Abstract
The focus of this work is on dynamical systems that are controlled over a
communication network, also denoted as Networked Control Systems (NCSs).
Such systems consist of a continuous-time plant and a discrete-time controller
that are connected via a communication network, such as e.g. controller area
network (CAN), wireless networks, or internet. Advantages of the use of such
a network are a reduction of installation and maintenance costs and a flexible
architecture. The reduction of the costs is achieved by using one (shared)
processor to control multiple plants, instead of using dedicated processors for
each plant. Adding or removing plants or controllers to the network is easy,
which explains the benefit in terms of a flexible architecture of the control system.
Moreover, the use of wireless networks obviously allows to separate the
controller and plant physically. Typical applications of NCSs are mobile sensor
networks, remote surgery, automated highway systems, and the cooperative
control of unmanned aerial vehicles. Disadvantages of the use of such networks
are the occurrence of time-varying delays, time-varying sampling intervals, and
packet dropouts, i.e. loss of data. Moreover, time-varying sampling intervals
and delays may also result from other sources than the communication network.
Namely, in many high-tech embedded systems, the processor is used for
both the control computation and other software tasks, such as interrupt and
error handling. This leads to variation in the computation time or variation in
the moment of asking for new sensor data, resulting in variable sampling intervals.
The amount of variation depends on the chosen software implementation,
the chosen architecture, and the processor load. A control design that can deal
with the variation in the time-delays, sampling intervals, and the occurrence
of packet dropout is important for the multidisciplinary design of high-tech
systems. Namely, such robustness properties of the control design represent a
relaxation on the demands from control engineering on the software and communication
network design.
In this thesis, a discrete-time model for linear NCSs is derived that considers
time-varying delays, time-varying sampling intervals, and packet dropouts.
Based on this model, examples of the destabilizing effect of variations in the
delay and variations in the sampling intervals are given to show the necessity of
stability conditions that consider the effects of time-varying delays, time-varying
sampling intervals, and packet dropouts. To derive such stability conditions, upper
and lower bounds of time-varying delays and sampling intervals are assumed,
as well as a maximum number for the subsequent packet dropouts. Based on
these assumptions, sufficient conditions in terms of linear matrix inequalities
(LMIs) are derived that guarantee global asymptotic stability of the NCS. Two
different control strategies, i.e. state feedback control and state-feedback control
including past control input information are considered. For both control
approaches, conditions in terms of LMIs are given for the controller synthesis
problem and a comparison of the applicability of both control approaches is
made. Besides the stability analysis and controller synthesis conditions, the
intersample behavior is investigated to ensure stability of the continuous-time
system between the sampling instants. An extension to the stability analysis
conditions is given that can be used to solve the approximate tracking problem
for NCSs with time-varying delays and sampling intervals and packet dropouts.
Only approximate tracking can be achieved because the time-varying delays,
sampling intervals, packet dropouts, and the use of a zero-order hold between
the controller and actuator cause an inexact feedforward, which induces a perturbation
on the tracking error dynamics. Sufficient conditions for the input-tostate
stability of the tracking error dynamics are provided and an upper bound
for the tracking error is given as a function of the plant properties, the control
design, and the bounds on the delays, the sampling interval and the number of
subsequent packet dropouts.
To validate the obtained stability and controller synthesis conditions experiments
are performed on a typical motion control example. First, measurements
are performed to validate the stability region, i.e. all stabilizing controllers, for
constant time-delays. Second, the destabilizing effect of time-variation of the
delays is shown in experiments. Third, the obtained stabilizing controllers for
time-varying delays, with constant sampling intervals are validated. A comparison
between the stability regions for constant delays and time-varying delays
shows that the stability conditions developed in this thesis are not overly conservative.
The delay combinations that result in instability in the measurements
confirm this observation.
Original language | English |
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Qualification | Doctor of Philosophy |
Awarding Institution |
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Supervisors/Advisors |
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Award date | 25 Jun 2008 |
Place of Publication | Eindhoven |
Publisher | |
Print ISBNs | 978-90-386-1304-8 |
DOIs | |
Publication status | Published - 2008 |