Abstract: Dead times can manifest in various control systems, posing a challenge due to their limiting eﬀect on

the maximum allowable gain required for system stability. Consequently, researchers have developed various

structure-based controllers to enhance control performance or mitigate the strong inﬂuences of the dead time

component. Among these structures are the Smith Predictor, Generalized Predictive Controller (GPC), and

fractional PID controllers. With the signiﬁcant advancements in networking and communication technology, the

application of networked control has gained importance. However, due to the diverse network characteristics,

additional variable delays are challenging to avoid. Modern control engineering oﬀers methods capable of

signiﬁcantly improving control performance, considering both theoretical and practical aspects.

Key-Words: Smith Predictor, GPC, Networked Control Systems

Received: April 26, 2024. Revised: October 6, 2024. Accepted: November 4, 2024. Published: December 5, 2024.

1 Introduction

Many processes in the industry, as well as in

other domains, exhibit dead times in their dynamic

behavior. Dead times primarily consist of delays

in information, energy transport, or communication

networks [1], [2]. They can also be caused

by processing time or the accumulation of time

delays across a series of interconnected dynamic

systems. In processes with dead time, a change in

the process setpoint aﬀects the controlled variable

only after the process’s dead time. Additionally,

disturbances become noticeable only after some time,

and it also takes time for the controller to respond

to these changes. Therefore, the analysis and

design of controllers for systems with dead time are

challenging [2], [3].

Time delay poses a signiﬁcant challenge in process

control and regulation as it can lead to undesirable

oscillatory behavior or even instability within the

system. Stability analysis and robust control

of time delay systems are therefore of both

theoretical and practical signiﬁcance [4]. Although

these are typically associated with disturbances

in Closed-loop control systems, some methods

intentionally integrate delays into control laws to

achieve stable behavior or improve control quality

[5].

Processes with signiﬁcant dead times are challenging

to control using standard controllers. By employing

a predictor structure, the performance of the

closed-loop system can be improved. These

predictor-based controllers, known as dead time

compensators, ﬁnd applications across various

technical domains, primarily in the process industry

[6], [7], but also in other areas such as robotics

[8] and internet congestion control [9]. These

controller structures were introduced to enhance the

performance of classical controllers (such as PI or

PID controllers) in systems with dead time.

The outline of the remaining paper is as follows:

Section 2 describes the PID controller, followed

by the Smith predictor in Section 3 and the GPC

controller in Section 4. Section 5 presents their

applications, and ﬁnally, Section 6 provides the

conclusion.

2 PID, PI Controllers

Many processes are regulated using classical

controllers such as Proportional Integral (PI) and

Proportional Integral Derivative (PID). However,

when the process exhibits dead time, tuning

the controller parameters becomes challenging.

Consequently, extensive eﬀorts have been made to

explore and derive better tuning rules for controller

parameters of processes with dead time [10], [11].

The ideal controller is deﬁned as follows [12]:

C(s)=Kc(1 +1

Tis) (1)

where Kcis the proportional gain and Tiis the time

constant and sthe Laplace operator. The Process is

assumed as:

P(s)=e−sτm(Km

1+Tms) (2)

This classical controller can be designed using

various methods, including the following rules [10]

as shown in Table 1:

Development and validation of control systems with variable dead

time for networked control systems.

MAROUANE OUADOUDI, MICHAEL H. SCHWARZ, JOSEF BÖRCSÖK

Dept. Computer architecture and system programming

University Kassel

Wilhelmsh¨oher Allee 71, 34121 Kassel

GERMANY

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Table 1: Tunings rules for PI controller [10], [11]

Rule KcTiComment

Ziegler

Nichols

(1992)

0,9Tm

Kmτm

0,33τm

τm

≤1

Astr¨

H¨

agglund

(1995)

0,63Tm

Kmτm

0,2τm

Chien,

et al.

(1952)

0,6Tm

Kmτm

4τm

τm

≤1

St. Clair

(1997)

0,333Tm

Kmτm

τm

≤3

The closed loop system of a process P(s)=G(s)e−Ls

controlled by a PID controller can be deﬁned as

follows:

Y(s)

R(s)=C(s)P(s)

1+C(s)P(s)

=C(s)G(s)e−Ls

1+C(s)G(s)e−Ls (3)

Generally, processes with small dead time can be

regulated using classical PI and PID controllers,

and suitable tuning of the controller parameters can

achieve a reasonable compromise between robustness

and performance [10]. However, as depicted in

Figure 1, processes with signiﬁcant dead times are

challenging to control with PI and PID controllers,

and determining the optimal control parameters

is diﬃcult. Consequently, the performance of

the control loop remains limited. The eﬀect of

disturbances on the controlled variable becomes

noticeable only after a certain time, hence it also takes

time for the response of the manipulated variable to

reﬂect in the controlled variable [3].

