## 1 Introduction
While offering enhanced performance, designing and tuning NPID controllers can often be more complex than their linear counterparts. A novel NPID controller that addresses this challenge was presented in [15; 16]. By scaling the error input to the integrator within the standard PID controller framework, the number of tuning parameters is maintained at three, simplifying the design and tuning process. To further improve control precision and stability, researchers have increasingly incorporated advanced control strategies including adaptive control and intelligent techniques like evolutionary algorithms, neural networks, and fuzzy logic. In [17], the authors investigated the design and performance of internal model control and model reference adaptive control (MRAC) for the linearized second-order model of a CSTR process. In [18], the authors explored an improved method for controlling the temperature of a continuous reactor; an improved Sparrow Algorithm was used to find the best settings of a PID controller. In [19], the authors proposed the use of a neuro-fuzzy control system, optimized by a metaheuristic technique, for precise temperature control in a chemical reactor during biodiesel production. In [20], the authors developed a type of adaptive controller for systems in which a linear part is followed by a nonlinear part. This controller uses both linear and nonlinear control methods to achieve better performance. This paper presents a fuzzy adaptive control scheme for continuous stirred tank reactors (CSTRs) subject to full-state constraints and actuator faults. Employing backstepping design in conjunction with an Integral Barrier Lyapunov Function (IBLF), the control strategy effectively addresses the limitations imposed by the full-state constraints. [PERSON] and [PERSON] [21] presented the design of a Model Reference Adaptive System (MRAS) utilizing the MIT rule. The MIT rule, employing a gradient-based method, adjusts the controller gain to minimize the discrepancy between the actual plant's behavior and the desired behavior defined by a reference model. In [22], the authors studied an adaptive neural network (NN) control strategy for CSTRs operating under the influence of time-varying delays and subject to full time-varying state constraints. The time-delayed terms are decomposed into a sum of positive continuous functions using a separation technique. Subsequently, Lyapunov-Krasovskii functionals are employed to effectively address the stability concerns arising from these positive continuous functions containing delayed states. In [23], the authors proposed two neural network (NN)-based adaptive control strategies for continuous stirred tank reactors (CSTRs) subject to input nonlinearities and unknown disturbances. The first approach incorporates a robust control term to mitigate the impact of input dead zones. The second approach utilizes an anti-windup compensator to alleviate the effects of actuator saturation. [PERSON] et al. [24] proposed an RBF-NPID control algorithm to improve the adaptive capability of the NPID controller for CSTRs. The RBF neural network is used to adjust nonlinear gains online to improve the control performance of the system. A characteristic of this approach is the adaptation of three nonlinear PID gains, which necessitates defining nine constants. [PERSON] et al. [25] presented a novel adaptive fuzzy control scheme for CSTRs that effectively addresses full-state constraints and actuator faults. The proposed controller utilizes IBLF to ensure that all state variables remain within their specified bounds. The adaptive fuzzy control mechanism is designed to compensate for uncertainties in the system dynamics. In [26], the authors proposed an approach that combined sliding mode control with an event-triggering mechanism to ensure stability and disturbance rejection under limited network resources. [PERSON] et al. [27] introduced a neural network-based PID controller for CSTR temperature regulation.