







































J. Anbazhagan et al. /Future Technology                                                                                  August 2025| Volume 04 | Issue 03 | Pages 
10-18 

10 

 

 

 

Article 

Optimized PID control for automated blood 

pressure management in post-operative care 
Jegatheesh Anbazhagan1*, Siddheswar Kar2, Krishna Prakash Arunachalam3,  

Aravinda Koithyar4 

1Department of Electronics and Communication Engineering, Infant Jesus College of Engineering, Tuticorin, India 
2Department of Electrical Engineering, Medicaps University, Indore, M.P, India 
3Departamento de Ciencias de la Construcción, Facultad de Ciencias de la Construcción Ordenamiento Territorial, 

Universidad Tecnológica Metropolitana, Santiago, Chile 
4Department of Electronics and Communication Engineering, New Horizon College of Engineering, Bengaluru, India 

A R T I C L E   I N F O 
 

Article history: 
Received 30 March 2025  
Received in revised form 
12 May 2025 
Accepted 25 May 2025 
 
Keywords:  
Blood pressure, Sodium nitroprusside, Prairie dog 
optimization, Proportional-integral-derivative 
controller, Infusion pump 
 
*Corresponding author 
Email address: 
jegatheeha@gmail.com 
 
 
DOI: 10.55670/fpll.futech.4.3.2 
 

A B S T R A C T 
 

Maintaining optimal Blood Pressure (BP) is vital, as abnormal BP levels pose 
substantial challenges to patient recovery in post-operative care. The manual 
administration of Sodium Nitroprusside (SNP) is a common approach to lower 
BP by relaxing peripheral vascular smooth muscles. Nevertheless, because of 
the inconsistency in drug sensitivity between patients, manual dosing is 
inaccurate and labour-intensive as it necessitates continuous expert 
monitoring. Therefore, this research adapts a control method to regulate BP in 
post-operative patients with hypertension. The Prairie Dog Optimization-based 
Proportional-Integral-Derivative (PDO-PID) controller adapts in real-time to 
the particular physiological responses of the patients, assuring precise and 
individualized SNP dosing. According to simulation results, the controller 
effectively controls BP levels over an extended time, generating an execution 
time of 63.613s and a reduced settling time of 1.05s. Corresponding SNP 
infusion levels are also effectively regulated, which is significantly smaller than 
the previous control approaches.  

1. Introduction 

Local Personalized hemodynamic management in the 
Intensive Care Unit (ICU) and Operating Room (OR) requires 
real-time cardiovascular system monitoring. Severe surgical 
organ failure results from poorly treated perioperative 
hypotension (low BP) and hypertension (high BP) [1]. 
According to estimates, elevated BP is the primary risk factor 
for 10.4 million deaths annually, and the number is 
continually growing. Acute blood pressure increases are 
frequently linked to major outcomes that need immediate 
medical attention [2, 3]. On the other hand, poor blood 
pressure control might endanger brain perfusion, which 
causes ischemia, infarction, and even neurological 
impairments. Optimizing blood pressure regulation before 
and after awake craniotomy is consequently a challenge in 
order to reduce the danger of bleeding as well as the 
possibility of neurological impairments. Continuous blood 
pressure monitoring is necessary, as certain patients require 
temporary anti-hypertensive medications following glioma 
excision via craniotomy, and invasive blood pressure 

monitoring is often limited to intermediate or critical care 
units [4-6]. Even with the introduction of numerous 
antihypertensive medications in recent decades and the 
identification of numerous traditional risk factors for 
hypertension, blood pressure (BP) management in modern 
society remains suboptimal, with one-fourth of hypertension 
sufferers failing to meet optimal BP targets [7, 8]. It has been 
demonstrated that appropriate blood pressure management 
considerably lowers the cardiovascular morbidity and all-
cause mortality linked to hypertension. In order to 
successfully prevent and treat hypertension, blood pressure 
needs to be checked on a normal and reliable basis [9-11]. One 
of the effective drugs to reduce Mean Arterial Blood Pressure 
(MABP) is SNP, an anti-hypertension vasodilator. Since 
patients respond differently to this pressure-controlling 
medication and the regulated release of the drug over an 
extended period of time, healthcare staff's manual control of 
MABP using SNP is frequently demanding, exhausting, and of 
low quality [12,13].  