Fig. 1: PI Controller

3 Smith Predictor

Predictor-based control structures have been utilized

in many control applications. The performance of the

closed loop system can be enhanced by employing a

predictor structure in two main cases [13]:

•when the process exhibits signiﬁcant dead time.

•when the future setpoint is known.

In the ﬁrst case, the main objective of the predictor is

to eliminate the eﬀects of dead time on the control

loop. In the second case, the predictive controller

enables prediction of the control process. In both

scenarios, the predictive strategy involves a process

model integrated into the controller’s structure.

Fig. 2: Smith Predictor

Figure 2 illustrates the complete controller C1(s). The

controller C0(s) is typically a PI or PID controller.

The predictor includes a transfer function model

without dead time Gn(s), along with a dead time

model e−Lns. Consequently, the complete process

model is expressed as Pn(s)=Gn(s)e−Lns[2].

C1(s)=C0(s)

1+C0(s)[Gn(s)−Pn(s)]

=C0(s)

1+C0(s)Gn(s)(1 −e−Lns)(4)

When Pn(s)=P(s) and L=Ln, the transfer function

of the closed loop system can be expressed as:

Y(s)

R(s)=C1(s)P(s)

1+C1(s)P(s)

=C1(s)G(s)e−Ls

1+C1(s)G(s)e−Ls

C0(s)

1+C0(s)Gn(s)(1 −e−Lns)G(s)e−Ls

1+C0(s)

1+C0(s)Gn(s)(1 −e−Lns)G(s)e−Ls

=C0(s)G(s)

1+C0(s)G(s)e−Ls (5)

Compared to the PID or PI control loop (Equation 3),

the characteristic equation depends on the dead time,

with the phase margin of the system reduced by the

additional phase of the dead time.

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3.1 Filtered Smith Predictor

Various approximation methods are employed in

process modeling, which may entail simplifying

higher order dynamics or approximating nonlinear

dynamics with linearized equations [14]. Since the

model merely represents an approximation of the

real process, thorough analysis of modeling errors

is indispensable to develop a reliable controller.

To enhance the control quality of the Smith

Predictor, ﬁlters are often employed, as depicted

in Figure 3 [15]. A ﬁltered Smith Predictor is

an extended version of the conventional predictor

circuit aimed at optimizing control quality in control

loops. Various ﬁltering techniques are integrated

to reduce disturbances and enable more accurate

prediction of process variables. Typically, low

pass ﬁlters, band pass ﬁlters, or Kalman ﬁlters are

used, depending on the speciﬁc system requirements

and the nature of disturbances. These ﬁlters help

eliminate noise, minimize signal distortions, and

increase the robustness of the control loop [16].

Fig. 3: Block diagram of the ﬁltered Smith Predictor

(FSP)

Dead time errors pose a signiﬁcant challenge to the

stability of the Smith Predictor. Thorough analysis

of the block diagram of the Smith Predictor in Figure

3 illustrates that when considering dead time errors,

periodic diﬀerences between actual and predicted

outputs are fed back to the controller. These errors

can jeopardize the stability of the closed-loop system

[2], [17]. A practical solution to this problem is

implementing a low-pass ﬁlter. The ﬁlter should be

designed to eﬀectively suppress oscillations in the

system output [18].

Table 2: Smith Predictor and ﬁltered Smith Predictor

controllers

SP FSP SP FSP

SP FSP 10% 10% 15% 15%

error error error error

IAE 49.8 49.79 55.5 53.7 66.1 56

The results from Table 2 suggest a general conclusion

that using a ﬁltered Smith Predictor provides

signiﬁcantly better results in terms of setpoint

tracking and sensitivity to modeling errors. However,

it is noted that this does not necessarily lead to

optimization of disturbance rejection and control

time.

Fig. 4: Smith Predictor Simulation

Figure 4 illustrates that by continuously adjusting

the manipulated variables and accurately predicting

future system states, the Smith Predictor enhances

control quality and ensures eﬀective system control.

Thus, the Smith Predictor proves to be an eﬃcient

dead time compensator for processes with long dead

times. The control algorithm of a Smith Predictor

typically involves a PI or PID controller, which is

also prediction based. A comparison between the

performance of the classical controller and the Smith

Predictor for processes with long dead times shows

that the Smith Predictor achieves the best results.

