Algorithm and Direct Search Matlab Toolbox for minimizing the following criteria:

(7)

For evaluation of parameters of the PI controller and the filter a simple genetic algorithm has been used with the population size 40, crossover fraction 0.8, elite count 2, max. generations count 20, variable ranges: 0.5<kp<20, 0.5< ki <20, 0<Tf< 0.6. The evolution yielded the following values: kp=IO.009, ki =7.7391, Tf= 0.2013.

IV. DESIGN OF PARALLEL FUZZY-PI CONTROLLER

As an alternative to previously propose the adaptive Smith predictor, the fuzzy-PI controller shown in Fig. 4 will be described and discussed. Fuzzy-PI controller is explained in [21] and we will expose some of the key features of that controller design.

Fig. 4. Fuzzy-PI controller

Fuzzy-PI controller scheme consists of the ordinary controller, the fuzzy controller and the plant. This scheme is simpler than the adaptive Smith predictor. In this study ordinary controller represents PI controller (5) and the output of fuzzy controller depends only on the value of e. The output of fuzzy controller is parameter P given by:

fJ = h(e(t)) (8)

where h is a nonlinear function that represents input-output mapping of fuzzy controller. Parameter P compensates effect of network-induced delay and improves performance of a nominal PI control by adjusting parameters of the PI

controller:

u(t) = fJkpe(t) + fJki f e(t)dt (9)

In order to improve the control performance and robustness we propose the parallel fuzzy-PI controller with additional input (Fig. 5). This form is similar to the previous one, but now parameter P depends on a value of error and error rate change - ec. Considered range of values for inputs e and ec of fuzzy controller are [-L, L] and [-Q, Q], respectively. Linguistic variables used in fuzzy controller are E and Ec for crisp values e and ec, respectively. Unlike the ASP that predicts time delay, fuzzy-PI does not predict time delay but compare system response to set point. Bigger time delay is, more rippled system response is what results with bigger signal error. In accordance to this statement there are seven linguistic values used for each linguistic variable: Positive Big (PB), Positive Middle (PM), Positive Small (PS), Zero (ZE), Negative Small (NS), Negative Middle (NM) and Negative Big (NB). Membership functions for linguistic variables are shown in Figs. 6 and 7. Fuzzy controller is Sugeno type, output membership functions are constants P� i= 1, ... ,5 (O<f3i<I). The one of possible choices for Pi is:

(10)

The set of rules shown in Table 1 was used in fuzzy controller. The arrangement of Pi in Table 1 reduces overshoots and ripples in velocity time responses. Also, the genetic algorithm was used for controller parameters tuning by identical way as in the case of adaptive Smith predictor. It yielded the following values: kp = 12.2235, ki = 10.4444, L=6.1673, Q=0.0698, PI =0.0824, P2=0.1283, P3=0.1453, P4 = 0.1736, Ps = 0.9988.

r

Fig. 5. Fuzzy-PI controller with error change input

·L ·2l13 .l13

Fig. 6. Membership functions of E

o E

l13 2113 L

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Fig. 7. Membership functions of Ee

TABLE I SET OF RULES FOR Fuzzy CONTROLLER USED IN FIG. 5

� E

NB NM NS ZE PS PM PB NB PI PI PI PI P2 P2 P3 NM PI PI PI P2 P2 P3 P4 NS /JI /JI /J2 /J2 /J3 /J4 /J4

�" ZE /JI /J2 /J2 /J3 /J4 /J4 /Js PS P2 P2 /J3 P4 /J4 /Js /Js PM /J2 /J3 /J4 P4 /Js /Js Ps PB P3 P4 /J4 /Js /Js /Js Ps

V. SIMULATION AND EXPERIMENTAL RESULTS

To investigate the control perfonnance and robustness of mentioned controllers various simulation and experimental studies were done under different conditions.

A. Simulation Results

The simulations have been conducted using Matlab/Simulink software. Sampling time is chosen to be 0.001 [s], time delay is generated using unifonn number sequence whose samples fluctuate +1- 20% of average time delay value, which is set to 0.125 [s] (Fig. 8). The choice of average time delay value is based on a motor drive time constant and a time delay measured during experiments.

0.16,---------------------,

� 0.15

1 014

� "0 0.13

.§ ] '2 0.12 " 8 � 0.11

Fig. 8. Signal of simulated communication delay

Figure 9 shows system responses obtained using Smith predictor with PI controller with adaptation, without adaptation and without adaptation and filtering. The best response is obtained using the adaptive Smith predictor with PI controller. Transition time takes less than 2s. System response obtained using adaptive Smith predictor without adaptation has the same rise time as ASP but as it reaches 90% of the set point it slows down. System response for all cases is over-damped.

Figure 10 shows system responses using parallel fuzzy-PI with one and two inputs. Better result is obtained using Parallel fuzzy-PI with additional input. In this case system response has small overshoot on the positive edge and no ringback on the negative edge. In other hand system response obtained using Parallel fuzzy-PI with two inputs has overshoot and ringback for positive and negative edge.

