Robert H. Chen

A generalized least-squares fault detection filter

A fault detection and identification algorithm is determined from a generalization of the least-squares derivation of the Kalman filter. The objective of the filter is to monitor a single fault called the target fault and block other faults which are called nuisance faults. The filter is derived from solving a min–max problem with a generalized least-squares cost criterion which explicitly makes the residual sensitive to the target fault, but insensitive to the nuisance faults. It is shown that this filter approximates the properties of the classical fault detection filter such that in the limit where the weighting on the nuisance faults is zero, the generalized least-squares fault detection filter becomes equivalent to the unknown input observer where there exists a reduced-order filter. Filter designs can be obtained for both linear time-invariant and time-varying systems. Copyright

Sensor and Actuator Fault Reconstruction

Many fault detection filters have been developed to detect and identify sensor and actuator faults by using analytical redundancy. An approach to further reconstruct sensor and actuator faults from the residual generated by the fault detection filter is proposed. The transfer matrix from the faults to the residual is derived in terms of the eigenvalues of the fault detection filter associated with the detection spaces of the faults and the invariant zeros of the faults. For each fault, all possible fault reconstruction processes are derived and parameterized by applying a projector to the transfer matrix and taking inverse. Then, the optimal fault reconstruction process is determined by minimizing the ratio of the H 2 norm of the projected transfer matrix from the disturbance over the H 2 norm of the projected transfer matrix from the fault. For the existence of the fault reconstruction process, the invariant zeros of the fault have to be in the left-half plane. Furthermore, for reconstructing a sensor fault, the system has to be detectable with respect to the other sensors.

Health monitoring of a satellite system

A health monitoring system based on analytical redundancy is developed for satellites on elliptical orbits. Analytical redundancy, which reduces the need for hardware redundancy, uses the modeled dynamic relationship between system inputs and measured system outputs to form a residual process that is used for detecting and identifying faults. First, the dynamics of the satellite including orbital mechanics and attitude dynamics is modeled as a periodic system. Then, periodic fault detection filters are designed to detect and identify the satellite’s actuator and sensor faults. In addition, parity equations are constructed using the algebraic redundant relationship among actuators and sensors. Furthermore, a residual processor is designed to generate the probability of each fault by using a sequential probability test. Finally, the health monitoring system, consisting of periodic fault detection filters, parity equations, and residual processor, is evaluated in the simulation in the presence of disturbances and uncertainty.

Homing Missile Guidance and Estimation Under Agile Target Acceleration

Two new algorithms for homing missile guidance and estimation in the two-dimensional intercept problem are proposed based on the assumption that certain targets execute evasive maneuvers orthogonal to their velocity vectors. The objectives of both algorithms are to estimate the engagement states in the presence of unknown target accelerations and guide the interceptor to hit the target based on these state estimates. Both algorithms are the integration of a fllter in cascade with a guidance law but constructed using difierent philosophies. One algorithm constructs the fllter that estimates the target acceleration and the guidance law based on a target model in which the magnitude of the target acceleration vector is assumed to be a sinusoidal function. The other algorithm constructs the fllter by blocking the dynamic efiect of the target acceleration and constructs the guidance law based on the anticipated worst possible target acceleration. These two algorithms form an interesting design trade between the inherent estimation lag and increased estimation uncertainty.

Optimal stochastic 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.

A vehicle health monitoring system evaluated experimentally on a passenger vehicle

A vehicle health monitoring system based on analytical redundancy, is developed for automated passenger vehicles. A residual generator and a residual processor are designed together to detect and identify actuator and sensor faults of the Buick LeSabre rapidly. The residual generator includes fault detection filters and parity equations. It uses the control commands and sensor measurements to generate the residuals, which have a unique static pattern in response to each fault. Then, the residual processor interrogates the residuals by matching them to one of several known patterns. It computes the probability of each hypothesis conditioned on the history of residuals. The fault detection latency is reduced by integrating the design of the residual generator and the residual processor. The vehicle health monitoring system is evaluated in real-time on a Buick LeSabre. The vehicle sensor and actuator faults are simulated artificially by the computer or created manually by the driver. In one experiment, a real intermittent sensor fault occurred and was immediately detected and identified. The real-time evaluation demonstrates that the vehicle health monitoring system can detect and identify actuator and sensor faults under various disturbances and uncertainties with almost minimal detection latency

