Fault-Tolerant Temperature Control Framework

• Fault-Tolerant Temperature Control Framework is a set of strategies combining modeling, estimation, fault detection, and adaptive control to maintain precise thermal regulation under faults.
• It integrates physical models, model-free estimators, and decentralized architectures to mitigate actuator, sensor, and component failures in diverse thermal applications.
• The framework demonstrates robust performance with reduced temperature RMSE, bounded gain parameters, and controlled fault propagation in industrial and building systems.

A fault-tolerant temperature control framework comprises a set of modeling, estimation, fault-detection, adaptation, and control strategies designed to maintain precise thermal regulation under the presence of actuator, sensor, or component failures, as well as model uncertainty and operational disturbances. Such frameworks have been developed and validated in high-stakes thermal systems including industrial power plants, building and greenhouse environments, and automotive HVAC and refrigeration contexts. Fault-tolerant architectures combine physical process models or model-free estimators, adaptive or robust control algorithms, and explicit or implicit mechanisms for fault accommodation. The prevailing frameworks exploit redundancy, physics-informed adaptation, real-time estimation, or decentralized clustering to deliver control performance and resilience beyond what conventional non-fault-adaptive architectures achieve.

1. System-Level Modeling and Fault Classes

Fault-tolerant temperature control frameworks are fundamentally tailored to the dynamics, critical variables, and fault modalities of the target thermal system. In thermal plants and power-generation applications, the underlying system dynamics are commonly represented by lumped-parameter or distributed-parameter models. For example, the steam turbine shell deflection control framework models the shell via a one-dimensional finite-difference discretization of the heat equation: $$\frac{1}{\alpha}\,\frac{dT_i}{dt} = \frac{1}{h^2}(T_{i-1} - 2T_i + T_{i+1}) + \frac{\dot q_i}{k}$$ with $T_i$ representing the temperature state of each shell element and $\dot q_i$ accumulating conduction from blanket heaters and convective exchange with the rotor (Geveci, 2017). In building thermal applications, reduced-order state-space models or first-order RC networks are adopted, and system faults may include partial actuator or sensor effectiveness loss, stuck relays, communication dropouts, or unmodeled large heat-loss paths (Xu et al., 2021, Chandan, 2021).

Actuator faults in these frameworks are often modeled as additive (e.g., stuck-on, stuck-off) or multiplicative (e.g., lost valve effectiveness) terms in the input signal. For instance, a loss of efficacy in a spray valve is captured as the transformation $u \mapsto (1-\phi)u$, with $\phi \in [0,1]$ representing the fault magnitude (Fanoodi et al., 3 Dec 2025). Sensor faults may be modeled as persistent bias, random spikes, or bursts (Xu et al., 2021).

2. Fault-Tolerance Mechanisms and Control Architectures

Control architectures for fault-tolerant temperature regulation exhibit diverse strategies to accommodate faults:

• Redundancy and Reallocation: In spatially-distributed heating systems (e.g., steam shell blankets), actuator-level faults such as zone outage or stuck actuators are mitigated by re-allocating thermal effort using remaining healthy actuators. The outer deflection loop actively shifts temperature references to compensate for unbalanced heat loss without requiring hardware reconfiguration for up to four simultaneous zone failures (Geveci, 2017).
• Adaptive and Physics-Informed Control: Frameworks such as the PINN-adaptive PI+feedforward control deploy a physics-informed neural network to continuously adapt control gains ($K_p$, $K_i$, $K_{ff}$) in real time, embedding first-principles (PDE) constraints in the loss function. This enables robust online tuning to changing plant responses under persistent actuator faults such as valve leakage (Fanoodi et al., 30 Nov 2025).
• Observer-Based Fault Estimation: Architectures incorporating a sliding mode observer (SMO) reconstruct unmeasured state variables in the presence of multiplicative faults, while a PINN estimates the time-varying fault parameter (e.g., loss of valve effectiveness) by enforcing model dynamics (Fanoodi et al., 3 Dec 2025).
• Model-Free Adaptive Estimation: In data-rich but model-impoverished contexts, ultra-local models with intelligent proportional (iP) or PI (iPI) control laws estimate total system dynamics and unknown disturbances in real time, directly absorbing actuator efficiency losses into the disturbance estimate and adaptively compensating faults without explicit diagnosis (Lafont et al., 2014).
• Decentralized and Hierarchical Control: In large-scale buildings, decentralized clustering and partitioned model predictive control (MPC) reduce fault propagation and confine actuator or sensor failures within clusters. The degree of architectural decentralization is selected through quantitative trade-off curves balancing performance (Optimality Loss Factor) and robustness (Fault-Propagation Metric) (Chandan, 2021).
• Learning-Based Fault Mitigation: Sensor fault tolerance in smart buildings is realized by chaining a temperature proposal generator (predictor neural network), a learned selector discriminating between raw and predicted temperatures, and a DQN-based controller; predictors are trained by model-assisted learning to enhance resilience under both IID and burst-type sensor faults (Xu et al., 2021).

