Advanced control techniques for the heart rate during treadmill exercise

Resumen

The objective of this work is to design a heart rate (HR) controller for a treadmill so that the HR of an individual running on it tracks a pre-specied, potentially timevarying profile specified by doctors for the cardiac recovery of the person. Initially, we consider a mathematical model relating the relationship between the speed of the treadmill and HR of the person running on it. An important issue in this model is the determination of its parameters. Thus, we first tackle the parameter estimation problem in this model which is formulated as an optimization one, that is solved through a heuristic technique known as Particle Swarm Optimization. This is the first time that this technique is used for the estimation of cardiac models and is a contribution of the thesis. Afterward, a super- twisting sliding mode controller is designed to perform the robust control of treadmill’s speed in the presence of potential unmodelled dynamics and 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, definitely 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. Finally, in the last part of this work, the objective is to design a discrete-time robust controller. Initially, a feedback linearization-based controller is designed, but it has poor robustness properties. In order to solve this problem, we propose another method consisting in the Joint parameter-state estimation based-control. However, this approach does not identify the parameters and it offers some oscillations. To solve all of these problems and regarding the previous Chapter, we used the discretetime sliding mode controller method to complete our study. In the first part of this Section, as designing a nonlinear model directly is hard, we decided to linearize the model and then discretize it. Furthermore, the continuous control is generated by a zero-order hold (ZOH). On the other hand, since the nonlinear model relationship describes a better relation between HR and speed, a nonlinear is used in the last part of this thesis. The final and best controller is a discrete-time super-twisting model that avoids chattering and achieves very good robustness and tracking in the system. The great systematic procedure to design of the controller, the perfect tracking and the avoidance of using an observer for this system are other advantages of this approach. The simulation results in this work that presented in the speed range of 2-14 km, a range that is not usually employed in previous studies to the control of the heart rate during treadmill exercise.