Optimal Intercept Missile Guidance Strategies with Autopilot Lag

In the linear-quadratic pursuit-evasion game, the pursuer (interceptor) wishes to minimize the terminal miss, whereas the evader (target) wishes to maximize it. Therefore, the optimal strategy of the interceptor is derived against the anticipated worst possible strategy of the target. If the interceptor has a lag, the current approach is to include this lag directly in the system dynamics, which are known to both players. In this problem formulation, the optimal cost could easily go to infinity, which means that the target will win the game. This is expected, because the target has knowledge about interceptors lag. To ensure the existence of an interceptor strategy, the weighting on the terminal miss has to be chosen small enough so that the optimal cost will remain finite. However, this manipulation prevents the target from maximizing the terminal miss and effectively constrains the target strategy. Therefore, the interceptor strategy is derived against the worst-case target strategy that is not really the worst case. In this paper, it is shown that this interceptor strategy performs poorly in realistic situations where the target tries to maximize the terminal miss. Instead, two new interceptor strategies are derived against target strategies that are determined without knowledge about the interceptors lag. These two optimal interceptor strategies improve the game-theoretic guidance law for homing missiles by correctly taking into account the autopilot lag.

Improved Endurance of Optimal Periodic Flight

For a class of subsonic aircraft, endurance can be improved signiflcantly by ∞ying in a periodic path rather than in steady state. The optimal periodic endurance problem is formulated where the performance criterion for endurance, fuel used over ∞ight time, is minimized and the aircraft is constrained to ∞y a periodic path while circles above a target on the ground. The optimal steady state endurance problem is formulated where the instantaneous fuel rate is minimized subject to the aircraft dynamics being in equilibrium. Both optimization problems are solved numerically. An example shows for an aircraft with maximal lift-to-drag ratio of 17.4 and thrust-to-weight ratio of 0.5, the endurance of the optimal periodic ∞ight is over three times of the endurance of the optimal steady state ∞ight. In order to mechanize the optimal periodic ∞ight, a periodic guidance law is developed.

Optimal stochastic multiple-fault detection filter

A class of robust fault detection filters is generalized from detecting single fault to multiple faults. This generalization is called the optimal stochastic multiple-fault detection filter since in the formulation, the unknown fault amplitudes are modeled as white noise. The residual space of the filter is divided into several subspaces and each subspace is sensitive to only one fault (target fault), but not to other faults (nuisance faults), in the sense that the transmission from nuisance faults to the target residual space is small while the transmission from target fault is large. It is shown that this filter approximates the properties of the classical fault detection filter such that in the limit where the nuisance fault weighting goes to infinity, the optimal stochastic multiple-fault detection filter is equivalent to the Beard-Jones fault detection filter when there is no complementary subspace. A numerical example also shows that this filter is an approximate Beard-Jones fault detection filter even when complementary subspace exists. This filter combines the advantages of the robust single-fault detection filter and Beard-Jones fault detection filter.

Optimization and Implementation of Periodic Cruise for a Hypersonic Vehicle

The optimal cruise trajectory for a detail designed hypersonic waverider vehicle is determined. Two possible local extrema are found representing the steady state and periodic cruise trajectories. The optimal steady state cruise is determined by minimizing the instantaneous fuel rate per distance subject to the dynamics being in equilibrium. The approximately optimal periodic cruise is determined by minimizing the fuel used over an optimal range period subject to a periodicity condition on the initial and terminal values of the altitude, velocity, and ∞ight path angle, assuming that the vehicle weight is given and held flxed over the range period. It is shown that if a door is placed over the inlet during the power-ofi phase increasing the drag by 50%, but increasing the lift by 35%, the periodic ∞ight over the cruise region is 13.27% better than ∞ying in steady state. Results for mechanizing the periodic ∞ight by a linear guidance rule allow the constant vehicle weight assumption to be removed, but retain the periodic cruise performance.