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In order to offer a reliable, fast, and offset-free tracking performance for the regulation of heart rate (HR) during treadmill exercise, a two-input single-output (2ISO) control system by simultaneously manipulating both treadmill speed and gradient is proposed. The decentralized integral controllability (DIC) analysis is extended to nonlinear and non-square processes especially for a 2ISO process, namely multi-loop integral controllability (MIC). The proposed multi-loop integral control-based HR regulation by manipulating treadmill speed and gradient is then validated through a comparative treadmill experiment that compares the system performance of the proposed 2ISO MIC control loop with that of single-input single-output (SISO) loops, speed/gradient-to-HR. The experimental validation presents that by simultaneously using two control inputs, the automated system can achieve the fastest HR tracking performance and stay close to the reference HR during steady state, while comparing with two SISO structures, and offer the fault-tolerant ability if the gains of the two multi-loop integral controllers are well tuned. It has a vital implication for the applications of exercise rehabilitation and fitness in relation to the automated control system.

Multi-Loop Integral Control-Based Heart Rate Regulation for Fast Tracking and Faulty-Tolerant Control Performance in Treadmill Exercises