Sathyendra Ghantasala

Brief paper: Robust actuator fault isolation and management in constrained uncertain parabolic PDE systems

This paper presents a methodology for the design of an integrated robust fault detection and isolation (FDI) and fault-tolerant control (FTC) architecture for distributed parameter systems modeled by nonlinear parabolic Partial Differential Equations (PDEs) with time-varying uncertain variables, actuator constraints and faults. The design is based on an approximate finite-dimensional system that captures the dominant dynamics of the PDE system. Initially, an invertible coordinate transformation-obtained through judicious actuator placement-is used to transform the approximate system into a form where the evolution of each state is excited directly by only one actuator. For each state, a robustly stabilizing bounded feedback controller that achieves an arbitrary degree of asymptotic attenuation of the effect of uncertainty is then synthesized and its constrained stability region is explicitly characterized in terms of the constraints, the actuator locations and the size of the uncertainty. A key idea in the controller synthesis is to shape the fault-free closed-loop response of each state in a prescribed fashion that facilitates the derivation of (1) dedicated FDI residuals and thresholds for each actuator, and (2) an explicit characterization of the state-space regions where FDI can be performed under uncertainty and constraints. A switching law is then derived to orchestrate actuator reconfiguration in a way that preserves robust closed-loop stability following FDI. Precise FDI rules and control reconfiguration criteria that account for model reduction errors are derived for the implementation of the FDI-FTC structure on the distributed parameter system. Finally, the results are demonstrated using a tubular reactor example.

Networked control of spatially distributed processes with sensor-controller communication constraints

This work presents a methodology for the design of a model-based networked control system for spatially distributed processes described by linear parabolic partial differential equations (PDEs) with measurement sensors that transmit their data to the controller/actuators over a bandwidth-limited communication network. The central design objective is to minimize the transfer of information from the sensors to the controller without sacrificing closed-loop stability. To accomplish this, a finite-dimensional model that captures the dominant dynamic modes of the PDE is embedded in the controller to provide it with an estimate of those modes when measurements are not transmitted through the network, and the model state is then updated using the actual measurements provided by the sensors at discrete time instances. Bringing together tools from switched systems, infinite-dimensional systems and singular perturbations, a precise characterization of the minimum stabilizing sensor-controller communication frequency is obtained under both state and output feedback control. The stability criteria are used to determine the optimal sensor and actuator configurations that maximize the networked closed-loop systems robustness to communication suspensions. The proposed methodology is illustrated using a simulation example.

Monitoring and fault-tolerant control of distributed power generation: Application to solid oxide fuel cells

This paper presents a hierarchical structure for fault detection and fault-tolerant control of distributed energy resources (DERs). The structure consists of distributed monitoring and control systems that perform local fault diagnosis and control system reconfiguration, together with a supervisor that communicates with the local controllers and provides high-level oversight and contingency measures in the event that local fault recovery is not possible. To realize this structure, an observer-based output feedback controller is initially designed for each DER to regulate its output in the absence of faults. The design accounts explicitly for practical implementation issues such as measurement sampling and plant-model mismatch. Fault detection is performed by comparing the output of the observer with that of the DER, and using the discrepancy as a residual. An explicit characterization of the minimum allowable sampling rate that guarantees both closed-loop stability and residual convergence in the absence of faults is obtained and used as the basis for deriving (1) a time-varying threshold on the residual which can be used to detect faults for a given sampling period, and (2) controller reconfiguration laws that determine the feasible fall-back control configurations that preserve stability. Finally, the design and implementation of the fault detection and fault-tolerant control architecture are demonstrated using a simulated model of a solid oxide fuel cell plant.