 

 

 

Future Technology 

Open Access Journal 

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August 2025| Volume 04 | Issue 03 | Pages 10-18 

Journal homepage: https://fupubco.com/futech 

 

ISSN 2832-0379 

mailto:jegatheeha@gmail.com
https://doi.org/10.55670/fpll.futech.4.3.2
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J. Anbazhagan et al. /Future Technology                                                                                  August 2025| Volume 04 | Issue 03 | Pages 10-18 

11 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Therefore, holding MAP within the ideal range is difficult 
for any patient receiving post-surgical drug infusion, such as 
SNP. In this situation, the medical practitioner uses manual 
control to preserve MAP at the proper level in a traditional 
and straightforward manner [14,15]. Predictive controllers 
and intelligent techniques work together to control systems 
with few inputs and outputs in a very effective and potent 
manner. Actually, the controller is aware of the limitations on 
both input and output, and it never generates an input signal 
that deviates from them. In general, controllers aim to 
regulate the quantity of medication administered to the body, 
which in turn regulates BP and lessens surgical and post-
operative problems [16]. A multi-model predictive controller 
that uses many models to properly forecast blood pressure 
behavior is developed in [17] to handle variances in patient 
situations. However, using more than one model adds to the 
computing effort, which makes it difficult for real-time 
applications. Therefore, this paper develops a PID controller 
for automatic BP regulation. To enhance the performance of a 
developed PID controller, an optimization algorithm is 
exploited. Particle Swarm Optimization (PSO) is represented 
in [18], minimizes a cost function that is determined by the 
system response and control objective. This improves control 
performance by enabling more effective and efficient tuning 
of the controller parameters. However, the final solution is 
impacted by the starting population's quality, and inaccurate 
initial estimations result in less-than-ideal outcomes or 
longer convergence times. By adjusting the controller's 
parameters, a Genetic algorithm is developed in [19] to 
enhance management of blood pressure performance. 
Suboptimal PID parameters result from its convergence to 
local optima rather than the global optimum. A PID controller 
is used in [20] with an Artificial Bee Colony (ABC) algorithm 
that improves performance. Nevertheless, implementing an 
ACO-based PID controller is more complex than other 
methods. As a result, this research proposes a PDO-based PID 
controller for regulating the BP. The main objectives of this 
research are: 

• Implementing the PID controller for regulating the blood 
pressure by adjusting medication dosages based on real-
time BP interpretations. 

• Incorporating the Prairie Dog Optimization for tuning the 
parameters of the PID controller.  

2. Proposed methodology  

Figure 1 depicts the BP management system with a PID 
controller, which has found extensive application in process 
control. The BP measurement sensor initially measures the 
patient's BP level. Then, the error generator block outputs the 
error signal between the measured and desired BP level.  

 
Figure 1. Block diagram of BP management system 

This error signal is given to the PID controller, and its 
parameters are tuned by the PDO algorithm. The PID 
controller sends an appropriate control signal for the correct 
administration of the medicine into the injection pump 
according to the error between the set-point and the patient's 
measured BP level. Subsequently, the proper amount of SNP 
is given to the patient, and this process is repeated until the 
desired BP level is reached.  

2.1 Blood pressure model 
Cardiac output, vascular resistance, and central venous 

BP all contribute to blood pressure, which is actually the 
average BP throughout a heart period. Maintaining MAP 
management is crucial for lowering hypertension disorders 
and preventing acute, life-threatening illnesses like stroke. 
MAP is more precise than the metabolic syndrome predicted 
by systolic, diastolic, and pulse pressure in older adults with 
hypertension. Now, the hypoxia-ischaemic brain damage is 
the leading cause of death in heart attacks. If the MAP is better 
than the automatic adjustment’s threshold, it results in 
excessive strain, which worsens brain injury and increases 
brain oedema. Conversely, if the MAP is under the automatic 
adjustment threshold, it induces further ischemia and brain 
damage. For these individuals to survive, blood pressure 
needs to be maintained within an ideal range by utilizing the 
link between blood pressure and oxygen saturation in the 
brain tissue. It is often used in general surgeries, hypotensive 
anaesthesia (anaesthesia by reducing BP) reduces 
intraoperative bleeding and necessitates postoperative blood 
transfusions. However, to control important physiological 
parameters, including awareness, heart rate, MAP, and 
breathing rate, this anaesthesia necessitates several 
medication injections. This control system's goal is to lower 
the patient's MAP by modifying the nitroprusside and 
medication dosage. This section provides the MAP model for 
controlling the patient's desired MAP through the infusion of 
SNP medicine. Figure 2 shows the general structure of the 
MAP model. The implemented model illustrates the 
relationship between the SNP medication infusion volumes 
and the MAP fluctuation for drug administration.  

