some long time delay sliding mode control approaches

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ISA Transactions 46 (2007) 95–101 www.elsevier.com/locate/isatrans Some long time delay sliding mode control approaches Oscar Camacho * , Rub´ en Rojas, Winston Garc´ ıa-Gab´ ın Grupo de Investigaci´ on en Nuevas Estrategias de Control Aplicadas, Escuela de Ingenier´ ıa El´ ectrica, Facultad de Ingenier´ ıa, Universidad de Los Andes, La Hechicera M´ erida 5101, Venezuela Received 7 December 2005; accepted 28 June 2006 Available online 9 January 2007 Abstract This paper presents a combined approach of predictive structures with sliding mode control (SMC). Control schemes have been proposed looking for performance and robustness improvement. These structures were designed for processes that can be approximated either by a first order plus time delay or an integral first order plus time delay model broadly used on chemical processes. The proposed schemes were tested for performance and robustness against set point changes and disturbances as compared with classical approaches. c 2006, ISA. Published by Elsevier Ltd. All rights reserved. Keywords: Chemical processes; Predictive structures; Sliding mode control; Time delay 1. Introduction The presence of time delays in many industrial processes is a well-recognized problem. Time lag, transportation lag, time delay and dead time are common phenomena in industrial processes. Time delay can be produced by measurement lag, analysis and computation time, communication lag or the transport time required for a fluid to flow through a pipe. The achievable performance of typical feedback control systems can decline if a process has a relatively large time delay compared to the dominant time constant [1]. Predictive structures and sliding mode controllers have been used to solve such problems. Primarily, internal model control (IMC) and the Smith predictor (SP) are the most popular predic- tive structures used for time delay compensation [2,3]. Further- more, when the process presents an integral behavior the origi- nal structures cannot be used since a constant load disturbance results in a steady-state error [4]. To overcome this obstacle dif- ferent approaches have been proposed [4,5]. Simulation studies have shown that the set point and load disturbances are either very oscillatory or highly damped when the process has a large time delay [6]. To deal with this additional problem new struc- tures were proposed, decoupling the disturbance from the set point response [5,7,8]. In general, these approaches have some * Corresponding author. Tel.: +58 274 2402903; fax: +58 274 2402903. E-mail address: [email protected] (O. Camacho). problems: they are sensitive to modeling errors, since the design requires the use of a process model, which can be difficult to ob- tain in practice. Modeling errors are unavoidable and they result in a mismatch between the model and the actual plant. Thus, the controllers designed using particular models may perform quite differently when they are implemented on the actual process. On the other hand, SMC has been used to design controllers based on its strength for dealing with model–plant mismatches [9]. Even though this controller has proved to be robust against modeling errors and disturbances, its overall performance was too sluggish. The aim of this paper is to summarize an approach that combines simple predictive structures with sliding modes. In that sense, three different controllers are presented to show the performance of this approach: an internal model based sliding mode controller (IM-SMCr), a time delay sliding mode con- troller (TDSMCr), and a Smith predictor based sliding mode controller (SPSMCr). So, the paper is organized as follows. Section 2 shows the background necessary for developing these controllers. Section 3 gives a brief description of the proposed controller design procedure. Section 4 presents some computer simulation results. Finally, some conclusions are offered. 2. Background 2.1. Models of the processes Nonlinear high order models describe most processes in industry. It is well known that a simplified model of a nonlinear 0019-0578/$ - see front matter c 2006, ISA. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.isatra.2006.06.002

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ISA Transactions 46 (2007) 95–101www.elsevier.com/locate/isatrans

Some long time delay sliding mode control approachesOscar Camacho∗, Ruben Rojas, Winston Garcıa-Gabın

Grupo de Investigacion en Nuevas Estrategias de Control Aplicadas, Escuela de Ingenierıa Electrica, Facultad de Ingenierıa, Universidad de Los Andes,La Hechicera Merida 5101, Venezuela

Received 7 December 2005; accepted 28 June 2006Available online 9 January 2007

Abstract

This paper presents a combined approach of predictive structures with sliding mode control (SMC). Control schemes have been proposedlooking for performance and robustness improvement. These structures were designed for processes that can be approximated either by a firstorder plus time delay or an integral first order plus time delay model broadly used on chemical processes. The proposed schemes were tested forperformance and robustness against set point changes and disturbances as compared with classical approaches.c© 2006, ISA. Published by Elsevier Ltd. All rights reserved.

