Delays and Networked Control Systems

Delays and Networked Control Systems
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The methodologies have been formulated based on several types of network behaviors and configurations in conjunction with different ways to treat the delay Yang, The concepts of one of these methodologies called Sampling Time Scheduling STS , to achieve optimization and communication performance in a CAN networked control system, were chosen to be applied in the case study presented in this paper.

As described in Hong , the STS methodology is used to appropriately select a sampling time for the devices of a distributed control system such that network delays do not significantly affect the control system performance and the system remains stable. This methodology was originally developed for multiple systems on a periodic delay network.

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The STS methodology defines the number of electronic control units on the network as M. The sampling times of all M devices on the network can be calculated from the sampling time of the most sensitive device based on the analysis of its worst-case delay bound. The STS methodology is formulated from the window concept illustrated in Fig.

The sampling time T 1 is computed from Eq. As described in the methodology, the other devices on the same network have to be indexed from the worst-case delay of the systems in an ascending order as ECU2 , The sampling times of ECU2 , In a generic case, all other sampling times are multiples of T1 as expressed by Eq. In addition, with the correct definition of the sampling times values of the devices, the optimality operation of the network can be achieved by this methodology, which is an advantage over other methodologies Tipsuwan and Chow, ; Li and Fang, The condition for this optimality is given by Eq.

According to Hong , the condition for optimality, in Eq.

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In this optimum condition, the network utilization is increased and the idleness is reduced without violating the messages timing requirements or deadlines. On the other hand, if the number of messages to be transmitted exceeds r, the messages miss their deadlines and the network becomes overloaded. This situation causes overlapping and loss of messages on the network.

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This edited monograph includes state-of-the-art contributions on continuous time dynamical networks with delays. The book is divided into four parts. The first. The purpose of this paper is to provide a complete diagnostic profile of the role of delays in networked control systems (NCS). It analyzes the impact of d.

For a NCS, performance is a function not only of the messages sampling times, but also of the traffic load on the network. In a network, as the sampling times decrease, performance improves until network saturation is reached. The proposal of this case study is to use the CAN mathematical model systemized to calculate the required data for the application of the STS methodology presented. The STS methodology will be used for the optimization of a CAN-based network applied to the control of a mobile robot.

The main idea is to ensure the correct choice of all the messages sampling times of the robot devices to achieve the largest possible value of the CAN network utilization and to obtain a good communication performance minimizing the network idleness for the CAN-based distributed control system studied. Characteristics of the Robot Control Network. In this section, network parameters are defined for the CAN-based network used for the distributed control of the mobile robot showed in Fig. The Fig. In applications of CAN-based networks, the electronic system that provides the interconnection between a device and the communication network is commonly called by electronic control unit ECU.

A set of messages is proposed in Table 1 referred to the devices connected to the CAN bus in the robot of Fig. Description of the Optimization Process. The data presented in Table 1 is used as data input for the mathematical model systemized for the CAN network. The mathematical model was implemented in a computational program more detailed described in Godoy This implementation represents one useful task that ease the analysis of the output data obtained with the utilization of the model systemized.

With the required data obtained by the use of the simulation software, the application of the STS methodology completes the optimization process for the control network analyzed. The flowchart of Fig. Based on the flowchart of Fig. With the application of the computational program, the output data of the bus utilization rates and time delays can be analyzed to verify the optimization possibility for the system. If the value for the CAN bus utilization is too low and the temporal requirement of the messages are satisfied, then the control system can be optimized the temporal requirement demands that the time delay of the messages be smaller than its message sampling time.

In this case, the network presents high level of idleness and the messages sampling times were not chosen correctly. Thus, in accordance with the STS methodology, an increase or decrease in the values of these messages sampling times can be achieved for the optimization of the CAN network.

SIAM Journal on Control and Optimization

With the optimization, the largest possible value for the bus utilization rate is achieved without problems to the system. Results and Discussions. The first results obtained with the input data in Table 1 for the mathematical model program Godoy, are shown in Table 2 for the mobile robot control. The results of Table 2 show that the value of the bus utilization rates is too low and the network presents high level of idleness. Slower values selected to the sampling times, before Point 1 in the diagram of Fig.

Thus, as described in the STS methodology, an increase in values for the messages sampling times can be achieved. Now, to demonstrate the utilization of the STS methodology and the optimization of the CAN-based network proposed in the case study, other applications columns 1, 2, 3 in Table 3 of the computational program are done with the correct input data values. The results in columns 1 and 2 of Table 3 represent two attempts to optimize the control system without the use of a control methodology, manually selecting other sampling times to the ECUs in the CAN bus.

These messages will not be transmitted in the CAN network harming the operation of the robot because, for example, the propulsion and guidance engines 3, which are commanded by messages 9 and 11, will not be controlled. This fact causes overlapping, saturation of the network and loss of messages on the CAN bus. In addition, an unacceptable performance for the control system is achieved with these faster values selected to the sampling times, after Point 2 in the diagram of Fig.


To correct this problem, the devices sampling times have to be chosen in agreement with the STS control methodology presented. The correct selection of the sampling times, with values between Points 1 and 2 in the diagram of Fig. Thus, the final parameters and the results obtained are shown in the column 3 of Table 3. This fact can be explained because of the time requirements related to the hardware of these devices, that imposes a minimum possible value for each sampling time for example the minimum sampling time of the compass is ms.

The sampling times selected in Table 3 represent these minimum values. The condition for the optimality presented in Eq. The little difference between the results can be explained by the sampling times of the ECUs 5, 6 and 7 that cannot be selected as defined in the STS methodology. The correct definition of the messages sampling times for the CAN-based control system, according to the methodology, are that network delays do not significantly affect the control system performance and the CAN-based system remains stable.

Due to the difficulties encountered with the determination of performance parameters such as transmission times, time delays, message sampling times and network utilization rates, predict the behavior of distributed control networks can be a challenging work. Since the behavior of NCS is determined by these design parameters, assigning the messages sampling times and calculating the network delays are important issues in NCS development. In addition, the network time delays can degrade the control performance and destabilize the NCS.

To control this problem, an application of a network methodology is required to diminish the network delay effect and to maintain the performance and stability of these systems. The detailed timing analysis presented and the mathematical model systemized to calculate performance parameters can provide information about the performance and operational behavior of CAN-based distributed control system and should be useful for designers of NCS.

The computational implementation of the CAN mathematical model systemized simplifies the determination of the network parameters and the performance analysis tasks of NCS, generating the required data and allowing the application of the selected sampling time scheduling STS methodology. The STS methodology was applied in a case study for the design of an embedded CAN-based network in a mobile robot to obtain an optimized configuration for the operation of the distributed system.

The results show that the optimization of the CAN-based system proposed in the case study can be achieved and the sampling times of the messages were chosen correctly. This condition is that network delays in the distributed communication system do not significantly affect the control system and ensure a better operational performance network utilization increased and idleness minimized for the CAN-based distributed control system. Al-Hammouri, A. S and Liberatore, V. Almutairi, N. Baillieul, J. Bosch, , "CAN 2. Cervin, A. Davis, R.

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source Tipsuwan, Y. Yang, T. Paper accepted February, Technical Editor: Glauco A. All the contents of this journal, except where otherwise noted, is licensed under a Creative Commons Attribution License. Services on Demand Journal. Analysis of CAN-Based Networks As described in Farsi, Ratcliff and Barbosa , CAN is a serial communication protocol developed mainly for applications in the automotive industry, but is also capable of offering good performance in other time-critical industrial applications.