Designing of intelligent PID controller for cardiac pacemaker using artificial bee colony algorithm

ABSTRACT

For real-time patient heart rate management, most widely used biomedical implantable devices in the cardiovascular system is the cardiac pacemaker (CP). A key factor in keeping the patient alive is the development of novel heart pacing techniques which can reduce the risk of cardiac arrhythmia. The present work is inspired to achieve this goal. To achieve an accurate, controlled, and regulated heart rate, a pacemaker with an intelligent proportional integral derivative (PID) controller is considered. The proposed PID controller is an integration of the traditional PID controller with appropriate tuning, that uses a swarm intelligence-based artificial bee colony (ABC) algorithm for handling the bio-electrical signals. To ensure the efficacy of the proposed controller experiments are conducted. MATLAB/Simulink software is used to test and simulate the suggested model and to adjust the controller gains. The simulation is performed in the time and frequency domain. The resulting pulse rate from the ABC-PID controller has a rise time (0.0985 s), settling time (0.3293 s), maximum overshoot (0.111367%), and MSE (0.0040565). External disturbances of various duty cycles are also introduced in the proposed CP control system. The proposed ABC-PID controller for implanted pacemakers reduces the risk of heart rate over-run.

KEYWORDS:

• Cardiac pacemaker
• proportional integral derivative
• artificial bee colony algorithm
• ABC-PID controller
• heart rate
• cardiac arrhythmias

1. Introduction

One of the worst diseases in the world is heart disease. It can be simply said that heart failure results from the heart’s inadequate pumping function (AHA, 2024). Diabetes, high blood pressure, and coronary issues that harm the heart are essentially the main causes of heart failure (NHLBI, 2024). Cardiovascular illnesses continue to afflict over half a billion people worldwide, accounting for 20.5 million deaths in 2021 – about a third of all fatalities worldwide and an overall rise above the anticipated 121 million heart disease deaths (WHF, 2023). On-time identification of heart working disorders and fast curing can rescue the patient and also can help to give them a normal life. It can be done by observing the bio-electrical (BE) signal pattern of the heart. A specific pattern of BE signals actuates the muscles of the heart and allows it to work in a rhythm. This rhythm is commonly known as heart rate (HR). It can be measured with some sensors and electronic instruments. The normal range of HR for an adult is 72–85 BPM (beats per minute), and it may go to 60–65 BPM with age (Favilla et al., 2018). This range is for normal activity conditions, but it may vary with the activity like running, playing, swimming, etc. During the active time, the heart needs to synchronize the HR with the activity.

The technique of sensing the BE signals and plotting them on a screen or a paper is known as Electro-Cardio-Graphy (ECG). It is a very common heart function monitoring process (Jafarnia-Dabanloo et al., 2007). The electrical signals sensed from the heart have a specific pattern of the waveform shown in Figure 1. For understanding purposes, these waveforms are globally named as P wave, R wave, and T wave. The R wave is the most important and is further divided into components QRS. Monitoring subsequent R waves plays a major role in diagnosing any disorder in heart function (Brockmann et al., 2022).

Figure 1. QRS compound.

The heart has its natural pacemaker known as the Sinoatrial (SA) node, which generates the BE signals and controls the HR. Any deficiency in this natural pacemaker may cause the loss of heart rhythm (Ansari et al., 2018). To overcome the effects of failure of natural rhythm the heart will be actuated by providing external natural rhythm like electrical signals (Arunachalam et al., 2016). These external signals are generated by an electronic instrument known as a pacemaker. The pacemaker continuously monitors the heart rhythm and in case of any abnormality, supports the heart by externally generated signals (Govind & Sekhar, 2014). To enhance the functional capability of the CP system, much research has been done on dynamic control techniques to modify and regulate the HR.

The best toolkit for control engineers to control the external pacemaker is the PID controller since it offers a quick response. The PID controller, on the other hand, has appeared as the simplest and most widely used traditional controller in industries as well as in the medical field (Dubey, 2021). The PID controller, a fuzzy-based controller, and the combination of other control approaches, such as F-PID (Fuzzy-PID), FO-PID (Fractional Order-PID) (Bajpai et al., 2017), etc., have all been utilized to improve the performance of pacemaker. To assess and choose the best controller for the intended pacemaker, the benefits and drawbacks of each controller are compared concerning the required output response parameters, which include the rising and settling time, maximum percentage of overshoot, and maximum allowable error. One prominent reason for unexpected death is cardiac arrhythmias. In the case of cardiac arrhythmias, a few seconds of the starting is most important to recover the heart function. An arrhythmia results in an irregular HR due to electrical impulses that are too fast (tachycardia), too slow (bradycardia), or chaotic, hence this condition presents a difficult design challenge for pacemakers.

Numerous studies have been drawn on pacemaker controllers to achieve quick response time and precise outcomes. Yadav et al. (2011) implemented a fuzzy controller for the CP controlling. The outcomes demonstrate how a fuzzy controller is better than the various conventional PID controllers as shown in Table 1. Still, it has an overshoot variation from 2.09 to 3.58%, and the settling time is 0. 7563 s. Shi (2013) designed a novel F-PID for dual-sensor CP systems. In contrast to the traditional fuzzy control approach, the response parameters produced by the F-PID were more consistent. However, the error value is 2.3–2.6%. Shi (2013) proposed an updated F-PID that responds more consistently and precisely and still has a maximum inaccuracy of 1.72–1.92%. Govind and Sekhar (2014) proposed an adaptive PID controlling scheme with MIT and Delta rules for HR regulating but, the system needs manual controlling of the learning rate of an adaptive correction factor. Arunachalam et al. (2016) proposed an FO-PID controller based on the ZN method with a 2% overshoot, 0.2761 s settling time, and a higher rise time than a conventional PID controller. Aghdam et al. (2017) used the neural network (NN) fused with the F-PID controller for CP controlling and achieved better outcomes over the F-PID. However, the settling time is 1.23 s and the maximum overshoot is 0.5%. Bajpai et al. (2017) used the GA method to tune the five parameters of the FO-PID controller for CP controlling, with a minimized settling time of 0.6432 s but the percentage overshoot is 0.9112. Momani et al. (2019) proposed an FO-PID controller based on the PSO optimization method via El-Khazali’s technique for HR regulation. However, the settling time and overshoot are 0.3573 s and 0.8597%, respectively. Nawikavatan et al. (2019) use a PID-accelerated (PIDA) spiritual search (SS) algorithm-based controller. The researcher has used the acceleration coefficient as the fourth parameter. The SS-based PIDA can regulate the HR with a faster response than the SS-based conventional PID, but the achieved overshoot is 1.4139%. Khan et al. (2020) used the concept of fuzzy logic with FO-PID for better performance of CP and got a percentage of error as 0.72, 3.14, 6.18, and 23.26 by fuzzy logic-based FO-PID, FO-PID, F-PID, and PID, respectively. A maximum percentage overshoot of 98.45 and 99.28 for males and females, respectively, was achieved by Khan et al. (2021). Kumar et al. (2022) proposed a fuzzy FO-proportional derivative with an integral controller based on the GWO optimization algorithm for finding the optimum controlling parameters of the CP system. Still, it has a 2.9601 settling time and 0.9857% overshoot.

