Control Configuration of Linear Multivariable Plants: Advanced RGA Based Techniques

Abstract

The RGA introduced in chapter 2 provides a powerful tool for measuring control loop interaction and it is a well established pairing technique in the industry, with decades of successful applications. Although, the presented RGA analysis is sufficient for many practical problems, it is for some cases necessary to extend the RGA concept to handle certain shortcomings. This chapter provides an overview of the advanced pairing techniques based on the different RGA extensions. The presented methodologies are:

The Dynamic Relative Gain Array. Dynamic relative gain is discussed in section 3.2.1. This is a dynamic extension of the RGA to improve the pairing capabilities of the steady state RGA in the cases where the RGA changes substantially with frequency and especially when the steady state RGA differs from the RGA at other key frequencies. In section 3.2.2, among the many different approaches, the static output feedback linear quadratic regulator problem strategy is chosen to develop the RGA dynamic extension. The Effective Relative Gain Array is another dynamic extension of the RGA presented in section 3.2.3, where the steady state gain and the response speed or plant bandwidth of the open loop transfer function are considered. Its key difference with the other RGA dynamic extensions is that no controller design or complex computations are necessary.

The Partial Relative Gain. The RGA in cases where selected loops are closed in a control system can lead to incorrect pairing selections. In fact, partially controlled plants can improve the designer’s knowledge of the plant under control. By investigating the relative gains of the uncontrolled part of the plant or the PRG, better pairing selections can be made. The notion of PRG is developed in section 3.3.

The Relative Interaction Array. Section 3.4 introduces the relative interaction array (RIA). It is similar to the RGA and is defined based on individual control loops and it can only measure interaction in individual loops. The interaction measure provided by the RGA and the RIA can lead to several pairs that may satisfy the pairing rules and are unable to propose the best choice. However, an overall interaction measure is defined along with the RIA which claims to lead to the best input-output pairing selection.

Block Pairing and Block Relative Gain. Fully decentralized control of highly interactive multivariable plants can result in poor closed loop performance. On the other hand, centralized controllers are not operationally desirable in certain complex multivariable plants where interaction is not heavily distributed through the plant and it is sever in some parts and less disturbing in the others. An effective design methodology in such cases is the block decentralized controllers. Block pairing discussed in section 3.5 is the first step in a successful block decentralized control system design.