2.5

1 2

0.5

r r �

- Setpoint

- ASP

- ASP (without adaptation)

- ASP (without adaptation and filtering)

4 6 8 10 Time [sJ

12 14

Fig. 9. Adaptive Smith predictor with implemented PI controller

3.5

82.5 e-

S 2 2-

f15 '* > 1

0.5

'"

r � f>.-

If \ A V

- Setpoint

- Parallel Fuzzy.PI

- Parallel Fuzzy-PI (additional input)

4 6 8 10 Time [sJ

Fig. 10. Comparison of parallel fuzzy-PI controllers

B. Experimental Results

12 14

16

16

In this section experimental results of the proposed control strategies are shown. The block structure of experimental control system is illustrated in Fig. 2. The controlled object is composed of DC motor drive and appropriate PWM-based actuator is shown in Fig. 11. The sampling time is 0. 001 [s]

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and average value of time delay is same in both feedforward and feedback loops (around 0. 125 [s]).

Fig. 11. Controlled object - DC motor drive and actuator

The experimental results obtained using adaptive Smith predictor with implemented PI controller are depicted in Fig. 12. The rise time takes less than 2 [s] wherein it was in the simulation and steady-state error is small. In this case it behaves as ASP with adaptation but with larger steady-state error. Response of ASP without adaptation and filtering is pretty rippled in comparison with other ones. Ripple is consequence of filter absence.

Figure 13 shows comparison of parallel fuzzy-PI controllers. Better results exhibits parallel fuzzy-PI controller with additional input. Experimental result shows that it has faster rise time and over-damped response. With appearance of fIrst positive edge of referent signal, the rise time of parallel fuzzy-PI controller with one input takes almost twice longer in comparison with parallel fuzzy-PI controller with additional input.

Comparison of all three mentioned controllers is given in Fig 14. Parallel fuzzy-PI controller with additional input gives much better results than others. System response in this case is over-damped, without overshoots and ringbacks. Also, the error signals of these controllers are illustrated in Fig. 15, which emphasize the superiority of parallel fuzzy-PI controller with additional input.

3.5,--�-�-�--�-�-�--�---,

5Z.5 e-

S 2 2S €15 o

� 1 - Setpoint

- ASP

0.5 - ASP (without adaptation)

- ASP (without adaptation and filtering) °0�ML�===4========�S====ICO====IZ====II4==�16

Time [sJ

Fig. 12. Adaptive Smith predictor with implemented PI controller

3.5,--�-�-�--�-�-�-��--,

Z.5

0.5 - Setpoint

- Parallel Fuzzy-PI

- Parallel F uzzy-PI (additional input) -0.50!-----:--'== 4===:::r6====::=S ===1 O:==== IO:= Z===14=� 16

Time [sJ

Fig. 13. Comparison of parallel fuzzy-PI controllers

3.5.--�-�-�-�-�-��-�---,

2.5 5 0-" 2 o � 1.5 f o � - Setpoint

0.5 - ASP - Parallel Fuzzy-PI

- Parallel F uzzy-PI (additional input) -0.50L--'----'========8 ===10===1"'2 ===II4==='J16

Time [sJ

Fig. 14. Comparison of adaptive Smith predictor and parallel fuzzy-PI controllers

- ASP

- Parallel Fuzzy-PI

- Parallel Fuzzy-PI (additional input)

-2

_3 L--�--L-�--L--�--L--L-� o 4 S 10 1Z 14 16 Time [sJ

Fig. 15. Error signal of adaptive Smith predictor and parallel fuzzy-PI controller

As a measure of quality, value of criteria J is calculated for all three controllers, in both simulations and experiments, and represented in Table 2. The parallel fuzzy-PI controller with additional input achieved the smallest values of J for simulation as well for the experiment, which indicates better control performance provided. Values of J for the experiment are much larger than for the simulation. It is expected because of measurement noise acting in physical model and uncertainty of identified motor drive system. Since the order

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of criteria values for analyzed controllers in simulation and experiment is the same, it confmns consistency between simulation and experimental results.

TABLE II COMPARISON OF CRITERIA VALUE FOR ASP, PARALLEL FUZzy-PI AND

PARALLEL Fuzzy -PI WIlli ADDITIONAL INPUT CONTROLLERS

I� Criteria value - J [xlO')

ASP ParaDel Parallel fuzzy-PI fuzzy-PI (additional input)

Simulation 7.2876 7.6223 6.7222

Experiment 19.023 19.528 18.689

VI. CONCLUSIONS

This paper addresses two approaches, adaptive Smith predictor and parallel fuzzy-PI controller, in solving problem of the NCS with time-varying delay tested on the DC motor drive. Analyzing achieved results it can be seen that both approaches have some advantages. With network delay increase, during experiments, the adaptive Smith gave better and robustness results in comparison with Parallel fuzzy-PI controllers because of the filter included in its controller scheme. However this design requires accurate mathematical model of a process and accurate estimation of total network delay, and sometimes this can be hard to achieve. Parallel fuzzy-PI based controller represents relatively less complex controller design. This design does not require information of network delay and accurate model description. If it is possible to tune parameters of fuzzy-PI controller online, then mathematical model of a process is not necessary to obtain. However for offline tuning of parameters, a mathematical model of the process is required. By comparing simulation and experimental results, it can be seen that parallel fuzzy-PI with additional input achieved better results than other exposed controllers. There are few limitations of this work which need to be addressed, especially in terms of conducting experiments. The influence of Pi order on system response should be undertaken in future studies. For more accurate experiment results a better method of estimation of network delay is required. Also method for synchronizing executions of simulations on master and slave node is required. This method is recommended to be implemented not on the same network which is used for feedback of the system. The influence of different values of sensor to controller delay and controller to actuator delay and double-ended synchronization of master and slave nodes will be undertaken future work.

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