3. Control and Fault-Compensation Algorithms

Control laws within fault-tolerant temperature regulation frameworks are chosen to maintain performance under both healthy and various fault scenarios:

• Relay and Two-Layer Deflection Feedback: In shell-deflection control, each of 20 heater zones implements a hysteretic relay law, with the outer-loop controller calculating deflection-induced temperature corrections:

$$T_{\mathrm{ref},i}(t) = T_{\mathrm{hold},i} + [\Delta T_{\mathrm{defl}}]_i$$

with $$\Delta T_{\mathrm{defl}} = K[y(t) - y_{\mathrm{des}}]$$ (Geveci, 2017).

• PI+Feedforward with PINN-Gain Adaptation: For HRSG superheaters, a PI+feedforward control law with gains $[K_p(\theta), K_i(\theta), K_{ff}(\theta)]$ is adaptively tuned by a PINN trained on tracking and physical-model-based losses:

$$L(\theta) = L_{\rm track}(\theta) + \mu L_{\rm phys}(\theta)$$

with online gradient updates ensuring adaptation to plant disturbances and valve leakage (Fanoodi et al., 30 Nov 2025).

• One-Sided Sliding Mode Control with PINN Compensation: The SMC scheme for HRSG temperature control corrects for valve degradation by scaling the control input using the estimated loss-of-effectiveness:

$u(t) = \frac{v(t)}{1-\hat\phi(t) + \epsilon}$

where $v(t)$ acts only when the plant exceeds the reference and $\hat\phi$ is estimated by the PINN (Fanoodi et al., 3 Dec 2025).

• Intelligent Proportional Model-Free Laws: The iP law,

$u = -\,\frac{F - \dot y^\star + K_P e}{\alpha}$

compensates actuator efficiency loss and tracks temperature setpoints without explicit model identification (Lafont et al., 2014).

• Learning-Based DQN with Proposal Selection: Fault-tolerant HVAC for buildings employs a learned selector to choose the most reliable temperature measurement before the DQN policy step, thus mitigating the impact of measurement faults during control updates (Xu et al., 2021).
• H-infinity Fault Compensation in Automotive HVAC: A Generalized Internal Model Control (GIMC) structure engages a fault compensator $Q(s)$, determined via $H_\infty$ optimization, to restore performance by minimizing the closed-loop effect of the identified actuator or sensor fault (Zhang, 2017).

4. Stability and Robustness Guarantees

Rigorous analysis underpins the stability and robustness credentials of fault-tolerant temperature control frameworks:

• Small-Gain and Boundedness Guarantees: In multi-loop relay control for distributed heating, inner-loop boundedness and outer-loop small-gain arguments ensure that deviations in deflection and temperature remain bounded under wide parameter and fault variations, as confirmed by Monte Carlo simulations (Geveci, 2017).
• Lyapunov-Based Adaptive Stability: Online PINN-PI frameworks provide Lyapunov functions combining tracking error and parameter estimation error. For instance:

$$V(e,\tilde\theta) = \frac{1}{2} e^2 + \frac{1}{2} \tilde\theta^T\Gamma^{-1}\tilde\theta$$

and show that for suitable $\Gamma$ and bounded leakage, the closed-loop system exhibits ultimate boundedness; tracking errors converge asymptotically under constant valve leakage (Fanoodi et al., 30 Nov 2025).