Table 1. Quantitative comparison of the literature review.

Author	Controller	Rise-time	Settling-time	Max. overshoot (%)
Yadav et al. (2011)	PID controller with ZN algorithm	0.0714	1.0204	23.55
Yadav et al. (2011)	PID controller with TL algorithm	0.0860	0.4098	11.73
Yadav et al. (2011)	PID controller with relay tuning algorithm	0.3621	1.0617	5.48
Yadav et al. (2011)	Fuzzy controller	0.3442	0.7563	2.09
Aghdam et al. (2017)	PID controller with the fusion of fuzzy and NN algorithm	1.63	1.23	0.5
Bajpai et al. (2017)	FO-PID controller with genetic algorithm (GA) algorithm	0.0908	0.6432	0.9112
Momani et al. (2019)	FO-PID controller with PSO via El-Khazali’s algorithm	0.2263	0.3573	0.8597
Nawikavatan et al. (2019)	PID controller with SS algorithm	0.3072	0.5899	4.6046
Nawikavatan et al. (2019)	PIDA with SS algorithm	0.1304	0.3368	1.4139
Kumar et al. (2022)	Fuzzy FO-proportional derivative + integral with GWO algorithm	0.3747	2.9601	0.9857

This paper used the ABC optimization algorithm to fine-tune the parameters of the PID controller to improve the stability of the CP control system. Swarm intelligence-based ABC algorithm widely used in various fields. Karaboga and Ozturk (2011) used the ABC algorithm for data clustering and the results show a comparative improvement in system efficiency. Pareek et al. (2014) proposed the ABC-based PID controller to tune the ball and hoop (fourth-order system) problem and has lower settling, rising, and peak times. Liao et al. (2014) applied an ABC-PID controller to enhance the performance index of a DC motor control system. Fang et al. (2017) used a combination of a back propagation neural network and the ABC method for course-controlling unmanned surface vehicles. Aytekin and Senberber (2017) used the ABC approach to find the ideal PID settings for higher-order oscillatory systems. The findings of the simulation indicate that the PID tuning method based on ABC may be effectively and effortlessly implemented for higher-order oscillatory systems. Bingul and Karahan (2018) proposed an enhanced ABC algorithm that combines chaos and cyclic exchange neighbourhood to tune the parameters of the FO-PID controller for the automated voltage regulator structure.

Furthermore, because of the restrictions of the tuning process, the FOPID controller is subpar. Numerous issues can be successfully solved using the ABC method (Aslan & Karaboga, 2020; Karaboga & Gorkemli, 2019). Wang et al. (2022) developed an extended ABC, to optimize PID controller gains with the balancing of explorative and exploitative to strengthen the PID controller’s performance for a steel strip deviation control system (SSDCS); in terms of convergence, dynamic adjustability, and resilience, simulation findings demonstrate that extended ABC-PID works better for SSDCS than four (ABC, PSO, Differential Evolution, and GA) bio-inspired algorithms based PID controllers. Du et al. (2022) propose a PID controller for the active magnetic bearings that are optimized using a reformative ABC algorithm and found more robustness in comparison to the classic PID, PSO-PID, DE-PID, and GA-PID. Dey et al. (2024) proposed a finite dimension repetitive controller for CP-controlling which is based on an artificial neural network also utilizing the principle of internal model and data processing carried out by using discrete wavelet transforms (DWT) in the repeated controller loop. Three significant drawbacks plague the DWT, despite its greatness in signal and image processing: shift sensitivity, inadequate directionality, and lack of phase information.

The literature study gives the idea that the most difficult challenge is to build a CP controller that can satisfy the necessary response parameters, like quick rising and settling time, minute percentage overshoot, and system errors. Moreover, minimum overshoot and error are the main goals of the pacemaker controller design. A quantitative comparison of the literature review is presented in Table 1.

Following reasons motivated to use ABC algorithm based PID controller for the pacemaker:

1. ABC offers fundamental characteristics including great flexibility, ease of conversion to other methods, rapid convergence, and robustness in addition to being straightforward to apply.

2. The ABC algorithm based PID controller had never been used for CP controlling until this work.

Thus, on the basis of characteristics of the ABC algorithm, the contributions of the proposed work are as follows:

1. The implementation of the proposed algorithm with the PID controller gives the improved CP system stability.

2. The overshoot, settling time, and MSE are minimized with compared to other considered algorithms.

3. The proposed system is implemented on hardware.

The remaining sections are arranged as follows: Section 2 presents the model description with mathematical modelling, basic steps of the optimization algorithm, and hardware design. Section 3 presents the simulation outcomes and superiority of the proposed ABC-PID controller compared to the existing controller. Finally, Section 4 gives the conclusion of the current work.

2. Model description and hardware design

2.1. Heart and pacemaker mathematical modelling

Numerous models, including mathematical (Katholi et al., 1977; McLernon et al., 2004), electrical (Vanderpol equations) (Gois & Savi, 2009; Grudziński & Żebrowski, 2004; Kaplan et al., 2008), YNI (Yanagihara, Noma, and Irisawa) model (Noma et al., 1977), and IPFM (Jafarnia-Dabanloo et al., 2007; Lak et al., 2010) have been developed for CP system. Mathematical modelling of the heart conduction system can be well defined by the YNI. The YNI model is a well-established and accurate SA replica of act possible production and proliferation in the heart. The YNI replica, like all other cardiac cell models, is pedestal on voltage clamp data and is of the Hodgkin–Huxley type model (Landau et al., 1990). The replica shown in Figure 2 depicts the current–voltage relationship and simulates the unprompted act possible (Yanagihara et al., 1980).

