A Time Delay System Case Study: Computer Integrated
Manufacturing and Management System Robustness
Jozef B. Lewoc*, Antoni Izworski** Slawomir Skowronski***
*BPBiT Leader (Leading Designer), ul Powst. Sl. 193/28, 53-138 Wroclaw, Poland **Wroclaw University of Technology, Wyb. Wyspianskiego 27, 50-370 Wroclaw, Poland ***Wroclaw University of Technology, Wyb. Wyspianskiego 27, 50-370 Wroclaw, Poland
Abstract: There is no commonly accepted approach to selection of a topology of a computer integrated
manufacturing and/or management system. The basic decisions are undertaken basing on the liking of some available hardware, without any consideration paid to any characteristics of the topology. The paper proposes selection of the topology basing on the system robustness comparison, using the μ function as the measure of robustness. Due to the fact that the systems are of the time delay character, calculation of μ is rather simple and the method may be used rather easily to solve the actual design problems. Copyright
IFAC 2009Keywords: Automatic control, manufacturing systems, management systems, computer integrated enterprises, communication systems, time delay systems, robustness, singularity.
1. INTRODUCTION
The problem of the communication media (communication network) topology in distributed control/monitoring systems (e.g. those applied in control and monitoring of the working media in large-scale manufacturing enterprises) is usually solved in a rather arbitrary way. The common opinion is that some kinds of standard local-area networks of the common-medium type, like Ethernet (Cisco Systems, 2006; NSF, 2002) are the best possible solution. Considering that such approach is highly inappropriate, some trials were made to select computer automation system topologies basing on their robustness. The first case study attempt was connected with a computer-based monitor of a big thermal power plant (Izworski 1991a, Izworski 1991b). When designing a novel computer integrated manufacturing and management system based on the Media subsystem (Franasik, 2001, Izworski 2006, Lewoc 2006), it was decided to use robustness (in the sense of automatic control (Doyle, 1982) and not of Artificial Intelligence (AUAI, 2002; Cozman, 1997)), and apply the very basic robustness measure, the μ function defined first by Doyle (1982).
The basic results of the very first case study performed for the Computer Integrated Manufacturing and Management (CIMM) systems (systems Media) were also published (Izworski 2003a,b). The authors of the case studies mentioned hereinabove thought it can be useful to present some more general case of a computer automation system of topology selected on the basis of its robustness. However, the software tools developed for the case study enabled to conduct some more general work: to compare working media control/manufacturing systems of various topologies but intended to provide the same services.
The subject of the investigations are the systems intended to monitor and control such variables as the working media (such as the electric power, fuel gas, solid and liquid fuels, cold and hot water, process steam, waste water, waste gas, etc.) (the Systems). After Doyle (1982), the structured singular value for the compensated plant subject to structured perturbations is used to analyse the robustness of the performance of such plant. Such approach has enabled to make comparisons of the Systems of different topologies on some rational basis in contrast to the arbitrary selections made by most computer system designers.
Such approach is hardly feasible for general automatic control systems because of very severe computational problems connected with accurate computation or even with approximation of µ (Fu, 1997). However, since the CIMM systems under investigation may be analysed as time delay systems, the approach is feasible and may be useful.
The paper presents some plots of the robustness measure adopted, the μ function, versus the data transfer cycle time. In accordance with the expectations, the “obsolete” star topology features with much higher robustness values in comparison with the “common-medium” (ring or bus) topology, at least when the fair comparison conditions are applied.
2. CONFIGURATION OF THE SYSTEM
Assuming that the variables in a manufacturing enterprise cover those mentioned in the Introduction of the presented paper, the schematic functional structure of the System may be presented as in Fig. 1. The problem is in how to interconnect the controllers dedicated to monitoring and control of individual variables and the higher level control and monitoring system providing services to the Automation
Department and inter-working with the Computer Integrated Management system of the enterprise since the System should be recognised as needing co-operation with future Computer Integrated Manufacturing and Management systems (Franasik, 2001, Izworski 2006, Lewoc 2006).
Actually, from the point of view of data transmission and robustness implied by that, there are two possible general arrangements of the communication system interconnecting
the individual controllers and the control and monitoring system: the star arrangement where all controllers are interconnected with the higher level system via individual transmission links (lines) and may interchange data with the computer almost simultaneously (in the macro time) (see Fig. 2), and the common-medium data network arrangement (see Fig. 3). The latter arrangement may be a bus with polling (e.g. RS 485, Modbus, Token Bus) or a ring (e.g. Ethernet, Token Ring, Proway).
TO COMPUTER NETWORK
OF THE ENTERPRISE
VISUALISATION
REPORT
PLANT UNDER MONITORING
COMMUNI-CATIONS &
MONITOR-ING
SYSTEM
Controller Variable 1 Controller Variable 2 Controller Variable 3 Controller Variable 4 Controller Variable 5 Controller Variable 6 Controller Variable Controller Variable nFig. 1. Architecture of the System
High level
system
Controller
1
Controller
n
...
Fig. 2. The System of the star topology
High level
system
Controller
1
Controller
n
...
3. THE MODELS
For the star topology case, the model of the control/monitoring loop is shown in Fig. 4.
z
nz
1...
G
SG
S,1G
S,nFig. 4. Basic diagram for the star topology
Considering the fact, that the Automation Department (included in the transfer function G(s)) is able to observe and act on a limited set of the components of the zk vectors at one time, it is possible to avoid analysing a high number of variables (exceeding several thousand entities for big enterprises (e.g. power plants)).