Networked control of Distributed Energy Resources: Application to solid oxide fuel cells

This paper presents a model-based networked control approach for managing Distributed Energy Resources (DERs) over communication networks. As a model system, we consider a solid oxide fuel cell (SOFC) plant that communicates with the central controller over a bandwidth-constrained communication network that is shared by several other DERs. The objective is to regulate the power output of the fuel cell while keeping the communication requirements with the controller to a minimum in order to reduce network utilization and minimize the susceptibility of the SOFC plant to possible communication disruptions in the network. Initially, an observer-based output feedback controller is designed to regulate the power output of the SOFC plant at a desired set-point by manipulating the inlet fuel flow rate. Network utilization is then reduced by minimizing the rate of transfer of information between the fuel cell and the supervisor without sacrificing stability or performance. To this end, a dynamic model of the fuel cell is embedded in the supervisor to approximate the dynamics of the fuel cell when measurements are not transmitted by the sensors, and the state of the model is updated using the observer-generated state estimate that is provided by the SOFC plant sensors at discrete time instances. An explicit characterization of the maximum allowable transfer time between the sensor suite of the fuel cell and the controller (i.e., the minimum allowable communication rate) is obtained in terms of model uncertainty and the choice of the control law. The characterization accounts for both stability and performance considerations. Finally, numerical simulations that demonstrate the implementation of the control architecture and its disturbance handling capabilities are presented.

Model-Based Fault Isolation and Reconfigurable Control of Transport-Reaction Processes with Actuator Faults

This paper presents a methodology for the design and implementation of integrated fault detection and isolation (FDI) and fault-tolerant control (FTC) systems for transport- reaction processes modeled by nonlinear parabolic partial differential equations (PDEs) with control constraints and actuator faults. Using a finite-dimensional system that captures the PDEs dominant dynamic modes, a family of nonlinear feedback controllers with well-characterized constrained stability regions are initially designed. Then, following a coordinate transformation that diagonalizes the input operator of the finite-dimensional system, a set of dedicated FDI filters - each replicating the fault-free behavior of a given state of the transformed system - are constructed. The choice of actuator locations ensures that each filters residual is sensitive to faults in only one actuator and decoupled from the rest. Following FDI, a set of actuator reconfiguration laws are derived to preserve closed-loop stability and minimize performance deterioration. Finally, the FDI-FTC architecture is implemented on the infinite-dimensional system, and appropriate FDI thresholds and actuator reconfiguration criteria are established to provide the necessary robustness against model reduction errors. Using singular perturbation techniques, these criteria are tied to the two time-scale separation between the slow and fast eigenvalues of the differential operator.

Fault-tolerant control of sampled-data nonlinear distributed parameter systems

This work presents an integrated fault detection and fault-tolerant control architecture for spatially-distributed systems described by highly-dissipative systems of nonlinear partial differential equations with actuator faults and sampled measurements. The architecture consists of a family of nonlinear feedback controllers, observer-based fault detection filters that account for the discrete measurement sampling, and a switching law that reconfigures the control actuators following fault detection. An approximate model that captures the dominant dynamics of the infinite-dimensional system is embedded in the control system to provide the controller and fault detection filter with estimates of the measured output between sampling instances. The model state is then updated using the actual measurements whenever they become available from the sensors. A sufficient condition for stability of the sampled-data nonlinear closed-loop system is derived in terms of the sampling rate, the model accuracy, the controller design parameters and the spatial placement of the control actuators. This characterization is used to derive rules for fault detection and actuator reconfiguration. The results are demonstrated through an application to the problem of stabilizing the zero solution of the Kuramoto-Sivashinsky equation.

Actuator fault detection and reconfiguration in distributed processes with measurement sampling constraints

This work develops a model-based approach for the detection and compensation of actuator faults in distributed processes described by parabolic PDEs with a limited number of measurements that are sampled at discrete time instances. Using an approximate finite-dimensional system that captures the dominant dynamics of the PDE, an observerbased output feedback controller that stabilizes the closed-loop system in the absence of faults is initially designed. The observer estimates are also used for fault detection by comparing the output of the observer with that of the process, and using the discrepancy as a residual. To compensate for measurement unavailability, a model of the approximate finite-dimensional system is embedded within the controller to provide the observer with estimates of the output measurements between sampling instances. The state of the model is then updated using the actual measurements whenever they become available from the sensors. By formulating the closed-loop system as a combined discrete-continuous system, an explicit characterization of the minimum allowable sampling rate that guarantees both closed-loop stability and residual convergence in the absence of faults is obtained in terms of the model accuracy, the controller design parameters and the spatial placement of the control actuators. This characterization is used as the basis for deriving (1) a time-varying threshold on the residual which can be used to detect faults for a given sampling period, and (2) an actuator reconfiguration law that determines the set of feasible fall-back actuators that preserve closed-loop stability under a given measurement sampling rate. Finally, the implementation of the fault detection and fault-tolerant control architecture on the infinite-dimensional system is analyzed using singular perturbations, and the results are demonstrated using a diffusion-reaction process example.