Figure 2. The cell membrane model (Keener & Sneyd, 1998).

It has four time-dependent currents and one that is not time-dependent (Shi et al., 2010). These are I_Na = Fast inward current (Sodium current), I_K = Potassium current, I_S = Slow inward current, I_H = Hyper-polarization activated current (Delayed inward current), I_L = Leakage current (Time independent). The conservation of trans-membrane currents is expressed in units of (µA/cm²) as follows: (1) $C_m\frac{\mathrm{dV}}{\mathrm{dt}}+I_{\mathrm{Na}}+I_K+I_S+I_H+I_L=I_{\text{app}}$(1) The I_S is a very important current in the YNI paradigm. This current is also responsible for the oscillation and the majority of the upstroke. The I_S steadily depolarizes the node after re-polarization by I_K in anticipation of a specified threshold being attained and a deed potential is begun in the fluctuation. As a result, the response of the YNI model, which is based on the currents that are sensed from the human body, produces a standard pulse. Other ionic currents also exist, including the chloride current, although they are tiny and grouped in the Hodgkin–Huxley hypothesis as the leakage current. Simplified form of Equation (1)(1) $C_m\frac{\mathrm{dV}}{\mathrm{dt}}+I_{\mathrm{Na}}+I_K+I_S+I_H+I_L=I_{\text{app}}$(1) is given in Equation (2)(2) $C_m\frac{\mathrm{dV}}{\mathrm{dt}}+I_{\text{ion}}=C_m\frac{\mathrm{dV}}{\mathrm{dt}}+\frac{V}{R_m}=I_{\text{app}}$(2) . (2) $C_m\frac{\mathrm{dV}}{\mathrm{dt}}+I_{\text{ion}}=C_m\frac{\mathrm{dV}}{\mathrm{dt}}+\frac{V}{R_m}=I_{\text{app}}$(2) Where: $I_{\text{ion}}=I_{\mathrm{Na}}+I_K+I_S+I_H+I_L$ = Ionic current = Leakage current (Time-dependent), C_m(µA/cm²) = Cell membrane capacitance, V(mV) = YNI model reaction (Membrane potential), R_m = Cell membrane Resistance, I_app = Outside Current.

In the theory of dynamics, entrainment among two beats is a famous miracle. It generally occurs when there is a stable enough connection between two interrelate oscillators. Frequency-entrainment (FE) is a method in which two related fluctuating schemes (such as ECG indicators and the YNI model’s reaction) with diverse eras operate separately, at the same time when they relate (Seidel & Herzel, 1998). Before going into synchrony, there is a phase error among ECG data and the entrained YNI-reaction after FE. A second-order system (SOS) is used to estimate the error, in which a simulation is used to perform PZ (pole-zero) scrutiny of the transfer function (TF) to determine the characteristics of lethal cardiac arrhythmia. The waveforms of ECG signals can be graphically recorded. The graphical interpretation helps in better understanding and mathematical analysis of signals. The cardiac muscles wield a force f(t) as a result of a disarticulation x(t) based on human activity (Quiroz-Juarez et al., 2018). During the displacement, the heart muscle is also subjected to viscous and torsional drags. As a result, the degree-of-difference equation can be used to depict the heart’s function as shown in Equation (3)(3) $M\frac{d^{2}x(t)}{d{t}^2}+B\frac{\mathrm{dx}(t)}{\mathrm{dt}}+\mathrm{Kx}(t)=f(t)$(3) . (3) $M\frac{d^{2}x(t)}{d{t}^2}+B\frac{\mathrm{dx}(t)}{\mathrm{dt}}+\mathrm{Kx}(t)=f(t)$(3) where: M = Cardiac muscle’s mass, B = Heart muscle’s viscous-drag (A constant), K = Heart muscle’s torsional-drag (A constant). Equation (4)(4) $\frac{X(s)}{F(s)}=\frac{w_n^2}{s^2+2\delta w_{n}s+w_n^2}$(4) shows, the Laplace transform representation of Equation (3)(3) $M\frac{d^{2}x(t)}{d{t}^2}+B\frac{\mathrm{dx}(t)}{\mathrm{dt}}+\mathrm{Kx}(t)=f(t)$(3) , which is a forward path TF of SOS. (4) $\frac{X(s)}{F(s)}=\frac{w_n^2}{s^2+2\delta w_{n}s+w_n^2}$(4) The comparison of Equations (3)(3) $M\frac{d^{2}x(t)}{d{t}^2}+B\frac{\mathrm{dx}(t)}{\mathrm{dt}}+\mathrm{Kx}(t)=f(t)$(3) and (4)(4) $\frac{X(s)}{F(s)}=\frac{w_n^2}{s^2+2\delta w_{n}s+w_n^2}$(4) gives the following results.

δ = The coefficient of damping oscillation = $\frac{B}{2\sqrt{M}}$, w_n = The un-damped natural frequency of oscillation = $\sqrt{\frac{1}{M}}=\sqrt{\frac{K}{M}}$, w_d = The damped frequency of oscillation = $w_n\left(\sqrt{1-{\delta }^2}\right)$.

This paper considers a person with normal condition (rest case) and the HR is 72 BPM. In this case, the damping frequency of heart oscillation will be $f_d=\frac{72}{60}=1.2\mathrm{Hz}$, $w_d=2\pi f_d=7.54\text{radian}/\text{second}$. In the rest case condition, the CP system should be an under-damp system. Hence consider δ = 0.8, therefore$w_n=\frac{w_d}{\sqrt{1-{\delta }^2}}=\frac{7.54}{\sqrt{1-0.64}}=12.57$. After putting the values of δ and w_n in Equation (4)(4) $\frac{X(s)}{F(s)}=\frac{w_n^2}{s^2+2\delta w_{n}s+w_n^2}$(4) , a new equation will be formed as Equation (5)(5) $\frac{w_n^2}{s(s+2\delta w_n)}=\frac{{12.57}^2}{s(s+2\ast 0.8\ast 12.57)}=\frac{158}{s^2+20.11s}$(5) : (5) $\frac{w_n^2}{s(s+2\delta w_n)}=\frac{{12.57}^2}{s(s+2\ast 0.8\ast 12.57)}=\frac{158}{s^2+20.11s}$(5) Equation (5)(5) $\frac{w_n^2}{s(s+2\delta w_n)}=\frac{{12.57}^2}{s(s+2\ast 0.8\ast 12.57)}=\frac{158}{s^2+20.11s}$(5) is likewise similar to the heart TF (Govind & Sekhar, 2014) which is: (6) $G_h(s)=\frac{169}{s(s+20.8)}$(6) As the damping coefficient and oscillation change with the human body activity, the numerator and denominator coefficients of the heart TF will also change. As demonstrated in Equation (3)(3) $M\frac{d^{2}x(t)}{d{t}^2}+B\frac{\mathrm{dx}(t)}{\mathrm{dt}}+\mathrm{Kx}(t)=f(t)$(3) , the dampness is induced by the viscous drag and torsional drag of the cardiac cell.

