5. Conclusion

Figure 8. Experimental data for HR step responses to either treadmill speed or gradient (open-loop test with gradient and

Figure 9. HR tracking performance comparison of SISO (speed) test with 2ISO.

Figure 10. HR tracking performance comparison of SISO (gradient) test with 2ISO.

HR).

286 Adaptive Robust Control Systems

This study investigates the benefits of using two controller inputs, the speed and gradient, for the regulation of HR during treadmill exercises. The main goal of HR control in treadmill exercises is to ensure a reliable, fast, and offset-free tracking, as well as to offer the faulty tolerance ability in the case of one of actuators (either treadmill speed or gradient) being out of service. For this purpose, we extended the concept of nonlinear decentralized integral controllability (DIC) to nonlinear 2ISO processes and presented a sufficient condition which only needs checking the steady state input-output relationship of controlled processes. Based on the proposed condition, we investigate the new defined multi-loop integral controllability (MIC) for walking, running, and walking-running zones. 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 multiloop 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.
