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Analysis and design of networked control loops

with synchronization at the actuation instants

Camilo Lozoya, Pau Mart´ ı, Manel Velasco and Josep M. Fuertes

Automatic Control Department

Technical University of Catalonia

Pau Gargallo 5, 08028 Barcelona, Spain

Email:{camilo.lozoya, pau.marti, manel.velasco, josep.m.fuertes}@upc.edu

Abstract—Varying time delays prevent successful operation

of control loops closed over communication networks, i.e. net-

worked control system (NCS). To mitigate the negative effects

of delays, existing research mainly focuses on deriving control

approaches/solutions built upon the assumption that the opera-

tion of control loops is synchronized at the sampling instants.

In this paper we propose an approach to design networked

control systems with synchronization at the actuation instants.

The immediate benefit is that the harmful effects that delays

within control loops have in stability/performance are removed.

However, the application of the proposed solution requires

accurate clock synchronization among the network nodes. This

requirement is discussed and analyzed for the specific case of

NCS based on the Controller Area Network (CAN).

I. INTRODUCTION

Control loops that are closed over communication networks

are known as networked control systems (NCS) [6]. In these

systems, control nodes such sensors, controllers and actuators

exchange the physically distributed control data through net-

works. The network is a fundamental component supporting

all the interactions among the nodes. The purpose of the

network is to deliver control messages in a reliable, secure,

efficient and timeliness fashion. For NCS, timeliness becomes

the most critical aspect because (varying) time delays prevent

the successful operation of the networked control loops [18].

To mitigate the negative effects of delays, existing research

(see [4] and [10] for surveys of recent results in NCS) mainly

focuses on deriving control approaches/solutionsbuilt upon the

assumption that the operation of control loops is synchronized

at the sampling instants. That is, the mathematical control

models that are used for analysis and design of controllers

assume periodic sampling. In addition, some of them treat time

delays as constant time intervals relative to sampling instants.

Therefore, if delays are time varying, simple control models

can not be applied.

In this paper we propose an approach to design networked

control systems where the key aspect is that all the control

operations are synchronized toward the actuation instants.

Rather than assuming periodic sampling, our approach de-

mands periodic actuation. Therefore, consecutive actuation

instants mark the sampling period. For a networked control

loop, the control operation is summarized as follows. After the

beginning of the sampling period, the plant must be sampled.

The sample is then sent to the controller, which executes the

control algorithm. Afterward, the control command is sent to

the actuator, that will apply it to the plant at the synchronized

actuation instant.

The benefit of this approach is that the harmful effects that

delays within control loops have in stability/performance are

removed if the controller is designed according to these new

operation rules. Note also that samples are not required to be

periodic. This also facilitates the implementation of control

systems where sampling periods are not constant such as in

the case of feedback scheduling approaches [13], or event-

based control systems [3].

However, the application of the proposed solution base

its operation on absolute time measurements, and therefore

requires accurate clock synchronization among the networked

nodes. Taking advantage of the IEEE1588 Precision Time Pro-

tocol (PTP) [12] standard, clock synchronizationis guaranteed.

This requirement is discussed and analyzed for the specific

case of NCS based on the Controller Area Network (CAN [5]).

The experimental results on clock synchronization, and the

simulation results of the operation of the control algorithm

synchronized at the actuation instants in NCS corroborate the

feasibility and effectiveness of the proposed approach.

The rest of this paper is structured as follows. Section II

introduces the preliminaries on NCS. Section III presents the

control theoretical aspects and the distributed control algorithm

of the design approach to networked control systems with

synchronization at the actuation instants. Section IV discuses

and analyzes clock synchronization issues and its application

to CAN. Sections V and VI describe the simulation setup and

results. Finally, section VII concludes the paper.

II. PRELIMINARIES

A. Networked control systems architecture

A common architecture for a single control loop in a NCS

is shown in Fig. 1, where sensor, controller and actuator nodes

exchange data via network messaging. Sending a message over

a network takes time. Therefore, for NCS, time delays are

introduced within each control loop. Mainly, three time delays

can be identified: delay between the sensor and the controller,

τsc, delay in the controller, τc, and delay between the controller

and the actuator, τca. The accumulated input/output (I/O) time

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Actuator

node

Process

Sensor

node

Controller

node

Network

h

τsc

k

τca

k

τc

k

u(t)

y(t)

Fig. 1.Common architecture for NCS

delay within each sampling period h is given by

τ = τsc+ τc+ τca,

(1)

where τsc and τca depends on the communication network,

and τc on the controller algorithm and processing node. In

this simple characterization we have assumed that sensing and

actuation operations do not add significant timing overhead

compared to (1). However, if their overhead is not negligible,

they can be added to the network delays.

