Design of an Indirect Adaptive Controller Based on Fuzzy Logic Control for Linear Cascade Systems Affected by Bounded Unknown Disturbances

This paper presents a novel indirect adaptive control scheme that integrates fuzzy logic with a virtual integral-based adaptive controller to enhance the tracking performance of linear cascade systems under bounded unknown disturbances. The proposed controller builds upon the established indirect adaptive control framework, employing a virtual state algorithm but augments it with a fuzzy inference mechanism that dynamically adjusts a key control parameter to improve robustness and adaptability. Gaussian membership functions and a Sugeno-type fuzzy inference system are employed to fine-tune the gain parameter based on real-time tracking error and its derivative. The control law incorporates parameter adaptation, a saturation function to replace discontinuous sign operations, and a fuzzy-tuned gain to mitigate chattering and improve transient response. Simulation results under severe disturbances demonstrate significant improvements in tracking accuracy and control smoothness. Specifically, the proposed fuzzy-based controller reduces steady-state tracking error by over 40%, minimizes control chattering, and maintains robust performance under disturbance amplitudes up to 185 units-conditions that severely degrade the performance of the non-fuzzy indirect adaptive controller. The effectiveness of the proposed algorithm is shown by handling model uncertainties and external perturbations in a two-level linear cascade system.