Abbreviation 
ABC Artificial bee colony 

ACO Ant Colony Optimization 

BP Blood Pressure 

DS digging strength 

GA Genetic Algorithm 

GWO Grey Wolf Optimizer 

IAE Integral Absolute Error 

ICU Intensive Care Unit 

ISE Integral Squared Error 

ITAE Integral Time Absolute Error 

MAP Mean Arterial Pressure 

MABP Mean Arterial Blood Pressure 

MPC Model Predictive Control 

MSE Mean Squared Error 

OF objective function 

OR Operating Room 

PID Proportional-Integral-Derivative 

PDO Prairie Dog Optimization 

PSO Particle Swarm Optimization 

SNP Sodium Nitroprusside 

SSA Salp Swarm Algorithm 



J. Anbazhagan et al. /Future Technology                                                                                  August 2025| Volume 04 | Issue 03 | Pages 10-18 

12 

 

 
Figure 2. MAP system 

The dynamic system is: 

𝐺𝑝 =
𝑌𝑝(𝑠)

𝐼𝑝(𝑠)
=

[𝑆𝑝(1+𝐿𝑝3𝑠)𝑒
−(𝜃𝑝)𝑠]

[((1+𝐿𝑝3𝑠)(1+𝐿𝑝2𝑠)−𝛿𝑝)](1+𝐿𝑝1𝑠)
          (1) 

In the dynamic model, 𝐼𝑝 represents the rate at which the drug 

is given, whereas 𝑌𝑝(𝑠)represents the variations in blood 

pressure brought on by the SNP drug's infusion. The rate of 
drug absorption into the patient's system is determined by 
the drug infusion time constants 𝐿𝑝1, 𝐿𝑝2 and 𝐿𝑝3. A fraction 

of the recirculated SNP drug is indicated by the parameter 𝛿𝑝, 

whilst the time interval between the drug infusion and its 
impact on blood pressure is denoted by 𝜃𝑝. Finally, 𝑆𝑝 shows 

that the patient's sensitivity to the medication affects their 
blood pressure. The MAP model is indicated by:  

𝑀𝐴𝑃𝑝(𝑡) = 𝑌𝑝(𝑡) + 𝐼𝑏𝑝(0)                            (2) 

Where the starting blood pressure is 𝐼𝑏𝑝(0). This research’s 

primary objective is to carefully give the drug SNP in order to 
manage MAP.   

2.2 PDO optimized PID controller  
To attain optimization, the PDO algorithm simulates the 

actions of 4 Prairie Dogs (PDs). The burrow-building and 
eating behaviors of the PDs are exploited to investigate the 
optimization problem domain. A plentiful supply of food 
serves as the basis for the PDs' tunnels. They look for 
alternative food sources or solutions throughout the colony 
or problem space as the current one runs out. Every time they 
find a new food source, they dig new tunnels around it. Two 
distinct warning sounds are exploited to elicit the PDs' unique 
responses. Anything from the occurrence of predators to the 
accessibility of food needs to be inferred from the sounds 
made by PDs. Due to their outstanding communication 
abilities, the PD can protect themselves from predators and 
meet their nutritional needs. These two distinct behaviors 
cause the PDs to congregate in a specific location when the 
PDO is implemented. From there, exploitation is done to 
detect better solutions.  

2.2.1 Initialization 
Similar to other population-based techniques, PDO 

starts the PDs' positions arbitrarily. The search agents are 
populations of PDs, and each PD is denoted by a vector in d-
dimensional space. Each PD in a coterie belongs to one of the 
n coteries. Each Coterie's (CT) location within a colony is,  

𝐶𝑇 =

[
 
 
 
 

𝐶𝑇1,1 𝐶𝑇1,2 ⋯ 𝐶𝑇1,𝑑−1 𝐶𝑇1,𝑑

𝐶𝑇2,1 𝐶𝑇2,2 ⋯ 𝐶𝑇2,𝑑−1 𝐶𝑇2,𝑑

⋮       ⋮ 𝐶𝑇𝑖,𝑗    ⋮             ⋮

𝐶𝑇𝑚,1 𝐶𝑇𝑚,2  ⋯ 𝐶𝑇𝑚,𝑑−1 𝐶𝑇𝑚,𝑑]
 
 
 
 

         (3) 

 
Where 𝐶𝑇𝑖,𝑗 is the 𝑗𝑡ℎ  dimension of 𝑖𝑡ℎcoterie. Each prairie 

dog's place within a coterie is represented by:  

 

PD =

[
 
 
 
 
𝑃𝐷1,1 𝑃𝐷1,2 ⋯ 𝑃𝐷1,𝑑−1 𝑃𝐷1,𝑑

𝑃𝐷2,1 𝑃𝐷2,2 ⋯ 𝑃𝐷2,𝑑−1 𝑃𝐷2,𝑑

⋮          ⋮    𝑃𝐷𝑖,𝑗        ⋮ ⋮

𝑃𝐷𝑛,1 𝑃𝐷𝑛,2 ⋯ 𝑃𝐷𝑛,𝑑−1 𝑃𝐷𝑛,𝑑]
 
 
 
 

         (4) 

 
Where 𝑃𝐷𝑖,𝑗is the 𝑖𝑡ℎ prairie dog in a coterie’s 𝑗𝑡ℎ  

dimension.Based on the expressions given below, a uniform 
distribution is exploited to distribute each PD and CT site. 