Pacemaker TF: The pacemaker signal is fed to the heart. The pacemaker is an I-order LT-variant scheme (Kwiatkowska et al., 2014) with the subsequent TF as shown in Equation (7)(7) $G_P(s)=\frac{k}{1+\mathrm{s\tau }}$(7) . (7) $G_P(s)=\frac{k}{1+\mathrm{s\tau }}$(7) Where: K = Steady-state gain = 1, τ = Time constant = $\frac{1}{2\pi f_d}=\frac{1}{2\pi \ast 1.2}$ which is approximately equal to 1/8. The derived pacemaker TF will be given in Equation (8)(8) $G_P(s)=\frac{8}{s+8}$(8) : (8) $G_P(s)=\frac{8}{s+8}$(8) As a result, the pacemaker functions like a frequency selector gadget which keeps high-frequency gestures from influencing a patient’s heart in cardiac arrhythmia. To solve the difficulties, the proposed ABC-PID controller activates the pacemaker.

2.1.1. State-space model of the CP system

The transfer function of the CP system can be modelled by a product of the heart TF (Equation (7)(7) $G_P(s)=\frac{k}{1+\mathrm{s\tau }}$(7) ) and the pacemaker TF (Equation (8)(8) $G_P(s)=\frac{8}{s+8}$(8) ) as follows: (9) $G_P(s)\ast G_h(s)=\frac{1352}{S^3+28.8S^2+166.4S}=\frac{Y(s)}{U(s)}$(9) By rewriting the Equation (9)(9) $G_P(s)\ast G_h(s)=\frac{1352}{S^3+28.8S^2+166.4S}=\frac{Y(s)}{U(s)}$(9) : (10) $(s^3+28.8s^2+166.4s)Y(s)=1352U(s)$(10) Equation (11)(11) $\frac{d^{3}y(t)}{d{t}^3}+28.8\frac{d^{2}y(t)}{d{t}^2}+166.4\frac{\mathrm{dy}(t)}{\mathrm{dt}}=1352u(t)$(11) shows the inverse Laplace transform of Equation (10)(10) $(s^3+28.8s^2+166.4s)Y(s)=1352U(s)$(10) . (11) $\frac{d^{3}y(t)}{d{t}^3}+28.8\frac{d^{2}y(t)}{d{t}^2}+166.4\frac{\mathrm{dy}(t)}{\mathrm{dt}}=1352u(t)$(11) Where y(t) is the output and u(t) is the input of the CP system. (12) $\begin{array}{rl}y(t)& =x_1\end{array}$(12) (13) $\begin{array}{rl}\frac{\mathrm{dy}(t)}{\mathrm{dt}}& =x_2={\dot{x}}_1\end{array}$(13) (14) $\begin{array}{rl}\frac{d^{2}y(t)}{d{t}^2}& =x_3={\dot{x}}_2\end{array}$(14) (15) $\begin{array}{rl}\frac{d^{3}y(t)}{d{t}^3}& =x_4={\dot{x}}_3\end{array}$(15) (16) $\begin{array}{rl}u(t)& =u\end{array}$(16)

Write and arrange the above differential equations in the form of state space equations as: (17) $\begin{array}{rl}& {\dot{x}}_3+28.8x_3+166.4x_2+0x_1=1352u\end{array}$(17) (18) $\begin{array}{rl}& {\dot{x}}_3=1352u-28.8x_3-166.4x_2-0x_1\end{array}$(18) The state space model of the CP system is given as: (19) $\begin{array}{rl}\dot{X}& =\mathrm{AX}+\mathrm{BU}\end{array}$(19) (20) $\begin{array}{rl}Y& =\mathrm{CX}+\mathrm{DU}\end{array}$(20) Where Equation (19)(19) $\begin{array}{rl}\dot{X}& =\mathrm{AX}+\mathrm{BU}\end{array}$(19) is the state equation and Equation (20)(20) $\begin{array}{rl}Y& =\mathrm{CX}+\mathrm{DU}\end{array}$(20) is the output equation.

The state vector is denoted by X and the differential state vector by $\dot{X}$. The input vector is denoted by U and the output vector by Y. The CP system matrix is denoted by A. The matrices for the input and output are B and C. The state space model of the CP system is: $\begin{array}{rl}\dot{X}& =\left[\begin{array}{c}{\dot{x}}_1\\ {\dot{x}}_2\\ {\dot{x}}_3\end{array}\right]=\left[\begin{array}{ccc}0& 1& 0\\ 0& 0& 1\\ 0& -166.4& -28.8\end{array}\right]\left[\begin{array}{c}{x}_1\\ x_2\\ x_3\end{array}\right]\\ & +\left[\begin{array}{c}0\\ 0\\ 1352\end{array}\right]u(t)\end{array}$Where $\begin{array}{rl}A& =\left[\begin{array}{ccc}0& 1& 0\\ 0& 0& 1\\ 0& -166.4& -28.8\end{array}\right],B=\left[\begin{array}{c}0\\ 0\\ 1352\end{array}\right],\\ x(t)& =\left[\begin{array}{c}{x}_1\\ x_2\\ x_3\end{array}\right]\end{array}$

