Analysis and design of networked control loops with synchronization at the actuation instants

Abstract

Varying time delays prevent successful operation of control loops closed over communication networks, i.e. networked 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 operation 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).

Full text

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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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