The Smith structure eliminates the inﬂuence of dead

time on the setpoint response, allowing for a balanced

compromise between robustness and performance

through appropriate controller tuning.

4 Generalized Model Predictor

Control

Single Input Single Output (SISO) process models

can be described using Equation 6 with backward

shift for the process output.

y(k)=P(z−1)u(k−1)

=z−dB(z−1)

A(z−1)u(k−1) (6)

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where u(k) and y(k) represent the control signal and

the model output, respectively, d is the time delay,

and [11].

A(z−1)=1+a1z−1+... +anaz−na

B(z−1)=b0+b1z−1+... +bnbz−nb(7)

The selection of the model process used to represent

deviations is crucial. A widely used model is the

Controlled Auto Regressive and Integrated Moving

Average (CARIMA) model. With the CARIMA

model (Equation 7), Generalized Predictive Control

(GPC) provides a deviation free response as it

considers both variable and constant future setpoints.

However, recursion of the Diophantine equation is

required for prediction [19]. Proper selection of the

prediction and control horizon as well as weighting

leads to optimal performance [20].

The diﬀerence between the measured and calculated

model output is deﬁned as [21]:

δ(k)=C(z−1)

D(z−1)e(k) (8)

where the polynomial D(z−1) 1contains the integrator,

e(k) represents white noise with zero mean, and the

polynomial C(z−1) is typically considered as one [22],

[23]:

ˆy(k)=y(k)+δ(k)

=z−dB(z−1)

A(z−1)u(k−1) +δ(k)

=z−dB(z−1)

A(z−1)u(k−1) +C(z−1)

D(z−1)e(k) (9)

With

C(z−1)=1+c1z−1+... +cncz−nc=1

D(z−1)= ∆A(z−1)

∆ = 1−z−1(10)

The disturbance signal e(k) can be either a

deterministic or a stochastic signal, but due to the ∆

operator, its mean is assumed to be zero [24]. This

leads to:

ˆy(k)=z−dB(z−1)

A(z−1)u(k−1) +

C(z−1)

∆A(z−1)e(k)

∆A(z−1)ˆy(k)=z−dB(z−1)∆u(k−1) +

C(z−1)e(k) (11)

Generalized Predictive Control (GPC) employs a

matrix approach, minimizing the cost function in

Equation 12. It is crucial to note that the prediction

horizon should be at least as large as the system’s

dead time to adequately consider delays. Often, it

is even chosen larger to provide additional safety and

compensate for potential model errors [25].

min J =

j=H1

[ˆy(k+j|k)−r(k+j)]2+

j=1

λj∆u(k+j−1|k)]2(12)

From this, the analytical solution follows:

∆u=(GTG+λI)−1GT(r−f) (13)

Fig. 5: Smith Predictor and GPC Simulation

The various control structures developed in this paper

are now comprehensively simulated to compare and

evaluate their performance. One of these control

methods is the Smith Predictor, complementing the

PI controller and achieving notable improvement.

Additionally, a Generalized Predictive Control (GPC)

has been implemented. Simulation results clearly

demonstrate that GPC exhibits higher control quality,

as shown both in Figure 5 and the results in Table

3. Furthermore, it responds more eﬀectively to

disturbances and setpoint changes, and compared to

other control algorithms, it has the shortest settling

time.

Table 3: Integral Absolute Error for GPC and Smith

Predictor

SP GPC

IAE 43,71 49.79

IAEs64.6 53,78

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5 Networked Control Systems

The signiﬁcant advancements in network technology

and data communication have propelled the

importance of networked and real time capable

control and regulation applications. Among

these applications are teleoperations, remote

controlled mobile robots, and factory automation,

all facilitated by interconnections between control

systems via network resources [26]. This trend is

further reinforced by the practical and systematic

maintenance capabilities of network applications

within the industry [27]. A notable modern industrial

application is the networked control system (NCS),

which enables a multitude of applications by

seamlessly connecting all sensors, actuators, and

controllers through networks [28].

Fig. 6: Representation of a networked control system

with B&R controllers.

The communication system used is depicted in

Figure 6. The PLCs are connected via access

point modules, which act as bridges and routers,

establishing the wireless network. The access point

receives commands, forwards them to the respective

PLC terminal, and then sends back the data.

