(504d) Uniting Safe-Parking and Reconfiguration-Based Approaches for Fault-Tolerant Control of Switched Nonlinear Process Systems

The operation of chemical processes is inherently complex due to the presence of nonlinearities, constraints, and uncertainty, which should be considered for control law designs. Furthermore, the occurrence of eventualities, such as actuator faults (failures in actuating equipments, such as pumps, valves, etc.), adds another layer of complexity. The economic losses, damage to the environment, and injury to personnel resulted from the common occurrence of faults have motivated extensive research on fault-detection and isolation (FDI) and fault-tolerant control (FTC). Economic considerations also drive the use of the same equipment to produce multiple product types. This gives rise to hybrid process behavior where the continuous process dynamics are present together with the occurrence of discrete events, such as changes in raw materials and product specifications. A class of systems exhibiting hybrid process behavior that has been paid significant attention recently is switched systems (e.g., [1, 2, 3]). It can be used to model several practical control problems that involve integration of supervisory logic-based control schemes and feedback control algorithms.

In many practical situations, the switched process system is required to follow a prescribed schedule, where the transition times are not decision variables. In [3], a predictive control framework was developed for the problem of control of switched nonlinear systems subject to input constraints that transit between the constituent modes (subsystems) at prescribed times. The basic idea is to design a Lyapunov-based model predictive controller for each mode and to incorporate stability constraints in the predictive controller design. The designed predictive controller provides guaranteed stabilization from an explicitly characterized set of initial conditions under input constraints. The stability constraints incorporated ensure that: (1) at the prescribed transition time the state of the closed-loop system resides in the stability region of the mode that the system is switched into and (2) the Lyapunov function for each mode is nonincreasing wherever the mode is reactivated. More recently, this framework has been extended to handle the presence of uncertainty in switching times and constituent mode dynamics in [4].

The ability to achieve a prescribed switching schedule, however, is also impeded by the occurrence of actuator faults. One of the prerequisites for implementing fault-tolerant control is to detect and isolate faults (if multiple actuators are used). Existing results on fault-detection include the design of fault-detection filters using historical data and using fundamental process models. Historical plant data can be used to construct indicators that identify deviations from normal operation to detect faults by statistical and pattern recognition techniques (e.g., [5, 6]). The problem of using fundamental process models for the purpose of detecting faults has been studied extensively for linear systems (e.g., [7]) and nonlinear systems (e.g., [8]). Recently, fault-detection and isolation filters have been developed in [9] that essentially capture the difference between the fault-free evolution and the observed (or estimated) evolution of the state variables to detect and isolate faults in control actuators for MIMO nonlinear process systems, where the failed actuator is the only one influencing at least some state variable (See [10] for SISO nonlinear process systems, for which fault-detection suffices).

The existing methods for dealing with faults after the FDI stage include the robust/reliable (e.g., [11]) and reconfiguration-based (e.g., [12, 9, 10]) fault-tolerant control approaches. The former relies on the robustness of the active control configuration, while the latter relies on available redundant control configurations identified off-line. Both these methods assume that the closed-loop operation at the nominal equilibrium point can be preserved in the presence of an actuator fault. Recently, a safe-parking framework of nonlinear process systems has been proposed to handle actuator faults that preclude the possibility of nominal operation in [13], where a safe-park point for (continuous) nonlinear process systems is defined as an equilibrium point subject to the failed actuator such that (1) the process state at the time of failure resides in its stability region and (2) it resides in the stability region of the nominal control configuration. The key idea is to park the process at a safe-park point and performance considerations are utilized in choosing the optimal safe-park point. More recently, the safe-parking framework has been extended to handle uncertainty and unavailability of measurements through state observer and output feedback design in [14].

The fault-detection and isolation filters devised in [9] can be utilized to detect and isolation actuator faults in the context of switched nonlinear process systems. While the safe-parking framework for (continuous) nonlinear process systems cannot be directly applied to control of switched nonlinear process systems due to the changing system dynamics resulted from prescribed transitions, its idea can be extended to account for the relation between safe-park points of the (continuous) subsystems. In addition, the multi-mode characteristic provides a possibility to achieve nominal operation in another mode when an actuator fault precludes the possibility of nominal operation in one mode. Motivated by these considerations, we unite safe-parking and reconfiguration-based approaches to handle actuator faults for switched nonlinear process systems subject to input constraints.

A fault-handling framework is developed to account for two possibilities: a fixed schedule and a flexible schedule, where the switching sequence and switching times are fixed for the former and they can be adjusted during the production process for the latter. In the absence of faults, it is assumed that nominal operation can be achieved in each mode through the Lyapunov-based predictive control design despite the prescribed switching. The actuator faults considered preclude the possibility of continued nominal operation in the mode where a fault takes place. For a fixed schedule, the consideration is to require that upon fault-occurrence the process be parked at a safe-park point of the mode where the fault takes place such that in the presence of the fault the process can also be parked at safe-park points of subsequent modes along the prescribed switching sequence and nominal operation can be resumed after the fault is rectified. This design considers changes in system dynamics due to the prescribed transitions and provides stronger conditions for choices of safe-park points of switched nonlinear process systems. For a flexible schedule, the consideration is to switch the process to a chosen mode (if available) where nominal operation can be achieved in the presence of the fault using either depleted primary control or backup control (through controller reconfiguration), starting from a safe-park point of the (continuous) subsystem operated in the mode where the fault takes place. Instead of safe-parking the process, the safe-park point is used to design a Lyapunov-based predictive controller that can be used to guide the process to enter the stability region of the chosen mode, starting from where nominal operation can be achieved even in the presence of the fault. The proposed method is illustrated by a switched nonlinear chemical process example.

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