Smith predictor based–sliding mode controller for integrating

7/29/2019 Smith predictor basedsliding mode controller for integrating

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Smith predictor basedsliding mode controller for integratingprocesses with elevated deadtime

Oscar Camacho,a,* Francisco De la Cruzb

a Postgrado en Automatizacion e Instrumentacion, Grupo en Nuevas Estrategias de Control Aplicado, Universidad de los Andes,

Merida 5101, Venezuelab Departamento de Ingeniera Electronica, Vice Rectorado Barquisimeto Universidad Nac. Exp. Politecnica

Antonio Jose de Sucre, Barquisimeto 3001, Venezuela

Received 23 October, 2002; accepted 25 August 2003

Abstract

An approach to control integrating processes with elevated deadtime using a Smith predictor sliding mode controlleris presented. A PID sliding surface and an integrating first-order plus deadtime model have been used to synthesize thecontroller. Since the performance of existing controllers with a Smith predictor decrease in the presence of modelingerrors, this paper presents a simple approach to combining the Smith predictor with the sliding mode concept, which isa proven, simple, and robust procedure. The proposed scheme has a set of tuning equations as a function of thecharacteristic parameters of the model. For implementation of our proposed approach, computer based industrialcontrollers that execute PID algorithms can be used. The performance and robustness of the proposed controller arecompared with the Matausek-Micic scheme for linear systems using simulations. 2004 ISAThe Instrumentation,Systems, and Automation Society.

Keywords: Sliding mode control; Smith predictor; Integrating process; Deadtime

1. Introduction

The presence of time delays in many industrial

processes is a well-recognized problem. The

achievable performance of typical feedback con-

trol systems can decline if a process has a rela-

tively large time delay compared to the dominant

time constant 1 . In the case of integral processes,

deadtime compensation is necessary in order to

enhance the performance of the control system.

ODwyer 2,3 considered a wide variety of

methods for the compensation of processes with

time delay, in both the continuous time and dis-

crete time domains. The compensators discussedare:

1. PID controllers and its variations.2. Lead, lag or lead-lag controllers.3. The Smith predictor 4 and its variations.4. Direct synthesis methods, which are typically

based on designing the controller to meet a re-quired output specification; pole placement con-trollers are an example.

5. Optimal controller design methods, which

may be based on a minimum variance or linearquadratic control strategy.

6. Predictive controllers.7. Other compensation strategies for processes

with time delays, including fuzzy implementation,neural networks, and expert systems.

The wide spectrum of methods covered and thedependence of the choice of compensator method

*Corresponding author. Tel: 58-274-2402891; fax:58-274-2402890. E-mail address: [email protected]

ISA

TRANSACTIONS

ISA Transactions 43 2004 257270

0019-0578/2004/$ - see front matter 2004 ISAThe Instrumentation, Systems, and Automation Society.


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on the application mean that an overall conclusionas to the best method to use is not appropriate.Viewing the compensation problem from a varietyof perspectives, it appears that the Smith predictor

is the optimal or a component of the optimalcontroller for dominant delay processes 2 . Inthose works, the compensation of integrating pro-cess with dead time is only achieved using PIDcontrollers, Smith predictors, or its variations.Other approaches have not been reported for thiskind of system.

The Smith predictor SP , or deadtime compen-

sator DTC , as it is also known, has many weak

points, including possible instability and poor per-

formance under modeling errors, and poor re-

sponse to disturbances 1 . In addition, the original

structure of the SP cannot reject constant load dis-

turbance for processes with integration 5 . Toovercome this obstacle many variations of SP have

been proposed.

Sliding mode control SMC is a robust and

simple procedure to develop controllers for linear

and nonlinear processes 6 . The design of a slid-

ing mode controller SMCr depends on the pro-

cess model, and the number of tuning parameters

is proportional to the model order. Camacho and

Smith 7 developed a simple and practical

method for the design of a SMCr based on a sim-

plified model of the actual process.