Detection, isolation and management of actuator faults in parabolic PDEs under uncertainty and constraints

This paper presents a methodology for the design of integrated robust fault detection and isolation (FDI) and fault-tolerant control (FTC) architecture for transport- reaction processes modeled by nonlinear parabolic partial differential equations (PDEs) with time-varying uncertain variables, actuator constraints and faults. The design is based on an approximate, finite-dimensional system that captures the dominant dynamic modes of the PDE. Initially, an invertible coordinate transformation, obtained with judicious actuator placement, is used to transform the approximate system into an equivalent form where the evolution of each dominant mode is excited directly by only one actuator and decoupled from the rest. For each mode, a robustly stabilizing bounded feedback controller that achieves an arbitrary degree of asymptotic attenuation of the effect of uncertainty is then synthesized and its constrained stability region is explicitly characterized in terms of the constraints, actuator locations and the size of uncertainty. A key idea in the controller synthesis is to shape the healthy closed-loop response of each mode in a prescribed fashion that decouples the effects of uncertainty and other modes on its dynamics, thus allowing (1) the derivation of performance-based FDI rules for each actuator, and (2) an explicit characterization of the state-space regions where FDI can be performed under uncertainty and constraints. Following FDI, a switching law is derived to orchestrate actuator reconfiguration in a way that preserves robust closed- loop stability. Finally, the theoretical results are demonstrated using a diffusion-reaction process example.

Integrating Actuator/Sensor Placement and Fault-Tolerant Output Feedback Control of Distributed Processes

A model-based fault-tolerant control (FTC) structure integrating nonlinear feedback control, state estimation, fault detection and isolation (FDI), and stability-based actuator reconfiguration is developed for distributed processes modeled by nonlinear parabolic PDEs with control constraints, actuator faults and limited state measurements. The design is based on an appropriate finite-dimensional model that approximates the dominant process dynamics. A key idea in the design is the judicious placement of control actuators and measurement sensors across the spatial domain in a way that enhances the FDI and fault-tolerance capabilities of the control system. Using singular perturbation techniques, precise FDI thresholds and control reconfiguration criteria accounting for model reduction and state estimation errors are derived to prevent false alarms when the FTC structure is implemented on the infinite-dimensional system. The criteria are tied to the separation between the slow and fast eigenvalues of the differential operator. Finally, the implementation of the developed architecture is demonstrated using a diffusion- reaction process example.

Stability-based actuator scheduling in distributed processes with control and communication constraints

This work focuses on control of distributed processes modeled by linear parabolic partial differential equations (PDEs) with constrained and quantized control inputs. Using a suitable finite-dimensional model that captures the PDEs dominant dynamics, we first characterize the inherent conflict in the control design objectives when both control constraints and quantization are simultaneously present, and the implications of this conflict for the spatial placement of the control actuators. At the heart of this conflict is the fact that control constraints limit the set of initial conditions starting from where stability can be achieved, while quantization constrains the set of terminal states that the system can be steered to. Using Lyapunov-based techniques, we explicitly characterize both the stability and terminal regions in terms of the control constraints, the quantization levels and the actuator spatial locations. The analysis reveals that the actuator configuration with the largest stability region also possesses the largest terminal region. This implies that steering the closed-loop state from large initial conditions to arbitrarily small terminal sets may not be possible using a single actuator configuration. To resolve this conflict, we devise an actuator scheduling strategy that orchestrates a finite number of transitions between different actuator configurations based on where the closed-loop state is with respect to the stability and terminal regions at any given time. The theoretical results are illustrated using a diffusion-reaction process example.