B. Underlying control model

The common approach to computer/networked control sys-

tems design has two steps. The first step is to obtain a discrete-

time model of the plant. The second step is to design a

discrete-time control law for the discrete-time plant model.

The traditional design approach mandates to periodically sam-

ple and actuate.

Consider the traditional mathematical description of a plant

given by the state-space model of a linear time-invariant

discrete-time system with sampling period h [2]

xk+1

=

=

Φ(h)xk+ Γ(h)uk

Cxk,yk

(2)

where xk is the plant state, uk and yk are the inputs and

outputs of the plant, matrix C ∈ Rp×nis the output matrix,

and matrices Φ(t) and Γ(t) are obtained using

Φ(t) = eAt,

Γ(t) =?t

0eAsBds,

(3)

with t = h, where A ∈ Rn×nand B ∈ Rn×mare the system

and input matrices of the continuous-time form

dx(t)

dt

y(t)

=

=

Ax(t) + Bu(t)

Cx(t).

(4)

For standard closed-loop operation of (2), the control com-

mand ukis given by

uk= Lxk

with L ∈ R1×n,

(5)

where L is the state feedback gain obtained using standard

control design methods from matrices Φ(h) and Γ(h).

The application of (5) to the plant mandates computing the

control command with zero time. This is physically impossi-

ble even for a processor-based closed-loop systems because

executing the control algorithm takes time.

Model (2) can be augmented to cope with a time delay

modeling an I/O latency that appears due to the computation

of the control algorithm or due to the insertion of a network

within a control loop, as in the case of NCS. The standard

model that incorporates a time delay τ, with τ ≤ h, is [2]

xk+1= Φ(h)xk+ Φ(h − τ)Γ(τ)uk−1+ Γ(h − τ)uk.

(6)

Model (6) has been often taken as the underlying simple

control model for design and analysis of NCS. This model

assumes a time reference given by the sampling instants with

a fixed time delay from sampling to actuation.

C. Discussion

The key aspect of the design procedure is that model (6)

describes the behavior of the analog plant at the sampling

instants. Moreover, the actuation instants are defined in terms

of the sampling instants. Therefore, the synchronism is given

by the sampling instants. Once a sample is taken, the control

command is computed assuming that the next sample will

occur after h time units (i.e., one sampling period), and

assuming that the actuation will occur after τ time units (i.e.,

one time delay). The operation of this model is usually violated

in networked control loops because varying time delay insert

time unpredictability from sampling to actuation.

To overcome this problem, [14] presented an approach to

NCS where controller and actuator are physically collocated in

the same node. This permits by using time-stamp techniques to

compute the correct control command regardless of the varying

I/O delays. The limitation is the assumption that controller

and actuator are in the same node. A more sophisticated

approach is found in [11] where in a NCS fully distributed, the

controller node computes several control commands that are

sent to the actuator node. The latter, applies to the plant the

adequate one according to time-stamps logics. This approach

however increases network traffic and computation overhead.

Alternatively, in [9] the use of synchronized I/O operations is

proposed. Although this solution removes the time variability,

in forces artificial input-output latencies within the loop.

Rather than using solutions based on (6), we propose to use

an equivalent model but synchronized at the actuation instants.

The analysis presented next extends previous work [15], which

was earlier suggested in [1], where a mathematical control

model with synchronization at the actuation instants was

presented. This model establishes new operation rules for

control algorithms. The extension presented in this paper relies

on analyzing if this model can be applied to NCS. That

is, we analyze which requirements this model imposes to

NCS, we show its feasibility, and we provide details on its

implementation.

III. NCS WITH SYNCHRONIZATION AT THE ACTUATION

INSTANT

A. Control model

We synchronize the operation of each control loop at the ac-

tuation instants. Hence, the time elapsed between consecutive

actuation instants, named tk−1and tk, is the sampling period,

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Fig. 2.Operation of the distributed control algorithm

h. Within this time interval, the system state is sampled, named

xs,k ∈ (tk−1,tk), and the sampling time recorded, ts,k. The

difference between this time and the next actuation time

τk= tk− ts,k

(7)

is used to estimate the state at the actuation instant as

ˆ xk= Φ(τk)xs,k+ Γ(τk)uk−1.