Keywords: Chemical processes; Predictive structures; Sliding mode control; Time delay

1. Introduction

The presence of time delays in many industrial processesis a well-recognized problem. Time lag, transportation lag,time delay and dead time are common phenomena in industrialprocesses. Time delay can be produced by measurement lag,analysis and computation time, communication lag or thetransport time required for a fluid to flow through a pipe. Theachievable performance of typical feedback control systems candecline if a process has a relatively large time delay comparedto the dominant time constant [1].

Predictive structures and sliding mode controllers have beenused to solve such problems. Primarily, internal model control(IMC) and the Smith predictor (SP) are the most popular predic-tive structures used for time delay compensation [2,3]. Further-more, when the process presents an integral behavior the origi-nal structures cannot be used since a constant load disturbanceresults in a steady-state error [4]. To overcome this obstacle dif-ferent approaches have been proposed [4,5]. Simulation studieshave shown that the set point and load disturbances are eithervery oscillatory or highly damped when the process has a largetime delay [6]. To deal with this additional problem new struc-tures were proposed, decoupling the disturbance from the setpoint response [5,7,8]. In general, these approaches have some

∗ Corresponding author. Tel.: +58 274 2402903; fax: +58 274 2402903.E-mail address: [email protected] (O. Camacho).

0019-0578/$ - see front matter c© 2006, ISA. Published by Elsevier Ltd. All rightsdoi:10.1016/j.isatra.2006.06.002

problems: they are sensitive to modeling errors, since the designrequires the use of a process model, which can be difficult to ob-tain in practice. Modeling errors are unavoidable and they resultin a mismatch between the model and the actual plant. Thus, thecontrollers designed using particular models may perform quitedifferently when they are implemented on the actual process.

On the other hand, SMC has been used to designcontrollers based on its strength for dealing with model–plantmismatches [9]. Even though this controller has proved to berobust against modeling errors and disturbances, its overallperformance was too sluggish.

The aim of this paper is to summarize an approach thatcombines simple predictive structures with sliding modes. Inthat sense, three different controllers are presented to show theperformance of this approach: an internal model based slidingmode controller (IM-SMCr), a time delay sliding mode con-troller (TDSMCr), and a Smith predictor based sliding modecontroller (SPSMCr). So, the paper is organized as follows.Section 2 shows the background necessary for developing thesecontrollers. Section 3 gives a brief description of the proposedcontroller design procedure. Section 4 presents some computersimulation results. Finally, some conclusions are offered.

2. Background

2.1. Models of the processes

Nonlinear high order models describe most processes inindustry. It is well known that a simplified model of a nonlinear

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96 O. Camacho et al. / ISA Transactions 46 (2007) 95–101

Fig. 1. Internal model control.

high order model can be used to design a controller. Inchemical processes the reaction curve is an often-used methodfor identifying dynamic models [10]. It is simple to use, andprovides adequate models for many applications. The curve isobtained by introducing a step change in the controller outputand recording the transmitter output. That curve allows modelparameter calculation. A first order plus time delay (FOPTD)model, Eq. (1), is able to adequately represent the dynamics ofmany chemical processes over a range of frequencies [11]:

Y (s)U (s)

=Km

τms + 1e−t0m s (1)

where Km, τm and t0m are the static gain, time constant and thetime delay of the model, respectively.