5.1 Analysis and Implementation

The use of network technologies enables easy

maintenance and scalability of the control system,

but it also leads to issues such as delays, data losses,

and packet collisions [29]. Another problem is that

the NCS performance can become unstable due to

the stochastic nature of network delay. Therefore,

it is challenging to directly apply linear analysis of

systems with delay and time. The network induced

overall delay, both in the control system and in the

drive, can signiﬁcantly aﬀect NCS performance [30].

The following Figure 7 illustrates the relationships

and provides a visual representation of the problem.

Fig. 7: Networked System

Now, the Smith Predictor and Generalized

Predictive Controller (GPC) are implemented

in Automation Studio™and transferred to the

controller, establishing communication between

the server and client. Simulations are conducted

in two steps or simulation conditions. The data is

exported from Automation Studio and represented

and evaluated in Matlab ®.

Fig. 8: Comparing Networked Systems

The analysis of Figure 8 illustrates that both the

Smith Predictor and GPC control systems achieve

the setpoint within a reasonable time and without

overshooting. Even with disturbances introduced at

the output, both controllers can fully compensate for

and suppress deviations. However, it is observed

that compared to the Smith Predictor, the GPC

exhibits superior control quality, resulting in shorter

control times, lower IAE values, and more eﬃcient

disturbance suppression.

In the second simulation (Figure 9), disturbances

are added to assess the system’s time delay

compensation. The goal is to evaluate the system’s

time delay compensation.

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Fig. 9: Comparing Networked Systems with Delay

The uncertainty of the time delay in this case shows

that the Smith Predictor exhibits stable behavior,

which is not the case for the GPC. Variation in the

time delay leads to system instability with the GPC,

although it showed better control performance than

the Smith Predictor in the case of constant time delay.

This indicates that the GPC is sensitive to time delay

uncertainties, and its robustness is clearly dependent

on the time delay.

When communicating over networks, additional

time delays can occur, signiﬁcantly inﬂuencing the

system’s behavior. This is because the sender

attempts to transmit a packet with constantly updated

information after each cycle. The receiver, in turn,

checks its input queue for newly received information

after each cycle. If no new packet is received,

the previous information is used. Thus, there is a

deviation between the current and the used system

information. Figure 10 depicts such a networked

control system using the Smith Predictor.

5.2 Approach for Time Delay

Compensation

Fig. 10: Adaptive Smith Predictor

As a solution, time delay detection (online delay

estimation) can be used with an adaptive Smith

Predictor, where delays between the sender and

the target system are identiﬁed through continuous

monitoring. The gathered information can be utilized

for adjustment and improvement of prediction.

Fig. 11: Adaptive Smith Predictor in Matlab®

In a real network, network induced delays and packet

losses depend on the current network load, which in

turn is inﬂuenced by factors such as message size,

data rate, transmission medium, and network cable

length. This paper demonstrates that time delays in

the communication of a networked control system

impair performance and can lead to instability.

An eﬀective solution for highly delayed control

systems is the adaptive Smith Predictor (Figure 11).

This approach is based on the analysis of network

information to enhance the performance and stability

of the system. The adaptive Smith Predictor can

utilize network information to adjust and optimize the

prediction delay accordingly.

Fig. 12: Adaptive Smith Predictors for PLC Control

6 Conclusion

This paper concludes that control systems with

dominant delays can only be controlled to a limited

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extent by simple feedback controllers. For high

performance or large relative dead times, a predictive

control strategy is required. For this purpose, a Smith

Predictor and a GPC were developed. The Smith

Predictor acts as an eﬀective dead time compensator

for processes with long dead times, providing

excellent prediction and compensation capabilities.

A comparison between classical controller and Smith

Predictor demonstrates the superiority of the latter for

long dead times. Furthermore, the GPC surpasses

both the Smith Predictor and the classical controller

in terms of control quality and disturbance rejection,

owing to its precise output prediction and optimized

control. The implementation of both approaches in

networked PLC controllers, as depicted in Figure

12, shows that the Smith Predictor exhibits stable

behavior with varying dead times. To enhance

its stability and performance with highly varying

delays, an adaptive Smith Predictor was developed,

which evaluates network information and adjusts the

prediction delay accordingly. Within this framework,

the adaptive Smith Predictor yielded signiﬁcant

control quality.

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Contribution of Individual Authors to the

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Policy)

The authors equally contributed in the present

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problem to the ﬁnal ﬁndings and solution.

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Conﬂict of Interest

The authors have no conﬂicts of interest to declare

that are relevant to the content of this article.

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