The SP performs well for eliminating deadtime

and the SMCr is a proven robust controller. It is

desired to combine them into a single control

structure that preserves the good qualities of both

techniques and improves the bad qualities of the

SP. A robust controller for integral processes with

deadtime, the Smith predictor sliding mode con-

troller SPSMCr , will be developed.

This paper is organized as follows: Section 2

introduces the basic concepts of the sliding mode

controller, the SP architecture and a review of the

modified SP for integrating processes that have

previously been proposed. Section 3 covers the de-

velopment of the SPSMCr based on an integrating

first-order process model with deadtime. Section 4

shows the SPSMCr implementation using a PID

algorithm of a computer based industrial control-

ler. Section 5 provides simulation results to illus-

trate the approach and to compare it with the

performance and robustness of a previous scheme.

Finally, some conclusions are presented in

Section 6.

2. Basic concepts

2.1. Sliding mode control (SMC)

Sliding mode control is a technique derivedfrom variable structure VSC which was origi-nally studied by Utkin 8 . A controller designedusing the SMC method is particularly appealingdue to its ability to deal with nonlinear systemsand time-varying systems 9 . The robustness tothe uncertainties becomes an important aspect indesigning any control system.

The idea behind SMC is to define a surfacealong which the process can slide to its desiredfinal value. Fig. 1 depicts the SMC objective. The

structure of the controller is intentionally alteredas its state crosses the surface in accordance with aprescribed control law. Thus the first step in SMCis to define the sliding surface S(t) which repre-sents a desired global behavior, like stability andtracking performance.

The S(t) selected in this work, presented bySlotine and Li 9 , is an integral-differential equa-tion acting on the tracking-error expression:

S t f e t , e t dt, de tdt

, , n , 1

where e(t) is the tracking error, that is, the differ-ence between the reference value or set point r(t)and the output measurement x(t) , namely, e(t)r(t)x(t) . is a tuning parameter, which helpsto define S(t) . This term is selected by the de-signer, and determines the performance of the sys-tem on the sliding surface. n is the system order.

The control objective is to ensure that the con-trolled variable be equal to its reference value atall times, meaning that e(t) and its derivatives

Fig. 1. Graphical interpretation of SMC.

258 Camacho, De La Cruz / ISA Transactions 43 (2004) 257270


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must be zero. Once the reference value is reached,Eq. 1 indicates that S(t) has reached a constantvalue, meaning that e(t) is zero at all times; it isdesired to set

dS t

dt0. 2

Once the sliding surface has been selected, atten-tion must be turned to design the control law thatdrives the controlled variable to its reference valueand satisfies Eq. 2 . The SMC control law M(t)consists of two additive parts: a continuous partUC(t) and a discontinuous part UD(t). That is,

M t UC t UD t . 3

The continuous part is given by

UC t fx t ,r t , 4

where fx(t),r(t) is a function of the controlledvariable and the reference value.

The discontinuous part is nonlinear and repre-sents the switching element of the control law.This part of the controller is discontinuous acrossthe sliding surface. Mainly, UD(t) is designedbased on a relaylike function i.e., UD(t)sgn( S(t) ), because it allows for changes be-tween the structures with a hypothetical infinitelyfast speed. In practice, however, it is impossible to

achieve the high switching control because of thepresence of finite time delays for control compu-tations or limitations of the physical actuators,thus causing chattering around of the sliding sur-face 8,9 . Chattering is a high-frequency oscilla-tion around the desired equilibrium point. It is un-desirable in practice, because it involves highcontrol activity and can excite high-frequency dy-namics ignored in the modeling of the system

9,10 . The aggressiveness to reach the sliding sur-face depends on the control gain i.e., , but if thecontroller is too aggressive it can collaborate withthe chattering. To reduce the chattering, one ap-proach is to replace the relaylike function by asaturation or sigma function, which can be writtenas follows:

UD

tK

D

S t

S t ,

5

where KD is the tuning parameter responsible forthe reaching mode. is a tuning parameter used toreduce the chattering problem. Fig. 2 shows theeffect of variations in the shape of saturationfunction. Fig. 3 shows the effect of KD variationson the system trajectory on the phase plane froman initial state to a final state.

