2.2. Subjects

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.

The Human Research Ethics Committee by University of Technology Sydney (UTS HREC 2009000227) approved the study, and an informed consent was obtained from all participants before each experiment. The physical characteristics of the participants are presented in Table 1. The subjects were required to take a light meal prior to the experiment activity and not to participate in any intense exercises one day before the experiment [14–16]. The environmental temperature during the experiments was set at 25C, and the humidity was at about 50% [17]. The HR monitor (HM131) was fitted to the middle of the chest of every subject by using electrode pads.

running in order to stabilize his/her desired HR level. As a result, simultaneous manipulating

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

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The Pan-Tompkins algorithm was applied to identify the P-peak of QRS complex during experiments, which is then used for calculations of HR values. This algorithm is inclusive of several filtering such as a band-pass filter, a differentiator, a squaring operation and a moving window integrator [9]. The band-pass filter is used to reduce noises in the raw ECG signals. After band-pass filtering, the high frequency components of ECG signals were extracted by using a five-point derivative function. The squaring operation was adopted to suppress P and T waves and further enhance the higher frequency QRS complexes. Finally, the moving window integrator provided a single peak output, P-peak, for each QRS complex. After implementing these steps and by implementing an adaptive threshold algorithm with false

peak detection capabilities, the HR signals can be detected accurately [18].

3.1. Multi-loop integral controllability analysis for HR responses to treadmill exercise

definition of MIC, which is a direct extension of DIC for a non-square 2ISO process [19].

<sup>y</sup> <sup>¼</sup> g xð Þ ; <sup>u</sup> <sup>y</sup> <sup>∈</sup><sup>Y</sup> <sup>⊂</sup>R<sup>1</sup>

with an input vector u∈ R<sup>2</sup> and an output vector y∈R<sup>1</sup>

(

In [8], the multi-loop PI controller has been designed for the regulation of HR for treadmill exercise. Now, we consider the case when one of the actuators is in faulty condition. First, we introduce a

As shown in Figure 1, assume the HR response can be described by the following equations

<sup>P</sup> <sup>x</sup>\_ <sup>¼</sup> f xð Þ ; <sup>u</sup> <sup>x</sup> <sup>∈</sup> <sup>X</sup> <sup>⊂</sup> Rn, u<sup>∈</sup> <sup>U</sup> <sup>⊂</sup>R<sup>2</sup>

where the state x tð Þ is determined by its initial value xð Þ0 and the input function u tð Þ. Considering the system (1) has equilibrium at origin, that is, fð Þ¼ 0; 0 0 and gð Þ¼ 0; 0 0, if the equilibrium xe is not at origin, a translation is then needed by redefining the state x as x � xe [19, 20].

(Multi-loop integral controllability for nonlinear 2ISO processes) Consider the closed loop system

i. For the nonlinear process P described by Eq. (1), if a multi-loop integral controller C exists, such that the unforced closed loop system (r ¼ 0) is globally asymptotically stable (GAS) for the equilibrium x ¼ 0 and such that the globally asymptotically stability is satisfied if each individual loop can be detuned independently by a factor ki (0 ≤ ki ≤ 1, i ¼ 1, 2), then the nonlinear process P is said to be multi-loop integral controllable (MIC)

:

(1)

of speed and gradient would be firmly beneficial.

2.4. Pan-Tompkins HR detection

3. Methodology

3.1.1. Definition 1

depicted in Figure 2.

for the equilibrium x ¼ 0.