𝐶𝑇𝑖,𝑗 = 𝑈(0,1) ∗ (𝑈𝐵𝑗 − 𝐿𝐵𝑗) + 𝐿𝐵𝑗              (5) 

𝑃𝐷𝑖,𝑗 = 𝑈(0,1) ∗ (𝑢𝑏𝑗 − 𝑙𝑏𝑗) + 𝑙𝑏𝑗          (6) 

Where 𝑈(0,1) is a uniformly distributed random number 

among 0 𝑎𝑛𝑑 1, 𝑢𝑏𝑗 =
𝑈𝐵𝐽 

𝑚
, 𝑙𝑏𝑗 =

𝐿𝐵𝐽

𝑚
. The upper and lower 

bounds of the optimization problem's 𝑗𝑡ℎ  dimensions are 
denoted by 𝑈𝐵𝐽  and 𝐿𝐵𝐽  respectively. The flowchart of the 

PDO algorithm is illustrated in Figure 3.  

 
Figure 3. Schematic diagram of PDO-PID controller  

2.2.2 Fitness Function Evaluation 
After receiving the solution vector, the fitness function 

estimates the fitness function value for the location of each 
PD. The obtained values are, 

f(PD) =

[
 
 
 
𝑓1([𝑃𝐷1,1 𝑃𝐷1,2 ⋯ 𝑃𝐷1,𝑑−1 𝑃𝐷1,𝑑])

𝑓2([𝑃𝐷2,1 𝑃𝐷2,2 ⋯ 𝑃𝐷2,𝑑−1 𝑃𝐷2,𝑑])
⋮         ⋮              ⋯            ⋮           ⋮

𝑓𝑛([𝑃𝐷𝑛,1 𝑃𝐷𝑛,2 ⋯ 𝑃𝐷𝑛,𝑑−1 𝑃𝐷𝑛,𝑑])]
 
 
 

        (7) 

The lowest fitness value is the best approach to the specified 
minimization issue. The fitness function values are preserved 
in a sorted array. The next three are assumed along with the 
optimum value for generating burrows that aid them in 
avoiding predators. 

2.2.3 Exploration 
A plentiful supply of food helps as the basis for PDs' 

tunnels. They look for alternative food sources or solutions 
throughout the colony or problem space as the current one 
runs out. Every time they find a new food source, they dig new 
tunnels around it. The burrows are vital for protecting the 
habitat from predators. Every PD resides in a colony, and each 
colony is separated into coteries with different colonial 
boundaries. Within their limits, the many coteries forage and 
dig burrows together only when a predator exists. PDO 
chooses between exploration and exploitation according to 4 
factors. The 4 phases of the highest number of repetitions 
include exploration and exploitation. Both of these 
exploratory methods rely on,  

𝑖𝑡𝑒𝑟 <
𝑀𝑎𝑥𝑖𝑡𝑒𝑟

4
and

𝑀𝑎𝑥𝑖𝑡𝑒𝑟

4
≤ 𝑖𝑡𝑒𝑟 <

𝑀𝑎𝑥𝑖𝑡𝑒𝑟

2
         (8) 

The two strategies for exploitation are based on:  



J. Anbazhagan et al. /Future Technology                                                                                  August 2025| Volume 04 | Issue 03 | Pages 10-18 

13 

 

𝑀𝑎𝑥𝑖𝑡𝑒𝑟

2
≤ 𝑖𝑡𝑒𝑟 ≤ 3

𝑀𝑎𝑥𝑖𝑡𝑒𝑟

4
and3

𝑀𝑎𝑥𝑖𝑡𝑒𝑟

4
≤ 𝑖𝑡𝑒𝑟 ≤ 𝑀𝑎𝑥𝑖𝑡𝑒𝑟         (9) 

The first strategy of coterie through the exploration phase is 
to have members search the ward for new food sources 
(Figure 4). The PDs' movements during their meal seeking are 
best captured by the Levy flight motion. This movement 
successfully examines a range of places despite preventing a 
comprehensive search of a specific location due to its 
characteristic large hops. To notify other people that food 
sources are found, they make distinctive sounds. In the 
algorithm’s exploration phase, foraging position updating is 
provided by: 

𝑃𝐷𝑖+1 = 𝐺𝐵𝑒𝑠𝑡𝑖,𝑗 − 𝑒𝐶𝐵𝑒𝑠𝑡𝑖,𝑗 × 𝜌 − 𝐶𝑃𝐷𝑖,𝑗 × 𝐿𝑒𝑣𝑦(𝑛)∀ 𝑖𝑡𝑒𝑟 <
𝑀𝑎𝑥𝑖𝑡𝑒𝑟

4
           (10) 

