A key issue in practical fault detection e lter applications is sensitivity to system disturbances and sensor noise. In this paper, a stabilizing fault detection e lter gain is found that bounds the H1 norm of the transfer matrix from system disturbances and sensor noise to the residual. For multidimensional faults, a residual direction is identie ed that enhances the fault signal-to-noise ratio while maintaining the H1 norm bound. By retaining the faultdetection e lterstructure,thepracticalapplicability oftheproposed approach isthesameasforfaultdetection e lter designs found by conventional eigenvector assignment. In contrast to an unknown input observer approach wherein noise is explicitly decoupled from the fault signal, a noise bounding approach does not impose additional geometric constraints on the e lter structure. This allows a given e lter to isolate more faults, an important feature because in practical applications low-order e lter dynamics are common. Further, the possibility of ill-conditioned e lter eigenvectors, occasionally imposed by geometric constraints, may be reduced.

H Bounded Fault Detection Filter

Properties of the optimal stochastic fault detection filter for fault detection and identification are determined. The objective of the filter is to monitor certain faults called target faults and block other faults which are called nuisance faults. This filter is derived by keeping the ratio of the transmission from nuisance fault to the transmission from target fault small. It is shown that this filter approximates the properties of the classical fault detection filter such that in the limit where the ratio of the transmissions is zero, the optimal stochastic fault detection filter is equivalent to the unknown input observer if all invariant zero directions are included with the nuisance fault directions. Detection filter designs can be obtained for both linear time-invariant and time-varying systems.

Optimal stochastic fault detection filter

http://users.cecs.anu.edu.au/~john/papers/JOUR/080.PDF

Robust frequency-shaped LQ control

This dissertation considers residual generation for robust fault detection of linear systems with control inputs, unknown disturbances and possible faults. First, multi-objective fault detection problems such as H−/H∞, H2/H∞ and H∞/H∞ have been formulated for linear continuous time-varying systems (LCTVS) in time domain for finite horizon and infinite horizon case, respectively. It is shown that under mild assumptions, the optimal solution is an observer determined by solving a standard differential Riccati equation (DRE). The solution is also extended to the case when the initial state for the system is unknown. Second, the parallel problems are also solved for linear discrete time-varying systems in time domain. The solution is again an observer whose gain is determined by solving a standard recursive difference Riccati equation (DDRE). The solution is also extended to the case when the initial state for the system is unknown. Third, for the general case in which Gd (the transfer matrix from disturbance to output) may be a tall or square transfer matrix, and Dd may not have full column rank for linear discrete time invariant systems (LDTIS), the common H−/H∞, H2/H∞ and H∞/H∞ frameworks are not applicable. Based on several novel definitions of norms over a certain subspace, we propose a new problem formulation with both disturbance decoupling and fault sensitivity optimization. It is shown that the solution is an observer determined by a generalized Riccati equation (or Riccati system, alternatively). To be more specific, with this

https://digitalcommons.lsu.edu/cgi/viewcontent.cgi?article=2836&context=gradschool_dissertations

Fault detection filter design for linear systems

The theory of a discrete-time parametric linear quadratic (PLQ) control is extended to a class of frequency-shaped performance measures. The incorporation of frequency-dependent weighting matrices allows the emphasis or de-emphasis of the importance of the system variables being penalized over specific bands of frequencies. Results are presented for constant-gain and dynamic output feedback configurations of frequency-shaping optimal control. The resultant control is applied to the design of active seat suspension control. The active suspension maximizes ride comfort by discriminatory minimization of average whole-body absorbed power over a band of frequencies that causes the most discomfort to a human being. >

Discrete-time frequency-shaping parametric LQ control with application to active seat suspension control

A fault detection filter is designed by minimising the response to confounding noises whilst keeping the fault response constant. A linear quadratic optimisation problem, related to /spl Hscr//sub 2/ and /spl Hscr//sub /spl infin// optimal control is used. The "Q" matrix of the associated Riccati equation is indefinite in contrast to the indefinite "R" matrix of /spl Hscr//sub /spl infin// control. We extend linear optimal control theory to solve the fault detection problem in this framework.

Fault detection: a quadratic optimisation approach

http://users.cecs.anu.edu.au/~john/papers/PROC/028.PDF

Frequency Shaped Linear Optimal Control with Transfer Function Riccati Equations

Loop transfer recovery is considered to be a special form of loop sensitivity shaping in this paper. This viewpoint suggests a design strategy which relaxes the requirement that the estimator or controller be unbiased. This strategy is illustrated using a stable, SISO example with a nonminimum phase zero. The approach still faces the design tradeoffs and limitations inherent in all feedback systems including those which apply to nonminimum phase plants. The formulation used here, however, suggests a different approach for dealing with these issues. >

Loop transfer recovery design using biased and unbiased controllers

It is argued that an unbiasedness constraint is not a requirement for effective loop transfer recovery (LTR). Controller design procedures are formulated which do not have this restriction and which permit the substitution of other relationships which can assist in the synthesis of the controller. These procedures offer the designer additional freedom in the synthesis of feedback controllers. In particular, they allow the synthesis of either unbiased or biased controllers in a framework that is more general than that offered by standard linear quadratic Gaussian (LQG)/LTR. Application to a simple nonminimum phase example shows that the additional flexibility offered by the methods discussed is useful for shaping sensitivity functions. While reflecting the fundamental limitations inherent in all feedback systems, the results obtained compare more than favorably with LQG/LTR designs. >

http://ieeexplore.ieee.org/iel5/164/5238/00203935.pdf

A method is presented for improving the tolerance of LQG (linear quadratic Gaussian) controllers to parameter errors. The improvement is achieved by introducing terms reflecting the structure of the errors into the linear quadratic regulator cost function and the process and measurement noise models. Adjusting the sizes of these additional terms permits a tradeoff between robustness and nominal performance. >

D.L. Mingori

Papers

Fault detection: a quadratic optimisation approach

Frequency Shaped Linear Optimal Control with Transfer Function Riccati Equations

Loop transfer recovery design using biased and unbiased controllers

Loop transfer recovery design using biased and unbiased controllers

Design of LQG controllers with reduced parameter sensitivity