Identification and Robust Control of Heart Rate During Treadmill Exercise at Large Speed Ranges

Abstract

The objective of this paper is to design a heart rate (HR) controller for a treadmill, so that the HR of an individual running on it tracks a pre-speci?ed, potentially time-varying pro?le speci?ed by doctors for the cardiac recovery of the person. Initially, a parameter estimation algorithm is presented with the aim at estimating the values of the parameters of a model relating the speed of the treadmill with the HR of an individual. The parameter estimation problem is formulated as an optimization one and solved by using Particle Swarm Optimization (PSO). Afterwards, a super- twisting sliding mode controller is designed to perform the robust control of treadmill’s speed in the presence of potential unmodelled dynamics or parametric uncertainties. Numerical examples show that the estimation procedure is able to obtain accurate values for the system’s parameters while the proposed control approach is able to obtain zero tracking error without chattering, de?nitely achieving the control objectives. In both cases the range of treadmill’s speed goes from 2 to 14 km/h, range that is not usually employed in previous studies.