Discrete-time observer-based state feedback control of heart rate during treadmill exercise

This paper designs a discrete-time state-feedback output tracking control for the heart rate during treadmill exercise. Initially, the nonlinear model describing the relationship between the heart rate and the speed of a treadmill is discretized. Afterwards, a feedback linearization-based control law is proposed to achieve perfect output tracking. The control objective is to make the runner's heart rate follow a heart rate reference profile set by especialists as reference. The set-up of the problem in discrete time allows taking into consideration the effect of sampling during the controller design procedure instead of relegating it to the implementation stage. It will be shown that a linear state feedback controller is enough to make the nonlinear model's output track the reference profile regardless its possibly complex time variation. Since the full state is not available for measurement a reduced order state observer is incorporated into the discrete-time control law. Then, the continuous control command is generated by using a zero order hold (ZOH). The designed control system is tested on the original continuous-time nonlinear model by computer simulation to demonstrate the effectiveness of the proposed method to achieve the required objective.