Fig. 2. Chattering reduction using a saturation function a: 0; b: 0.01; c: 0.1; d: 1.0 .

259Camacho, De La Cruz / ISA Transactions 43 (2004) 257270


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In summary, the control law usually results in afast motion to bring the state onto the sliding sur-face, and a slower motion to proceed until a de-sired state is reached.

2.2. Smith predictor: Basic concepts and

previous schemes for integrating processes

As stated before, SP is a popular scheme fordeadtime compensation. Fig. 4 shows the architec-ture of the SP. The process transfer function isGp(s)G(s)e

t0s which is assumed to consist ofa rational stable transfer function G(s) and adeadtime t0 . A model of the process without dead-time, Gm(s) , is used to predict the effect of the

control action on the process output and to in-crease the performance of the system. The differ-ence between the output of the process and themodel is fed back in order to correct modelingerrors and load disturbances.

If there is no process/model mismatch, Gm(s)G(s) and t0mt0 , then the modeling errorem(t)y (t)y m(t)0. Since the deadtime isseparated from the model, and e m0, the feed-back only consists of the model without delay.Therefore the deadtime is isolated and compen-sated 1 , and thus, for controller design purposes,it can be ignored. However, the SP cannot be usedwith its original structure to control processes withintegration since a constant load disturbance re-

Fig. 3. Graphical interpretation for KD variations. K1K2K3.

Fig. 4. Smith predictor scheme.



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sults in a steady-state error 5 . To overcome thisobstacle many variations of SP have been pro-posed.

Watanabe and Ito 5 proposed a modification of

the SP as shown in Fig. 5. The system can reject aload disturbance if the time delay of the process is

exactly known. Otherwise, there will be a small

steady-state error 12 . Simulations studies have

shown that the setpoint and load disturbances are

either very oscillatory or highly damped when the

process has a large dead time 13 .

Astrom et al. 13 proposed a new SP structure,as shown in Fig. 6, where the disturbance response

is decoupled from the setpoint response. The con-

troller has four adjustable parameters but a sys-

tematic tuning method was not given. The authorsconsidered only the restricted integrating process

G(s)et0s/s .

Zhang and Sun 12 improved the results of As-

trom et al. retaining the separation nature of loadresponse from the setpoint response. The structure

of the modified SP is shown in Fig. 7. M(s) was

recommended as

M s s Mo s

1sT1Mo s et0s

,

Mo s T2T sT

s1 2Ts. 6

Eq. 6 contains a positive feedback loop that is apotential instability source, resulting in limited ro-bustness 15 . Zhang and Sun rely on a generalguideline to tune Kr and rather than a systematicapproach 16 . The proposed scheme does not pro-vide much better performance than Astroms 12 .When the process is described by a high-ordermodel, the controller is a derivative or a derivativewith lag and a more complex M(s) will result.

Matausek and Micic 17,18 proposed a modi-fied SP and gave a simple controller tuningmethod. Their scheme, given in Fig. 8, has a con-troller to remove the load disturbance although thesetpoint and load responses cannot be decoupled.In a first paper 17 , F(s) is a proportional con-troller Ko , obtaining a simple structure with threeadjustable parameters. However, for high values

Fig. 6. The SP structure proposed by Astrom et al.

Fig. 5. The modified SP proposed by Watanabe and Ito.



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of the deadtime, the scheme has poor disturbancerejection 19 and becomes significantly oscilla-

tory with time delay deviation 15 .A second Matausek and Micics modified SP

18 , where F(s) is a lead-lag compensator, pro-vides considerably faster load disturbance rejec-tion but requires a trial-and-error procedure of themain controller gain in a tradeoff between closed-loop system performance and stability/robustness.This scheme will be used to compare the proposedcontroller.