It may be assumed that all transfer functions GS,1, … GS,n are of the pure time delay character (the communication system introduces nothing else than time delays, being a pure time delay system; possible transmission errors may be thought about as some system failures needing separate analysis). The disturbance matrix is given by (1):
n i d s Sdiag
e
i i 1 ) (
(1) where dj is a multiplicative disturbance of the time delay type.For the common-medium arrangement case, the control loop diagram is shown in Fig. 5 and the equivalent diagram in Fig. 6.
...
...
Zn Z1...
GS __ G R,1 __ G R,1 __ G R,nFig. 5. The common-medium arrangement: Basic diagram
In this case, the disturbance matrix is given by formula (2). n i d T s R i m m m
e
diag
1 1
(2) In either case, a simple transfer function G(s) meeting the demand for stability defined by Doyle (1982) is adopted. When a simple integrating type action of the plant is assumed in conformity with actual applications in any Automation Departments, G(s) may be given by the formula (3):
k i i R k RG
k
k
n
G
1 , ,;
1
;
1
,...,
(3) zn z1...
G S G R,1 G R,nFig. 6. The common-medium case: The equivalent diagram
According to Doyle (1982) and Ferreres (1999), the structured singular value is defined by formulae (4) and (5) for the star arrangement case and the common-medium case, respectively.
1 ,.., 1)
det
:
cos
1
2
min
(
)
(
0
1
S i i n i SG
t
G
(4)
1 1 ,.., 1)
det
:
cos
1
2
min
(
)
(
0
1
R i m m i n i CMG
T
t
i
G
(5)The value of ω is derived, in either case, from the condition that ω = π/2ti. To derive the formulae (4) and (5), it was assumed (in conformity with actual applications) that di = d, i = 1,…,n.
4. ROBUSTNESS EVALUATION 4.1. Assumptions concerning transmission delays
To ensure fair comparisons, it was assumed that the data entities transmitted via the communication network have the same data field lengths (1 KB) while the overall data entity lengths (including data and control information) are
defined by relevant data transmission protocols. This means, that for the star arrangement case, the asynchronous transfer mode (one start bit, one stop bit and 1 parity bit for each 8-bit byte plus two bytes for longitudinal check sum) is assumed while two synchronising octets (flags), ca 10% for bit stuffing (insertion/deletion of 0 after a series of five 1’s, to enable detection of flags) plus 32 bits for the redundancy check + 4 control octets are assumed for the common-medium arrangement.
4.2. Robustness evaluation cases
Case 1. This case provides the “fair” comparison of
robustness for the two communication network arrangement cases. The μ values (μS for the star arrangement and μCM for the common-medium arrangement) versus the data transfer rate r are presented in Figs. 7, 8 and 9, for n = 2, 4 and 8, respectively.
r
CM
SFig. 7. μ values versus transmission rate. “Fair” comparison. n = 2.
r
CM
SFig. 8. μ values versus transmission rate. “Fair” comparison. n =4.
Within the full transmission rate range investigated, the star arrangement was much better in the sense of robustness than the common-medium arrangement.
Case 2. In this case, it was assumed that the
common-medium arrangement operated at the transmission speed of 10 Mb/second and the transmission rate in the star arrangement was changed in the region of several orders of magnitude lower. The plots of μS versus transmission rate r and μCM (constant value) are shown in Fig. 10.
Sr
CMFig. 9. μ values versus transmission rate. “Fair” comparison. n =8.
r
CM(r=10
7b/s)
SFig. 10. μS values versus low transmission rates; μCM = constant.
The star arrangement operating at rather low transmission rates (several Kb/second) is more robust than the common-mode competitor operating at 10 Mb/second (and even at higher transmission rates). This means, in practice, another improvement in robustness due to the possibility to employ communication equipment operating at lower transmission rates, that, at least in theory, should have intrinsically higher hardware robustness.
The lower limit of the permissible transmission rate is defined, of course, by the requirements of the application for the time resolution. Nevertheless, in real Working Media Engineers’ Departments, the requirements are not too severe. Therefore, it is feasible to employ low or medium transmission rate equipment.
5. CONCLUSIONS
For distributed computer control and monitoring systems similar to the system Media described, the star arrangement is much more robust than the common-medium one, when the “fair” comparison conditions are applied.
For the typical number of controllers installed, the star arrangement operating at the transmission rate of several thousand baud is more robust than the corresponding common-medium arrangement operating at 10 Mb/second or at even higher transmission rates.
In spite of that it is rather difficult to the compute or even approximate the μ function (Fu, 1997; Ferreres, 1999), the robustness evaluation methods based on the very initial robustness measure, the μ function defined already by Doyle (1989), seams to be an interesting option for designing the topology of distributed control systems similar to the system Media, which are time delay systems. The basic reason for that is the fact that for systems constituted of pure time delay components, as is the case for topology of computer systems, it is not needed to find eigen-values since on the unitary circle, all values are eigen-values. Therefore, the calculations needed to evaluate robustness are simple and straightforward (actually, the HP calculator was the only computing tool needed to conduct all calculations for this paper).
Thus, due to the inherent simplicity, the method enables really to eliminate the methods used in actual practice, that are rather arbitrary or, in the best case, supported entirely on the system availability and individual preferences of the system designers.
The results obtained for the case studies for the power plant monitor (Izworski 1991a,b) and the Computer Integrated Manufacturing and Management systems (Izworski 2006, Lewoc 2006) may be rather easily transferred to more general computer automation systems. This is implied, mainly, by the fact that the same or similar communication systems are of influence on the data transmission processes and, consequently, on robustness of the system under investigation.
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