For processes presenting an integrating behavior, anintegrating first order plus time delay (IFOPTD) process model,Eq. (2), must be considered:

Y (s)U (s)

=Km

s(τms + 1)e−t0m s . (2)

In both equations, Y (s) is the Laplace transform of thecontrolled variable (transmitter output), and U (s) is the Laplacetransform of the manipulated variable (controller output). BothY (s) and U (s) are deviation variables.

2.2. Predictive structures

2.2.1. Internal model structureThe internal model structure is shown in Fig. 1. The idea

behind this scheme is firstly to obtain a model of the process,and then to decompose it into two parts, a directly invertibleterm G−

m(s), and another, noninvertible term G+m(s). Thus, the

model can be represented in the following way:

Gm(s) = G+m(s)G−

m(s). (3)

The noninvertible part has an inverse that is not causal or isunstable, such as time delay or unstable poles. On the otherhand, the invertible component is causal and stable, whichallows one to design a realizable controller [12,13].

Therefore, the IMC procedure eliminates all elements inthe process model that can produce an unrealizable controller.Thus, the design of the controller takes into consideration onlythe invertible one.

Fig. 2. Smith predictor scheme.

Fig. 3. Graphical interpretation of SMC.

2.2.2. Smith predictor structureThe Smith predictor structure is shown in Fig. 2. In it, y(t)

is the process output, r(t) is the set point or reference input,G−

m(s) is the invertible part of the process model, ym(t) is theprocess model output and em(t) is the output modeling error.So, the SP incorporates a model of the process, and thus itis able to predict its output. This allows the controller to bedesigned as though the system is delay free, therefore retainingthe simple tuning features of PID controllers [12,13].

The closed-loop transfer function of the system, comingfrom the previous figure, can be written as

Y (s)U (s)

=Gc(s)G p(s)

1 + Gc(s)G−m(s) + Gc(s)[G p(s) − Gm(s)]

(4)

where Gc(s), G p(s) and Gm(s) are the controller, process andprocess model transfer functions, respectively. If the modeland the process match, the characteristic equation will notcontain a time delay, because G p(s) and Gm(s) will cancel.Therefore, in this case, the characteristic equation involves onlythe expression 1 + Gc(s)G−

m(s), which allows an aggressiveadjustment of the manipulated variable. Obviously, the trueprocess is never known exactly, and therefore the performanceshould decrease.

2.3. Sliding mode control

Sliding mode control is a technique derived from variablestructure control (VSC) which was originally studied byUtkin [14]. A controller designed using the SMC methodis particularly appealing due to its ability to deal withnonlinear systems and time-varying systems, showing a robustbehavior [15].

The idea behind SMC is to define a surface along whichthe process output can slide to its desired final value. Fig. 3

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O. Camacho et al. / ISA Transactions 46 (2007) 95–101 97

depicts the SMC objective. The structure of the controlleris intentionally altered as its state crosses the surface inaccordance with a prescribed control law. Thus, the first stepin SMC is to define the sliding surface, S(t), which represents adesired global behavior, like stability and tracking performance.

The sliding surfaces used to derive the different con-trol schemes presented in this work are based on anintegral–differential equation acting on the tracking-error ex-pression [15]:

S(t) = sign(Km) f(

e(t),∫

e(t)dt,de(t)

dt, λ, n

)(5)

where e(t) is the tracking error, that is, the differencebetween the reference value or set point, r(t), and the outputmeasurement, y(t), namely e(t) = r(t) − y(t). λ is a tuningparameter, which helps to define S(t). This term is selectedby the designer, and determines the performance of the systemon the sliding surface. n is the model’s order, and thereforeonce its value is included in the sliding surface it does notappear explicitly. The sign(Km) function was included in thesliding surface equation to guarantee the appropriate action ofthe controller [9]. Note that sign(Km) only depends on the staticgain of the plant model; for that reason it never switches, givingjust a positive or negative sign multiplying f (•).

