Discrete-time sliding mode control of heart rate during treadmill exercise

A Barrier Function-Based Integral Sliding Mode Control of Heart Rate During Treadmill Exercise

“…ISMCbf in Eq. ( 40) is compared to QSMC designed in the study [14] and also to STSMC designed in the study [15]. The two controllers from the literature are employed here as designed in the original work but with the current output and error equation definitions.…”

“…where, 𝜌 = 2.121, 𝑦̇𝑟 is the derivative of 𝑦 𝑟 [14], 𝜖 1 = 0.05. As for STSMC, the final control law is given as follows [15]:…”

“…The following nonlinear model describes HR response to the treadmill speed during an exercise [15,11,3]:…”

“…It was shown that SMC performed better than an existing controller from the literature. In other study, Esmaeili et al [15] designed a Super-Twisting based SMC (STSMC) to track a pre-defined HR profile. They employed particle swarm optimization to re identify the nonlinear model of the research [3] on ten subjects.…”

“…ISMCbf is continuous and chattering-free since the barrier function is differentiable. To show the efficiency of the proposed approach, ISMCbf is compared to other controllers designed in previous studies: QSMC [14] and STSMC [15]. This comparison is useful as QSMC outperformed an existing reference controller and STSMC outperformed PID performance that was designed in another earlier study.…”