2.2. Controller specification and design

The major objective of this paper is to betterment the controlling of the pacemaker electrical signals. This is accomplished by adjusting the output BE signals y(t) of CP, using a PID controller and a feedback loop channel, after the input BE signals have been initialized. A widely used controller known as the PID controller accepts the error signal e(t) as an integration with input (Taran et al., 2020). The discrepancy between y(t) and r(t) is e(t) (Luo et al., 2023). By minimizing e(t), the controller changes the process control inputs as shown in Figure 3. Based on the characteristics equation of the system, PID parameter values must be modified (Swarnkar & Goud, 2020). The u(t) taken as a whole control function of PID constraints (K_p, K_i, and K_d) which is given in Equation (21)(21) $u(t)=K_{p}e(t)+K_i{\int }_0^{t}e(t)\mathrm{dt}+K_d\frac{d}{\mathrm{dt}}e(t)$(21) (Time domain analysis): (21) $u(t)=K_{p}e(t)+K_i{\int }_0^{t}e(t)\mathrm{dt}+K_d\frac{d}{\mathrm{dt}}e(t)$(21) where K_p is a proportional controller, this controller modifies the CP output according to the error that exists between the measured HR and the set-point HR at the moment; K_i is an integral controller, this controller modifies the CP output according to error accumulation over time also increase the CP system stability and aid in the elimination of steady-state error; K_d is a derivative controller, this controller modifies the CP output according to how quickly the error is changing, also reduce the oscillations and enhance the stability of the CP system.

Figure 3. A schematic representation of a PID controller with a cardiac pacemaker.

In terms of the Laplace domain, the PID controller TF model for Equation (21)(21) $u(t)=K_{p}e(t)+K_i{\int }_0^{t}e(t)\mathrm{dt}+K_d\frac{d}{\mathrm{dt}}e(t)$(21) is: (22) $G_{\text{PID}}(s)=K_p+\frac{K_i}{s}+K_d(s)$(22)

2.3. Hardware implementation of the CP controller

The pacemaker hardware system developed around the ATmega328 micro-controller platform shown in Figure 4 to explain the entire system. To control cardiac arrhythmia, the output of pacemaker pulse frequency varies according to the sensed BPM (beats per minute). A heartbeat sensor is used to detect pulse rate and provide feedback to the control system, and it makes the closed loop to effectively control the CP output. In normal conditions (60–80 BPM) pacemaker will not be in action. In the case of Bradycardia (lower than 60 BPM), the pacemaker’s output pulse frequency increases and in the case of Tachycardia (higher than 80 BPM) the frequency goes low to normalize the HR. A DSO and LED indicators are used to visualize the output frequency of the Pacemaker. Figures 5–7 show the experimental setup and input–output in different arrhythmia conditions. When the HR of a humanist under the normal range, pacemaker action is not required (Figure 5). The pacemaker is in action in case of tachycardia (Figure 6), and bradycardia (Figure 7). In case of any pulse rate irregularity, the pacemaker feeds externally generated electrical signals to regulate the HR of a patient.

Figure 4. Circuit diagram of an intelligent cardiac pacemaker controller.

Figure 5. Normal heart rate.

Figure 6. Output in case of tachycardia.

Figure 7. Output in case of bradycardia.

2.4. Traditional technique (TL) for PID controller tuning

B. D. Tyrus and W. I. Luyben proposed the Tyrus-Luyben approach in 1997. TL tuning method is more conservative than the ZN method; hence it performs better with tiny values for dead time (Tyreus & Luyben, 1992). When the amount of dead time is high, the performance is sluggish. In this method, only the important frequency point of the process is employed to adjust the PID constraints (K_p, K_i, K_d). It tunes the PID constraints using the ultimate Period (UP) and ultimate Gain (UG). The tuning procedure to calculate the UG and UP i.e. K_U and P_U, respectively is a go-behind (Kumar & Garg, 2015).

• First Step: Look for a sign of process improvement.

• Second Step: Proportional control should be implemented.

• Third Step: Raise the proportional gain until getting a stable periodic oscillation.

• Fourth Step: Make a note of the UG.

• K_U: The Oscillation’s gain, P_U: The distance between two crests that follow each other.

• Fifth Step: Calculate the control settings as TL specifies.

2.5. Genetic algorithm for PID controller tuning

GA is an optimization method based on the heuristic approach concept. This method was developed to start solving optimization issues in the field of soft computing, based on the idea of Darwin’s principle of the survival of the fittest. To tune the CP system controlling parameters, the GA optimization algorithm follows the three basic steps: reproduction, crossover, and mutation (Wang et al., 2021).

2.6. Artificial bee colony technique for PID controller tuning

An appropriate selection of tuning techniques is necessary to optimize the PID output (Dubey et al., 2022). There are various gain-tuning techniques available to get improved output such as conventional tuning techniques and intelligent tuning techniques. For linear time-invariant, conventional techniques guarantee secure and pleasing action (Dubey et al., 2021; Goud et al., 2021). Still, if the patient’s condition is carried out beyond the specified range, in such type of cases; traditional techniques cannot guarantee excellent control concert when operating points or ecological variables change. Also, it takes a lot of effort and money to use. To address this issue, a great deal of exertion has gone into combining intelligent aspects of metaheuristic techniques with PID controllers to automate the controller parameters (Goud & Swarnkar, 2019a, 2019b).

Dervis Karaboga first put forth the ABC algorithm in 2005 (Ahmad & Choubey, 2017), and it was stirred by the foraging behaviour of honeybees invented by Karaboga and Akay (2009). The labour (working and not working) and source of quality food are basic components of this ABC. The identity association and communal intelligence are accomplished through the iterative process of picking the wealthy food resources and dumping deprived resources given by Karaboga and Basturk (2007). The same scheme is artificially mimicked in ABC to achieve optimized results. In ABC, the colony of agents (artificial forager bees) searches for the optimized value (food resource) in the company of high nectar value (quality of source) to minimize the objective function and substitute the poor food sources. This process is based on the working bee’s (observer and lookout) communication. Figure 8 shows the flow chart of the ABC Algorithm.

Figure 8. Flow chart of the ABC optimization algorithm.

2.7. CP system modelling with optimized PID controller

K_p (present gain), K_i (past gain) and K_d (future gain) are three independent gain factors in the PID controller architecture. PID tuning is required to get the initial standards of K_p, K_i, and K_d. Tuning PID’s constraints is an important aspect of a control system. In the actual world, three types of bee’s forage for food (values of PID parameters) in a honeybee colony (CP PID system): worker bees, observer bees, and lookout bees. There is just one worker bee per food source. In other words, the amount of food sources and working bees are equal. An abandoned food source’s worker bee transforms into a lookout bee. A particular food source that depends on a number of factors is connected to working bees, including how close it is to the nest, how rich or concentrated it is in energy, and how simple it is to take this energy. A single quantity can be used to simply express how profitable a food source is. Working bees are in-charge of looking for suitable food sources and acquiring the necessary data. They then utilize the waggle dances to communicate details such as distance, direction, and profitability with additional bees waiting within the beehive.

