The Covid-19 pandemic which appeared as an outbreak in Wuhan (China) in 2019 [1]-[6] has spread over the world and led to devastating consequences not only for insanity but also for economy, society, and people’s lives. This pandemic has caused crisis and paralysis in the medical system in every country that suffers from the outbreak of Covid-19, even the most developed nation is no exception. On the health-care aspect, the Covid-19 affects directly to the human respiratory system, especially those who have underlying medical conditions. Thus, the demand for medical ventilators in general and simple ventilators in specific rises quickly [7] as a consequence to assist patients with respiration [8] . During this period, myriad types of medical ventilators are designed and manufactured with different principles; some of which use the CAM mechanism [9], and others use pneumatics [10] or bag valve mark ventilators [11]. Another breed of the medical ventilator is also used widely as a simple ventilator [12]. This type of ventilator helps to resolve problems associated with the need for ventilators such as inter-and intrahospital transport [13], protocolized weaning from ventilation [14], or patients in a persistent vegetative state (PVS).

In general, a medical ventilator consists of two important main components, the air compressor, and the control unit. Among these two main units, the air compressor has more effects on the operating principles of the ventilator. Beside the mentioned mechanisms above, the air compressor using a piston mechanism, especially a double-acting pistons, gives excellent performance through time [15]. This kind of air compressor gives the advantage to generate a consistent airflow during the piston’s cycle, therefore, there is no idle time in the control process. In addition, the double-acting pistons mechanism has the ability to operate smoothly with nearly zero noise and high stability, thus, its application is widely spread and prioritized in designing medical ventilators. The second component of the medical ventilator is the control unit. In present ventilators, various control units are studied and applied, some typical control units are adaptive neuro-fuzzy control [16], and model-free control [17]. The application of a specific control unit on the ventilator system requires a model that describes the dynamic behavior of the system accurately. This paper presents a model identification of two double-acting pistons pump (DAPP) [18][19]. The first order plus dead time (FOPDT) model is used for this identification process.

The contents of this paper are organized as follows: Section 2 describes the overall system of the DAPP used in the ventilator. Then, the model identification process by applying the FOPDT model is presented in Section 3. After that, Section 4 provides experimental tests along with results and discussion. At the end of this paper, conclusions and future work is mentioned in Section 5.

Figure 1 describes the operation process of DAPP system. In which, the DAPP is driven by a brushless direct current (BLDC) motor. The flexible tube that is responsible for air transmission between each part of the system is made of medical specialized silicon. The DAPP also uses two types of exhausting valves. The first type is the overflow valve. The overflow valve gives the ability for the DAPP system to exhaust the air when the pressure in the system increases above the limit pressure. This helps to protect the system from being damaged. The other exhausting valve is the positive end-expiratory pressure (PEEP) valve, which is used for maintaining the residual pressure existing in the patient’s lung at the end of the expiration phase. This PEEP valve plays an important role in assisting patient’s breath and avoiding collapsed lungs which has the possibility of augmenting the mortality rate of patients [20]-[23]. Besides these exhausting valves, a mass flow sensor SFM 3020 manufactured by SENSIRON is included in the system with the purpose of retrieving airflow data on the outlet. The pumped mixed air must be filtered by a heat moisture exchanger filter (HMEF) before entering patient’s respiratory system. The HMEF contributes to humidification, warming-inspired air. It also helps to capture airborne particles and prevent bacteria or viruses from flowing into the patient. Additionally, the usage of the HMEF can help to isolate the contaminated airflow from the patient to the DAPP system during the exhalation.

Figure 1: 
Operation process of two double-acting pistons pump system

Upon present literature in the model identification and control field, the FOPDT model still receives considerable attraction due to its simplicity and well performance in fitting many industrial processes. A FOPDT model can be written as follow:

where τ_p is the time constant; y(t) is the response signal of the system; K_p is the process gain or the steady state gain; u(t) is the input signal of the system and θ_p is the dead time. By calculating three parameters τ_p, K_p, θ_p based on the sample data, the DAPP system can be identified in form of an estimated FOPDT model. Numerous methods were studied and applied in determining or approximating these parameters [24]-[27]. Among them, there is a class of methods that use the step response of the system to estimate the FOPDT model. Typically, the graphical method and area method was introduced by document [28] to estimate FOPDT model based on the step response. The two-points method [29] is also a simple one for this application. However, all three mentioned methods were sensitive with noise, and a novel method was proposed in the document [30] in which the least-squares method was applied to calculate the parameters of the FOPDT model.

In this paper, the graphical method is adopted for model identification of the DAPP system because of the simplicity of the method and the low-noise characteristic of the DAPP. According to this method, the parameters τ_p, K_p, θ_p are identified based on the step response of the DAPP system. Let’s define u_ss, y_ss respectively as the steady state input and the output signal of the system. Assume that two separated steady-state output signals y_ss1,y_ss2 with respect to two steady-state signals u_ss1, u_ss2 are recorded through experimental tests. The process gain K_p can be determined as the following equation.

From the step response graph, the process dead time θ_p is defined as the time period between the beginning when the system is excited by a step input and the time when the state transition of the system is initialized. With this definition, the dead time can be estimated visually by one when conducting the experimental tests or calculated by using the intercept of the tangent line with the horizontal axis.