• Unified Observer-Controller-PINN Lyapunov Functions: For closed-loop frameworks comprising observer, PINN, and SMC, a composite Lyapunov function demonstrates uniform ultimate boundedness (UUB) of all error states and PINN weights even under multiplicative valve faults (Fanoodi et al., 3 Dec 2025).
• Passivity and $H_\infty$ Performance: Automotive GIMC-based FTC framework guarantees stability and limits the $L_2$-gain from faults/disturbances to plant outputs by construction of the robustifying path $Q(s)$, ensuring the closed-loop performance stays below strict bounds for all modeled plant variations (Zhang, 2017).
• Analytical Fault Propagation Bounds: In decentralized building thermal control, the Fault-Propagation Metric quantifies the worst-case spread of a zone fault across the system as a function of control partitioning, thus providing an explicit design handle for robust architecture selection (Chandan, 2021).

5. Implementation Strategies and Quantitative Outcomes

Implementations of fault-tolerant temperature control frameworks span embedded real-time controllers, field deployments, high-fidelity plant co-simulation, and learning pipelines:

• Embedded Real-Time and Zone Redundancy: The relay+deflection framework for turbine shells executes faster than real time on a GE Mark VIe controller. Zone granularity (20 heaters) is configured to match structural geometry, guaranteeing redundancy up to four heater faults (Geveci, 2017).
• Field Validation with Industrial Plant Data: HRSG PINN-PI+FF control demonstrates reduction in temperature RMSE (4.8°C to 1.7°C), elimination of overshoot, and allows higher power setpoint under valve leakage in operational combined-cycle power plants. PINN gain parameters remain bounded and readapt within ~100 s after fault disturbances (Fanoodi et al., 30 Nov 2025). The SMC-SMO-PINN controller maintains steam temperature errors below 1°C and settling time of ~45 s even at 40% valve effectiveness loss, outperforming PID in both transient suppression and steady-state tracking (Fanoodi et al., 3 Dec 2025).
• Model-Free Adaptation in Stochastic Environments: In greenhouse trials, model-free iP control maintains internal temperature within ±0.5°C even under 25%–50% actuator degradation; tracking error remains invariant and no gain retuning is required (Lafont et al., 2014).
• Learning-Assisted Data-Efficient Controllers: Model-assisted learning for sensor-fault tolerant HVAC achieves 70–98% reductions in temperature violation rates with only 25% of fully-labeled data required by the baseline approach, while energy cost remains within 2% of optimal (Xu et al., 2021).
• Decentralized Control Partitioning: Clustering algorithms for building MPC identify optimal “knees” in the trade-off curves, distributing zones into clusters to balance performance loss and contain fault propagation, as confirmed by co-simulation in EnergyPlus and analytical OLF/FPM measurements (Chandan, 2021).

6. Applications and Generalization Across Domains

Fault-tolerant temperature control frameworks generalize across diverse thermal domains:

• Power Plant Thermo-mechanical Systems: High-redundancy, model-driven, and structure-sensitive feedback is critical to safety and efficiency in turbine shells and HRSGs (Geveci, 2017, Fanoodi et al., 30 Nov 2025, Fanoodi et al., 3 Dec 2025).
• Automotive and Transport Refrigeration: FTC enabled by physically-motivated plant models and robust H-infinity design; explicit FDI schemes provide actuator and sensor isolation (Zhang, 2017).
• Smart Building HVAC: Sensor fault accommodation via model-assisted machine learning, decentralized model-based or learning-driven architectures, and real-time proposal selection; robust performance under measurement faults and network disruptions (Xu et al., 2021, Chandan, 2021).
• Agricultural Environments: Real-time model-free adaptation, with direct relevance to other SISO or small-scale MIMO temperature-driven processes (Lafont et al., 2014).

These frameworks are unified by their pursuit of closed-loop boundedness, real-time adaptability, and explicit or implicit use of redundancy in architecture or signal processing. Future research is likely to focus on integrating physics-informed learning with advanced fault detection/isolation, convex and data-driven decentralized architectures, and standardized robustness certification across increasingly networked and autonomous thermal systems.