The control objective is to ensure that the controlled variablebe equal to its reference value at all times, meaning that e(t)and its derivatives must be zero. Once the reference value isreached, S(t) has reached a constant value; it is desired to set

dS(t)dt

= 0. (6)

Once the sliding surface has been selected, attention mustbe turned to designing the control law that drives the controlledvariable to its reference value and satisfies Eq. (6). The controllaw, U (t), consists of two additive parts: a continuous part,UC (t), and a discontinuous part, UD(t). That is

U (t) = UC (t) + UD(t). (7)

The continuous part is given by

UC (t) = f (y(t), r(t)) (8)

where f (y(t), r(t)) is a function of the controlled variable andthe reference value.

The discontinuous part is nonlinear and represents theswitching element of the control law. This part of the controlleris discontinuous across the sliding surface. Mainly, UD(t) isdesigned on the basis of a relay-like function (i.e. UD(t) =

αsign(S(t))), because it allows for changes between thestructures with a hypothetical infinitely fast speed. In practice,however, it is impossible to achieve the high switching controlbecause of the presence of finite time delays for controlcomputations or limitations of the physical actuators, thuscausing chattering around of the sliding surface [14,15].Chattering is a high frequency oscillation around the desiredequilibrium point. It is undesirable in practice, because itinvolves high control activity and can excite high frequency

Fig. 4. Proposed scheme of IM based SMC.

dynamics ignored in the modeling of the system [15]. Theaggressiveness for reaching the sliding surface depends on thecontrol gain (i.e. α), but if the controller is too aggressive it cancollaborate with the chattering. To reduce the chattering, oneapproach is to replace the relay-like function by a saturation orsigma function, which can be written as follows:

UD(t) = K DS(t)

|S(t)| + δ(9)

where K D is the tuning parameter responsible for the reachingmode. δ is a tuning parameter used to reduce the chatteringproblem. In summary, the control law usually results in a fastmotion to bring the state onto the sliding surface, and a slowermotion to proceed until a desired state is reached.

3. Controller design

In this section the syntheses of the sliding mode controllersusing the different predictive structures are presented.The controllers are developed for processes that can beapproximated by FOPTD and IFOPTD models.

3.1. Internal model based sliding mode controller

The design of a sliding mode controller (SMCr) from anFOPTD model was described by Camacho and Smith [11] buttheir approach requires some assumptions and approximationsto deal with the time delay term. The internal model basedsliding mode controller (IM-SMCr) approach takes advantageof choosing the invertible part of the model process to designthe controller.

Fig. 4 shows the proposed scheme. The nonlinear processwas modeled as an FOPTD. As was suggested in Section 2.2.1,the model can be separated into two parts:

G+m = e−t0m s (10)

G−m =

Km

τms + 1(11)

where G−m(s) eliminates the time delay term from the model;

this simplification facilitates the SMC design.Let us propose the following sliding surface:

S(t) = e−m (t) + λ

∫ t

0e(t)dt (12)

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98 O. Camacho et al. / ISA Transactions 46 (2007) 95–101

where

e−m (t) = r(t) − y−

m (t) (13)e(t) = r(t) − y(t) (14)

where y−m (t) is the model output without time delay.

Now, following the procedure described in [11], the SMCris obtained:

U (t) =τm

Km

[y−

m (t)τm

+ λe(t)]

+ K DS(t)

|S(t)| + δ(15)

S(t) = sign(Km)

[e−

m (t) + λ

∫ t

0e(t)dt

]. (16)

To complete the SMCr design, it is necessary to establisha set of tuning equations. For the tuning equations as firstestimates, using the Nelder–Mead searching algorithm [16,17],the following equations were obtained:

λ ≤1

τm + t0m(17)

K D ≥0.8

|Km |

(τm

t0m

)0.76

(18)

δ = 0.68 + 0.12|Km |K Dλ. (19)

These equations have a fixed structure depending on theλ parameter and the characteristic parameters of the FOPTDmodel which is an advantage from the process control tuningpoint of view. For an industrial application, Eq. (16) can beimplemented by a PI algorithm [18].