The Tian and Gaos control scheme 15 has thesame structure as Astroms SP and a parameterstuning as in Ref. 18 . The structure of this SPincludes four controllers, as shown in Fig. 9.

A local proportional feedback Ko is introducedto prestabilize the integrator process. The intro-duction of Go(s) eliminates the effect of Ko onsetpoint tracking. To compensate the phase lagcaused by integrator and time delay aproportional-derivative controller G c(s) is sug-gested, where

G o s 1KoKp

set0s; G c s Kc 1Tds .

7

This structure behaves slightly better than the lat-est Matausek and Micics scheme setpoint ITAEindex reduction 0.5% 15 , despite the addedstructural complexity, and their tuning strategy canbe applied to only pure integrator plus time delaymodels 16 .

3. Smith predictor based sliding mode

controller for integrating processes

The Smith predictor based sliding mode control-ler SPSMCr proposed in this paper uses the stan-dard SP architecture while the controller is a slid-ing mode controller SMC . The block diagram ofthe proposed scheme is shown in Fig. 10. As men-tioned, the original structure of SP is ineffectivefor integrator processes because it cannot reject a

Fig. 7. The structure of Zhan and Suns SP.

Fig. 8. Modified SP proposed by Matausek and Micic.



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constant load disturbance 5 and proportional-derivative controller G d(s) is used for load distur-bance rejection, where

G d s Ko Tds1 . 8

This controller will be discussed later.To develop SPSMCr, an integrating first-order

plus deadtime IFOPDT process model given inEq. 9 is considered,

Gp s G s et0s

K

s s1et0s, 9

where Kis the process gain, t0 is the process dead-time, and is the process time constant. If there isno process/model mismatch, the model transferfunction without deadtime is

Gm s X

1s

M s

Km

s ms1, 10

where Km is the model gain and m is the modeltime constant.

Since the deadtime term has been isolated usinga SP structure, we can ignore it in the SMC de-sign. Then, transforming Eq. 10 into differentialequation form,

m

d2X1 t

dt2

dX1 t

dtKmM t 11

and

d2X1 t

dt2

1

mKmM t

dX1 t

dt . 12

In this case, we use an IFOPDT process and n2. Then, from Eq. 1 , we selected as S(t) anintegral-differential equation acting on the track-ing error expression represented by

S t de t

dt1e t 0

0

t

e t dt. 13

Eq. 13 represents a PID surface. The parameters

1 and 0 can be chosen independently and, in ourcase, they were selected to obtain an overdampedresponse.

From Eq. 2 ,

dS t

dt

d2e t

dt2 1

de t

dt 0e t 0

14

Fig. 9. Tian and Gaos control scheme.

Fig. 10. Smith predictor based sliding mode controller.



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but e(t)R(t)X1(t) and substituting into theabove equation gives

d2R t

dt2

d2X1 t

dt2

1

dR t

dt

1

dX1 t

dt

0e t 0. 15

Camacho 11 has shown that the derivates of thereference value can be discarded without any ef-fect on the control performance. Thus

d2X1 t

dt21

dX1 t

dt0e t . 16

Substituting Eq. 12 into Eq. 16 ,

1 dX1 t

dt 0e t 1

mKmM t dX

1 tdt .

17

Thus the continuous part of the controller is

UC t 1

Km 1m 1

dX1 t

dtm0e t .

18

Then, the complete SPSMCr can be represented as

M t 1

Km 1m 1

dX1 t

dtm 0e t

KDS t

S t 19

with

S t sgn K dX1 tdt 1e t

00

t

e t dt . 20

The function sgn(K) in Eq. 20 is included in the

sliding surface equation to guarantee the appropri-ate action of the controller for the given system.Note that sgn(K) only depends on the static gainof the plant; therefore it never switches 6 .