(8)

Finally, making use of ˆ xk, the control command is computed

as

uk= Lˆ xk

with L ∈ R1×n

(9)

where L is the original controller gain as in (5). The control

command ukis held constant within actuation instants.

A control strategy using (7)-(9) relies on the time reference

given by the actuation instants, if uk is applied to the plant

by hardware interrupts. In addition, samples are not required

to be periodic because τkin (7) can vary at each closed-loop

operation. The interested reader is referred to [15] for further

reading on this control model.

B. Distributed control algorithm

The operation of a distributed control algorithm based on

(7)-(9) relies on distributed absolute time measurements and

control messages, as illustrated in Figure 2. Grey boxes with

A, S, or C represent the execution of the code in the actuator,

sensor or controller, respectively. And grey boxes with 1, 2,

or 3 represent the three messages required at each closed loop

operation.

At each actuation, the actuator node, after applying to

the plant the control signal, e.g. uk−1, generates the next

actuation instant tk, which is sent to the sensor (message

1). The sensor, upon reception of this message, samples the

plant xs,k and records the absolute sampling time ts,k. The

latter, together with tk is used to compute τk. Both xs,k

and τk are sent (message 2) to the controller node. Upon

reception of this message, the controller node estimates the

plant state that will apply at tk, eq. (8), and computes the

control command uk, eq. (9). The latter is sent to the actuator

(message 3), that will apply it to the plant at the synchronized

(e.g., by hardware interrupt) actuation instant. The pseudo-

code required to execute a networked control loop using the

presented algorithm is shown in Figure 3.

Algorithm 1: Sensor Node - Triggered by a message

begin

while (no message(from my actuator)) do nothing

tk:= read message()

(xs,k,ts,k) := read input with time stamp()

τk:= tk− ts,k

send message(to controller,xs,k,τk)

end

Algorithm 2: Controller Node - Triggered by a message

begin

while (no message(from my sensor)) do nothing

(xs,k,τk) := read message()

ˆ xk:= Φ(τk)xs,k+ Γ(τk)uk−1

uk:= Lˆ xk

uk−1:= uk

send message(to actuator,uk)

end

Algorithm 3: Actuator Node - Synchronized by h

begin

while (no message(from my controller)) do nothing

uk:= read message()

wait for actuation interrupt

send output(uk)

tk:= tk+ h

send message(to my sensor,tk)

end

Fig. 3. Sensor, controller and actuator nodes pseudo-code

IV. FEASIBILITY ANALYSIS

Time measurements and messaging become crucial for

the successful operation of the distributed control algorithm.

Therefore, clock synchronization and network scheduling are

key aspects.

A. Clock synchronization

In our NCS based on CAN, we assume that nodes are

synchronized using the IEEE 1588 PTP protocol. The protocol

synchronizes slaves’ clocks to a master clock ensuring that

events and time-stamps in all devices use the same time base.

To corroborate the correctness of this assumption, we briefly

describe the implementation of the PTP protocol using low-

cost CAN-enabled microcontrollers connected via CAN. The

targeted clock precision is in the order of sub-milliseconds,

being enough for many control applications. The interested

reader is referred to [16] for further information.

In our distributed system, although any node could play as

a master (in terms of clock synchronization), we implemented

the master in the controller node. This permits to have sensor

and actuator nodes perfectly synchronized because synchro-

nization messages will arrive at both nodes within the same

bit time, as mandated by CAN. Remember that these nodes

are the ones that perform absolute time measurements.

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Fig. 4.Experimental set-up and synchronization results

Figure 4 shows the hardware set-up (top) and part of the

experimental results (bottom). In the set-up we used two CCS

CAN prototype boards1connected through CAN. Each board

itself has four nodes connected via CAN. The first node is

a PIC18F4580 which includes an integrated CAN peripheral.

The second node is a PIC16F876A connected to an MCP2510,

an external CAN peripheral which is connected to a micro-

controller over SPI. Both nodes are connected to a 20MHz

oscillator. The last two nodes, which have not been used in our

experiments, are MCP25050s, stand-alone CAN expanders.

In particular, one PIC18F in one board plays the master

clock role, and PIC18F and PIC16F in the other board play

as slaves. The bus speed was set to 125Kbps. The real-time

clock maintained in each node had a resolution of 0.1ms. After

the application of the PTP protocol, the time in the master

and in one of the slaves was read, and displayed in PC-based

monitors.

