Safe and profitable operation of chemical plants relies, among other things, on controller designs that account for the inherently complex dynamics of the chemical processes involved (manifested as nonlinearities), operational issues such as constraints and uncertainties, as well as are robust with respect to abnormalities (arising, for example, due to faults in sensors/actuators). This work considers the problem of establishing robustness of feedback controls with respect to asynchronous sensor data losses in the presence of constraints in the manipulated inputs. In a previous work [1], sensor faults arising due to communication losses were modeled as delays in implementing the control action and a reconfiguration strategy was devised to achieve fault-tolerance subject to faults in the control actuators. In [2] a reconfiguration based approach was utilized for the purpose of achieving fault-tolerance that explicitly accounts for the unavailability of some of the states for measurement, system nonlinearity as well as the presence of input constraints. In [2], however, the measurements were assumed to be continuously available, and sensor failures and sensor data losses (intermittent unavailability of measurements) arising due to, for example, packet losses in communication lines, were not considered. In [3] the problem of availability of sensor measurements at different (known) rates is considered (multi-rate sampling). Sensor data losses, arising due to sampling, measurement or communication irregularities are more likely to be manifested as intermittent availability of measurements, where only an average rate of availability of measurements is known, but not the exact times when the measurements will be available. When explicitly considered, this problem of intermittent sensor data losses (asynchronous measurements) can be handled as a robustness issue. Specifically, for a given stabilizing control law, a bound on the sensor data loss rate is computed such that if the sensor data loss rate is within this bound, closed–loop stability is preserved. For unconstrained systems, such a bound for the data loss rate can be defined over an infinite time interval (e.g., see [4] and the references therein). For constrained systems, however, a data loss rate defined over an infinite time interval does not allow for the computation of such a bound.

Motivated by the above, in this work we consider the problem of fault-tolerant control of nonlinear process systems subject to input constraints and sensor faults. We employ a reconfiguration-based approach, wherein, for a given process, a set of candidate control configurations are first identified. To illustrate the importance of accounting for process nonlinearity and constraints, we first consider sensor faults manifested as complete loss of measurements (faults that necessitate taking corrective action to fix the sensors). We address the problem of determining which candidate control configuration should be implemented in the closed–loop system to achieve stability after the sensor is recovered (this analysis is carried out under the assumption of continuous availability of measurements when the sensor is functioning). We then consider the problem in the presence of intermittent sensor data losses, and for a given process, model the sensor data losses and analyze the stability properties in the presence of input constraints and sensor data losses (appropriately defining the sensor data loss rate). After characterizing the stability properties of each candidate configuration, we utilize this information in implementing fault-tolerant control. Specifically, for each control configuration, the characterization of the stability region (i.e., the set of initial conditions starting from where closed–loop stabilization under continuous availability of measurements is guaranteed) and the maximum allowable data loss rate is utilized in taking corrective action, i.e., to trigger reconfiguration, as well as in making the decision as to which backup configuration should be employed in the closed–loop system to maintain stability. We use a chemical reactor example to illustrate our theoretical results.

References:

[1] El-Farra, N. H., A. Gani, and P. D. Christofides. Fault-tolerant control of process systems using communication networks. AIChE J., 51:1665–1682, 2005.

[2] Mhaskar, P., A. Gani, N. H. El-Farra, C. McFall, P. D. Christofides, and J. F. Davis. Integrated fault-detection and fault-tolerant control for process systems. AIChE J., 52, 2129-2148, 2006.

[3] Tatiraju, S., M. Soroush, and B. A. Ogunnaike. Multirate nonlinear state estimation with application to a polymerization reactor. AIChE J., 45:769–780, 1999.

[4] Hassibi, A., S. P. Boyd, and J. P. How. Control of asynchronous dynamical systems with rate constraints on events. In Proceedings of 38th IEEE Conference on Decision and Control, pages 1345–1351, Phoenix, AZ, 1999.