Eqs. 19 and 20 define the controller equa-tions to be used in the SPSMCr, which can besimplified by setting

11

m time 1. 21

Furthermore, to assure that the sliding surface be-haves as a critical or overdamped system, 0should be

01

2

4 time 2. 22

Numerous simulations showed that the values of1 and 0 are a function of the controllability re-lationship, CRt0/m , and the following valuesprovide satisfactory system performance and ro-bustness with time delay deviation:

14

m time

1

if CR4

1.5

m time 1 if CR4,

23

0 1

2

8 time 2. 24

The parameters and KD have a relationshipwith system speed, overshot, and chattering.Based on previous approaches 6,11,14 where theNelder-Mead searching algorithm was used, thetuning parameters of the controller discontinuouspart are

KD0.75

Km t0

m

0.76

fraction CO ,

25

2 0.680.12 Km KD 1

fraction TO/time . 26

3.1. Disturbance rejection

As mentioned, many modified SP for integratorprocesses with different structures have been pro-posed in the literature to remove the steady-stateerror produced by a constant load disturbance.



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Tian and Gao 15 and Matausek and Micic 18added derivative action to their proposed DTC toovercome this problem. A proportional-derivativecontroller G d(s), given in Eq. 8 , is used in the

proposed SPSMCr to enable the load disturbancerejection. The parameters of this controller, using0.4, pm641.117 rad, as recommendedin Ref. 18 , are

Ko

2pm

Km m t0 1 2pm

2

2

0.7239

Km

mt

0

, 27

Td mt0 0.4 mt0 . 28

4. SPSMCr implementation using a PID

algorithm

Computer based industrial controllers that ex-ecute PID algorithms programmable logic con-trollers and remote terminal units can be used forSPSMCr implementation. The more common PIDalgorithm is based on the following equation:

M V t KcD

dCV t

dt e t

1

i0

t

e t dt

, 29

where M V(t) is the manipulated variable, i is theintegral time, D is the derivative term, and CV(t)

is the controlled variable. Note that the derivativeterm is calculated using the measured controlled

variable, not the error. Fig. 11 shows the blockdiagram that implements an algorithm for a PID.As can be observed, Eqs. 20 and 29 are simi-

lar. The term X1(t) in Eq. 20 is the same CV(t)in Eq. 29 . Therefore, to represent the sliding sur-face S(t) , the next step is to tune the PID based onthe SPSMCr tuning equations as follows:

Kc 1 ,

i1/0 , 30

D1/1 .

With these equations the PID algorithm can bechanged, representing S(t) .

Then, to achieve the implementation, the slidingsurface value S(t) is calculated from the PID out-put. Because the continuous and discontinuousparts of the controller are algebraic equations, theyare easily programmable. The block diagram thatimplements an algorithm for the SPSMCr isshown in Fig. 12.

Fig. 11. Implementation of PID algorithm in an industrial

controller.

Fig. 12. Implementation of SPSMCr using an industrial controller.



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Fig. 13. System responses to a setpoint change for different 1 values. : 11.33; : 12.67; : 10.33.

Fig. 14. System responses to a setpoint change for different 0 values. : 00.22; : 00.44; : 00.056.



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5. Simulation results

To illustrate the SPSMCr performance, two ex-amples are given. In example 1, the system re-

sponse to different parameter values is presentedto show the relationship with the system perfor-mance. In example 2, the response of an integrat-ing system with a long deadtime is shown and theresults are compared to those obtained using theproposed controller in Ref. 18 .

Example 1

Let us consider a process with IFOPDT transferfunction G1(s) ,

G 1 s 1

s 3s

1

e6s, 31

with CRt0/2. Using Eqs. 23 26 , the pa-rameters of SPSMCr are

14

m

4

31.333, 0

12

80.222,

KD0.75

K t0

m

0.76

0.75

1 6

3

0.76

0.443,

2 * 0.680.12 KmKD 1

2 * 0.680.12 1 0.443 1.333 1.5,

Ko0.7239

Km m t0

0.7239

1 360.0809,

Td0.4 mt0 0.4 9 3.6.

