1. Introduction

Obesity, which leads to diabetes and cardiovascular disease (CVD), is one of the major threats to human health. It is well recognized that regular exercise is the most efficient way to reduce

© The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons © 2018 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

the possibility of both type 2 Diabetes and CVD [1]. The development of automated exercise assisted equipment can greatly enhance the efficiency of exercises and reduce the requirement of supervision. An easy-to-measure indication of exercise strength is heart rate (HR). One of the most efficient ways for the manipulation of exercise intensity for either the training of athletes or rehabilitation patients is to simulate the HR in order to follow a pre-designed HR profile. As a result, an automated control system can offer numerous benefits for different groups of users. For instance, it will provide assistance for patients with cardiac diseases who might be prescribed treadmill exercise rehabilitation. It also can be used for training the athletes and safely regulating the exercise intensity within a suitable profile in order to achieve the predefined HR ranges. It has been well documented that by determining one's maximum and minimum values of HR responses the exercise profile can be individually designed [2]. Specifically, rehabilitation patients will be guided to perform the exercise in terms of 50–60% of the maximum HR, 60–70% of the maximum HR zone then suitable for subjects who target weight control, and the range between 70 and 90% is preferred for the cardio-endurance exercise. In the study, a two-input single-output (2ISO) control system is proposed, which can specially further improve the efficiency of treadmill exercises for different subject groups as well as diversify more reliable and safe treadmill exercise protocols.

for a 2ISO process, namely multi-loop integral controllability (MIC). The proposed multi-loop integral control-based HR regulation by manipulating treadmill speed and gradient is then validated through a comparative treadmill experiment that compares the system performance of the proposed 2ISO MIC control loop with that of single-input single-output (SISO) loops, speed/gradient-to-HR. The real treadmill experiment is used to experimentally validate if MIC in the HR range is valid. Results show that, compared with two SISO loops, the 2ISO MIC control loop can achieve the fastest HR tracking performance, reach up to the reference HR during the steady state, as well as offer the fault-tolerant ability in the case of one of the gains of multi-loop integral controllers being out of service. It has a vital implication for the applica-

Multi-Loop Integral Control-Based Heart Rate Regulation for Fast Tracking and Faulty-Tolerant Control…

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tions of exercise rehabilitation and fitness in relation to the automated control system.

In this study, the HR data during experiments were collected by a portable sensor, Alive Heart Monitor (HM131) manufactured by Alive Technologies. It consists of one HR sensor and one triaxial accelerometer. The HR data acquired from the internal HR sensor are used in the study. The sampling rate for HR data collections is 300 samples/s. A Bluetooth SPP connection is used to transmit the instantaneous HR data to the laptop-based control program that is designed and implemented based on LabVIEW (National Instrument). The treadmill Powerjog J series is set up for experiments, the speed and gradient of which is controlled and able to be accessed via the RS232 protocol. Figure 1 shows the schematic diagram for the experimental equipment

Eight healthy non-smoking males were invited to join the experiments. They were free from any known cardiac or metabolic disorders, hypertension, and were not under any medication.

Figure 1. The schematic diagram for the experimental equipment setup.

2. Experiments

setup.

2.2. Subjects

2.1. Experimental settings

Recently, most studies [3–6] only consider using one manipulate variable (treadmill speed or gradient) to regulate HR responses. In [7, 8], for exercise testing and rehabilitation of subjects with impaired exercise tolerance, ramp type protocols were proposed by simultaneously manipulating both speed and gradient (without feedback), which could produce a low initial metabolic rate that then increases the work rate linearly to reach the subject's limit of tolerance in approximately 10 min. In [9], a multi-loop proportion-integral (PI) controller based HR tracking system has been presented, which independently tuned both treadmill speed and gradient in closed loop, and achieved good performance. However, in paper [9], it is assumed that the HR response to treadmill exercise is in linear range, and only linear modeling and control approaches have been presented. The experimental evidences of the advantages of using both speed and gradient to regulate HR are therefore only valid in a certain linear response range.

This study introduces the 2ISO HR process which employs two actuators, treadmill speed and gradient, to regulate the HR response. Such process control has the following merits. First of all, it can increase the non-saturation range. For example, practical systems always have physical limitations and therefore have limited non-saturation range. If simultaneously executing multiple actuators, the output range can be extended. On the other hand, it can increase the maximum gain of the actuator so that the fast tracking or regulation of manipulated variable can be achieved [9]. Also, redundancy of actuators can facilitate fault accommodation for the implementation of faulttolerant control strategies. As the stability of the closed loop system can be practically achieved by adding suitable constraints in control inputs and their derivatives, the achievable performance (especially in steady state) is more important for most industrial control processes.

For the regulation of HR, multi-loop PI controllers were developed [9] in order to achieve zero steady-state tracking error. For multi-loop PI control of square process, Skogestad and Morari [10] introduced the concept of decentralized integral controllability (DIC). DIC analysis [11–13] determines the stability, integral control ability, and faulty-tolerant control of the multi-loop system. This study extends the DIC analysis for nonlinear and non-square processes especially for a 2ISO process, namely multi-loop integral controllability (MIC). The proposed multi-loop integral control-based HR regulation by manipulating treadmill speed and gradient is then validated through a comparative treadmill experiment that compares the system performance of the proposed 2ISO MIC control loop with that of single-input single-output (SISO) loops, speed/gradient-to-HR. The real treadmill experiment is used to experimentally validate if MIC in the HR range is valid. Results show that, compared with two SISO loops, the 2ISO MIC control loop can achieve the fastest HR tracking performance, reach up to the reference HR during the steady state, as well as offer the fault-tolerant ability in the case of one of the gains of multi-loop integral controllers being out of service. It has a vital implication for the applications of exercise rehabilitation and fitness in relation to the automated control system.