𝑃𝐷𝑖+1,𝑗+1 = 𝐺𝐵𝑒𝑠𝑡𝑖,𝑗 × 𝑟𝑃𝐷 × 𝐷𝑆 × 𝐿𝑒𝑣𝑦(𝑛) ∀
𝑀𝑎𝑥𝑖𝑡𝑒𝑟

4
≤

𝑖𝑡𝑒𝑟 <
𝑀𝑎𝑥𝑖𝑡𝑒𝑟

2
          (11) 

Where 𝐺𝐵𝑒𝑠𝑡𝑖,𝑗  denotes the best solution presently available 

worldwide, and 𝑒𝐶𝐵𝑒𝑠𝑡𝑖,𝑗  assesses the consequences of the 

most effective solution presently acquired worldwide. 𝐶𝑃𝐷𝑖,𝑗 

represents the randomized cumulative effect of all PDs, 𝜌 
indicates the experiment's customized food supply alert set at 
0.1 𝑘𝐻𝑧, and 𝑟𝑃𝐷 indicates the position of a random solution. 
The coterie's digging strength, denoted by 𝐷𝑆, which has a 
random value, is determined by the quality of the food source. 
The Levy distribution, 𝐿𝑒𝑣𝑦(𝑛) is well known for promoting 
more effective and superior problem search space 
exploration.  

𝑒𝐶𝐵𝑒𝑠𝑡𝑖,𝑗 = 𝐺𝐵𝑒𝑠𝑡𝑖,𝑗 × ∆ +
𝑃𝐷𝑖,𝑗×𝑚𝑒𝑎𝑛(𝑃𝐷𝑛,𝑚)

𝐺𝐵𝑒𝑠𝑡𝑖,𝑗×(𝑈𝐵𝑗−𝐿𝐵𝑗)+∆
       (12) 

𝐶𝑃𝐷𝑖,𝑗 =
𝐺𝐵𝑒𝑠𝑡𝑖,𝑗−𝑟𝑃𝐷𝑖,𝑗

𝐺𝐵𝑒𝑠𝑡𝑖,𝑗+∆
                                            (13) 

𝐷𝑆 = 1.5 × 𝑟 × (1 −
𝑖𝑡𝑒𝑟

𝑀𝑎𝑥𝑖𝑡𝑒𝑟
)
(2

𝑖𝑡𝑒𝑟

𝑚𝑎𝑥𝑖𝑡𝑒𝑟
)
      (14) 

Where 𝑟 introduces the stochastic property to validate 
exploration and takes the value of either 1 𝑜𝑟 − 1 depending 
on the present iteration, and ∆ denotes a small number that 
indicates discrepancies that arise among the PDs. 𝑀𝑎𝑥𝑖𝑡𝑒𝑟is 
the maximum number of iterations, and 𝑖𝑡𝑒𝑟 is the present 
iteration. To guarantee exploration, the 𝑟 adds the stochastic 
property. Depending on the iteration, it takes the value 
of 1 𝑜𝑟 − 1. 

 
Figure 4. Exploration and exploitation strategy  

2.2.4 Exploitation 
The PDO capitalizes on PDs' varying responses to two 

distinct alarms or communication noises. Anything from the 
presence of predators to the availability of food is inferred 
from the sounds made by PDs. Because of their outstanding 
communication abilities, the PDs are able to protect 
themselves from predators and meet their nutritional needs. 
Furthermore, only PDs near the bird's path hide, with the 
others staying in their burrows to observe if the transmission 
indicates a hawk as the predator. The PDs congregate in one 
position due to these two distinct behaviors, or in the case of 
PDO implementation, a potential site where further search is 
conducted to uncover better or almost ideal solutions. The 
exploitation processes used by PDO are intended to 
thoroughly search the potential areas discovered during the 
exploration stage, as seen in Figure 3. The PDO alternates 
between these two tactics under the conditions,  

𝑀𝑎𝑥𝑖𝑡𝑒𝑟

2
≤ 𝑖𝑡𝑒𝑟 ≤ 3

𝑀𝑎𝑥𝑖𝑡𝑒𝑟

4
and3

𝑀𝑎𝑥𝑖𝑡𝑒𝑟

4
≤ 𝑖𝑡𝑒𝑟 ≤ 𝑀𝑎𝑥𝑖𝑡𝑒𝑟       (15) 

𝑃𝐷𝑖+1,𝑗+1 = 𝐺𝐵𝑒𝑠𝑡𝑖,𝑗 − 𝑒𝐶𝐵𝑒𝑠𝑡𝑖,𝑗 × 휀 − 𝐶𝑃𝐷𝑖,𝑗 ×

𝑟𝑎𝑛𝑑∀
𝑀𝑎𝑥𝑖𝑡𝑒𝑟

2
≤ 𝑖𝑡𝑒𝑟 ≤ 3

𝑀𝑎𝑥𝑖𝑡𝑒𝑟

4
        (16) 