Figs. 13 and 14 show the process output to a set-point change when 1 and 0 variations were in-troduced. In these figures, the dotted lines corre-spond to responses using the values obtained withEqs. 23 and 24 . The smaller values of 1 in-crease speed and overshoot. The smaller values of 0 increase speed response and decrease settlingtime. Numerous simulations showed that as speedincreases, the system robustness decreases.

Fig. 15 shows the system responses to a setpoint

change when reductions of value were intro-duced. Fig. 15 a corresponds to the value ob-tained with Eq. 25 . Fig. 15 b corresponds to0. The smaller increases speed and chatter-ing.

Fig. 16 shows the system responses to a setpointchange when reductions of KD value were intro-duced. In this figure, the solid lines correspond toresponses to KD value using Eq. 26 . A larger KDincrease speed and overshot system and thesmaller KD values increase settling time.

Example 2

Let us consider a process with a transfer func-tion G 2(s) , which has been investigated in Refs.

15,1719 ,

Fig. 15. System responses using SPSMCr for G1(s): a

1.5 and b 0.



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G 2 s

1

s s1 0.5s 1 0.2s1 0.1s 1 e20s

. 32

The corresponding IFOPDT model is

G 2m s 1

s 1.28s1e20.64s 33

with CR16.125.In this example, the SPSMCr is compared to the

controller proposed in Ref. 18 and denoted byMM99. For MM99, the equivalent time constantTe is set to 2.4 as in Ref. 18 to improve robust-

ness. The rest of the parameters of MM99 andSPSMCr are given in Table 1. A unit step setpoint

s introduced at time t0 and a load disturbanced0.1 is introduced at time t70. When themodel is exact, Fig. 17 a shows the response of

both control schemes. Fig. 17 b shows the effectof a 20% deadtime modeling error on system per-formance. The MM99 scheme becomes unstable.

6. Conclusions

In this paper, a robust control scheme for inte-grating systems with deadtime using a Smith pre-dictor sliding mode controller SPSMCr has beenpresented. Sliding mode control improves robust-ness and stability to the scheme while the Smithpredictor isolates and compensates the deadtime.

This new method allows for a robust controllerwhile compensating for the deadtime within theprocess. The robustness of the steady-state perfor-mance is improved by the sliding mode with 20%modeling errors. This controller combines the sim-plicity of the SP architecture implementation andthe robustness of a sliding mode controller. Be-sides, the disturbance rejection for integrator pro-cesses of the original structure of SP has been im-proved, adding a proportional-derivative controller

Fig. 16. System responses to a setpoint change for different KD values. : KD0.44; : KD0.25; :

KD3.54.

Table 1

Controller tuning parameters for process G2(s).

MM99 SPSMCr

Tr Kr Ko Td 1 0 KD Ko Td

2.4 0.417 0.027 10.56 1.172 0.172 0.09 0.139 0.033 8.77



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originally proposed by Matausek and Micic 18 .The new proposed controller has a simple tuningprocedure if an IFOPDT model is available.

References

1 Tan, K. K., Lee, T. H., and Leu, F. M., Predictive PIversus Smith control for dead-time compensation. ISATrans. 40, 1729 2001 .

2 ODwyer, A., The estimation and compensation of

processes with time delays. Ph.D. thesis, Dublin CityUniversity, Ireland, 1996.

3 ODwyer, A., A survey of techniques for the estima-tion and compensation of processes with time delay.Technical Report Number: AOD. 00.03, Dublin Insti-tute of Technology, Ireland, 2000.

4 Smith, O. J. M., Close control loops with dead time.Chem. Eng. Prog. 53, 217219 1957 .

5 Watanabe, K. and Ito, M., A process-model control forlinear systems with delay. IEEE Trans. Autom. Control26, 12611269 1981 .

Fig. 17. Responses of the proposed SPSMCr and MM99 for G2(s). a Nominal case, b 10% error in t0 .