Following that, observer bees choose healthy food sources (desired values of PID parameters) based on the nectar details (ECG feedback) provided via working bees to more explore the foods. After a set number of spins, if the quality (desired HR) is not improved, the hired bee will leave the food supply. The working bee transforms into a lookout bee (deciding new range for control parameters) after reaching the amount of abandoned that is considered as a limit, an essential ABC algorithm controlling parameters, and fresh food supplies are then haphazardly looked for in the vicinity of the beehive, as depicted in Figure 9. A food source’s position in the ABC algorithm indicates a potential optimum problem solution, and its nectar content indicates the effectiveness (fitness) of the associated explanation. Additionally, it is planned that the number of working, or observer bees will be equivalent to the population’s amount of the solution.

Figure 9. CP controlling flowchart using optimized PID controller.

The following steps are carried out to design the PID using ABC (Pareek et al., 2014):

1. Initial Phase: In this phase, the ABC method generates a beginning population P of the potential food source solution that is spread at random. Worker bees or observer bees make up the same amount of food sources (nf). Within the range of the parameter limits, each initial solution f_i = (f_i,1, f_i,2, …  … f_i,D) is generated at random and these can be resolute by Equation (23)(23) $f_{i,j}=B_{L,j}+\text{ rand}(0,1)\ast (B_{U,j}\text{--}{B}_{L,j})$(23) : (23) $f_{i,j}=B_{L,j}+\text{ rand}(0,1)\ast (B_{U,j}\text{--}{B}_{L,j})$(23)

i = 1, 2, … , nf; j = 1, 2, … , D; and D is a parameter for optimization(PID parameters). The j dimensions for the lower and upper bounds are B_L,j, and B_U,j, respectively.

1. Worker Bee Phase: Bees discover the nearest high nectar value food resources E_i,j (novel constraints of PID) through Equation (23)(23) $f_{i,j}=B_{L,j}+\text{ rand}(0,1)\ast (B_{U,j}\text{--}{B}_{L,j})$(23) . (24) $E_{i,j}=f_{i,j}+\text{ rand}(-1,1)\ast (f_{i,j}\text{--}{f}_{k,j});\{i^{1}k\}$(24)

k = {1, 2, … , nf}. In the ABC method, f_i represents the location where a food source is located, and E_i denotes a fresh possibility for the food source.

1. Observer Bee Phase: Based on objective function i.e. MSE, the observer bees select the food source. The food collection’s priority will increase with a greater nectar value as given in Equation (25)(25) $p_i=\frac{\text{fitness}(i)}{{\sum }_{j=1}^{\mathrm{nf}}\text{fitness}(j)}$(25) . (25) $p_i=\frac{\text{fitness}(i)}{{\sum }_{j=1}^{\mathrm{nf}}\text{fitness}(j)}$(25)

2. Lookout Bee Phase: If the observer bees fail to find better food, the working bees play the role of lookout bees and start the iteration process as per the Equation (23)(23) $f_{i,j}=B_{L,j}+\text{ rand}(0,1)\ast (B_{U,j}\text{--}{B}_{L,j})$(23) .

3. Last Phase: The search finishes when the allotted number of iterations has passed and chooses the best source (desired HR) from the list of search results.

Control deeds can be offered according to individual process needs, by tuning these three constants of a PID controller. The output voltage signal and its frequency are the controllable values of the controller in the pacemaker control system. Feedback ECG signal from the heart is used to produce the desired output of the pacemaker. The controller’s reaction can be measured in terms of the output’s transient and steady-state concert constraints, which are as follows: rise time, settling time, maximum overshoot, and MSE. Figure 10 depicts a pacemaker modelling, where pacemaker is cascaded with a heart and PID controller.

Figure 10. Cascading arrangement of cardiac pacemaker controller.

The fitness or objective function at this point is to reduce the MSE by tweaking PID parameters as much as possible. The population’s bee (ABC) will be determined once using the objective function. ABC comprises three numbers corresponding to the three gains that must be modified for the PID regulator to behave properly. The MSE evaluation involves calculating the performance of each swarm particle. Equation (26)(26) $\text{fitnes}{\text{s}}_k=\frac{1}{J(\text{MS}{\text{E}}_k)}$(26) estimates the fitness of the objective function. (26) $\text{fitnes}{\text{s}}_k=\frac{1}{J(\text{MS}{\text{E}}_k)}$(26) Where $J(\text{MS}{\text{E}}_k)$ is the value of MSE, which is delivered by kth possible solution using PID gain,$K_p^k$, $K_i^k$ and $K_d^k$. $J(\mathrm{MS}{E}_k)$, has the expression which is given in Equation (27)(27) $\text{MSE}=\frac{1}{t}{\int }_0^{t}t{e}^2(t)\mathrm{dt}$(27) . (27) $\text{MSE}=\frac{1}{t}{\int }_0^{t}t{e}^2(t)\mathrm{dt}$(27) e(t) is equal to [r(t)−y(t)]. r(t) indicates the desired value of the human HR and y(t) is the actual value of the human heart (later-than PID tuning).

This objective function is implemented in the appearance of MSE, and its goal is to reconcile the system as quickly as feasible. The high overshoot value of y(t) can be reduced by dropping the higher boundary value of K_P, however, this would lengthen the time it takes to settle. This problem can be overcome by selecting the ABC-PID tuning strategies as shown in Figure 11.

Figure 11. CP controlling model using ABC-PID controller.

2.8. Convergence fitness of the ABC-PID controller

Figure 12 depicts the finest fitness value of convergence of the ABC algorithm. The finest fitness achieved the constant value at generation 38. From generation 38 to generation 50, the ideal fitness will remain the same.

Figure 12. Fitness convergence for the ABC-PID controller.

3. Discussion on simulation results

The results of the MATLAB Simulink are included in this section, along with a thorough comparative study that shows how well the ABC-PID controller design is best over the other techniques. As the system stability depends on settling time, percentage overshoot, and error whereas the rise time has very little importance. The simulation is done in time and frequency domain both. This simulation compares the achieved ABC-PID results with TL, GA, and CP systems without a PID controller. Proposed CP system Simulink model is shown in Figure 13. Here the forward path consists of three blocks which are pacemaker TF, PID controller, and heart TF. A unity negative feedback is given to calculate the error e(t). Step input is considered as a base (desired HR) input. To tune the PID controller TL, GA, and ABC tuning techniques are used and compared. For considered CP system the following points describe the basic simulation setup and the outcomes of different controllers considered in this work. Furthermore, these outcomes will be compared with proposed ABC-PID outcomes for the same CP system.

