Proportional-integral observer in robust control, fault detection, and decentralized control of dynamic systems

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

Rejecting Plant Input Disturbances with PI Adaptive Observers

Under Construction Conventional proportional adaptive observers are unable to reject slowly varying measurement disturbances; estimation error does not converge with time to zero. The bias caused by the disturbances The measurement disturbances bias both the state and parameter estimates. Adding an offset based on the integral of the state estimate error to the observer equation allows the observer to Keywords: Disturbance Rejection, PI Adaptive Observers 1 Northeastern University, Department of Mechanical, Industrial and Manufacturing Engineering, Boston, MA 02115 USA . Email address is [email protected] 2 Northeastern University, Department of Electrical and Computer Engineering, Boston, MA 02115 USA . Email address is [email protected] DRAFT 2 1. Introduction State feedback control designed with Linear Quadratic Regulator (LQR) techniques has impressive robustness properties, but requires access to system state variables. When state variables of a linear system are unavailab..

A Design Procedure for Robust Actuator and Sensor Fault Detection

This paper considers the design of an integrated observer structure termed as Proportional Integral Fading Unknown Input Observer (PIFUIO). The advantages of PIO and UIO observers are used in robust fault detection. The UIO decouples the unknown input disturbance while PIO allows to estimates the faults. It is shown that the fading term of this observer plays a distinct role in reliable estimation of faults decoupled from the unknown disturbance or vice versa. The robust detection of sensor fault is also considered with the presence of unknown inputs. Indirect and direct design procedures for sensor fault detection are provided. Numerical examples are included to illustrate the advantage of PIFUIO

Fault diagnosis in a class of differential-algebraic systems

An Iterative Learning Observer (ILO) is proposed for fault diagnosis in a class of differential-algebraic nonlinear systems described by so-called semi-explicit form with index 1. The main feature of this ILO-based fault diagnosis strategy is that the ILO can estimate both system states and algebraic variable. This is important since both fault detection and estimation can be achieved. As a result the ILO can still track the post-fault system. Moreover, the ILO input can be used to isolate faults. The simulation study presented shows the effectiveness of this ILO-based fault detection and estimation strategy for differential-algebraic systems

Robust decentralized PI observer for linear interconnected systems

This paper considers 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 design process requires a suitable modification of a decentralized PI observer design comprised of a set of local PI observers for the decoupled subsystems. The modification ensures a desired convergence rate for the overall PI observer and generally involves the use of additional inputs, which account for the interconnection effects, into the local PI observers. © 2011 IEEE