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6 Camacho, O., Rojas, R., and Garca, W. M., Variablestructure control applied to chemical processes withinverse response. ISA Trans. 38, 5572 1999 .

7 Camacho, O. and Smith, C. A., Sliding mode control:An approach to regulate nonlinear chemical process.

ISA Trans. 39, 205218 2000 . 8 Utkin, V. I., Variable structure systems with sliding

modes. IEEE Trans. Autom. Control AC-22, 212222 1997 .

9 Slotine, J. J. and Li, W., Applied Nonlinear Control.Prentice-Hall, Englewood Cliffs, NJ, 1991.

10 Camacho, O. and Rojas, R., A general sliding modecontroller for nonlinear chemical processes. Trans.ASME 122, 650655 2000 .

11 Camacho, O., A New Approach to Design and TuneSliding Mode Controller for Chemical Process. Ph.D.Dissertation, University of South Florida, 1996.

12 Zhang, W. D. and Sun, Y. X., Modified Smith predic-tor for controlling integrator/time delay processes. Ind.Eng. Chem. Res. 35, 27692772 1996 .

13 Astrom, K. J., Hang, C. C., and Lim, B. C., A newsmith predictor for controlling a process with an inte-grator and long dead-time. IEEE Trans. Autom. Con-trol 39, 343345 1994 .

14 Camacho, O., Rojas, R., Garca, W., and Alvarez, A.,Sliding Mode Control: A Robust Approach to Integrat-ing Systems with Dead Time. Proc. Second IEEE Int.Caracas Conf on Devices, Circuits and Systems,ICCDSC-98, Margarita, Venezuela, 1998.

15 Tian, Y. and Gao, F., Control of integrator processeswith dominant time delay. Ind. Eng. Chem. Res. 38,29792983 1999 .

16 Kwak, H. J., Sung, S. W., and Lee, I., Modified Smithpredictors for integrating processes: Comparisons andproposition. Ind. Eng. Chem. Res. 40, 15001506

2001 . 17 Matausek, M. R. and Micic, A. D., A modified Smith

predictor for controlling a process with an integratorand long dead-time. IEEE Trans. Autom. Control 41,11991203 1996 .

18 Matausek, M. R. and Micic, A. D., On the modifiedSmith predictor for controlling a process with an inte-

grator and long dead-time. IEEE Trans. Autom. Con-trol 44, 16031606 1999 .

19 Normay-Rico, J. E. and Camacho, E. F., Robust tuningof dead-time compensators for processes with an inte-grator and long dead-time. IEEE Trans. Autom. Con-

trol 44, 15971603 1996 .

Oscar Camacho received theElectrical Engineering, andM.S. in Control Engineeringdegrees from Universidad deLos Andes ULA , Merida,Venezuela in 1984 and 1992,respectively, and the M.E. andPh.D. in Chemical Engineeringat University of South Florida

USF , Tampa-Florida, in 1994and 1996, respectively. He hasheld teaching and research po-sitions at U LA, C IED -

PDVSA, and USF. His currentresearch interests include sliding mode control, deadtime compensa-tion, and hybrid systems. He is the author of more than 50 publicationsin journals and conference proceedings.

Francisco De la Cruz re-ceived the Electronic Engi-neering degree from the Insti-tuto Universitario Politecnico

IUP de Barquisimeto, Ven-ezuela in 1980 and the Masterdegree in Electronic Engineer-ing from the Universidad Si-mon Bolivar, Caracas, Venezu-ela in 1990. Since 1980, hehas been at the Department

of Electronic Engineering,Uni versidad Pol it ecnica

UNEXPO , Barquisimeto,Venezuela. He is currently working towards the Doctoral Degree inApplied Sciences, Universidad de Los Andes, Merida, Venezuela. Hiscurrent research interests include systems with delays, sliding mode

control, and predictive control.


Smith predictor based–sliding mode controller for integrating

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