In Figure 4 both monitors show the same type of informa-

tion. On the left of each monitor, they show the PC time, which

is a time stamp feature provided by the monitor. Then, after the

arrow, and starting by Master time or Slave time, it is displayed

the read time. The time is displayed in d:h:min:sec:ms:ms:µs.

1https://www.ccsinfo.com/.

In fact, microseconds (µs) are not shown, but their hundreds.

As it can be seen both clocks mark the same time, and the

achieved synchronization is of the order of 0.1ms.

B. Schedulability issues

At this stage we assume that each node executes the single

code illustrated in Fig. 3. However, the application of the

proposed algorithm can perfectly operate on multi-task nodes.

This simplification permits us to focus on the messaging.

Figure 2 illustrates that messages latencies can vary as long

as actuation is synchronized at the expected times, and all

required operations occur within each period h. In addition,

the implementation of the clock synchronization adds control

messages in the network.

The CAN protocol specifies that the identifier with the

lowest binary number has the highest priority. Bus access

conflicts are resolved by arbitration of the identifiers. Taking

into account these rules, the following guidelines for designing

feasible NCS including several control loops, all using the

presented algorithm, are as follows:

• Clock synchronization messages should have the highest

priorities

• All messages sent by actuator nodes should have the next

level of priorities. Recall that these messages trigger the

operation of each networked control loop.

• All messages sent by sensor nodes should have the next

level of priorities.

• Finally, all messages sent by controllers should have the

lower priorities.

These guidelines indicate that messages identifiers should be

coded using message classes, similar to the CAN application

profile for NCS presented in [17].

Looking at message schedulability, periods, deadlines and

offsets should be defined by each class of messages. Schedu-

lability should then be performed using existing results such

as [7]. Future work will cope with this problem.

V. SIMULATION SET-UP

A simulation set-up has been designed in order to evaluate

the presented algorithm. Simulations have been carried out

with the TrueTime simulator [8].

The controlled plant used in the simulations is a ball and

beam in the form of a double integrator. The plant is controlled

by a NCS composed by three nodes: sensor, controller and

actuator. The ball and beam state space description is

˙ x(t) =

?

0

0

1

0

?

x(t) +

?

0

1

?

u(t),

(10)

where the system output is x1, the ball position. The control

objective is to keep the ball position at zero coordinate,

regardless of the perturbations affecting the system.

Control performance is measured during each simulation

period (tsim) using a continuous standard quadratic cost

function

?tsim

0

J =

?xT(t)Qx(t) + uT(t)Ru(t)?dt.

(11)

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Rcv Snd

A/D

x’ = Ax + Bu

y = Cx + Du

Rcv SndRcvSnd

D/A Schd

Rcv1 Snd1 Rcv2 Snd2 Rcv3 Snd3

Network

Sensor

ControllerActuator

Plant

+

+

Pulse

Scheduler

Cost Function

Fig. 5. Simulation model

where the weighting matrices are specified as

Q =

?

1

0

0

1

?

andR = 1.

For simulation purposes, it is assumed that the plant states are

available and therefore there is no need for observers.

Control is achieved by a controller designed to place the

continuous closed loop poles at s1,2 = −2.0 ± 5.0i. The

discrete-time controller is obtained by standard pole place-

ment, considering an specific actuation period of h = 300ms.

The basic TrueTime simulation model is shown in Figure 5.

The three nodes (sensor, controller and actuator), implemented

using a TrueTime kernel, are connected to a TrueTime CAN

network block (configured at 125Kbps), in order to be able

to exchange messages. The perturbations are provided by a

programmable pulse element connected to the plant input.

Performance is measured from the plant output and repre-

sented as a cost function. Also it is important to notice, that in

order to provide synchronization at actuation instants, the only

periodic task to be executed is located in the actuator node. In

this distributed schema, each node executes the pseudo-code

presented in subsection III-B.

VI. SIMULATION RESULTS

This section summarizes the simulation results of the CAN-

based NCS using the presented control algorithm with syn-

chronization at the actuation instants. The simulations results

are divided in two groups. First, the algorithm is evaluated

considering a distributed system that presents variable network

induced time-delays. Then, the analysis focuses on the nega-

tive effects on control performance caused by the differences

in the time measurements if no perfect clock synchronization

is available among nodes.

