Control over communication networks : modeling, analysis, and synthesis

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.