(687e) Safe-Parking of Nonlinear Process Systems: Handling Uncertainty and Lack of Measurements

The operation and control of chemical processes is experiencing increased reliance on automation with the enhanced availability of sensors and actuators and communication infrastructure. The increased availability of information has opened up several opportunities in making better use of the available resources and coordinating safety measures across the plant. The resulting interdependence of processing units, both materially and in terms of information flow, has also placed more emphasis on the need to preserve safe plant operation in the event of eventualities and contain the effects of faults to local processing units. Even under `normal' operating conditions, chemical processes exhibit significant complexity (manifested as nonlinearities) and have to account for operational issues such as constraints and disturbances and availability of limited measurements. Operation of chemical processes to meet profitability as well as safety requirements, therefore, relies on adequate design and maintenance, appropriate monitoring systems to detect and diagnose eventualities, and the presence of correcting mechanisms that, having been `informed' of an eventuality, prevent or minimize loss of performance, shutdowns, or hazardous situations while accounting for process nonlinearity, disturbances, constraints and availability of limited measurements.

The extensive economic, personnel and environmental damage caused by the faults (it is estimated that the U.S. petrochemical industry looses an estimated 20 billion per year due to faults [1]) as well as the practical inevitability of fault occurrence has motivated several researchers to consider the problem of handling of faults. The first step in handling of faults is the ability to detect and isolate the faults. Statistical and pattern recognition techniques for data analysis and interpretation (e.g., [2,3]) use historical plant-data to construct indicators that identify deviations from normal operation to detect faults. The problem of using fundamental process models for the purpose of detecting faults has been studied extensively in the context of both linear and nonlinear systems (e.g., [4,5]).

Having detected and isolated a fault, the existing results on fault handling have essentially focussed on continued operation at the nominal operating point, under the assumption of sufficiency of the depleted control action to preserve nominal operation. Under this assumption, one approach dictates fault-accommodation via robust/reliable control designs (e.g., see [6]) that allow continued operation at the nominal operating point. To handle the situation when the fault causes such significant depletion of the control action that prevents the handling of fault via controller re-tuning, other approaches assume the existence of redundant control configurations to preserve closed--loop stability. In the choice of redundant control configuration, however, the presence of nonlinearity, input constraints and uncertainty, as well as the hybrid nature of the closed--loop system must be accounted for.

The development of reconfiguration--based approaches has been facilitated by the development of extensive research on control of nonlinear and switched systems (see, e.g., [7, 8, 9]). These include Lyapunov-based nonlinear control designs (for a review, see [7]) that provide an explicit characterization of the stability region in the presence of constraints as well as model predictive control designs that allow incorporation of performance considerations in the control design and provide stability guarantees based on the assumption of initial feasibility of the optimization problem. Recently, model predictive controllers have been designed [8,9] that allow explicit characterization of the stability region, via mimicking the stability properties of Lyapunov-based bounded controllers, without assuming initial feasibility of the optimization problem. More recently, a model predictive controller has been designed [10] that by better utilizing the constraint handling capabilities of model predictive controllers enhances the set of initial conditions from where stability is achieved. The work in [10], however, does not explicitly consider uncertainty and assumes the availability of complete state information. One of the contributions of the present work is the generalization of the predictive controller of [10]to explicitly consider uncertainty and availability of limited measurements for subsequent use within a fault-handling framework.

In [11, 12, 13] reconfiguration-based fault-tolerant control structures have been developed that guarantee preserving of closed--loop stability, while accounting for process nonlinearity, constraints and performance. Specifically, closed--loop stability is preserved (having first detected and isolated the occurrence of a fault) via implementing a backup control configuration chosen such that 1) the state at the time of the failure resides in the stability region of the candidate backup control configuration and 2) the backup configuration does not use the failed control actuator. However, all the reconfiguration-based fault-tolerant control designs of [11, 12, 13] assume the existence of a backup, redundant control configuration. The scenario where a fault results in temporary loss of stability that cannot be handled by redundant control loops has not been explicitly addressed. In the absence of a framework for handling such faults, ad-hoc approaches could result in temporarily shutting down the process which can have substantially negative economic ramifications. Recently, in [14] a 'safe-parking' framework was developed to handle faults that necessitate fault rectification via identifying `safe-park' points where the process is stabilized accounting for process nonlinearity and constraints, and also ensures smooth resumption of nominal operation upon fault-recovery. Specifically, a candidate parking point is termed a safe-park point if 1) the process state at the time of failure resides in the stability region of the safe-park candidate (subject to depleted control action), and 2) the safe-park candidate resides within the stability region of the nominal control configuration. The safe-parking framework in [14], however assumes availability of the entire state information as well as precise process dynamics knowledge. Availability of limited measurements and the presence of disturbances and uncertainty, however, can destabilize even nominal operation and also invalidate the guarantees of safe-parking and resumption of smooth operation upon fault-recovery.

Motivated by the above considerations, this work considers the problem of handling faults in control of nonlinear process systems subject to input constraints, uncertainty and unavailability of measurements. A framework is developed to handle faults that preclude the possibility of continued operation at the nominal equilibrium point using robust or reconfiguration-based fault-tolerant control approaches and necessitate fault-rectification. The key consideration is to operate the plant using the depleted control at an appropriate `safe-park' point to prevent onset of hazardous situations as well as enable smooth resumption of nominal operation upon fault-recovery, while accounting for practical issues such as nonlinearity, constraints, uncertainty and availability of limited measurements. First, we consider the presence of constraints and uncertainty and develop a robust Lyapunov-based model predictive controller in designing the safe-parking algorithm that preserves closed--loop stability upon fault recovery. The framework utilizes the stability region characterization in selecting `safe-park' points from the safe-park candidates (equilibrium points subject to failed actuators). Then we consider the problem of availability of limited measurements. An output feedback Lyapunov-based model predictive controller, utilizing an appropriately designed state observer (to estimate the unmeasured states), is formulated and its stability region explicitly characterized. An algorithm is then presented that accounts for the unavailability of the state measurements in the safe-parking framework as well as controller design. The proposed framework is illustrated using a chemical reactor example and demonstrated on a styrene polymerization process.

References

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