3.2. Time delay sliding mode controller

The time delay sliding mode controller (TDSMCr) wasdeveloped using an approach similar to that presented in theprevious subsection. In this case the Smith predictor structurewas used and a different controller was obtained [12,13].

When the nonlinear process is modeled as an FOPTD, thedelay free part, G−

m(s), can be used to design the controller.This simplifies the procedure of obtaining a conventional SMCrwithout delay compensation.

Then, the following proportional sliding surface wasproposed:

S(t) = KS · e1(t) (20)

where KS is a design gain and e1(t) is the SP-like error(e1(t) = r(t) − (y−

m (t) + em(t))) that it is reduced to thedifference between the reference, r(t), and the free delaymodel output, y−

m (t), when a perfect model matching isconsidered, i.e. em(t) = 0. Thus, the process time delay is notconsidered, shortening the controller design. Although previousconsiderations are not so real, it is assumed that the controllerrobustness will compensate for this.

The TDSMCr obtained is given by the following equation:

U (t) =τm

Km

[dr(t)

dt+

y−m (t)τm

]+ K D

S(t)|S(t)| + δ

(21)

Fig. 5. Smith predictor based sliding mode controller.

where S(t) is the following sliding surface:

S(t) = KS · sign(Km) · e1(t) (22)

and the KS parameter is responsible for the controlleraggressiveness, KS > 0.

To complete the controller design, it is necessary to have aset of tuning equations. The tunings for first estimate valueswere determined using time-domain performance methods [5],resulting in the following equations:

K D =0.72|Km |

(τm

t0m

)0.76

(23)

δ = 0.68 + 0.12|Km |K Dt0m + τm

t0mτm(24)

KS = 15K P (25)

where K P can be calculated as the controller gain of a PID con-troller. Thus, the value chosen for this parameter depends on thetuning equations used, giving a more aggressive controller if theZiegler–Nichols are chosen instead of Dahlin equations [2].

3.3. The Smith predictor based sliding mode controller forintegrating processes

The Smith predictor based sliding mode controller(SPSMCr) presented uses the standard SP architecture whilethe controller is a sliding mode controller (SMC). The blockdiagram of the proposed scheme is shown in Fig. 5. It is wellknown that the original SP controller is not effective for integralprocesses because it cannot reject a constant load disturbance.Many modified SP for integral processes with differentstructures have been proposed in the literature to remove thesteady-state error produced by a constant load disturbance. Tianand Gao [20], and Matausek and Micic [8] added derivativeaction, Gd(s), to their proposed TDC to overcome this problem.This was also considered in our approach.

Gd(s) = KO(τds + 1). (26)

To develop the SPSMCr, an integrating first order plus timedelay (IFOPTD) process model was considered. The modeltransfer function without time delay can be written as

G−m(s) =

Km

s(τms + 1). (27)

Again assuming perfect model matching, em(t) = 0. Thus,the time delay part is not considered in the SMC design. Then,

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O. Camacho et al. / ISA Transactions 46 (2007) 95–101 99

the complete SPSMCr can be represented as

U (t) =1

Km

[(1 − τmλ1)

dy−m (t)dt

+ τmλ0e−m (t)

]+ K D

S(t)|S(t)| + δ

(28)

with

S(t) = sign(Km)

[−

dy−m (t)dt

+ λ1e−m (t) + λ0

∫ t

0e−

m (t)dt]

(29)

where y−m (t) is the G−

m output and e−m (t) = r(t) − y−

m (t).Eqs. (28) and (29) define the SPSMCr. In this case thetuning equations for first estimate values were determinedfrom a systematic set of simulations as a function of thecontrollability relationship, CR =

t0τm

. The following valuesprovide satisfactory system performance and robustness againstmodeling errors [19]:

λ1 =

4τm

[=][time]−1 if CR ≤ 4

1.5τm

[=][time]−1 if CR ≥ 4(30)

λ0 =λ2

18

[=][time]−2 (31)

K D =0.75|Km |

(t0τm

)−0.76

[=][fraction CO] (32)

δ = 2[0.68 + 0.12(|Km |K Dλ1)][=][fraction TO/time]. (33)

A proportional-derivative controller given in Eq. (26) isused in the proposed SPSMCr. The parameters of the Gd(s)controller for enabling the load disturbance rejection werefound as recommended by Matausek and Micic [8]:

K0 =0.7239

Km(τm + t0m)(34)

τd = 0.4(τm + t0m). (35)

4. Simulation results

To illustrate the performance of the proposed controllers ahigh order model with long time delay of a system is given, foreach case. The different controllers were tested when set pointand disturbances changes were applied to the process. Finally,IM-SMCr was compared against IMC and SMC; TDSMCr wascompared against a dead time compensator (DTC), and forthis comparison an SP was used as a DTC; and SPSMCr wascompared against a predictive controller structure proposed byMatausek and Micic (MM99) [8].

4.1. Internal model based sliding mode controller

In this case a fourth order system with time delay and acontrollability ratio above 1 was used (t0m/τm ≈ 4.38):

G(s) =e−5s

(s + 1)(0.5s + 1)(0.25s + 1)(0.125s + 1). (36)

Fig. 6. Process response for set point and disturbance changes.

Table 1Controller tuning parameters

IM-SMC Values SMC Values IMC Values

λ 0.10 λ0 0.19 τm 1.5K D 0.90 λ1 0.87 Km 1.0δ 0.69 K D 0.21 τ f 1.8

δ 0.70

For this system a FOPTD model was obtained by using thereaction curve procedure [3],

Gm(s) =e−5.68s

(1.3s + 1). (37)

In Table 1 are shown the tuning values for each controller.These values were kept constant in all simulations. The tuningvalues for the SMCr were obtained as given in Camacho [9,17]and those for the IMCr were obtained as given in Marlin [2],where τm is the model time constant, Km is the model staticgain, and τ f is the robustness filter time constant (see Fig. 1).

Figs. 6 and 7 shows the process and controller outputs whena set point change was introduced at time t = 0 units of time(UT) and a disturbance change was applied at time t = 100 UT.It is observed that the IM-SMC and IMC controllers presentedvery close behavior, while the SMC controller presented aslower and oscillatory response, with a higher overshoot.

4.2. Time delay sliding mode controller

In this case a fourth order system with long time delay and acontrollability ratio above 1 was used (t0m/τm ≈ 8.22):

G(s) =e−10s

(s + 1)(0.5s + 1)(0.25s + 1)(0.125s + 1). (38)

For this system a FOPTD model was obtained by using thereaction curve procedure,

Gm(s) =e−10.68s

(1.3s + 1). (39)

100 O. Camacho et al. / ISA Transactions 46 (2007) 95–101

Fig. 7. Controller output when set point and disturbance changes were applied.

Fig. 8. Process response for set point change applied to G(s).

Table 2Tuning parameters

DTC G(s) DTSMC G(s)

Kc 0.07 Ks 1.07Ti 1.5 K D 0.164Td 5.25 δ 0.695

In Table 2 the tuning values for each controller are shown.These values were kept constant in all simulations. The tuningvalues for the PID adjustment in the DTC were obtainedusing the Dahlin equations [3] and for the TDSMC, usingEqs. (23)–(25).

The system with both controllers, DTC and DTSMC, wastested against set point changes and disturbances. Fig. 8 showsthe system responses when a set point change of 10% wassimulated; both responses were overdamped, but the DTSMCproduces a faster response than that given by the DTC. Fig. 9depicts the responses for the same system when a disturbanceof 5% is simulated at time t = 400 UT, similar to the set pointchange result; the DTSMC presents a better performance thanthe DTC.