Figure 13. Proposed model of CP system with PID controller.

3.1. Analysis of simulation without external disturbance

3.1.1. Simulation of TL-PID controller

Table 2 shows the tuned PID parameters generated with the TL algorithm. These tuned PID parameters are further used to control the CP system. Received simulated results for K_U (ultimate gain) and P_U (ultimate period) are 2.0530 and 0.4871, respectively.

Table 2. TL parameters for the CP system controlling.

PID’s parameters →	KP	$K_i=\frac{K_P}{T_i}$	$K_d=K_P\ast T_d$
TL-PID →	$\frac{K_U}{2.2}$	$2.2P_U$	$\frac{P_U}{6.3}$

TL Tuned PID parameters shown in Table 3 are generated with the help of Table 2. During the simulation the TL algorithm given the results as rise time 0.1295 s, overshoot 0.245381%, settling time 1.4209 s, and MSE is 0.0856345. The graphical representation of TL performance is shown in Figure 14.

Figure 14. Comparative analysis of CP system performance with different control techniques.

Table 3. The PID parameters for the CP system obtained by various algorithms.

Control methods →
Response parameters ↓	TL-PID controller	GA-PID controller	ABC-PID controller
Kp	1.6112	2.208	1.9343
Ki	1.5036	2.063	0.1998
Kd	0.1246	0.2604	0.2458

3.1.2. Simulation of GA-PID controller

Necessary GA parameters for calculating the tuning parameters of PID controller are given in Table 4. GA tuned PID parameters are shown in Table 3. During the simulation the GA algorithm given the results as rise time 0.1152 s, overshoot of 0.220432%, and settling time 0.5611 s and MSE is 0.050376. The graphical representation of GA performance is shown in Figure 14.

Table 4. GA parameters for the CP system controlling.

Population size	50
Iteration	50
Crossover operator	Arithmetic
Optimization variables	03

3.1.3. Simulation of ABC-PID controller

The ABC algorithm’s key parameters are displayed in Table 5. With the help of these parameters, PID is tuned smartly according to the heart’s activity as given in Table 3. During the simulation the ABC algorithm given the results as rise time 0.0985 s, overshoot of 0.111367%, settling time 0.3293 s, and MSE is 0.0040565. The graphical representation of GA performance is shown in Figure 14.

Table 5. ABC parameters for the CP system controlling.

BL,j	[1 0 0]
BU,j	[2 1 1]
fi,j (colony size)	20
fi = (fi,j)/2	10
i (iterations)	50
Abandonment limit (trial limit)	36
an (acceleration coefficient)	1

As per the Table 6, the simulation results show that the proposed ABC-PID gives better results compared to other considered algorithms.

Table 6. Comparison of the CP’s transient response analysis results for different controllers.

Control methods →
Response specifications ↓	Without controller	TL-PID controller	GA-PID controller	ABC-PID controller
Rise-time (s) (0.10–0.90)	0.1908	0.1295	0.1152	0.0985
Max. overshoot (%)	0.346568	0.245381	0.220432	0.111367
Settling time (s) (±2%)	1.5414	1.4209	0.5611	0.3293
Settling time (min.)	0.8735	0.9087	0.9085	0.9083
Settling time (max.)	1.3466	1.2454	1.1878	1.1114
Peak time (s)	0.4843	0.3142	0.2843	0.2102
Peak	1.3466	1.2454	1.2078	1.1114

3.2. Frequency domain simulation analysis

Figure 15 depicts a Nyquist Diagram (or Nyquist plot), which is a frequency response plot used to measure the stability of the CP system with feedback. Stability is assessed using the number of (−1, 0) point encirclements. Real axis crossings can be utilized to determine the range of gains that the system will be stable through. The graph of the Nyquist plot also shows that the ABC-PID controller is more stable than the TL-PID, GA-PID, and CP system without PID controller.

Figure 15. CP system Nyquist diagram with different controllers.

Figure 16 depicts a Bode plot (Hendrik Wade Bode: 1930), which is a magnitude graph (in dB) or phase of the TF versus frequency (in rad/s) used to resolve the stability of a CP system. The graph of the Bode plot shows that the gain margin and phase margin of the ABC-PID controller are more than the TL-PID, GA-PID, and CP system without PID controller. Therefore ABC-PID controller is more stable than the other simulated controllers.

Figure 16. CP system stability with Bode-diagram using various PID controller tuning methods.

3.3. Analysis of simulation with external disturbance

To evaluate the system robustness, three external disturbances with different duty cycles are introduced. Figure 17 shows the CP Simulink model with external disturbances and Table 7 shows the parameters of disturbance signal.

Figure 17. Proposed model of CP controlled (with external disturbances) PID controller.

Table 7. External disturbance parameters.

Signal parameters	Value 1	Value 2	Value 3
Amplitude	1 mV	1 mV	1 mV
Period	3 s	3 s	3 s
Pulse width	0.01	0.1	0.25
Phase delay	2 s	2 s	2 s

3.3.1. Simulation of robustness

The ability of the suggested controller to suppress disturbances can be used to measure their resilience. Figures 18–20 illustrate how the proposed controller react to a pulse disturbance introduced to the CP system at the varied duty cycle. The ABC-PID controller can successfully reduce the effect of disturbances, as shown in Figures 18–20.

Figure 18. CP controller output comparisons with external disturbances of 0.01% duty cycle.

Figure 19. CP controller output comparisons with external disturbances of 0.1% duty cycle.

Figure 20. CP controller output comparisons with external disturbances of 0.25% duty cycle.

