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Passivity-based process control introduces an emerging area in process control — control design and system analysis based on the concept of passive systems. This monograph presents in a systematic approach the recent developments in robust, decentralized, and fault-tolerant process control, as well as process controllability analysis and nonlinear process control.

This chapter introduces the concepts of passive and dissipative systems which lay the foundation of the developments described in this book. Most of the definitions follow Willems [138, 139], Byrnes . [24] and Sepulchre . [110] with possibly different notations. The implication of passivity is discussed in terms of the input-output behavior and stability of the process system.

In Chapter 2, we have seen that input feedforward passivity (IFP) is a phase related property. Therefore, it is possible to characterize the uncertainties in terms of their IFP so that both the phase and gain information of the uncertainties can be used, leading to a potentially less conservative control design approach. Robust control design methods based on the passivity uncertainty bound are presented in this chapter, along with case studies and illustrative examples. The developments are for linear systems, leading to systematic approaches that can be readily applied to process control practice.

A passive process can be stabilized by a decentralized passive controller. Therefore, the degree of passivity can imply how interactions between different loops in a multivariable process can affect the stability of the decentralized control system. In this chapter, an interaction analysis approach based on passivity is introduced. This includes steady-state and dynamic interaction analysis for both multiloop (fully decentralized) control and multi-unit (block diagonal) control. Passivity-based decentralized control design approaches are also presented.

We have seen in Chapter 4 that the concept of passivity can be used to develop decentralized control approaches. A passivity-based decentralized controller, if properly designed, can also achieve fault tolerance. For example, for a given multivariable linear strictly passive process, a decentralized passive controller can maintain the stability of a closed-loop control system when one or more controller loops fail simply because the decentralized passive controller remains passive when one or more elements are detuned or taken out of service. Motivated by this observation, a passivity-based decentralized fault-tolerant control framework was developed [16, 17, 148, 149]. In this chapter, we will present the main results of this approach, including fault-tolerant control systems design with zero or minimum control loop redundancy.

Process control has been playing an important role in process industries as increased process integration and tight operating conditions are putting greater demands on control system performance. For a given process system, the control performance achievable can be quantified by the input-output controllability measure. Controllability analysis can be used in the process design stage to reveal controllability problems. In this chapter, we will introduce a controllability analysis approach based on passivity.

General passivity-based control is difficult without physical insights. Even at the origin of passivity-based control, the physical analogies of stored and retrievable energy of mechanical systems have been used fruitfully. Later, the notions and techniques to apply the fundamental physical description to design controllers emerged particularly in the area of mechanical systems and robotics [115, 130]. Inspired by this fruitful connection, this chapter is devoted to the thermodynamic foundation of process control.