A. NCS with time-delays

The objective of this set of simulations is to evaluate

the performance of the NCS with the presented algorithm

(eq. (7)-(9)) compared to the case where the control loop

is synchronized at the sampling instants and the controller

designed considering a constant time delay, i.e., the traditional

case, eq. (6). For the simulation, we have considered that each

control loop node presents timing variations caused by network

delays. To obtain comprehensive results, we have limited the

maximum value for timing variations to 20ms. For simulation

02468 1012

−0.5

−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

0.5

Position (m)

Time (s)

sampling synchronized model

actuation synchronized model

ideal response

Fig. 6.Ball and beam transient response

2468

Simulation Cycles

1012 14161820

0

20

40

60

80

100

120

Accumulative Cost

ideal response

actuation synchronized model

sampling synchronized model

Fig. 7.Accumulated control performance

purposes, an ideal response has been incorporated. The ideal

response considers no network delays, and an immediate

control response (controller execution time equals to zero),

as specified by (5). As shown in Fig. 6, the transient response

of the control loop using actuation synchronized model is very

close to the ideal response.

The accumulated control cost is reported in Fig. 7. The

control performance is measured by (11), and the simulation

is executed several times considering different perturbations

amplitudes and perturbations time-offsets. This explains why

the slops of the displayed curves is not constants. It is

important to remark that a lower cost represents a better con-

trol performance. The actuation synchronized model achieves

better control performance since the timing variations due to

network delays are absorbed by the underlying control model

and performance is therefore not seriously affected.

B. NCS with clock variations

The purpose of this set of simulations is to analyze the

impact on the operation of the presented control algorithm

(eq. (7)-(9)) when the time reference is different among sensor,

controller and actuator nodes.

Recall that the next actuation instant tk and the sampling

instant ts,kare obtained in different nodes (actuator and sensor

nodes respectively). If both internal clocks are not exactly

synchronized then the calculated τk used by the controller

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−90−60 −300 306090

0

1

2

3

4

5

6

7

8

9

10

Cost Function (J)

Clock offset (ms)

Network based

Processor based

Fig. 8. Control performance impact of de-synchronized clocks.

will not correspond to the actual τk. Let τkdenote the actual

value of the time elapsed from sampling to actuation, and ˆ τk

the expected elapsed time for perfectly synchronized clocks.

Different scenarios can be distinguished:

1) The expected time elapsed from sampling to actuation

equals the actual one, i.e. ˆ τk = τk. That is, all clocks

are perfectly synchronized.

2) The expected time elapsed from sampling to actuation is

greater or less than the actual one, i.e. ˆ τk> τkor ˆ τk<

τk. In this case, clocks are not perfectly synchronized.

These scenarios are evaluated in this set of simulations.

Figure 8 summarizes the results. A negative value in the x-axis

indicates that estimated value is greater than actual (ˆ τk> τk),

a positive value in the x-axis indicates that estimated value

is less than the actual (ˆ τk < τk), and the zero value in

the x-axis means that both values are equal (ˆ τk = τk). In

this set of simulations, the ideal control performance value,

named processor based, is the case of a processor-based

system, which contains a unique/centralized time reference.

Hence, no de-synchronization exists and its performance is

always the same. The best performance is achieved when the

estimated value equals the actual one, and the performance

degrades exponentially when the difference between these

values increases, independently if the difference is negative

or positive.

Note also that from Figure 8 we can conclude that for

this plant, having a clock synchronization between nodes with

a sub-millisecond precision is more that enough to ensure

correct operation of the distributed algorithm.

Finally we notice that the best performance in the NCS

equals the performance of the processor-based system. There-

fore, we can conclude that the negative effects of net-

work time delays on control performance are efficiently re-

moved/absorbed by the presented control algorithm.

VII. CONCLUSIONS

This paper has presented a novel control model for imple-

menting networked control loops whose messages are subject

to time varying delays. The key aspect of the proposed model

is that the control loop operation relies on synchronized

actuation instants. A detailed explanation of the distributed

control algorithm based on this new model has been given.

The operation of the control algorithm is based on absolute

time measurements. Therefore, clock synchronization becomes

very important. We have given experimental evidence that

clock synchronizationbetween networked nodes based on low-

cost microcontrollers can easily achieve a sub-millisecond

precision. Finally, simulation results have corroborated that

a) the preseted control approach to NCS removes the harmful

effects that varying time delays have in control performance

and b) the required clock synchronization can be in the order

of sub-milliseconds to ensure its successful operation.

Future work will focus on a more formal schedulability

analysis as well as on a prototype implementation of a NCS

making use of the presented control algorithm.

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