During the case of external disturbance, the output of the pacemaker loses its synchronization which means the high overshoot occurs, causing a severe effect on heart function. The robust controller must have the ability to fast recover (minimum settling time) the proper functioning and protect the patient’s life. The above simulation with disturbances is performed to check the robustness of the considered system with different tuning algorithms. The rise time, maximum overshoot, and settling time of the proposed ABC-PID controller with a disturbance of 0.01% duty cycle is 0.1341 s, 1.5323%, and 2.0099 s, respectively as shown in Table 8. With a disturbance of 0.1% duty cycle, the response parameters are 0.1341 s, 1.5745%, and 2.0099 s as rise time, maximum overshoot, and settling time, respectively as shown in Table 9. When the disturbance increases to 0.25% duty cycle, the rise time, maximum overshoot, and settling time are 0.1341 s, 6.3381%, and 2.1710 s, respectively as shown in Table 10. Here the simulation results show that the proposed algorithm gives a more stable system compared to other algorithms. The comparative settling time and maximum overshoot are minimum which shows the proposed system is more stable and has a fast recovery ability compared to other simulated algorithms. Another thing noticed is that the system without a PID controller has the maximum overshoot percentage and also shows the under-shoot with external disturbance of 0.25% duty cycle, which is highly undesirable, and the system becomes unstable.

Table 8. Comparison of the CP’s transient response analysis results with external disturbance of 0.01% duty cycle.

Control methods →
Response specifications ↓	Without controller	TL-PID controller	GA-PID controller	ABC-PID controller
Rise-time (s) (0.10–0.90)	0.2435	0.1538	0.1152	0.1341
Max. overshoot (%)	19.2503	17.9627	8.7146	1.5323
Max. undershoot (%)	0	0	0	0
Settling time (s) (±2%)	2.8910	2.7936	2.5622	2.0099
Settling time (min.)	0.0290	0.0473	0.0388	0.0046
Settling time (max.)	1.1935	1.1796	1.0871	1.0191
Peak time (s)	1.5863	1.3972	1.2878	1.2878
Peak	1.1935	1.1796	1.0871	1.0191

Table 9. Comparison of the CP’s transient response analysis results with external disturbance of 0.1% duty cycle.

Control methods →
Response specifications ↓	Without controller	TL-PID controller	GA-PID controller	ABC-PID controller
Rise-time (s) (0.10–0.90)	0.2434	0.1538	0.1352	0.1341
Max. overshoot (%)	19.3195	18.0091	8.7814	1.5745
Max. undershoot (%)	0	0	0	0
Settling time (s) (±2%)	2.8910	2.7936	2.5622	2.0099
Settling time (min.)	0.0479	0.0473	0.0388	0.0086
Settling time (max.)	1.1932	1.1801	1.0878	1.0195
Peak time (s)	1.5774	1.3836	1.2843	1.2843
Peak	1.1932	1.1801	1.0878	1.0195

Table 10. Comparison of the CP’s transient response analysis results with external disturbance of 0.25% duty cycle.

Control methods →
Response specifications ↓	Without controller	TL-PID controller	GA-PID controller	ABC-PID controller
Rise-time (s) (0.10–0.90)	0.2435	0.1537	0.1152	0.1341
Max. overshoot (%)	19.2509	17.9799	14.4544	6.3381
Max. undershoot (%)	3.0117	0	0	0
Settling time (s) (±2%)	2.3495	2.2411	2.5037	2.1710
Settling time (min.)	0.0579	0.0475	0.0388	0.0046
Settling time (max.)	1.1925	1.1796	1.2445	1.0673
Peak time (s)	1.5863	1.3972	2.0729	2.0655
Peak	1.1925	1.1796	1.2445	1.0673

3.4. Comparative analysis of the proposed controller with the previously related controller

Table 11 shows the comparison analysis of the proposed controller with previously used diverse controller types with diverse tuning methods. The quantitative results in Table 11 represents that the proposed ABC-PID controller attains better response associated with the required HR in terms of the settling time and maximum percentage overshoot compared to the existing controllers. The proposed controller achieves an extremely accurate and closed match pacing rate with a very little percentage overshoot and settling time with an acceptable rise time.

Table 11. Comparison of the proposed ABC-PID controller with the previously related controller.

Controller	Rise time	Settling time	Overshoot
Fuzzy controller (Yadav et al., 2011)	0.3442 s	0.7563 s	2.09%
PID controller with the fusion of fuzzy and NN (Aghdam et al., 2017)	1.63 s	1.23 s	0.5%
FO-PID controller with genetic algorithm (GA) (Bajpai et al., 2017)	0.0908 s	0.6432 s	0.9112%
FO-PID controller with PSO via El-Khazali’s approach (Momani et al., 2019)	0.2263 s	0.3573 s	0.8597%
PIDA controller with SS (Nawikavatan et al., 2019)	0.1304 s	0.3368 s	1.4139%
Fuzzy fractional order proportional derivative + integral (FFOPD + I) controller with GWO algorithm (Kumar et al., 2022)	0.3747 s	2.9601 s	0.9857%
Proposed ABC-PID controller	0.0985	0.3293	0.111367%

4. Conclusion

It is inevitable to make certain significant choices while designing a PID control system, such as choosing between slow control with no overshoot and fast control with a significant overshoot. In the case of cardiac arrhythmias, a few seconds of the starting is most important to recover the heart function. In this paper, the ABC algorithm is applied to optimize the PID controller parameters of the cardiac pacemaker. The system is simulated in time and frequency domains and to check the robustness and efficiency of the proposed system some disturbances are also applied. Analysis of CP system done by using unity negative feedback. After that a PID controller is cascaded with CP system and various algorithms like TL, GA and ABC are used to tune the PID controller. Simulation results show that the system stability is improved with the proposed ABC-PID controller compared to controllers with other existing algorithms like TL, GA. The proposed ABC-PID controller also shows better results when compared with the other PID tuning techniques such as fuzzy, NN, PSO, SS, and GWO (Table 1). On the best side, settling time and overshoot simultaneously reduced when utilizing the proposed ABC algorithm based PID methodology for the CP system in comparison to alternative techniques. A laboratory experiment is also performed on the designed hardware to ensure the system’s feasibility. In the future, the system can also be designed for dynamic cases.

Author’s contributions

Vandana Dubey: Writing original draft, formal analysis, methodology, performed implementation of all experiments and simulations.

Harsh Goud: Supervision – mathematical modelling, reviewed the research paper.

Prakash Chandra Sharma: Supervision – prototype designing of methodology, reviewed the research paper, cross verify and validation of the manuscript, author of correspondence for the article.

S. Anjana: Prepared all the figures and visualization, cross verify, content flow/English language and grammar.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability

Data will be made available on request.

Additional information

Funding

This work was supported by Manipal Academy of Higher Education.