After determining parameters K_p and θ_p, Equation (1) can be rewritten in form of:

By shifting the time origin of the step response to an amount that equals the dead time, the dead time θ_p , which is the alternative time origin, can be neglected in Equation (1) (θ_p = 0 ). Hence, at the time t = τ_p, the airflow output of the DAPP system is calculated as

According to Equation (4), by identifying the time t_0.632 when the airflow output reaches 63.2% of the steady state output value y_ss, the time constant is derived by the difference t_0.632 − θ_p.

The whole identification process is summarized in form of a pseudo-code algorithm and shown in Table 1.

The aim of this section is to provide experimental features of the tests which are conducted for collecting input-output data from the DAPP system. Furthermore, the model identification process of the DAPP system with the collected data is presented. And at the end of this section, the results and validation of the identified model are illustrated and discussed.

Figure 2: 
The two double-acting pistons pump in experimental tests.

4.3 Results and validation

The entire experimental tests and the calculated parameters in each scenario are also included in Table 2.

Table 2: 
Results of experimental tests

Test No.	∆u (%)	∆y (ml/s)	Kp	θp (s)	τp
1	10	173	347	0.04	0.03
2	15	344	459	0.04	0.03
3	20	521	521	0.04	0.03
4	25	681	545	0.04	0.03
5	30	818	545	0.04	0.026
6	35	961	549	0.04	0.026
7	40	1041	520	0.04	0.03
8	45	1149	511	0.04	0.03
9	50	1348	539	0.04	0.033
10	55	1476	537	0.04	0.03

For a full explanation of the above table, a brief view of the step response graph is indeed needed. Figure 3 shows the output response curve and the corresponding step input which belong to the 1^st test scenario. It can be seen from the figure that the system took a small period of time to start the state transition. This amount of time results from the inertia relying on the pump system itself which prevents the system from responding to the input voltage signal immediately. By this means, the dead time θ_p acts the same way as the delay time in Figure 3. As consequently, it can be estimated as 0.04 seconds.

Figure 3: 
Output response in the 1^st test scenario

After the derivation of the dead time, the time constant is computed by following the algorithm in Table 1. Hence, τ = t_0.632 − θ_p ≈ 0.07 − 0.04 = 0.03 (s).

As can be seen from Table 2, the parameters τ_p among the scenarios oscillate around an equilibrium point (≈ 0.03 seconds) and the dead time θ_p remains constant as 0.04 seconds throughout every scenario. On the other hand, the process gain K_p tends to change its value in low levels of airflow (< 500 ml/s) due to the nonlinear characteristics of the DAPP at a low level of airflow. When the BLDC motor reaches the high level of duty cycle (> 20%), where the high level of airflow (> 500 ml/s) is generated by the DAPP. The gain K_pstarts to fluctuate between 511 and 549 with a mean value of about 533. This means that the DAPP system has linear characteristics in a high level of airflow. Therefore, the FOPDT model will be used for designing the controller of the DAPP system in high levels of airflow (> 500 ml/s). The final FOPDT model is derived as follows, after extracting the mean value from each parameter.

y˙t=-10.03yt+5330.03ut-0.04

(5)

For the objectives of validation, the mean squared error (MSE) is used to evaluate the estimated model’s performance. The equation of MSE is defined as

MSEr=∑y^SSi-ySSi2∑ySS2i

(6)

where y^ss is the steady state output airflow of the estimated FOPDT model in Equation (5); y_ss is the steady state output airflow of the DAPP system that is measured by the mass flow sensor, i denotes the number of samples in steady state in the r^th scenario. The MSE score of the FOPDT model with the 2^nd group of data is summarized in Table 3 below. Figure 4 below shows the comparative evaluation between the output airflow of the estimated FOPDT model and the airflow measured by the sensor in 10^thscenario.

Table 3: 
MSE scores of the FOPDT model with the 2^nd group of data

Test No.	MSE
1	0.004479545
2	0.004493375
3	0.003943517
4	0.002815366
5	0.002896781
6	0.005190154
7	0.00262155
8	0.001692255

Figure 4: 
Comparison of output airflow in 10^th scenario

From Figure 4, one restriction of the FOPDT model could be pointed out, that is the estimated output values do not fit well with fluctuation in steady-state. This disadvantage could be troublesome when designing an airflow controller that requires high accuracy because some peak values might do harm to the system itself. Alternatively, using a model with higher order or applying another identification method is one of the solutions. However, with the objective of controlling the volume that is pumped into the patient’s lung, this estimated FOPDT model can be useful. In future work, research and studies on the volume controller based on this estimated FOPDT model will be conducted. Tuning the model parameter is also a branch to be concerned.

This paper presented an alternative method of system identification for medical ventilators. The FOPDT model was described and an algorithm was established to determine the parameters. The estimated model was then validated with the aspect of performance in the approximation system. Some restrictions of the model also are discussed. In future work, the volume parameters of the DAPP are going to be experimentally performed with the prosthetic lung and the change in output impedance (change in the internal resistance of the prosthetic lung). In addition, the intelligent controller is applied for DAPP to observe and update the coefficients to ensure in two situations: the volume is constant or the volume changes based on the impedance change of the prosthetic lung.