𝑃𝐷𝑖+1,𝑗+1 = 𝐺𝐵𝑒𝑠𝑡𝑖,𝑗 × 𝑃𝐸 × 𝑟𝑎𝑛𝑑 ∀3
𝑀𝑎𝑥𝑖𝑡𝑒𝑟

4
≤ 𝑖𝑡𝑒𝑟 < 𝑀𝑎𝑥𝑖𝑡𝑒𝑟

           (17) 
Figure 5 represents the flowchart of the PDO algorithm. 
Whereas 𝐺𝐵𝑒𝑠𝑡𝑖,𝑗  is the most successful worldwide solution to 

date, 𝑒𝐶𝐵𝑒𝑠𝑡𝑖,𝑗 examines the effects of the most recent finest 

solution. The predator effect is represented by 𝑃𝐸, 𝑟𝑎𝑛𝑑 is a 
random integer between 0 𝑎𝑛𝑑 1, 𝐶𝑃𝐷𝑖,𝑗 is the combined 

influence of all PD in the colony, and 휀 is a minor value that 
indicates the quality of the food that is available. 

𝑃𝐸 = 1.5 × (1 −
𝑖𝑡𝑒𝑟

𝑀𝑎𝑥𝑖𝑡𝑒𝑟
)
(2

𝑖𝑡𝑒𝑟

𝑀𝑎𝑥𝑖𝑡𝑒𝑟
)
        (18) 

 

 
Figure 5. Flowchart of the PDO algorithm 



J. Anbazhagan et al. /Future Technology                                                                                  August 2025| Volume 04 | Issue 03 | Pages 10-18 

14 

 

2.2.5 Implementation of PDO-based PID controller 
The PDO approach is used in this study to get the best 

possible blood pressure control. The PDO technique is used to 
calculate the gain values of the optimal PID parameters. The 
objective functions are minimized using the Integral Time 
Absolute Error (ITAE) standard. The objective function is: 

𝑂𝐹 = ∫ ((𝐸𝑟(𝑡))
2
𝑑𝑡)

𝑡

0
         (19) 

BP management involves maintaining a patient's BP within 
desired levels by continuously monitoring and regulating the 
output of a pump. The expression for the PID controller is, 

𝑢(𝑡) = 𝐾𝑝𝑒(𝑡) + 𝐾𝑖 ∫ 𝑒(𝑡)𝑑𝑡 + 𝐾𝑑
𝑑𝑒(𝑡)

𝑑𝑡

𝑡

0
       (20) 

Where the error signal is represented by 𝑒(𝑡) = 𝑟(𝑡) − 𝑦(𝑡) , 
control signal is indicated by 𝑢(𝑡) and proportional, integral, 
and derivative gains are denoted by 𝐾𝑝 , 𝐾𝑖and 𝐾𝑑 .This method 

assures optimal BP control by integrating the PDO algorithm’s 
ability to balance exploration and exploitation for tuning the 
PID parameters. Figure 3 depicts the schematic diagram of 
PDO-PID controller.       

2.3 Infusion pump  
A basic infusion pump is permitted if the input voltage 

adjustment at the pump equals the variation in the infusion 
rate at the output.  

�̇�(𝑡) = 𝑣(𝑡)          (21) 

The pump’s transfer function is: 

𝐺𝑏(𝑆) =
𝑈(𝑆)

𝑉(𝑆)
=

1

𝑆
         (22) 

From the perspective of input/output, the infusion pump has 
an impulse response ℎ(𝑡) = 1for𝑡 ≥ 0. 

2.4 Patient 
Under the influence of SNP, the patient’s MAP is denoted 

by:  

𝑀𝐴𝑃(𝑡) = 𝑃𝑂(𝑡) − ∆𝑃(𝑡) + 𝑣(𝑡)        (23) 

Where 𝑣(𝑡) is a stochastic background noise, 𝑃(𝑡) is the 
pressure differential because of the infusion of SNP, and 𝑃𝑂 is 
the initial BP, also known as the background pressure. 𝑃𝑂is 
taken as constant in this paper. The relationship between the 
change in BP,𝛥𝑃(𝑠) and the drug infusion rate, 𝐼(𝑠) is 
described by the following continuous-time deterministic 
model: 

∆𝑃(𝑆) =
𝐾𝑒−𝑇𝑖𝑠(1+𝛼𝑒−𝑇𝐶𝑠)

1+𝜏𝑠
𝐼(𝑆)                            (24) 

Where 𝜏 a time constant, 𝑇𝑖  is the initial transport delay, 𝑇𝐶  is 
the recirculation time delay, 𝛼 is the recirculation constant, 
and 𝐾 is the sensitivity of the drug. The relevant discrete-time 
deterministic model is,  

∆𝑃(𝑡) =
𝑞−𝑑(𝑏𝑜+𝑏𝑚𝑞−𝑚)

1−𝑎1𝑞
−1 𝐼(𝑡); 𝑏𝑜 > 0                               (25) 

Parameters 𝑏𝑜, 𝑏𝑚, 𝑎1, 𝑑 and 𝑚 are taken from the sampled 
form of the continuous-time model, where 𝑞−1 represents a 
unit delay operator. Table 1 lists a range of typical values for 
the model's parameters for various patients.  
The parameters 𝐾, 𝛼, 𝑎𝑛𝑑 𝜏 change during the infusion 
process, time delays for a particular patient are unknown but 
are presumed to be consistent over an extended period of 
time. The following model is used in this work, which assumes 
that the parameters change exponentially.  

