Loop Pairing Analysis
Despite the availability of sophisticated methods for designing multivariable control systems, decentralized control remains dominant in industry applications, because of its simplicity in design and ease of implementation, tuning, and maintenance with le
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Despite the availability of sophisticated methods for designing multivariable control systems, decentralized control remains dominant in industry applications, because of its simplicity in design and ease of implementation, tuning, and maintenance with less cost [29, 30]: (i) Hardware simplicity: The cost of implementation of a decentralized control system is significantly lower than that of a centralized controller. A centralized control system for an n × n plant consists of n! individual single-input single-output transfer functions, which significantly increases the complexity of the controller hardware. Furthermore, if the controlled and/or manipulated variables are physically far apart, a full controller could require numerous expensive communication links. (ii) Design and tuning simplicity: Decentralized controllers involve far fewer parameters, resulting in a significant reduction in the time and cost of tuning. (iii) Flexibility in operation: A decentralized structure allows operating personnel to restructure the control system by bringing subsystems in and out of service individually, which allows the system to handle changing control objectives during different operating conditions. However, the potential disadvantage of using the limited control structure is the deteriorated closed-loop performance caused by interactions among loops as a result of the existence of nonzero off-diagonal elements in the transfer function matrix. Therefore, the primary task in the design of decentralized control systems is to determine loop pairings that have minimum cross interactions among individual loops. Consequently, the resulting multiple control loops mostly resemble their SISO counterparts such that controller tuning can be facilitated by SISO design techniques [31]. This chapter aims to obtain a new loop paring criterion which may result in minimum loop interactions.
2.1 Introduction Since the pioneering work of Bristol [32], the relative gain array (RGA) based techniques for control-loop configuration have found widespread industry applications, including blending, energy conservation, and distillation columns, etc [13,33,34,35]. The Q.-G. Wang et al.: PID Control for Multivariable Processes, LNCIS 373, pp. 9–38, 2008. c Springer-Verlag Berlin Heidelberg 2008 springerlink.com
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2 Loop Pairing Analysis
RGA-based techniques have many important advantages, such as very simple calculation because it is the only process steady-state gain matrix involved and independent scaling due to its ratio nature, etc [36]. To simultaneously consider the closed-loop properties, the RGA-based pairing rules are often used in conjunction with the Niederlinski index (NI) [37] to guarantee the system stability [31, 13, 36, 38, 39, 40]. However, it has been pointed out that this RGA- and NI-based loop-pairing criterion is a necessary and sufficient condition only for a 2 × 2 system; it becomes a necessary condition for 3 × 3 and higher dimensional systems [36,41]. Moreover, it is very difficult to determine which pairing has less
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