Fig. 9. Process response for disturbance change applied to G(s).

Fig. 10. Responses of the proposed SPSMCr and MM99 for G(s). Nominalcase.

4.3. The Smith predictor based sliding mode controller forintegrating processes

In this case a fourth order system with long time delay and acontrollability ratio above 1 was used (t0/τ ≈ 11):

G(s) =e−20s

s(s + 1)(0.5s + 1)(0.2s + 1)(0.1s + 1)(40)

and the corresponding IFOPTD model was

Gm(s) =e−20.64s

s(1.28s + 1). (41)

For MM99, the equivalent time constant, Te, is set to 2.4 UTas in [8] to improve robustness. The rest of the parameters ofthe MM99 and SPSMCr are given in Table 3. A unit step inputwas introduced at time t = 0 UT and a −10% load disturbanceat time t = 70 UT. Fig. 10 shows the system response whenboth control schemes were used. Fig. 11 shows the effect of a20% time delay modeling error on the system performance. TheMM99 scheme becomes unstable.

O. Camacho et al. / ISA Transactions 46 (2007) 95–101 101

Fig. 11. Responses of the proposed SPSMCr and MM99 for G(s). 20% errorin t0.

Table 3Controller tuning parameters for process G(s)

MM99 SPSMCrTr Kr Ko Td λ1 λ0 K D δ Ko Td

2.4 0.417 0.027 10.56 1.172 0.172 0.09 0.139 0.033 8.77

5. Conclusions

A combined approach of predictive structures with slidingmode control was presented. This control schemes showedthe benefits for dealing with long time delays using thepredictive structure plus the robustness of the sliding modetheory. The proposed structures work well for processes thatcan be approximated either by a first order plus time delayor an integral first order plus time delay model, broadlyused on chemical processes. The proposed schemes showed abetter performance and robustness against set point changesand disturbances when they were compared with classicalapproaches. The use of simple predictive structures and theprovision of tuning equations make implementation easy andgive a good starting point for the adjustment.

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[20] Tian Y, Gao F. Control of integrator processes with dominant time delay.Industrial Engineering Chemistry Research 1999;38:2979–83.

Oscar Camacho received an Electrical Engineeringand M.S. in Control Engineering degrees fromUniversidad de Los Andes (ULA), Merida, Venezuela,in 1984 and 1992, respectively, and an M.E. andPh.D. in Chemical Engineering at University ofSouth Florida (USF), Tampa, Florida, in 1994 and1996, respectively. He has held teaching and researchpositions at ULA, PDVSA, and USF. His currentresearch interest includes sliding mode control, dead

time compensation, and fault detection systems. He is the author of more than60 publications in journals and conference proceedings.

Ruben Rojas received a Systems Engineering degreefrom Universidad de Los Andes (ULA), Merida,Venezuela, in 1986, and an M.Sc. and Ph.D. inBiomedical Engineering at University of lows (UI),Iowa City, Iowa, in 1994 and 1997, respectively. Hehas held teaching and research positions at ULA. Hiscurrent research interest includes sliding mode control,dead time compensation, mathematical modeling, andidentification. He is the author of more than 50

publications in journals and conference proceedings.

Winston Garcıa-Gabın received an Electrical Engi-neering, and M.S. in Automation and Instrumenta-tion degrees from Universidad de Los Andes, Merida,Venezuela, in 1994 and 1998, respectively, and a Ph.D.in Industrial Engineering at University of Seville,Spain, in 2002. He has held teaching and research po-sitions at the Electrical Engineering School at Univer-sidad de Los Andes. His current research interests in-clude sliding mode control, model predictive control,

and time delay systems. He is the author of more than 50 publications in jour-nals and conference proceedings. He has been in consultancy work, as well aslecturing in short courses for companies.