Table 1. Values for the model's parameters 

 

𝑝𝑎𝑟(𝑘) = 𝑝𝑎𝑟(0) (2 − 𝑒−𝑘
𝛾⁄ )        (26) 

Where 𝛾 is the change in the time constant and 𝑝𝑎𝑟(𝑡)is the 
parameter of the continuous-time modelfor increasing and 
decreasing the parameter value. As a result, the controller is 
able to manage time-varying parameters and initially 
unknown time delays when it is adjusted for a specific patient.  

3. Results and discussion 

In this section, a dynamics model of MAP is chosen and 
executed as a controlled system in a simulated environment 
in order to assess the performance of developed control 
architecture managed the medicine infusion SNP rate to 
regulate MAP. The comparison of developed research with 
conventional approaches for BP management is also included 
in this section. 

The open-loop system’s unit step response for the BP 
management system is displayed in Figure 6. It shows how 
the system reacts without any feedback control when 
subjected to a unit step input. The response reveals a slow rise 
in output, with a significant delay and extended settling time, 
indicating poor dynamic performance and a lack of regulation 
in controlling BP.  

Figure 7 illustrates the system response to the intended 
output. The patient's BP is 40 mmHg at the first appointment. 
Following the intended output, the system response 
immediately returns blood pressure to normal. It compares 
the MBP with the reference signal over time. The graph 
demonstrates that the PDO-PID controller successfully tracks 
varying reference BP levels with minimal overshoot and rapid 
settling, even during step changes. This indicates that the 
proposed controller is capable of maintaining BP within the 
desired ranges effectively and adaptively, ensuring precise 
and responsive regulation suitable for post-operative 
hypertension management. 

Figure 6. Step response  

 

Parameters Maximum Nominal  Minimum 

𝑇𝑐(𝑠) 75 45 30 

𝑇𝑖(𝑠) 60 40 20 

𝜏(𝑠) 60 40 20 

𝛼 0.4 0.1 0 

𝐾 9 1 0.25 



J. Anbazhagan et al. /Future Technology                                                                                  August 2025| Volume 04 | Issue 03 | Pages 10-18 

15 

 

Figure 7. Output response 

The impact of the prediction horizon (P) on the response 
of the system is represented in Figure 8. The signal gets laxer 
and has an inferior jump than lesser values as the horizon 
grows, but the computational volume also increases. 
However, this increase slows down the system. The system 
speed increases as the prediction horizon lowers, while the 
quantity of jumps grows in the other direction. Figure 9(A) 
denotes the output response for the PDO-based PID 
controller. It compares the MBP with disturbance and the 
reference signal over varying time. In addition to the 
heartbeat, injection device, percentage of injection substance, 
and neurological system, the disturbance is assumed to be 
sinusoidal. This disturbance has an amplitude of 10. The 
influence of drug-induced disturbance has been abolished, as 
seen in Figure 9 (B).  

Figures 10 and 11 display the output and control signal 
of the developed control system. Figure 10 shows the system 
output stabilizing around 1.2 mmHg shortly after the 75-
second mark, maintaining steady performance with negligible 
fluctuations, which reflects the controller's rapid settling and 
robust stability.  

Figure 11 illustrates the SNP drug infusion rate used to 
achieve this control. Initially, the infusion rate exhibits some 
oscillations as the controller adapts to the system dynamics, 
but it quickly stabilizes to a constant rate of around 0.6 mL/h, 
indicating efficient and consistent drug administration with 
minimal overshoot. The PDO-PID controller satisfies the 
constraint of the drug infusion rate limitation.Both the output 
and control signal are varied initially and maintained a steady 
value. 

