Proportional-Integral Observer in Robust Control, Fault Detection, and Decentralized Control of Dynamic Systems

Abstract

Abstract. This chapter initially reviews observer theory as it was developed over the past few decades. The state observer and its order reduction including functional observer in connection to state feedback control design are briefly discussed. The robustness of observer-based controller design is also explored. The loss of robustness due to the inclusion of observer in optimal linear quadratic regulator (LQR) and its recovery procedure (LTR) are summarized. The subsequent development of new observer structures such as disturbance observer (DO), unknown input observer (UIO), and proportional-integral observer (PIO) for disturbance estimation and fault detection is highlighted. Throughout the chapter we concentrate mainly on important advantages of PI-observer. Finally, we consider the problem of designing a decentralized PI observer with prescribed degree of convergence for a set of interconnected systems. Under the assumption of linear interactions, we provide a direct design procedure for the PI observer which can effectively be used in disturbance estimation and observer-based control design enhancing the robustness properties. In this connection we also extend the results to the case of designing controllers that attenuate the disturbance while preserving the stability. It is shown that the design can be formulated in terms of LMI which efficiently solve the problem.

The Unknown Input Observer and its Advantages with Examples

“…The problem of designing observers for a linear system with both known and unknown inputs has been studied since the 1970's [1], [2], [4]. The motivation for studying this problem is that in practice, for a variety of reasons, many plants are modeled with disturbance terms as shown in Eq 1.1.…”

Complete characterisation of disturbance estimation and fault detection for positive systems

“…Observers have found broad application in estimation and control of dynamic systems [1][2][3] (see also the references therein). A major advantage of observers is in disturbance estimation and fault detection [3,4]. Among different observer structures, unknown input observer (UIO) and proportional-integral observer (PIO) are well-qualified candidates for this purpose.…”

Stabilization, estimation and control of linear dynamical systems with positivity and symmetry constraints

“…Apart from positive stabilization that can be employed for a general system, the problem of observer design has additional restrictions when positivity constraints are imposed. Observers have found broad application in estimation and control of dynamic systems [18][19][20]. A major advantage of observers is in disturbance estimation and fault detection [20,21].…”

“…Observers have found broad application in estimation and control of dynamic systems [18][19][20]. A major advantage of observers is in disturbance estimation and fault detection [20,21]. Among different observer structures, UIO and PIO are well-qualified candidates for this purpose.…”

“…The PI observer that was successfully used in the past and offered several advantages [20,39] is combined with UIO to solve the robust fault detection problem for regular and positive systems.…”