 

 
Figure 8. MAP for diverse values of P 

 

(a) 

(b) 

Figure 9. (a) Output response for PDO-based PID (b) Impact of drug 
disturbance on the patient 

 

 
Figure 10. Output response with PDO-PID controller 

 

 
Figure 11. Control signal corresponding to the PDO-PID controller 

 



J. Anbazhagan et al. /Future Technology                                                                                  August 2025| Volume 04 | Issue 03 | Pages 10-18 

16 

 

Figure 12 demonstrates the performance of the 
developed controller with MPC. Additionally, it should be 
mentioned that the system always reacts more quickly than 
other controllers. This control strategy is suitable for various 
patients due to notable advancements in system 
responsiveness. While the MPC demonstrates a faster rise 
time and initially reaches the target output more quickly, the 
PDO-PID controller shows better long-term stability and 
reduced overshoot. The PDO-PID approach offers a smoother 
and more gradual transition, minimizing aggressive control 
actions and thus ensuring safer and more sustainable drug 
delivery, making it particularly suitable for sensitive 
physiological systems such as blood pressure regulation in 
post-operative patients. Figure 13 presents a comparative 
analysis between ABC-PID [21] and PDO-PID, based on 
settling time and peak time. From the analysis, PDO-PID is a 
slightly more efficient controller due to its lower settling time 
(1.05) while maintaining the lower peak time (0.203) as ABC-
PID, which stabilizes the system slightly faster. 

 
Figure 12. Step response (MAP) for controllers 

 

 
Figure 13. Analysis among controllers 

Table 2 provides a performance comparison between Genetic 
Algorithm (GA)-based Model Predictive Control (MPC) [22-
25] and the developed controller according to Integral 
Squared Error (ISE), Integral Absolute Error (IAE), Mean 
Squared Error (MSE), and Execution time. PDO-PID 
outperforms GA-based MPC by showing lower absolute error, 
ensuring that PDO-PID provides a more accurate and stable 
response. The developed controller consistently performs 
better across all performance metrics compared to GA-based 
MPC. 

Table 2. Performance analysis among controllers 

Control Approaches GA based MPC PDO-PID 

IAE 4.42 3.87 

ISE 2.10 2.01 

MSE 0.011 0.01 

Execution time  66.9531 63.613 

 

An analysis of the transient response between the ABC-
PID [22] and the PDO-PID controller is represented in Figure 
14. The ABC-PID has a rise time of 0.0985, whereas PDO-PID 
has a significantly lower rise time of 0.051, which suggests 
that PDO-PID responds faster to changes in input and reaches 
the desired state more quickly. The PDO-PID also exhibits 
lower overshoot (0.1021), meaning it introduces fewer 
fluctuations and maintains better system stability. A 
comparative analysis of steady-state error across three 
different control approaches, like Grey Wolf Optimizer 
(GWO), Salp Swarm Algorithm (SSA), and the proposed 
method, is revealed in Table 3. It is a critical metric in control 
systems, particularly in blood pressure management, as it 
determines the accuracy of the system in sustaining the 
desired pressure level. The proposed method outperforms 
SSA and GWO in terms of steady-state error, particularly in 
normal and insensitive cases, indicating a more reliable and 
precise blood pressure regulation system.  

 
Figure 14. Comparison of transient response 

 

Table 3. Comparison among algorithms 

Error steady state(𝑚𝑚𝐻𝑔) 

Cases SSA [24] GWO [25] Proposed 

Sensitive  2.58 × 10−5 7.492 × 10−5 2.91 × 10−5 

Normal  2.61 × 10−5 3.838 × 10−5 2.23 × 10−5 

Insensitive 0.00044 0.000689 0.00035 

 

4. Conclusion  

This research work proposes a novel optimized PID controller 
for blood pressure management. The PID controller decides 
the amount of SNR drug rate that is delivered to the patient, 
ensuring the BP is managed properly. By tuning the 
parameters of the PID controller, the PDO enhances the 
performance of the PID controller with less settling time and 
overshoot. By the injection pump's physical constraints, the 
MAP stabilizes at about 80 mm Hg after bringing the blood 
pressure down to a normal control level. According to the 
results, PDO-based PID performs better than the PID 



J. Anbazhagan et al. /Future Technology                                                                                  August 2025| Volume 04 | Issue 03 | Pages 10-18 

17 

 

controller with the control signal's delay and limit. The 
proposed research guarantees that the MAP remains at its 
predefined rate of 100 mmHg during surgical procedures, 
post-surgery recuperation, or anaesthesia administration by 
precisely administering the recommended amount of the SNP 
medicine. By calculating the SNP infusion rate, the simulation 
results have validated that a PID controller with PDO is 
helpful in controlling blood pressure. This method provided 
much improved performance than other approaches, mainly 
to cover an extensive range of patients.  

Ethical issue 
The authors are aware of and comply with best practices in 
publication ethics, specifically with regard to authorship 
(avoidance of guest authorship), dual submission, 
manipulation of figures, competing interests, and compliance 
with policies on research ethics. The authors adhere to 
publication requirements that the submitted work is original 
and has not been published elsewhere. 

Data availability statement 
Datasets analyzed during the current study are available and 

can be provided upon a reasonable request from the 

corresponding author. 

Conflict of interest 

The authors declare no potential conflict of interest. 

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